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N1Fen/Abncu/cSR2qa95+nvvM3OnuCu/p6Tldv6pzqmizKTYIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQMBJAlUQ9Jy0C42CAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAgCWAoMeFAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAGHCSDoOWwcmgYBCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABBD2uAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQg4TABBz2Hj0DQIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIIOhxDUAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEDAYQIIeg4bh6ZBAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAEGPawACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACDhNA0HPYODQNAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAgh6XAMQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQcJgAgp7DxqFpEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEEDQ4xqAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAgMMEEPQcNg5NgwAEIAABCEAAAhCAAASiI/DVV1+p2267Tc2ePVvVrVtXrbfeetFVnkdNm222mTr66KNV69at1brrrpvHmeEfunjxYvXUU0+pJ554Qq1atSr8CvOsYfXq1Wr58uWqXr166tRTT1Xt2rXLswQOhwAEIAABCEAAAhCAAAQgEA8BBL14uFMrBCAAAQhAAAIQgAAEIOAYgfvvv1/16NHDCj4ilFWpUsWxFv7VnKpVq6pDDz1UjRo1Sm2//fZOtfHxxx9XZ511lvr++++V1tqptqUaI6LeOuusozp16qQmTpzorHCbai+vEIAABCAAAQhAAAIQgAAEhACCHtcBBCAAAQhAAAIQgAAEIAABQ2DmzJmqa9eudmVZjRo1VK1atZzjIiJj48aNrfAoba1du7ZTbfzvf/+rrrvuOnXfffeplStXOtU2acwff/xhBVt5Pemkk9S0adOUCKRsEIAABCAAAQhAAAIQgAAEXCeAoOe6hWgfBCAAAQhAAAIQgAAEIBAJAVmhd9ppp9kwll26dFH9+vWLpN58K6lWrZoNCVqnTh3nVhGKUPbLL7+opUuXOrlC780331SjR49Wb7/9thX0br/9dufCluZ7PXA8BCAAAQhAAAIQgAAEIFAaBBD0SsPO9BICEIAABCAAAQhAAAIQyEJABL3u3bsrEcz69u2rhg8fnuUMdieNwEsvvaTOO+88NWfOHAS9pBmP9kIAAhCAAAQgAAEIQKDECSDolfgFQPchAAEIQAACEIAABCAAgb8IIOj5fyUg6PlvY3oIAQhAAAIQgAAEIAABXwkg6PlqWfoFAQhAAAIQgAAEIAABCORFAEEvL1yJPBhBL5Fmo9EQgAAEIAABCEAAAhCAgCGAoMdlAAEIQAACEIAABCAAAQhAwBBA0PP/MkDQ89/G9BACEIAABCAAAQhAAAK+EkDQ89Wy9AsCEIAABCAAAQhAAAIQyIsAgl5euBJ5MIJeIs1GoyEAAQhAAAIQgAAEIAABQwBBj8sAAhCAAAQgAAEIQAACEICAIYCg5/9lgKDnv43pIQQgAAEIQAACEIAABHwlgKDnq2XpFwQgAAEIQAACEIAABCCQFwEEvbxwJfJgBL1Emo1GQwACEIAABCAAAQhAAAKGAIIelwEEIAABCEAAAhCAAAQgAAFDAEHP/8sAQc9/G9NDCEAAAhCAAAQgAAEI+EoAQc9Xy9IvCEAAAhCAAAQgAAEIQCAvAgh6eeFK5MEIeok0G42GAAQgAAEIQAACEIAABAwBBD0uAwhAAAIQgAAEIAABCEAAAoYAgp7/lwGCnv82pocQgAAEIAABCEAAAhDwlQCCnq+WpV8QgAAEIAABCEAAAhCAQF4EEPTywpXIgxH0Emk2Gg0BCEAAAhCAAAQgAAEIGAIIelwGEIAABCAAAQhAAAIQgAAEDAEEPf8vAwQ9/21MDyEAAQhAAAIQgAAEIOArAQQ9Xy1LvyAAAQhAAAIQgAAEIACBvAgg6OWFK5EHI+gl0mw0GgIQgAAEIAABCEAAAhAwBBD0uAwgAAEIQAACEIAABCAAAQgYAgh6/l8GCHr+25geQgACEIAABCAAAQhAwFcCCHq+WpZ+QQACEIAABCAAAQhAAAJ5EUDQywtXIg9G0Euk2Wg0BCAAAQhAAAIQgAAEIGAIIOhxGUAAAhCAAAQgAAEIQAACEDAEEPT8vwwQ9Py3MT2EAAQgkCLwyy+/qA8//FAtWbJE1a5dO/Uxr54Q+PPPP9Uff/yhGjZsqHbeeWdPekU3IAABCFROAEGvcj7shQAEIAABCEAAAhCAAARKhACCnv+GRtDz38b0EAIQgIAQ+Pnnn9W0adPU2LFjlQg/66yzDmA8JKC1Vttss43q37+/6tChg4c9pEsQgAAEyhJA0CvLg/8gAAEIQAACEIAABCAAgRIlgKDnv+ER9Py3MT2EAAQgIARkZd7IkSPVjBkzAOI5gRo1aqhu3bqpSZMmed5TugcBCECAkJtcAxCAAAQgAAEIQAACEIAABCwBBD3/LwQEPf9tTA8hAAEICIHPP//crs6bPHmyDcl48MEHq5122gk4nhD47bff1JtvvqkeeeQR1bRpU3Xuueeqs846y5Pe0Q0IQAACmQmwQi8zG/ZAAAIQgAAESoKA5B2YO3euev7559Xmm2+uqlWrVhL9drmTq1evVosXL1Y1a9ZUHTt2VHXq1HG5ubQNAt4QCFvQ++yzz9Qzzzyj1l13XVW3bl1vuAXdERmkk7xHW2yxhTriiCNUlSpVAqsCQS8wlBQEgbwI4G/mhSuSg333N7/88kt1xRVXqIkTJ6p99tlHXXbZZaply5aRsKWS8AmIrzB9+nQbarN58+ZqyJAhqkePHuFXTA0QgAAEYiaAoBezAageAhCAAAQgEDeBhx9+WPXt21etWLECMS9uY6TVn8r10alTJ3XllVem7eEtBCAQFoEwBb33339fjRkzRj3++ONWoCKXT2YrSj4cGWhu0KCBOuOMM+xgXeaj89uDoJcfL46GQFAE8DeDIhlsOT77m+mCXtu2bdX48eMR9IK9fGItTQS9W2+91foJCHqxmoLKIQCBiAkg6EUMnOogAAEIQAACrhGQmY2dO3d2rVm05/8TEEHvjjvugAcEIBABgTAFPVkFPWDAAPX2229H0BM/qpCcOF27dlU33HBDYB1C0AsMJQVBIC8C+Jt54Yr8YB/9TQS9yC+jSCtE0IsUN5VBAAIOEUDQc8gYNAUCEIAABCAQBwHJOyArIL777ju11157qZ49e8bRDOpMI/Dqq6+qm266SVWtWlV16dJFTZ06NW0vbyEAgbAIhCnoiZA3bNgwm+ulRYsWSgZPN9lkk7C6kthyZbXIyy+/rG677TbVpEkTNWjQIHXOOecE1h8EvcBQUhAE8iIg/uaZZ56pFixYgL+ZF7nwDvbd30TQC+/acaFkBD0XrEAbIACBOAgg6MVBnTohAAEIQAACDhGQ8G+9e/dWP/30k10JMXbsWIdaV5pNkRxbMoj91VdfqVNPPVXdeOONpQmCXkMgYgJhCnrz5s1TI0aMUFLH4Ycfrq655hrVqFGjiHvofnWSZ2vGjBn2d6lZs2Zq8ODBqlevXoE1HEEvMJQUBIG8CIi/2adPH7Vw4UL8zbzIhXew+JsDBw5U8+fPtzaZMmVKeJXFUDKCXgzQI6wSQS9C2FQFAQg4RQBBzylz0BgIQAACEIBA9ARSgt7ixYvt6jzJL8EWLwEZYOnXr5/69NNPvRxgiZcutUMgM4GoBL327duryZMnI+hVYAoR9KZNm6a6d++uEPQqAMRHEEgogVmzZlmhftGiRer0009XEyZMSGhP/Gm27/4mgp4/12pFPUHQq4gKn0EAAqVAAEGvFKxMHyEAAQhAAAKVEEDQqwROTLt8H2CJCSvVQiArAQS9rIhCPwBBL3TEVACBWAgg6MWCvdJKffc3EfQqNX/idyLoJd6EdAACECiQAIJegeA4DQIQgAAEIOALAQQ99yzp+wCLe8RpEQT+IoCgF/+VgKAXvw1oAQTCIICgFwbV4sr03d9E0Cvu+nD9bAQ91y1E+yAAgbAIIOiFRZZyIQABCEAAAgkhgKDnnqF8H2BxjzgtgsBfBBD04r8SEPTitwEtgEAYBBD0wqBaXJm++5sIesVdH66fjaDnuoVoHwQgEBYBBL2wyFIuBCAAAQhAICEEEPTcM5TvAyzuEadFEPiLAIJe/FcCgl78NqAFEAiDAIJeGFSLK9N3fxNBr7jrw/WzEfRctxDtgwAEwiKAoBcWWcqFAAQgAAEIJIQAgp57hvJ9gMU94rQIAn8RQNCL/0pA0IvfBrQAAmEQQNALg2pxZfrubyLoFXd9FHr2woUL1YMPPqg+/PBDdfLJJ6uWLVsWWlSl5yHoVYqHnRCAgMcEEPQ8Ni5dg4APBGRQ588//1TVq1dPXHe01mr16tWqSpUqap111klc+2lw6RBA0HPP1r4PsLhHnBZB4C8CCHrxXwkIevHbgBZAIAwCCHphUC2uTN/9TQS94q6PQs7+3//+p+677z41ePBgte6666o+ffrY94WUle0cBL1shNgPAQh4S8AMOLNBAAIQcJLAnDlzdPv27XWnTp30u+++62QbMzXKOJf6oYce0m3atNFDhgzRS5cuzXQon0MgdgKPPfaYbtq0qa5Tp44eOHBg7O2hAVr/5z//0S1atNDrrbee7tmzJ0ggAIGICDzwwAO6fv36epNNNtGXXnppoLW+8847umPHjto8WFr/5ttvvw20fF8K+/333/XUqVMtp2bNmulJkyYF2rWXX35Zt27dWpsJV9bHNJOvAi2fwiAAgYoJmAlkesstt7T+5oABAyo+iE8jJeC7v/nFF19oIyjZ35O2bdvq119/PVK+pViZ+DodOnSwv7E77bSTvueee0LDYMRDPWXKFGvf5s2b65tuuim0uigYAhCAgEsEWKHnrVRLxyCQfAIzZ85U3bp1U2YwRw0fPlwdd9xxienUTz/9pMwAlDKDgco4suriiy9WxxxzTGLaT0NLiwAr9Nyzt+8zpt0jTosg8BcBI7IpI+qpxYsXqxNPPFFtu+22gaGZN2+eGjFihJJVgGbCkpo8ebJq1KhRYOX7UlDYK/R+/vln9dRTT6m33npLHXXUUcqIe76gox8QcJoAK/TcM4/v/iYr9KK95pYtW6amTZumzj//fBupSMJtjhs3TtWrVy+UhrBCLxSsFAoBCCSAAIJeAoxEEyFQigQkzObtt9+uTjvtNLXVVltZp9CsUkkMChmMuvvuu1Xv3r1tyFDpx5VXXqmqVq2amD7Q0NIhgKDnnq19H2BxjzgtgsBfBMT/WLlypZLfcbNq2YaLCooNgl5uJMMW9MzsWmtjCQu2/vrrK7MSOreGcRQEIFAUAQS9ovCFcrLv/iaCXiiXTcZCX3nlFWWiE6nnn39e7bnnnmrUqFGqXbt2NgVJxpOK2IGgVwQ8ToUABBJNAEEv0eaj8RDwl0DYgzlRkHvjjTfUBRdcoJ5++ml14IEHqvHjx6vdd989iqqpAwJ5EUDQywtXJAf7PsASCUQqgYBjBBD0cjOIDz5gbj3lKAiUFgEEPffs7bu/iaAX3TUnEYpM+EsboahmzZqqR48eauTIkUreh7Uh6IVFlnIhAAHXCSDouW4h2geBEiXgw2COhOuaOHGiDbe5xRZbqEGDBql+/fqVqEXptssEEPTcs47vAyzuEadFEAifAIJebox98AFz6ylHQaC0CCDouWdv3/1NBL1orjlZ+f7ss8+q/v37q3fffVe1adPGTmZu1apVqA1A0AsVL4VDAAIOE0DQc9g4NA0CpUwgisEcCbX0ww8/qK+++kp99913avny5apu3bqqcePGyiRVVvXr1y/KBKtXr1YilJx99tnq66+/Vscff7zNqyd1sEHAJQIIei5Z46+2+D7A4h5xWgSB8Akg6OXGOAofMLeWcBQEIBAkAQS9IGkGU5bv/iaCXjDXSbZSvvnmG3X11VfbPxlD6du3rxo8eHDoIa0R9LJZhv0QgICvBBD0fLUs/YJAwgmENZgjs8dExHviiSfUAw88oGRwTYQ9qU8EuHXWWUdVq1ZNbbLJJqp169bq//7v/9Q+++yjateuXRDRjz76yMaOl3yALVu2VJdddpk67LDDCiqLkyAQFgEEvbDIFl6u7wMshZPhTAgklwCCXm62C8sHzK12joIABMIigKAXFtnCy/Xd30TQK/zayPVMyT386KOP2khE8+fPt2MdIu5tu+22uRZR8HEIegWj40QIQCDhBBD0Em5Amg8BXwmEMZgjK/Aee+wxdeWVV6rPPvvMJmfea6+91LHHHqtatGihqlevblfqzZkzx4p9n3/+udpwww3VfvvtZ2eZ7b///nkndF65cqWaNm2aXaUnomCvXr2swOer3ehXMgkg6LlnN98HWNwjTosgED4BBL3cGIfhA+ZWM0dBAAJhEkDQC5NuYWX77m8i6BV2XeRz1qeffqr+9a9/qVtvvVWl0oyceeaZqmrVqvkUU9CxCHoFYeMkCEDABwJmtQobBCAAAecI/P7773rq1Kna3Gd1s2bN9KRJk4pq448//qiNkKe33HJLbYQ7bUQ6fd999+kFCxboFStWaDN4pM0KPW1W6+klS5ZoM+imhw8frhs2bKhNImdthD9tnFQt7cpnkzJnz56t9957b21W/+mjjjpKGzExnyI4FgKhEzBCt27atKmuU6eOHjhwYOj1UUF2Av/5z3+0mWig11tvPd2zZ8/sJ3AEBCDgPIF33nlHd+zY0fo27du3199++63zbY6jgUH7gHH0gTohAIHyBMwEMvssJv7mgAEDyh/AJ5ET8N3f/OKLL3SfPn3s727btm3166+/HjljnytctWqVNpOX9cYbb6xNlCNtUozY8ZWo+ixjN1OmTLH2NSlT9E033RRV1dQDAQhAIFYCKtbaqRwCEIBABgJBDuaY0A/6ggsusI7muuuuq8WZf+GFF7RZPZehdm0FPhEBr732WivqiYO60047WYdRRLp8NhNTXp977rnW0dxuu+2sMJjP+RwLgbAJIOiFTTj/8n0fYMmfCGdAIPkEEPRys2GQPmBuNXIUBCAQBQEEvSgo51eH7/4mgl5+10O+R4tf06FDB12lShW944476unTp2sTgjPfYgo+HkGvYHScCAEIJJwAITd9WGZJHyDgIYGgwi39/PPP6rbbblOXXHKJWrx4sdp+++3V0KFD1UknnZQ1SbO5v9sQnBMnTlRjxoyxlPfcc0910UUXKTOzPmfqElf+/vvvV71791YS9rNLly7KCIU2xGfOhXAgBEIk4ErITQlR+8Ybb6innnpKmQFdm89SclqaVWr2+yKv8n8qhIt8t+Q4yYMpIVdSf/KZhMs96KCDVKtWrcqRq6geKTv9L9d6NtpoI1uP5MgMcvM9BFKQrCgLAkkh4ErIzZ9++kk999xz6q233rLo5H4nfxJ6PHWfregemLrHpl7lXmsmStkcwZJzWPIQB7EF5QMG0RbKgAAEgiPgSsjNivxAuefJ/S/9Poi/GZzt4yqJkJvhkV+2bJlNLXL++ecrM+FZnXzyyWrcuHGqXr164VW6Vsnij0iozzPOOEOZFXpqyJAhqkePHmsdxb8QgAAEPCSQcEGS5kMAAp4SMINERYfclNlhMhNUVsWZ27cNtdm1a1dtRL6cqUkZzz//vDb582wZ5kHPhpL46quvci5DDnz77bf10UcfbWevtWnTRr/yyit5nc/BEAiTgCsr9CQcbd++fXXdunX1BhtsYF/NQ6E24pw2wpmuX7++XWnboEEDLX8S3kU+k31yjBybOlfC644cObJCbP/9738DrWfUqFEV1lPMh77PmC6GDedCIKkEXFmhJ37Nvvvua++Xcs+Uv2z3WrnfVnSvlXPNIJ6WqAZBbUH4gEG1hXIgAIHgCLiyQg9/82+b+u5vskLvb1sH/W7OnDn6gAMOsGMkZtKzNoK9TWESdD2VlccKvcrosA8CEPCZACv0PBRp6RIEfCAQxOxsmZE3fvx4ZfLvKVnJI6vzLrzwQtW5c2dlwkLkjElW9kkZsjJPts0331z1799fDRo0KOdyli5dqm688UY1ePBgtemmm9rzzzvvvJzbwIEQCJOAKyv0fv31V7tiRFaOmNyWSv5fuHCh+uijj9SHH36oTJ6Gchhk9nTjxo3tCpFGjRopk/PSzrCW9+YhU+2www7lzim0niZNmpSpR2ZzV1ZPuYrz+IAVennA4lAIJISAKyv0fvjhB7tCT+6rMrtdVtrJqj1pn/yJD7b2JqvvxH/ZY4891BZbbKFq165tV0ubXFj2vnjggQeuWT299rn5/h+ED5hvnRwPAQiET8CVFXqF+oH4m+FfI0HXwAq9oIn+VZ74DCZ3nbr00kvts5esijMTKe37cGqsuFRW6FXMhU8hAIESIOCzWknfIACB5BIodna2rKx78MEHtRHf7KwxczvX7dq1059++mneUKQsEzJTm4EsW5bk4TvqqKP0J598knNZknfviSee0EZc0HL+cccdp41QkfP5HAiBMAm4skJPvicy01JW0RohXZuHRW0Gnm3OS0myLt/j9D9Zxde9e3dtBD/9/fff2+PlvCVLlmgTBkbLfaSiLVM9s2fPtt/N9DrkvaxA6dmzp/7444/zqqeiunP9zPcZ07ly4DgI+ETAlRV64teYSRP2Xin3zEWLFtkVdmYigTYhxcvcZ+UeaMQ7feqpp+r33ntPL1iwYM29Vs795ZdftJlsEaiZivUBA20MhUEAAoERcGWFXiY/UHKs428GZm4nCmKFXvBmkO+PPKfsvPPO1l+Q6EOvvfZa8BXlUCIr9HKAxCEQgICXBJSXvaJTEIBA4gkUO5gjg/tmRZ02M8qto2lW0ujTTjtNm1lcBbF59dVX9T/+8Y81g1zbbrutvuWWW/IqS8L8iSggg2O77babFRzzKoCDIRASAVcEvUzdM6tItFlZu+b7lxLc9tlnH21W8wUW3uWDDz7QnTp1KlePhKYTsU8eYKPaEPSiIk09EIiOgCuCXqYey732lFNOKXcP3HvvvfWzzz6rRQiMYivWB4yijdQBAQjkT8AVQS9Ty/E3e2ZCk9jPEfSCN93XX3+tzz33XC3jKzLhWVIciLAWx4agFwd16oQABFwggKDnghVoAwQgUI5AsYM5kqPuoIMOWjMo1bBhQ33ZZZeVqyfXD2Q1nqwESgkJNWrUsOJcPrPS5dibb75Z16pVy+YHMyE7Ixscy7WfHFeaBFwX9GTGtAwop75/8ipi/YknnmhX4gVltYrqkRW1J510kl6+fHlQ1eRUDoJeTpg4CAKJIuC6oPfyyy+vyRmcut+m7oGy6jmqrVgfMKp2Ug8EIJAfAdcFvYr8QPzN/Gzs2tEIesFaxITEtpOSmzZtqk0KE3344YfbCCbB1pJ7aQh6ubPiSAhAwC8CCHp+2ZPeQMAbAsUM5si5d9xxhzZ5XdYIAFtttZW+4YYbCuYjIaaGDBmypjxxYNu2bZt3eIlU8mg5X0KAyoogNgjETcBlQU9Wxc2cOVPXq1dvzfdPBpo33nhjPWzYsMBWzVVWz/DhwwOrJ1dbI+jlSorjIJAcAq4LehJevH79+qHea3OxVjE+YC7lcwwEIBAPAZcFvcr8QPzNeK6XIGpF0AuC4t9lpCY5y2SfZs2a6euuuy5jioO/zwrvHYJeeGwpGQIQcJsAgp7b9qF1EChZAsUM5nz33Xd66NChdtZYaoa55K6bPn16wTyXLl2qx48fX2aQa5ttttFTp07Nq0zJB3bxxRfbcrbeemttkknndT4HQyAMAi4LepJPb+zYsWW+z/K93nHHHfWdd94ZGI6o6sm1wQh6uZLiOAgkh4DLgp74ORMmTFgTqjzlP7Vo0SLQe20u1irGB8ylfI6BAATiIeCyoBeVHxhVPbla2Hd/E0Ev1ysh+3ESbWjatGl2UqWE25R8kzLpOc4NQS9O+tQNAQjESQBBL0761A0BCGQkUMxgznvvvWdD8aUGo+RVctY9/PDDGevLtkNy7910001lBL2NNtpIX3DBBdlOLbNfwlTIDPjNN99cV69eXXfr1k2vWLGizDH8A4GoCbgs6MlMUMl/mf59lvcSUlcGx4PaPv300zJhdVP1BV1Pru31fYAlVw4cBwGfCLgs6KXn+U3d/1L32nnz5kVqhmJ8wEgbSmUQgEBeBFwW9PA317PpJPIyaAIORtALzkjiw3To0MFOspSJlTJZOqrcupl6gaCXiQyfQwACvhNA0PPdwvQPAgklUMxgzuzZs3WrVq3KCACSf+vZZ58tmIaEYZEwnpJHITXQJaEmOnfurPPJoycNEMHxhBNOsOXsu++++vnnny+4XZwIgSAIuCzoVZTPRL57nTp10r/++msQ3bdlvPjii1q+j6nvt7yGUU+uDUbQy5UUx0EgOQRcFvQkf17r1q2duAcW4wMm52qgpRAoPQIuC3r4mwh6pfeNzL3Hsor/+uuv17Vr19a1atXSPXr00EuWLMm9gJCORNALCSzFQgACzhNA0HPeRDQQAqVJoJjBnAceeMCGgkgfmD/ggAP0m2++WRTMe+65xzqw6eUedthhWma157MtX75cX3vttbpq1ap6k0020SNHjszndI6FQOAEXBX0KstnEnReu/vuu0/Lqtv077fk6Qu6nlyNh6CXKym3j1u8eLGdTDJp0iR9ySWX2Fyso0eP1rfddpt+66238p4Q4nZvaV02Ai4LehXlz2vQoIEeMWJE5DlEi/EBs9mA/e4T4L7pvo0KbaGrgh7+Zgu93noIeoVe16Vw3pw5c7SMp8hz0p577qlnzZoVuW9QEWcEvYqo8BkEIFAKBBD0SsHK9BECCSRQ6GCOhH2Q2O7pK+nE8Tz00EP1Rx99VBQJGezacMMNywz477///lpmteezyUPjM888Y8OAygogCV3x7bff5lMEx0IgUAKuCnqZ8owEndPpl19+sTky175vBJ2nLx+jIejlQ8utY2Vw4fXXX9f9+vXTu+++uw2xLOJwvXr19AYbbGB/R2QyR9OmTfWBBx5or72vvvrKrU7QmlAIuCroVZY/76677gqFRWWFFuoDVlYm+9wmwH3TbfsE1TpXBT38TQS9oK5xH8tZuHChHjVqlE0XIr7soEGDAo2SUgwzBL1i6HEuBCCQZAIIekm2Hm2HgMcECh3MkRB8Eg4ifZWNvC9kJd3aeCta+bfHHntoeTjNd5PB27PPPtu2c6eddtJ33313vkVwPAQCI+CqoFdZPpMgczpVljtKBuDj2BD04qBefJ2fffaZXYW3zTbb6Dp16tiwrWv/HqX/X61aNbsydL/99rN5WmUFN5u/BFwV9DLdAw8++GD97rvvRm6QQn3AyBtKhYEQ4L4ZCMZEFOKqoIe/iaCXiC9QDI2UicjyTLLzzjvbcYs2bdro1157LYaWVFwlgl7FXPgUAhDwnwCCnv82pocQSCSBQgdzJEzP5ZdfXk7QO/zww/Xnn39eFIsHH3zQhshMH4yVFTwzZszIu1zpnySSrlu3rl5//fWtuPfHH3/kXQ4nQCAIAq4KelHlM3Epd1TKngh6KRLJeJX79yuvvGJXXMt9vUqVKuV+h9J/O9Z+LyGYt9hiC33uuefqBQsWJKPTtDJvAq4KenIPlIgD6ddlKk/wypUr8+5nsScU6gMWWy/nR0uA+2a0vF2ozVVBD38TQc+F74eLbZg/f75dkScT0DbddFObKkRENFc2BD1XLEE7IACBqAkg6EVNnPogAIGcCBQ6mCMDoeeff36ZQSkZoDriiCP0l19+mVPdmQ56+OGHrSObPuC11VZb6RtuuCHTKZV+LiHZZOWgDPzKLPi5c+dWejw7IRAWARcFPZkReu+999owhenfOcnpFHReu4pW38aZP0/sjKAX1tUefLkS6lkGAyV8Zo0aNcr9/qRfv5W9l5CvksexV69eiHrBm8mJEl0V9DLlz5O8j3FshfqAcbSVOgsjwH2zMG5JP8tFQQ9/8z9aQtmTQy/p367g2y+TLmRCs4SIl/EKmSD98ccfB19RESUi6BUBj1MhAIFEE0DQS7T5aDwE/CVQ6GCOzCLr379/uQHVI488Usu+YrZHHnlEN2rUqEzZsqLi6quvLqjYRYsW2Xj0MsArjvK1115bUDmcBIFiCbgo6FWWzyTInE6SO+rKK68sl3czzvx5Yk8EvWKv6ujOF5Hm2GOPtYNhlQl2ueyTARPJrzd06FC9bNmy6DpBTZEQcFHQy5RDVAZ44woHXqgPGIkRqSQQAtw3A8GYuEJcFPTwNxH0EvdFiqjBEoq2e/fuNnx8s2bN9HXXXafl99mlDUHPJWvQFghAIEoCCHpR0qYuCEAgZwKFDubIKryzzjqrjOgmg6hHHXWU/vrrr3Ouv6IDH330Ud2kSZMyZTdu3FiPHz++osOzfiazk0UklFV+Esaic+fOWgbW2CAQNQEXBb3UQ+TaIkjQOZ0kd8+ZZ55Z5nstdR500EFaBhzj2hD04iKfX73fffedHjZsmK5Vq1a5a2jtazfX/2Wl3g477KBvvvnm/BrD0c4TcFHQcy1/nhixUB/Q+QuABloC3DdL90JwUdDD30TQK91vZOaer1q1Sk+bNk1LxBIZpzj++OOdjB6BoJfZhuyBAAT8JoCg57d96R0EEkug0MEcyZPXu3fvcgOrIuh9++23RfFIiR7pg7KyYm/MmDEFl/vRRx/pU0891ba3VatW+sknnyy4LE6EQKEEUtd2nTp19MCBAwstJtDzXnzxRb3PPvuU+S6HkdNpzpw5um3btuXq6dSpk/71118D7VM+hSHo5UMrnmMlTNesWbP0tttuW+b6Sf+NKPS95NTr2LFj0aGi4yFDrZkIuCjouZY/T9gV6gNm4s7n7hDgvumOLeJoiYuCHv4mgl4c3wXX6xR/pUOHDjbUpkQtmT59upbJyK5tCHquWYT2QAACURFA0IuKNPVAAAJ5ESh0MEdmmp9xxhnlBlfbt29f9KwyET0kxGb6AK0kh7788svz6lv6wStXrtRTpkzR1atX1/Xr19cXXXRR+m7eQyASAq4JepXlMxkxYkSgTCQ3hIQ4TP9ex50/TzqIoBeomUMp7JtvvtHnnXeeFvEt/foJ6r2EN5o0aVIobafQeAi4KOhVlD9P7olx5c8TyxTqA8ZjVWrNhwD3zXxo+Xesa4Ie/qb//uYXX3yh+/TpY/00mcAnOezZKicg6Qiuv/56Xbt2bRuBokePHnrJkiWVnxTTXgS9mMBTLQQgEDsBBL3YTUADIACBiggUOpiTKXyeCHrFrtCTkJsSYjN9sHazzTbTo0ePrqgLOX0mD5IvvPCCXYkkYdaknfLgwQaBKAm4Juil8pnIdyL9+xZ0Tqfly5fra665xrn8eWJ7BL0ovwGF1SWrO9u0aVPmGk2/Xot9v9566+nTTjtNS9gjNj8IuCboZcqft9NOO8WWP08sXagP6MdV4ncvuG/6bd9svXNN0MPf9N/fRNDL9q0svz89esmee+5po1HImIWLG4Kei1ahTRCAQBQEEPSioEwdEIBA3gQKHcwRp71v377lBliDCLkp+e4kxGb6IO3mm2+ur7jiirz7l36CCI2DBw+25W6//fY2Xn36ft5DIGwCrgl6UeUzyXS/iDt/ntgbQS/sq7648iXs0N1336032GCDMr8J6b8PQbw/8MAD9dtvv11cYznbGQKuCXqZ8uf94x//0O+9915s3Ar1AWNrMBXnRID7Zk6YvD7INUEPf9N/fxNBL79bysKFC/WoUaNs9KB69erpQYMGxZqCIFvrEfSyEWI/BCDgK4Eq0jEz4MAGAQhAwCkCf/zxhzKJmFX37t2VCTumjOClevXqlbWN8+fPV+PHj1dm1U2ZY4888kg1efJkZVbYlfk8n3+MoKd69uypvv/++zWnNWnSRA0YMMD+rfkwzzdmgEOZkFfKCJFq2bJlyuTUs+03qzPyLCm6w03uP3X11VerZ555JrpKqSk0AitWrFA//vijkmuxc+fO6rbbbgutrlwKfumll9S5556rXnnllTKHmxWxao899lA1atQo83mh/5iQMurDDz9UJgTYmiJMnj514oknqptuuknVrFlzzedRvzGCnurXr5/6+OOP1V577aVOOumkqJtAfZUQ+O2339Srr76q7r33XpkcV8mRxe2S3ywzIUWZ/CXFFcTZThAwIpmaMWOGMquDlVmRb/0SM1EotraZWfjKhI1Vcs9NbSaErL3f3HjjjYHda1Nl5/qa7gOacOTKCIxq//33z/V0jnOUAPdNRw0TYbPmzp2rbr/9dmUiMKiuXbvae2CE1ZerCn9TKfE3zz77bPXpp59af1N8YJ+2L7/8Uj300EPKRPFRJuSmHSdo2bJl4rtoJr4oeX6TsYP0P/Ev5M/kAbffM5MfXZnQmUpe09/LZ/KcI889qU382WeffVb1799fvfvuu8pEobC8WrVqlTrEuVf5Xbn11luVSbmimjdvroYMGaJMiFDn2kmDIAABCARNAEEvaKKUBwEIBEIgfTAnH0HPrHZTV155pXU+0xtyxBFHKJOLSDVt2jT947zey8OACHoifKQ2KU+Eh7POOiv1UUGvZta+Gj58uH3gEOd53LhxylXn+fPPP1dXXXWVuvnmm+0DQ0Ed5iRnCXTq1EndcccdsbVPHiZF4JaHMRMKqUw75KFTBpurVKlS5vNC/zHhY5Tca+Q1tZn8eVZcl+9jUPWkys7n1eT2U6effrr66aeflMmxaR/G8zmfY8MlINepCYVpB0zCrEmu+Vq1aimXJ3iE2X/fyjYzydf8brZr106ZHDV2ACqufj7wwAP2Xrt48eI1TTD586xPc/HFF6/5LOo3MlApE0vkHigD/zLoGNREjqj7Qn1/E+C++TeLUn2XugeKfyX+poh7cW34m3+R993fTAlfMmlx1113VSY/rPrnP/8Z12WXV73Sdhl3EDHSrDRc8ycipXwu++UZRv6kf6n3qVepTPxI+R1N/0t9Jv6liTZkJ0/LeIsIfrNnz1b33HOPksk0MtlYJlW77IMi6OV1SXEwBCDgEQEEPY+MSVcg4BOBQgU9GfyWAbIRI0aUwXHYYYfZz7feeusyn+fzT/oDT+q8bbfdVg0dOlR169Yt9VFBr+lC5M4772zFvWOPPbagssI+adGiRWrixIlq2LBhYVdF+TEQiFvQMzmdlKwMOf/888sIbSKeH3PMMcrk0QuEisxqff7559V9991XpjxZCSXXdtwzlE3OTnXmmWcquTewQQAC/hE4/PDD7USjLbfcMpbOyQplWYksK/Rk8C+1mfx51oeK0weRQUqJ0sAs+5RVeIWAfwTwN/E3o76qZbLs5Zdfrg455JCoq86pvpUrVyqZOPvGG2+oN998U8mEX4kiIkK4CFfyJ7+P8ioCnojSxWwi8slESRHs5E/+lzbIM5JEiOjQoYONErHLLrsoiZIS50THTP1E0MtEhs8hAAHfCSDo+W5h+geBhBIoVNCTEBMyQCVhMNO3Qw89VF133XVKBLhCt4pmsouDK+Jhx44dCy3WnieO+4UXXqiefPJJdfDBB9uQm0EJF0U1rIKTZeDPxNdXJq+TDc9SwSF8lDACcv3Jaoj111/fDqBKONW4NpPTSY0ePVpNnTq1TBPkeyHhdLfZZpsynxf6j8x0nTBhgl1pml6GyZ9nV6DKdzvOLT0EkoSbk/CbbO4QkN8aEV3DDk8rYZ0l3OqBBx7oTuc9b8nLL79sV/rLIJeExZQwxEFtEkL3lltuUfPmzbODZBIKXGbHx7HJjP8xY8bYCRTp9cv9RsKWxxnmNd0H3HTTTZWIixI6Pajtgw8+UP/+97+VhA+XEGwiaspAJlu4BLhvhss3CaW/8MILNgqJRB4QwR5/8yoVt7/59NNPWx9TQm6K0CXhN33aZGLcXXfdZUOLtm7d2j5LSCh7Fzb5rZP2SYqBF1980Qp5CxYssKKaCGsSCUKOkU1+o2Slet26dcv9mVx35T6TZzoR/WTyjkQ8kQmTmf5kv9yfRRxLbeIDSRmyis/ki1YyKVpCXwtDWeko7XBhQ9BzwQq0AQIQiIMAgl4c1KkTAhDISiB9MCefkJvp56VXEsQg/cyZM22+B4lJn9rkgUDEBxEbCt2kzRLaonfv3naWvOQNvOKKK1S1atUKLTL082RGYGqGYOiVUUHoBJ544gl1zjnn2Ic+CSsrwllcm+QzkcFVye2U2uSh8uSTT7YDzzIIFMQmD8+yClBCy6Q2CUHjQv48aY/kpxQRTwZYTjnlFLuSJ9VOXuMnIL8DIsysPXkk6JbttttudsV2kGJG0G30rTxZjS+5WOS+I7/LF110UWBdFCHv0ksvVQ8//HDsOfQy5c+Te+2UKVNiDXGZ7suJDzho0CAb8jwoQ4hoK9EV5HfghBNOsN9luf+zhUuA+2a4fJNQ+uOPP25D+oqwICF1ZWJVXBv+5l/k0/3NLl262CgscdkkjHolPKU818jvmgs59OT5WVbhiZAqf5JbV3Lgyao4EfFEhJNNnnckOonkDpeVhfIqE4Dktyr1JyJfpvepSSpSnvzJhNz01/T3cm+WdAfin8jvr+TXkxV7EpVHnvllZZ6MS6QEPplos88++yiJNLDvvvva8Jxh2C6XMhH0cqHEMRCAgJcEzA2aDQIQgIBzBIyzq80KHYkjoc1gjjb573Ju4913363NbDJ7rpwvf2Y2mTYDNzmXsfaBxrnVZvBWG4e2TLkHHHCAfuutt9Y+PK//zYOGNrMhbdkm3KY2wmFe53MwBIol8Nhjj2nz0KhN7gQ9cODAYosr+HzzsKnvvfdebWaalvmemZxO2jxkFlxuRSeaFbfa5MsrU4/8b3LnaWlH3JtZoafNKl1tHqi1EVnjbg71r0Ugda1utNFGZa6h1G9OUK9mtrw2q4nWqp1/wyRgwvDae1CDBg30iBEjAq3KhM/SZkW/vWbM6j9tZuYHWn4+hZnBO7329duwYUM9cuTIfIoJ5dhifMBcGmRWQmgzCGntYFbAavHx2MInwH0zfMau12AEPW3CDFt/00yIia25qWsRf1Nr3/1NE5FD9+nTx97vjaCnX3/99ViuO5MWRMsYhZk4qLfaaittctRps+JuzdiCvN9hhx20SeOhTWoLbSaeaBkj+P7777VZZaeNcBVau8U3MeE1bVvM6nxtUh9Y3/ORRx7RJg2BNsKdNiLemrYaEVEb0U+bMJzaiI36ggsu0Cbai5bf7qg3E45UG7HW2rd58+baRGqKugnUBwEIQCAWAjLjgg0CEICAcwSKGcx56qmn9Pbbb28du9Sg6t57763NDMSC+2nCUOirrrqqTJlStkmqrcVBL2Z79tlntQm3Yp1kcabFcWeDQJQEXBH0TMgXbVanajOrtMx3zeR0ClTolgfjK6+8slw98hB75513Rok+Y12+D7Bk7HiCdrz66qvarM4uc62mfnOCeJXBHRFzZbCCLToCpSDomdUx2qxYKHcPdGVSUTE+YC5XCoJeLpTCOYb7Zjhck1KqK4Ie/ubfV4zv/macgp5MFjGpBLQJb61NuEotk2Zq1qxpn/llkrBMqjnssMP0v/71L23yelsB78cff9RmxV5k4pg8E11//fVWoJMJ0SYUrl6yZImd3Cj+p7w3YUCtwCeTLs866yw7biETDsXXFXHPhN/UIqbJBBkT5cAKkH9fYeG+Q9ALly+lQwAC7hJA0HPXNrQMAiVNoJjBHFkxJzPf0wdUd999dy2zzArdTM44fckll5QpUwZbe/XqpU3IikKLtQ67yVWjTRgLO/Nt1KhRRZVXcEM4saQJuCLomfCS2oScLfM9k++xyemk33///cBsZHJHaRNSr1w9JjSvllmqLmy+D7C4wLjYNvzwww/64osvXjNjOf03J4j3Jl+kXalebDs5Pz8CpSDoyQCjiMVrX6dyr3VhRWgxPmAu1kbQy4VSOMdw3wyHa1JKdUXQw9/8+4rx3d+MQ9CT1XRz587VJly0jbax4YYbahPG2/7mmnx0WqIvyPO/jFmIWCaTbOR3L47NhN/WsnJR/IE999xTz5o1q8JIJbKq1YQEtROZTchQe5xJ16C32247OzlIBEoRKxs1aqQPPfRQbfLUarnfh70h6IVNmPIhAAFXCSDouWoZ2gWBEidQzGDO/Pnzdf/+/csMVImzedtttxVMVcqU0DDpg18SZkJm3BWzmbj5+vjjj7flSvgnGWRig0DUBFwR9NIHWVPfNXkANjnk7ENkUFwkjE2bNm3KfJ9lhmmnTp20ySMRVDVFleP7AEtRcBw5WWZey4pwmTCSul6DepVJHjLTOYrBEEdwOtOMUhD0TO4ou1og/XqVe+2pp56qV61aFbstivEBc2l8+m8NITdzIRbcMdw3g2OZxJJcEfTS7wGp+yD+pp8h3qMU9ERckpCeEuJTVqyJeCdRR+Rviy220CY3to0YJOG2ZRVe3OGeZcKyTCY2+fpsqHERIHN5DhJxT/oqUYpkEpCkSWnXrt2alCeyek/Clsuz1nXXXWdFy7DuVwh6YZGlXAhAwHUCCHquW4j2QaBECRQzmGOSSlvnMT3fXePGjW14qUJxfvLJJzamfeqhT1532203/dBDDxVapJ39Jnm8JCa9ONKyMknazgaBqAm4IOil8pnILNb075nkz5PVsUFukjvK5fx50lcEvSAtHl5ZMpgxevRomwcl/bot9r2EYRZhqZgV4OH12u+SS0HQy5Q/77LLLnPCuMX4gLl0IH0wH0EvF2LBHsN9M1ieSSrNBUEPf7PsFeO7vxmFoCe/WW+//bY+++yz9dZbb23DV8o4hEzOklDW4ifKij2594WZC6+sZSv/T74HYntpn/isIr699tprlZ9UwV7xU2X8QiY/y/Nkly5d1jxjSf/leUvKnjx5shYBMegNQS9oopQHAQgkhQCCXlIsRTshUGIEihnMEQf1iSeesImlU4OqkvR8yJAhBVMUJ1zy5aXKEye92Hx33333nb7wwgvtrD0JrSahKdggEAcBFwQ9CTczbtw4+31Ifc/kVfLnSRL5oLYk5M+Tvvo+wBKUPeMuRwYyPv74Yxu+MH0SSfo1nO/7Jk2a6LFjxzLBIybj+i7oVZY/T/LjuLAV4wPm0n4EvVwohXcM983w2LpesguCHv5m2avEd38zTEFPxhwkjP+wYcPsuEOdOnVsGHaZqLvXXnvZ3HQyKViuubhX45W1urYCnKzIS6X9GDlyZFE5m4WFiGsSWWL27Nk2197mm29ux06kDlmxJ/kC77nnnpxWAa7d3kz/I+hlIsPnEICA7wQQ9Hy3MP2DQEIJFDuYk+68y2CqhNPr3LlzwWH7nnvuObsiLzUwK6uGLr300qJWT6SH/RMHV3LasEEgDgIuCHqSz0QSsae+Y6nXgw8+WL/77ruBYUlC/jzprO8DLIEZ1IGC5PdKQiwdd9xx5QTp1HWc66v8tgwdOlQvWrTIgZ6VZhN8F/TE1zj99NPL3Wslp48L+fPkqivWB8x25SLoZSMU/n7um+EzdrEGFwQ9/M2yV4bv/mb6mIDkihN/LYht8eLFNp3HfvvtZ8NVSlhNCTXZqlUrPWnSJCv0SVhNEbpc20RcfPDBB3XTpk2tAHn44YfbyWlBtVNWIcpqRAnvLasWJRqR+MHCR0KPnnbaafqNN94IhA2CXlBWoxwIQCBpBBD0kmYx2guBEiFQ7GCOOJLTp0/X6eH7ChUGxBGXFUIy6y41KCuz7p555pmCrSE5aiTefK1atWwbzz///NiSYRfcCU70hoALgl76AGvqe1asEF+RgdKF9PR6XMqfJ+32fYClItsk+TP5zZk3b57Nm1KjRo01vxWpayyXVwnTdNVVV9lBEBcHgJJsn3za7rug53r+PLFVsT5gNnun/94QcjMbrfD2c98Mj62rJbsg6KV//1O/zfibLazY0rNnT1cvnYLbFbSgJ2KYhNcUUaphw4Z2hZtcPzvssIONNCKCsatCXgqirBqUVB/S7mbNmtlUJfK7G/QmZYqw9+yzz+quXbvanIISzWL99dfXe+yxh7766qv1kiVLiqoWQa8ofJwMAQgkmACCXoKNR9Mh4DOBIAZzxNk++uij1wysSlhLEdHy3SQ05gUXXGBnsMmDnwh7Mtssl6TRmepKnx26++6760cffTTToXwOgdAJxC3oiXghod7SBXj5rkl4lhEjRgTaf8lb6Xr+POkwgl6gZo+kMPnd+vrrr2345L333jvn1XoSEvqEE07QTz31lJaQsGzxEvBd0HM9f55YPwgfsLKrKH1AH0GvMlLh7+O+GT5jl2qIW9DD3yx/NfjubwYp6In4dMstt+g999zTilLyrCKiXr9+/azIJ6E1XZ+QJZOKp02bZp+FJBTm8ccfrxcsWFD+wgjwE5m8IXXMnDlTywRrERKrVq1qV+6dcsopdrVeodUh6BVKjvMgAIGkE0DQS7oFaT8EPCUQxGDOypUr9YwZM2xoB3G4JZ79qaeeauPY54PthRdesHHwpQz523fffbV8VswmOf6aN29uHdoTTzxRS9gONgjERSBuQS9TPpMWLVrou+66KzAsScmfJx32fYAlMKM6VpAM5Cxfvlx/+OGHdgKJhOFs1KjRmoklqd8RCTsks7llcsjDDz+sv//++6JylziGIdHN8VnQk3vt+PHjy4nNu+yyi5Z+u7IF4QNW1hcEvcroRL+P+2b0zOOqMW5BD3+zvOV99zeDEPTkHiX5klPhI0WMknGFgw46SMtEQVmF5lqOvPKW/uuTd955R3fo0MFOVN5xxx1tRCPJaxr2JgxlbEb8Y0lb0rhxY9sGiVYkk+D+/e9/FzRZGkEvbMtRPgQg4CoBBD1XLUO7IFDiBIIazPnxxx/1ZZddplMh0Lbaais9ceJEnavjKg8BMutOBl9lIHbLLbe0IdFkdluhm4h3Y8aMsTPTmjRpoidMmOD8bL5C+8p5ySAQt6CXvmI1JXjIqzwoSxjDoDbJn3fmmWeWE1ekHnnAdWnzfYDFJdZhtEV+Y1asWGGFOrm+n376ad2tWzd77W233Xb6+uuv119++aUdBCrm9ySMtpd6mT4LepXlz/voo4+cMX1QPmCmDiHoZSIT7+dr3zcfeeQR3bFjR3vf3HXXXfUdd9zBfTNeExVde9yCHv5meRP67m8WK+iJjyYTcSXPbCr9xmabbaYlXYaErhSRKimbTGwU/7N27do27YfkLi825GW+fZf7vIyFSHQiyd2XWq0nufUGDhyov/rqq7yKRNDLCxcHQwACHhFA0PPImHQFAj4RCGowR5zGDz74YM1Aqsyok1lgsiIi2/bzzz/bmPIbbbSRHUyQMH3nnXeeXrRoUbZTK93/1ltv6SOPPNKWecABB+g333yz0uPZCYGwCcQt6KUPrqYEPXnACzqv3Zw5c3Tbtm3tdy/MeoKwl+8DLEEwSlIZP/zwgx4+fLi99nbbbbecfoOS1D+f2uqzoFdR/jwJuSW5bVwSloPyATNdl+m/OYTczEQp/s9lIL5v3772vrn//vtr+Q1nSzaBuAW99O9+mH4g/qY712kxUvJmBAAAGkpJREFUgp6svJOJwDIRSyb3psYR7r77bitKyThDkrb061LChs6aNSu2ScXic8gYzYUXXmjDf66zzjq6bt26dvVgPpGQEPSSdAXSVghAIEgCCHpB0qQsCEAgMAJBDuZIWZJPTwasZKWeOOQyqC8zwySme0Wb5M274oortKzok+TNkjB63LhxWlb8SciIQjcJx3HnnXfaXGGSELpPnz5ODaIV2i/OSzaBOAU9+T7JAHpKOE8NsIiALgJIMd+3ta3y4IMP2rx8qTrkNYx61q63kP8R9Aqh5u45MigkIYbkmpO8qbLyhM1NAj4LehXlz9t00031qFGjnDJGkD5gRR1LH9RH0KuIkBufyUoNiZIh983WrVvrV1991Y2G0YqCCcQp6OFvVmw23/3NQgU9OU8m8kqOvJTYJKk7ZEzh119/rRimw58uXLjQ/tZLqFDJ3Txo0KDY+yHjItIuWX0tAqPc62WsZp999tG33367zaebDSmCXjZC7IcABHwlgKDnq2XpFwQSTiDowRwR7iS8mYS3lLCZ4syKSNe9e3ctD5cyaCDhHyTs3pQpU/QRRxxhBQaZuS4r+mSAT/IuFLvNnz9fDxgwwIqEkj9p+vTpxRbJ+RAomkCcgl6mfCaS10HE76C2ZcuW2XC58lAuD4ypv6DrCaq9vg+wBMUpKeUg6CXFUtr+3stgV4MGDfSIESMCbbj4GKkQgu3bt9fffvttoOVXVlhl+fNE6HNpC9oHXLtvCHprE3HzfwQ9N+1STKviFPTwNyu2nO/+Zr6Cngi/c+fOtVFCNthgA/u80LRpUyuGLViwIDG58tKtLX0SO++88862P23atNGvvfZa+iGxvZe2SYh6WZV34okn2lWQMv4iqyLHjh2r5fmtsg1BrzI67IMABHwmgKDns3XpGwQSTCCMwRwJiyEPcxJySsI7yEwwCe0gcfBF3Nt66621xG+XFTubbLKJPuyww/QNN9ygJa9MUDPxnnvuOb3HHntYQU8G87755psEW4mm+0IgTkGvsnwmQea1+/zzz3Xv3r3XCHkpQc/F/HlyXfk+wOLLdyfXfiDo5Uoq/uN8XaEn99rTTz+93D3w0EMPtX5O/OT/bkEYPuDfpWuNoJdOw933CHru2qbQlsUp6OFvVmw13/3NfAQ9+e2ZPXu2bteunc0xJ5MA5bl9xowZWlJxiPiUxE0mFMuKPBHKZFX+yJEjtQhhLm0y+VrGXCQ3oYzPSOqFxo0b6yFDhthVfJnaiqCXiQyfQwACvhNA0PPdwvQPAgklEOZgjpQtCaBlgF8EtqlTp+rRo0fb8H5XXXWVvuuuu2xYH5mFt3z5ch1UfHwpSxJRS8hPEQxl5r+EmmCDQNwE4hT0nn/+ed2yZcsyg8zyAC1h0GTGZlDbyy+/rGVGakrIk1ep5+STTw5MsA+qrVKO7wMsQbJKQlkIekmw0l9t9FXQk0HKVq1albkHyoBZ586dnRvYC9MHFCsj6CXj+4iglww75dPKOAU9/M2KLeW7v5mroCfCkOSU23fffW0kH3lelwkvMlYQ5PNIxVYI71MZa5CUA7LKUNKIHH744frjjz8Or8IiSpa2yviLjMeImCfPaRIt4ayzzso4CRpBrwjgnAoBCCSaAIJeos1H4yHgL4GwB3OEnMyyk3rESZeVeyLyLV26VK9cuTIUoe3999+3IoUICRLG85lnnvHXgPQsUQTiEvTk+3bttdfqmjVrlhlkrlOnjg1NG9RMWPmOy2rbWrVqlatn4MCBTs649X2AJVFfkAAai6AXAMSIivBR0JN77TXXXJPxHhgR2pyrCdsHRNDL2RSxHoigFyv+UCqPS9DD38xsTt/9zVwEvVWrVumHH37YRu+RVWzyvHDCCSfYVByurWTLbMmK93zyySc2xYhM4JGIRNddd11OuekqLi38T+XZT8Zkbr31Vr399ttbEVLyrPfq1Ut//fXX5RqAoFcOCR9AAAIlQgBBr0QMTTchkDQCYQ/mRM1DnNOHHnpIb7755naFniTVzhYTPuo2Ul/pEohC0JNQKhKu5scff9SfffaZfvrpp/XgwYN18+bNy4hsInjLQ2fbtm31o48+anNfihgionsuD9VyjOTDlHrkIV5mZA8fPrzSeqT/kmMzn3rCvlp8H2AJm59r5SPouWaRzO1JuqAn90AZDPv++++1DOTJALrk7t1qq63swFj6KmW510rYYTlGQl3JOXKflolNQU2oyEw6856wfUAEvczsXdqDoOeSNYJpSxSCHv5mfrby3d+UZ4E+ffrYZw15tnj99dfLAJJIPMJAUnFUrVpVS968bt26aQnRKr9FSd5EqJw2bZpNJyJC5fHHH29XwLneJ/E/ZJxk5syZa1KVbLPNNvrGG28s13QEvXJI+AACECgRAgh6JWJougmBpBEIezAnah4//PCDHjZsmBUqZFBt0qRJsQ6WRd1/6nObQJiCngwsT548Wbdo0cLmqZTrf8stt9SNGjWyD80yoJw+wJx6X6NGDZvfUo6VcyTHpTxsjxs3rkKYUo98r3bYYYcy9YiIXq9ePfvdS5Wd/pqpnvHjx1dYT1Qf+j7AEhVHV+pB0HPFEtnbkVRBT0Jo9evXz85ol/ul3DclxJbkCZZVzxK6Kv3el3qfugfKsal77bbbbmtzjorvEscWtg+IoBeHVfOvE0Evf2aunxGmoIe/WZj1ffc3swl6InqJUCSCl+RuO+OMM+wkv6BSbhRmlWDOklzkHTp0sJN5dtxxRz19+vTAUokE08LKS5EIK/KMevDBB+v99tvPTvRc+wwEvbWJ8D8EIFAqBBD0SsXS9BMCCSMQ9mBO1DheeeUVfeCBB9rBtEMOOUR/8MEHUTeB+iCQkUCYgt7ChQv1ZZddZlemysOyhNcUgU3ySEp+BBlA3m677awQJ2KczMCUz7bYYgs7EC1hVmrXrm3Pb9KkiR47dmyF/ZB6JMm75LwIop4rrriiwnqi+tD3AZaoOLpSD4KeK5bI3o6kCnpz5861A3cySULugeuvv77ecMMNdcOGDTPea1OCX/369a3oJ+KerFCQ+3SXLl00gl7264UjwiOAoBce27hKDlPQw98szKq++5vZBD1ZDSbC19ChQ7VM5pP7jg9inoSZvf766+0zlIQQ7dGjh129X9hVEt9ZEjHgm2++0fPnz68wlyGCXny2oWYIQCBeAlWkejNDkw0CEICAUwRMUmRlQkSo7t27KxPvXZnQfMrETneqjbk2xoR+UTNmzFB9+/ZVZqBMnX766Wr06NHKDLjlWgTHQSBUAmaARfXu3VuZUJWqZ8+eyjzQBlafeShWJlymWrRokS3TJGRXFf2lVyiuSUV/8v0xYqAyg9Tph9v3UdVTruKQPjA5NpVZbaNMyB/VtWtXNWXKlJBqotgoCMj1P3HiRGVWaqvdd99dGfFZHXXUUVFUTR15Erj//vut7yG/0fK7bUL25llC5sPnzZunRowYoaSO9u3bK7N6WZnVyplPyGOPGdSy91kzo92eVdF9Vj5L31L3WTOgae+5sk8+k+PMRArVoEEDZQTC9FMieR+2D/jSSy+p8847T82ZM0eddNJJ6vbbb4+ln5HATHAlZgDX+iMm/6Nq3bq1fb/XXnsluEc0fdasWdbflN9EeR6aMGFCYFCi8gOjqicwMFkK8t3fNCH1lZmkZ30wE3LT3kdatmxZhoqZSKyWL19ufwfkt8+saC+zP4n/mMnE6vzzz1ezZ89WJsKJGjVqlGrXrp39fU9ifzK1WcZZTL49ZVZWKpPGQQ0ZMkQZ8TLT4XwOAQhAwB8C5qGNDQIQgIBzBHxaoSf5wiR8hxkg07vuuqt+4IEHnONNg0qbQJgr9EqbbOG9933GdOFkknkmK/SSY7ekrtBLDuHsLQ3bByTkZnYbuHAEK/RcsEKwbQhzhV6wLS2d0nz3N7Ot0PPR0rJa1Qh4unr16jYqyqBBg/Svv/7qY1dtfnUz6dFGQZK87DfddJOX/aRTEIAABNYmQMjNtYnwPwQg4ASBsAdzouzkU089ZUMKSv6aY445RouTzQYBlwgg6Llkjb/a4vsAi3vEw20Rgl64fIMsHUEvSJqFlRW2D4igV5hdoj4LQS9q4uHXh6AXPuN8a/Dd3yw1QU9CiIpNd955ZytytWnTRr/22mv5XhaJOZ6Qm4kxFQ2FAAQCJoCgFzBQioMABIIhEPZgTjCtzF7Kzz//rMeNG2dz0piwWnrMmDFexOXP3nOOSBIBBD33rOX7AIt7xMNtEYJeuHyDLB1BL0iahZUVtg+IoFeYXaI+C0EvauLh14egFz7jfGvw3d8sNUFPVuJNmjTJ5tLddNNNbX5xEb183RD0fLUs/YIABLIRQNDLRoj9EIBALATCHsyJqlNz587VRx99tJ0hZ/J/aBPPPqqqqQcCORNA0MsZVWQH+j7AEhlIRypC0HPEEDk0A0EvB0ghHxK2D4igF7IBAyoeQS8gkA4Vg6DnkDH+f1N89zdLTdAzOR61yYuo//nPf+qhQ4dqk0PQvYsuwBYh6AUIk6IgAIFEEUDQS5S5aCwESodA2IM5UZAUh/qee+7R9evX1zVr1tQ9e/bUK1eujKJq6oBAXgQQ9PLCFcnBvg+wRALRoUoQ9BwyRpamIOhlARTB7rB9QAS9CIwYQBUIegFAdKwIBD3HDGKa47u/WWqCnlxhskrvu+++04sWLfI+MhCCnnv3FFoEAQhEQwBBLxrO1AIBCORJIOzBnDybU9Dh33zzjT733HO15M7bbrvt9K233lpQOZwEgbAJIOiFTTj/8n0fYMmfSLLPQNBLjv0Q9OK3Vdg+IIJe/DbOpQUIerlQStYxCHru2ct3f7MUBT33rrLwWoSgFx5bSoYABNwmgKDntn1oHQRKlkDYgzlRgJ09e7Zu1aqVDbd5xBFHaHmgYIOAiwQQ9Nyziu8DLO4RD7dFCHrh8g2ydAS9IGkWVlbYPiCCXmF2ifosBL2oiYdfH4Je+IzzrcF3fxNBL98rIlnHI+gly160FgIQCI4Agl5wLCkJAhAIkICEq5QVbUopvfXWW+sbb7wxwNLDL2rFihU2IXX16tVtyM0LL7xQ//HHH+FXTA0QKIAAgl4B0EI+xfcBlpDxOVc8gp5zJsnYIAS9jGgi24GgFxlqpytC0HPaPAU1DkGvIGyhnuS7v4mgF+rlE3vhCHqxm4AGQAACMRFA0IsJPNVCAALZCdx99926Vq1aukWLFlreJ2lbuHChvuSSS6wguddee9n8BElqP20tLQIIeu7Z2/cBFveIh9siBL1w+QZZOoJekDQLKwtBrzBuvp2FoOebRbVG0HPPpr77mwh67l1zQbYIQS9ImpQFAQgkiQCCXpKsRVshUGIEPvzwQz1kyBA9bNgwPX/+/ET1Xlbjvfzyy7p///566tSpNjl1ojpAY0uKAIKee+b2fYDFPeLhtghBL1y+QZaOoBckzcLKQtArjJtvZyHo+WZRBD0XLeq7v4mg5+JVF1ybEPSCY0lJEIBAsggg6CXLXrQWAiVF4LffftOLFy+2f0kMV7lq1Sq9aNEivWzZspKyG51NHgEEPfds5vsAi3vEw20Rgl64fIMsHUEvSJqFlYWgVxg3385C0PPNogh6LlrUd38TQc/Fqy64NiHoBceSkiAAgWQRQNBLlr1oLQQgAAEIQCBwAgh6gSMtukDfB1iKBpSwAhD0kmOwF198Ue+777423Pddd90VaMPfeecd3bFjRxuOu3379vrbb78NtHxfCgtb0Pvkk0909+7ddYMGDfSIESN8weZdPxD0vDMpITcdNKnv/iaCnoMXXYBNQtALECZFQQACiSJQRVqr2CAAAQhAAAIQKFkCJqeJ6t27tzIrYlXPnj3V+PHjS5aFKx1/5plnVL9+/dSnn36qunbtqqZMmeJK02hHAQTMam01ceJEZUJIq913312NHDlSHXXUUQWUxClhE/j111+VEXzU0qVLra3q1KkTWJXz5s1TRkBS999/vzKCnpo8ebJq1KhRYOX7UpCJyqCmTZumjOimmjVrpgYPHqx69eoVWPeMYKjMIK/65ptvlMnTrBo2bBhY2RQUHAETbt/6I9dcc41q3bq1fW/yUgdXASVFTmDWrFnW35TfxNNPP11NmDAh8jZQYVkCvvubX375pbriiiusD9a2bVt7H2nZsmVZCPyXWAImopO69dZb1RlnnKGaN2+uTLoW1aNHj8T2h4ZDAAIQyJUAgl6upDgOAhCAAAQg4CkBBD33DOv7AIt7xMNtEYJeuHyDLv3PP/9Uq1evVtWqVQu0aAS93HCGLehJK8TG8ic2rlKlSm4N46hICSDoRYo7ksoQ9CLBnFclvvubCHp5XQ6JOxhBL3Emo8EQgEBABBD0AgJJMRCAAAQgAIGkEkDQc89yvg+wuEc83BYh6IXLNymlI+jlZqkoBL3cWsJRcRJA0IuTfjh1I+iFw7WYUn33NxH0irk63D8XQc99G9FCCEAgHAIIeuFwpVQIQAACEIBAYggg6LlnKt8HWNwjHm6LEPTC5ZuU0hH0crMUgl5unHw/CkHPPwsj6LlnU9/9TQQ99665IFuEoBckTcqCAASSRABBL0nWoq0QgAAEIACBEAgg6IUAtcgifR9gKRJP4k5H0EucyUJpMIJeblgR9HLj5PtRCHr+WRhBzz2b+u5vIui5d80F2SIEvSBpUhYEIJAkAgh6SbIWbYUABCAAAQiEQOC+++5Tp512mlq+fLlq0aKFOvLII0OohSLzIfDxxx+rxx57TP3++++qU6dO6vbbb8/ndI51jACCnmMGiak5b7/9tho2bJh65JFHVOPGjdVBBx2kGjVqFFNr3K1WBL13331XPfnkk6pJkyZqwIAB9s/dFtOyMAgg6IVBNd4yxd/s3r27WrZsGf5mvKZYU7vv/iaC3hpTe/kGQc9Ls9IpCEAgBwIIejlA4hAIQAACEICAzwRmzJihTjnlFLV69WpVrVo1VbNmTZ+7m4i+iZC3cuVK21YR9O64445EtJtGVkwAQa9iLqX26cyZM1W3bt3UihUr1LrrrquqV6+uqlatWmoYcuqvDNKtWrXK8unSpYuaOnVqTudxkD8EEPT8sWWqJ/ibKRLuvPrubyLouXOthdESBL0wqFImBCCQBAIIekmwEm2EAAQgAAEIhEhg9uzZatCgQeqNN94IsRaKLoRA3bp11RlnnKHGjh1byOmc4wgBBD1HDBFzMz777DM1ZswYdeONN8bckuRUv8suu6gRI0aojh07JqfRtDQQAgh6gWB0qpAXXnjB+puvv/66U+2iMUqJv3nmmWfa3yifeCDo+WTN8n1B0CvPhE8gAIHSIICgVxp2ppcQgAAEIACBjARkFcQPP/ygli5dalfpZTyQHZESqFKlilpvvfXUxhtvbP8irZzKAiWAoBcozsQWJqEklyxZon788Ucl79kqJ7DOOuuo2rVrq4YNG6patWpVfjB7vSOAoOedSe2qW/xN9+zqs7+JoOfe9RZkixD0gqRJWRCAQJIIIOglyVq0FQIQgAAEIBAiAa21kj82NwjIAItsqVc3WkUrCiGAoFcINX/P4V6bm23l3sf9LzdWPh6FoOejVf/qE/dAt2ybus+mXt1qXXGt+fzzz+2qwylTptiUAjvuuKOSld9sfhD43//+pyQP5Jtvvmlz7krEmXPOOcePztELCEAAApUQQNCrBA67IAABCEAAAhCAAAQgUCwBBL1iCXI+BCBQagQQ9ErN4vQXAsETkDCvAwcOXJNWQPLWSvQLNj8IyOQAiXgguSDFtuTc9cOu9AICEMhOAEEvOyOOgAAEIAABCEAAAhCAQMEEEPQKRseJEIBAiRJA0CtRw9NtCARI4KefflITJ05Uw4cPtyu+q1WrpmrUqBFgDRQVJwER9ETMk/QRrVq1Updffrk65JBD4mwSdUMAAhCIhACCXiSYqQQCEIAABCAAAQhAoFQJIOiVquXpNwQgUCgBBL1CyXEeBCCQIrB69WqbI1xy18omYUUlPyubHwRS4XvltWbNmqpBgwYItn6Yll5AAAJZCCDoZQHEbghAAAIQgAAEIAABCBRDAEGvGHqcCwEIlCIBBL1StDp9hgAEIAABCEAAAhDIRgBBLxsh9kMAAhCAAAQgAAEIQKAIAgh6RcDjVAhAoCQJIOiVpNnpNAQgAAEIQAACEIBAFgIIelkAsRsCEIAABCAAAQhAAALFEEDQK4Ye50IAAqVIAEGvFK1OnyEAAQhAAAIQgAAEshFA0MtGiP0QgAAEIAABCEAAAhAoggCCXhHwOBUCEChJAgh6JWl2Og0BCEAAAhCAAAQgkIUAgl4WQOyGAAQgAAEIQAACEIBAMQQQ9Iqhx7kQgEApEkDQK0Wr02cIQAACEIAABCAAgWwEEPSyEWI/BCAAAQhAAAIQgAAEiiCAoFcEPE6FAARKkgCCXkmanU5DAAIQgAAEIAABCGQhgKCXBRC7IQABCEAAAhCAAAQgUAwBBL1i6HEuBCBQigQQ9ErR6vQZAhCAAAQgAAEIQCAbAQS9bITYDwEIQAACEIAABCAAgSIIIOgVAY9TIQCBkiSAoFeSZqfTEIAABCAAAQhAAAJZCCDoZQHEbghAAAIQgAAEIAABCBRDAEGvGHqcCwEIlCIBBL1StDp9hgAEIAABCEAAAhDIRgBBLxsh9kMAAhCAAAQgAAEIQKAIAgh6RcDjVAhAoCQJIOiVpNnpNAQgAAEIQAACEIBAFgIIelkAsRsCEIAABCAAAQhAAALFEEDQK4Ye50IAAqVIAEGvFK1OnyEAAQhAAAIQgAAEshFA0MtGiP0QgAAEIAABCEAAAhAoggCCXhHwOBUCEChJAgh6JWl2Og0BCEAAAhCAAAQgkIUAgl4WQOyGAAQgAAEIQAACEIBAMQQQ9Iqhx7kQgEApEkDQK0Wr02cIQAACEIAABCAAgWwEEPSyEWI/BCAAAQhAAAIQgAAEiiCAoFcEPE6FAARKkgCCXkmanU5DAAIQgAAEIAABCGQh8P8AAAD//2TqMa0AAEAASURBVO3dCbxWU////xUpiZShIqGQhIhSZjJHlDskNIjQgBQyJilS3YaIDGlChlsZcyNTSAPiRpO6u5MQKSRj1n+91+9/ne+pc67ONex9nX3t67Ufj+OcrrP32ms/12Vf+6zPWp9VwbrNsCGAAAIIIIAAAggggEAoAitXrjQjR440N954o2nSpIkZOHCgOfnkk0M5F4UigAACcRBYunSpGT58uLn77rvNYYcd5n8+6KCD4nBpXAMCCCCAAAIIIIAAAhkLVCCgl7EdByKAAAIIIIAAAgggUKYAAb0yidgBAQQQWE+AgN56HPwDAQQQQAABBBBAAAEvQECPNwICCCCAAAIIIIAAAiEKENALEZeiEUAglgIE9GLZrFwUAggggAACCCCAQJYCBPSyBORwBBBAAAEEEEAAAQQ2JkBAb2M6/A4BBBAoKUBAr6QJryCAAAIIIIAAAgggQECP9wACCCCAAAIIIIAAAiEKENALETfgon/77TezYMECs2rVKqP1uqpUqRLwGSiuvAXWrVtn/vvf/5r//e9/Zr/99jPbbbddeVeJ85ciQECvFBReQgABBBBAAAEEECh4AQJ6Bf8WAAABBBBAAAEEEEAgTAECemHqBlv222+/ba655hrzxx9/mB49epjOnTsHewJKK3eBzz77zAwdOtSorc8++2xzyy23mAoVKpR7vajA+gIE9Nb34F8IIIAAAggggAACCEiAgB7vAwQQQAABBBBAAAEEQhQgoBcibsBFT5482VxwwQVm0003NT179jQ33HBDwGeguPIWmD59urnqqqvMu+++azp06GDGjRtnNtlkk/KuFuffQICA3gYg/BMBBBBAAAEEEEAAASdAQI+3AQIIIIAAAggggAACIQoQ0AsRN+CiJ02aZM4//3yz2Wab+Rl6/fv3D/gMFFfeAgrkXXnllUaBvfbt25sJEyb4AG5514vzry9AQG99D/6FAAIIIIAAAggggIAECOjxPkAAAQQQQAABBBBAIEQBAnoh4gZcNAG9gEEjWBwBvQg2SilVIqBXCgovIYAAAggggAACCBS8AAG9gn8LAIAAAggggAACCCAQpgABvTB1gy2bgF6wnlEsjYBeFFulZJ0I6JU04RUEEEAAAQQQQAABBAjo8R5AAAEEEEAAAQQQQCBEAQJ6IeIGXDQBvYBBI1gcAb0INkopVSKgVwoKLyGAAAIIIIAAAggUvAABvYJ/CwCAAAIIIIAAAgggEKYAAb0wdYMtm4BesJ5RLI2AXhRbpWSdCOiVNOEVBBBAAAEEEEAAAQQI6PEeQAABBBBAAAEEEEAgRAECeiHiBlw0Ab2AQSNYHAG9CDZKKVUioFcKCi8hgAACCCCAAAIIFLwAAb2CfwsAgAACCCCAAAIIIBCmAAG9MHWDLZuAXrCeUSyNgF4UW6VknQjolTThFQQQQAABBBBAAAEECOjxHkAAAQQQQAABBBBAIEQBAnoh4gZcNAG9gEEjWBwBvQg2SilVIqBXCgovIYAAAggggAACCBS8AAG9gn8LAIAAAggggAACCCAQpgABvTB1gy2bgF6wnlEsjYBeFFulZJ0I6JU04RUEEEAAAQQQQAABBAjo8R5AAAEEEEAAAQQQQCBEAQJ6IeIGXDQBvYBBI1gcAb0INkopVSKgVwoKLyGAAAIIIIAAAggUvAABvYJ/CwCAAAIIIIAAAgggEKYAAb0wdYMtm4BesJ5RLI2AXhRbpWSdCOiVNOEVBBBAAAEEEEAAAQQI6PEeQAABBBBAAAEEEEAgRAECeiHiBlw0Ab2AQSNYHAG9CDZKKVUioFcKCi8hgAACCCCAAAIIFLwAAb2CfwsAgAACCCCAAAIIIBCmAAG9MHWDLZuAXrCeUSyNgF4UW6VknQjolTThFQQQQAABBBBAAAEECOjxHkAAAQQQQAABBBBAIEQBAnoh4gZcNAG9gEEjWBwBvQg2SilVIqBXCgovIYAAAggggAACCBS8AAG9gn8LAIAAAggggAACCCAQpgABvTB1gy2bgF6wnlEsjYBeFFulZJ0I6JU04RUEEEAAAQQQQAABBAjo8R5AAAEEEEAAAQQQQCBEAQJ6IeIGXDQBvYBBI1gcAb0INkopVSKgVwoKLyGAAAIIIIAAAggUvAABvYJ/CwCAAAIIIIAAAgggEKYAAb0wdYMtm4BesJ5RLI2AXhRbpWSdCOiVNOEVBBBAAAEEEEAAAQQI6PEeQAABBBBAAAEEEEAgRAECeiHiBlw0Ab2AQSNYHAG9CDZKKVUioFcKCi8hgAACCCCAAAIIFLwAAb2CfwsAgAACCCCAAAIIIBCmAAG9MHWDLZuAXrCeUSyNgF4UW6VknQjolTThFQQQQAABBBBAAAEECOjxHkAAAQQQQAABBBBAIEQBAnoh4gZcNAG9gEEjWBwBvQg2SilVIqBXCgovIYAAAggggAACCBS8AAG9gn8LAIAAAggggAACCCAQpgABvTB1gy2bgF6wnlEsjYBeFFulZJ0I6JU04RUEEEAAAQQQQAABBAjo8R5AAAEEEEAAAQQQQCBEAQJ6IeIGXDQBvYBBI1gcAb0INkopVSKgVwoKLyGAAAIIIIAAAggUvAABvYJ/CwCAAAIIIIAAAgggEKYAAb0wdYMtm4BesJ5RLI2AXhRbpWSdCOiVNOEVBBBAAAEEEEAAAQQI6PEeQAABBBBAAAEEEEAgRAECeiHiBlw0Ab2AQSNYHAG9CDZKKVUioFcKCi8hgAACCCCAAAIIFLwAAb2CfwsAgAACCCCAAAIIIBCmAAG9MHWDLZuAXrCeUSyNgF4UW6VknQjolTThFQQQQAABBBBAAAEECOjxHkAAAQQQQAABBBBAIEQBAnoh4gZcNAG9gEEjWBwBvQg2SilVIqBXCgovIYAAAggggAACCBS8AAG9gn8LAIAAAggggAACCCAQpgABvTB1gy2bgF6wnlEsjYBeFFulZJ0I6JU04RUEEEAAAQQQQAABBAjo8R5AAAEEEEAAAQQQQCBEAQJ6IeIGXDQBvYBBI1gcAb0INkopVSKgVwoKLyGAAAIIIIAAAggUvAABvYJ/CwCAAAIIIIAAAgggEKYAAb0wdYMtm4BesJ5RLI2AXhRbpWSdCOiVNOEVBBBIX+DHH3808+fPN6tWrTJVq1ZNvwCOiLTA33//bf78809Tq1Yts88++0S6rlQOAQQQCEqAgF5QkpSDAAIIIIAAAggggEApAgT0SkGJ6EsE9CLaMAFWi4BegJghFkVAL0RcikagQARWr15txo8fb26//Xazbt06s8kmmxTIlRfWZVprTYMGDczll19uTjvttMK6eK4WAQQKUoCAXkE2OxeNAAIIIIAAAgggkCsBAnq5ks7+PAT0sjeMegkE9KLeQv+vfgT08qOdqCUCURb4/PPPzcCBA83EiROjXE3qFoBA5cqVTefOnc39998fQGkUgQACCERbgIBetNuH2iGAAAIIIIAAAgjkuQABvfxpQAJ6+dNWmdaUgF6mcrk9joBebr05GwJxFFi8eLGfnTdq1ChTs2ZN07JlS7P33nvH8VIL8pqUavODDz4wL774otl5551N3759Ta9evQrSgotGAIHCEiCgV1jtzdUigAACCCCAAAII5FiAgF6OwbM43TPPPGO6dOliKlWqZLp3724GDBiQRWkcGkWBd955x3f6zZgxw5x11lk+Hdtmm20WxaoWdJ0I6BV083PxCAQisGTJEjN06FAzcuRI06JFC3PLLbeYpk2bBlI2hZS/wB9//GEee+wxn2pz9913N/369TNdu3Yt/4pRAwQQQCBkAQJ6IQNTPAIIIIAAAggggEBhCxDQy5/2X7hwodFI/hUrVvhR3s2aNcufylPTlAS+/fZb3wE4bdo0c95555k2bdqYChUqpHQsO+VOgIBe7qw5EwJxFSge0DviiCPM8OHDCejFqLEV0Bs7dqzp1q2bIaAXo4blUhBAoEwBAnplErEDAggggAACCCCAAAKZCxDQy9wu10f+9ddf5qeffjL6Xr16dT9TL9d14HzhCvz9999mzZo1Zu3ataZatWpmiy22CPeElJ6RAAG9jNg4CAEEigkQ0CuGEcMfCejFsFG5JAQQSEmAgF5KTOyEAAIIIIAAAggggEBmAgT0MnPjKAQQKFwBAnqF2/ZcOQJBCRDQC0oymuUQ0Itmu1ArBBAIX4CAXvjGnAEBBBBAAAEEEECggAUI6BVw43PpCCCQkQABvYzYOAgBBIoJENArhhHDHwnoxbBRuSQEEEhJgIBeSkzshAACCCCAAAIIIIBAZgIE9DJz4ygEEChcAQJ6hdv2XDkCQQkQ0AtKMprlENCLZrtQKwQQCF+AgF74xpwBAQQQQAABBBBAoIAFCOgVcONz6QggkJEAAb2M2DgIAQSKCRDQK4YRwx8J6MWwUbkkBBBISYCAXkpM7IQAAggggAACCCCAQGYCBPQyc+MoBBAoXAECeoXb9lw5AkEJENALSjKa5RDQi2a7UCsEEAhfgIBe+MacAQEEEEAAAQQQQKCABQjoFXDjc+kIIJCRAAG9jNg4CAEEigkQ0CuGEcMfCejFsFG5JAQQSEmAgF5KTOyEAAIIIIAAAggggEBmAgT0MnPjKAQQKFwBAnqF2/ZcOQJBCRDQC0oymuUQ0Itmu1ArBBAIX4CAXvjGnAEBBBBAAAEEEECggAUI6BVw43PpCCCQkQABvYzYOAgBBIoJENArhpHDH7/77jvz3HPPmblz55r27dubpk2bhnJ2AnqhsFIoAgjkgQABvTxoJKqIQCEL/PXXX2bdunWmcuXKecdgrTV///23qVChgtlkk03yrv5UGAEEEEAgGAECesE4UgoCCBSOAAG9wmlrrhSBsAQI6IUlm7zc33//3UyaNMlceeWVZtNNNzXdu3c3V111VfIDsvgNAb0s8DgUAQTyWoCAXl43H5VHIN4C77//vhk0aJCpVq2aueaaa8w+++yTNxf8559/mpdfftkMHTrUHHrooebaa681W221Vd7Un4oigAACCAQnQEAvOEtKQgCBwhAgoFcY7cxVIhCmAAG9MHVLL/uTTz4xN910k5k8ebLZe++9zY033mjOOOOM0nfO8lUCelkCcjgCCOStAAG9vG06Ko5A/AWefvpp07lzZ1OvXj3Tv39/065du7y56O+//97cd9995uabb/aByBtuuMGcfvrpeVN/KooAAgggEJwAAb3gLCkJAQQKQ4CAXmG0M1eJQJgCBPTC1C1Z9po1a8y4cePM1Vdf7bMsnX322Wb48OGmevXqJXcO4BUCegEgUgQCCOSlAAG9vGw2Ko1A/AWUZnPChAmmS5cupn79+v6h8MILL8ybC1eq0CeffNJccskl/mFW13HHHXeYihUr5s01UFEEEEAAgWAECOgF40gpCCBQOAIE9AqnrblSBMISIKAXlmzp5SrDUr9+/cxbb71lDjzwQHPLLbeYE044wS9BUvoR2b1KQC87P45GAIH8FSCgl79tR80RiLWAAmLjx483559/vp+hp7zrF198cV5d8+zZs32qzddee80cddRRfnRakyZN8uoaqCwCCCCAQPYCBPSyN6QEBBAoLAECeoXV3lwtAmEIENALQ7X0MvWsO2rUKJ+hqEqVKr4fRwE9/RzWRkAvLFnKRQCBqAsQ0It6C1E/BApUIA4BvR9++MGMHDnSKN3mzjvvbPr06WMuvfTSAm1RLhsBBBAoPAFrrdGaquqYVifHsGHD/HoiGr3cpk0bs8UWW5hNNtmk8GC4YgQQQCCJgO6b6qSdN2+eueuuu8wjjzximjVrZgYMGGCOOOII3znMfTMJHi8jgMB6AgT01uMI7R+6b7/xxhumd+/eRmvoHX744f6Z96CDDgrtnCqYgF6ovBSOAAIRFiCgF+HGoWoIFLJALgJ6v//+u/n222/N//73P/P1118b5XzfeuutzU477WR23313s+2222bVBH///beZMmWK6dWrl/nyyy/9YtBaV0/nYEMAAQQQiJ+APkfmzp1rZs6caebMmWMWLlzoP2d+++038+OPP5pVq1aZSpUqmW222cZsueWW/muXXXYxe+21l++wVnqiunXrEuSL31uDK0IAgVIE1An8008/mU8//dTMmDHDdwQvWrTIrFixwui+uXr1av/7zTff3D+XaxBEtWrVzK677uoHRyjQd8ABB5gddtghtJRupVSblxBAIE8ECOjlpqGWLVvmB2BoEIb6UHr06GGUYUnPvGFuBPTC1KVsBBCIsgABvSi3DnVDoIAFwgroqeNAQbx///vfZvLkyb7jQIE9nU8BOI343WyzzUzNmjXNYYcdZlq3bm1atGjhO10zaQ6NLh40aJBfD7Bp06ZFeeQzKYtjEEAAAQSiJ7B27Vr/WfLcc8+ZN99806hTQ6+pMzrx+ZKs1onPnMqVK/tZJ9WrVzeNGjUyp5xyijn22GP97O5kx/I6AgggkK8CP//8s1Fqet03p02bZr755hvz66+/+vumOmj1XJ5s031TncS6byrAV6NGDbPffvuZU0891RzlUtzXrl072aG8jgACBSZAQC/8Bl+3bp158cUXzWWXXeYHSmvNPAX2GjRoEPrJCeiFTswJEEAgogIE9CLaMFQLgUIXCCOgp5kTL730krnjjjuMRv9WqFDBKA3EP/7xDz/KVx0Dmqk3ffp0H+xbvHix7yQ45JBD/CizQw89NO3Rv+qc0FqAmqWn2RhaB1ABPjYEEEAAgfwWUIf0W2+9ZcaMGeNn5GkGngJ5iY5ofaZst912platWn5m9nfffednoajzec899/SDRzQLRa9rFooGlehzScdttdVWfrb4SSedZM4991w/gy+/tag9AgggYIzS0WtQnZ6NlZZNs/N031SHsO5/mom3/fbb+4F1em5evny5WbBggX9NM5m1nwbm6b6pYzVQTwE+3Tc1c08zntu2bWvat29vdnWz+NgQQKCwBZYsWWKGDh3ql8FQyt7hw4cbDbJlC05A2SiGDBnin4cTy4xcdNFFpmLFisGdJElJBPSSwPAyAgjEXoCAXuybmAtEID8Fgg7o6Q//Rx991I8WU9BOac369u3rZ98pBaY6AtQhoLWO1LGgFJn/+te/zP333+87DPbdd18f1OvQoUNaD6fqaHjnnXfMlVdeaWbNmmXUOXv33Xeb+vXr52fDUGsEEECgwAU0806p4bQmngJ66qDWa5rdrY4MrRuir/33398PClGHhjqex40bZ26//XajzxOlITr66KN98E+z+LTG3rvvvutnqnz00Ue+zE033dQPBNHnhQaedOzY0afjLHB+Lh8BBPJQQIPqdL/UfVP3Tw2A0L1Pz9+77bZb0X1T90cNaNB9U4E77f/QQw+Z5s2bm/79+/v7p4J6elb/73//65+xNcPv448/NhpkoeN0vAZN6Jn9rLPO8sHBPCSjygggEIAAAb0AEDdShO7jTz/9tF87T2nltT60+jqUBjkXGwG9XChzDgQQiKIAAb0otgp1QgAB38mp0bvnn3++qVevnu/81Oy2TDYF5xSYe+CBB/z6RZppp1lyGp2nkcClbeosUCftE0884dNk6md1Dlx66aXmggsuSGum3ldffWXuvPNOvzC0yrj22mt9x2xp5+U1BBBAAIFoCmiAhmZ3P/jgg+app54qShGnQSFK83bOOef4wSLqTFYauCpVqhSthbdy5Uo/OvzGG280TZo0MQMHDjQnn3yyv1CVq0Es6qD+5Zdf/IwUzWCZOHGi+eyzz3wZmnmilHLdunXznSUqmw0BBBCIuoCepz///HN//3v++efN999/7wN5mr2stGwKuCmIp9l4VatWLRpgp+vSQAfNplHnsNLg62dl1tCm+6YG4emeqS+th/3CCy/4juUvvvjCB/aUwlhr7HXv3t2ceOKJaQ3I8yfhPwggkPcCBPTCbULNtL7pppt8diPNor7++uv9fV0DpXOxEdDLhTLnQACBSAq4h2E2BBBAIHIC7o90O3r0aOtunNYF9Ox9992XUR3dSDHrcrjbbbbZxpfVsGFDO3bsWOtGk5VZnkt/Zl0wzl533XXWjfj1X26EsHUdEmUeW3wH11FrXeevdZ0X1gUQ7YUXXmjdbI7iu/AzAggggECEBVyHsXVrPVkXuLMuuGZdajjrOqBtq1at7DPPPGNdWjjrUiwnvQLXiW1vvvlm/znkAnrWdTwn3VefGS4Fp3WdJHbw4MHWrUHij3MzAK1LJ2ddCmfrOqyTHs8vEEAAgSgIuFl41mXHsC6o5u+XeqZ3QTbrgnjWDVqwbgbeRp+HXZDOuoF0/v7nAnrWzexLeln6u8ENvrNuXT7br18/W7duXX+cmwFo99hjD/8sr/s0GwIIFJaAm8lrXVDf3w9cyk3rMuYUFkCIV+tmRdt7773X39/dQDPrBmJb9b3kclOfjhu07dt39913t25Gdy5Pz7kQQACBchPQ6DY2BBBAIHICQQT03KhgO2XKFOtmxRX9Ud+pUyffUZrqBasMlyLIull9voxKlSrZM844w6qTIZ3NpVCzp556qu8EdqnY7Pvvv5/O4eyLAAIIIFBOAgrG3XPPPdalhbP6DNAADwXl3Ew9u2zZso0G8hJVTieglzgmEdjT50WPHj38wBQFEhVQbN26tXVp5hK78h0BBBCIlICCZy4bhq1Tp46/Z+reqWfpxx9/3H7zzTcpDaxLJ6CXuHjdNxXY07P7eeedZ92sP+tmivj7p5tFbV1qzsSufEcAgQIQIKAXXiNPnz7dHnnkkb6PxC1n4vtdNCA6lxsBvVxqcy4EEIiSAAG9KLUGdUEAgSKBIAJ6eoDv2bOndesQ+QdNzc5zaTxtug+aLlWaveWWW3wZGl2szgm3uHZa5WiU8rBhw3ynwo477mjdOkpF18oPCCCAAALRFFixYoW/d9euXdvfv2vUqGG7du1qNUjDrQmVcqUzCeglCtfnoTrA1RHu0s35zyLN9j7mmGPsa6+9ltiN7wgggEAkBFyqe+vSyxcNQqhVq5a94oor7Lx586xLLZxyHTMJ6CUKd2nYrOrh1uCzjRo18gPqFNw77bTT/Cy+xH58RwCBeAsQ0AunffVcq0EbmgWtmde6x6dzfw+qVgT0gpKkHAQQyDcBAnr51mLUF4ECEcg2oKeZdc8++6wPvikIp6/jjz/eLly4MG1BlTVp0iSrDl2VowChW/vILliwIOWyFERUeiGXW94f365dO/vdd9+lfDw7IoAAAgjkVkBpL0eOHOnv/ZoZp3SXt912mw+uaRZIOls2AT2dR58h6ih59913fbo6fQ6pE8WtC2U1QpoNAQQQiIKA0mgqVbAGP+iZWYPp3DrWVvdAPU+ns2UT0NN5dN9USrhXXnnF3yt1H3frm9ozzzzTzp07N52qsC8CCOSpAAG94BtO99apU6faxo0b+/u8sg9tLCVy8DX4vxIJ6P2fBT8hgEBhCRDQK6z25moRyBuBbAN6ms3gFmX2MyrUoaC1h7p06WI1YjeTTQ+pmg2hsvSlNY3GjBmTVlFa80jr5+n4/fff3wcc0yqAnRFAAAEEciKgdU6ffPJJn2ZTncBKtzlixIi0UjYXr2i2Ab1EWfoMmzNnjl+nRGnk1Dndvn171tRLAPEdAQTKTeCnn37yqYh32GEHPyNu3333tY899pgPqmVSqWwDeolz6n6uwRBt27b1z+BKW3zRRRf5wRmJffiOAALxFCCgF3y7avZz3759ff+KBjwPHDgwpTTKwdfE+vOyhl4YspSJAAJRFyCgF/UWon4IFKhAtgE9rTl09NFHFwXglO5HaTMz3TQbTws9JwJ6Snem4Jw6CVLdtO8jjzziO2DVmdCnT5+0Ryunei72QwABBBDITCCxdurBBx/sZ1TvtNNOfsaJUidnugUV0NP59fk4e/Zsv56rPpM0E+byyy/PONiY6TVxHAIIIJAQ0H3phRdeKEpvuccee/h0l7/88ktil7S/BxXQ04k1i+ONN97wg/M0SEOd0DfddFNaz/FpXwAHIIBAuQsQ0Au2CZShQlmQdt11Vz9wQ5ki5s+fH+xJ0iiNGXppYLErAgjESoCAXqyak4tBID4C2QT0dOyjjz5qt9pqq6IAXP369X3Kn0yFli9fbvv161dUnjoDjjjiCDtz5sy0ikwsHq3jlQL0888/T+t4dkYAAQQQCFdAqdg6duxoK1Wq5NcF6dWrV9YpkoMM6OnqNVNP6+cddthhvkOlXr169q677mKQSLhvDUpHAIEkAh988IFt1aqVrVixog+W9e/f32rGXjZbkAE91UMD6yZPnmz32Wcfn8FD3ydMmJBNFTkWAQQiLkBAL9gG0iBnrSWt1O969rznnnv8QLNgz5J6aQT0UrdiTwQQiJcAAb14tSdXg0BsBLIJ6H399df2mmuu8Z2ciRl1WrtOaX8y3dQpMXz48KKAnsrV6OPRo0enVaTWFrnhhht8OUrhphQRbAgggAAC0RBYuXKlHTZsmB8QooCeUrRp7VWtF5LNFnRAT3XRmnr6XNvFre2njhUF915//fVsqsmxCCCAQNoCX331lX/urlKliq1atart3Lmz1UC4bLegA3qqj2Za33fffXbbbbf16eJOOukkn8Y427pyPAIIRFOAgF5w7aJBERoEsf322/vBG+3atQvkXp9NDQnoZaPHsQggkM8CBPTyufWoOwIxFsgmoPfpp5/as846a73gm9ase/755zMW02yIhx56aL0yt9lmG3vttdemVabSVEyaNMnWqVPHVq5c2Xd6ZJOOKK2TszMCCCCAQFIBpdp8+eWXrQaAaNBGs2bN7Kuvvmp13852CyOgpzqtWLHCp5NWGmitp6eO9O+++y7b6nI8AgggkJKAOlO13qhSEyv7hNLdKyVwtoMgdPIwAnqq19KlS33ae61DuvXWW9vevXtbnsVTam52QiDvBAjoBddkH3/8sR/opnt9o0aN/KAyPTuX50ZArzz1OTcCCJSnAAG98tTn3AggkFQgm4De22+/7TtiE7Pz9L158+Z+7YykJyzjF+oAUBpP/fGfKFczIs4555y0199QwPHMM8/05WiNprfeequMs/NrBBBAAIGwBTQTT2ujKmWcBl3cdttt9tdffw3ktGEF9NSRMmfOnKL19LJNLx3IxVIIAggUjECig1fPx8pc8eCDD/qUwEEAhBHQU700SOOdd94pWk+vcePG9qmnngqiypSBAAIREyCgF0yD/Pzzz/bee++1W265pdVs7PPPP9+uWrUqmMKzKIWAXhZ4HIoAAnktQEAvr5uPyiMQX4FsAnpaH2O77bYrCrwpAHfkkUdare+RzaY/9jUDIhHQ0/cTTjjBfvHFF2kVu2bNGjtixAjfaVyzZk07cODAtI5nZwQQQACBYAXUIaD0lYk0Qqeffrr98ssvAztJWAE9VVB1f/rpp33qTQUjW7dubbXGCRsCCCAQpkDxDl49H6uDV2mLg9rCCuipfpqR9/DDD1tl21DGjA4dOlilxWdDAIF4CRDQC6Y9p0+f7vtT1P9x4IEH2ilTpgQyEzvb2hHQy1aQ4xFAIF8FCOjla8tRbwRiLpBpQE+zFcaPH7/eTDo9eB533HF23rx5WakpVWaNGjXWC+gdeuih9r333kurXM320zpHSgOqWX5t2rSxWn+EDQEEEECgfAQ+//xz36EbVhqhMAN6ElPwsU+fPj7lnWYXah1AtswEtA6v1rfVYJvFixdnVghHRVpA6yI/88wzPm36jBkzItEpGWmwJJWbNWuWPf744/1zcdOmTe0rr7wSqGWYAT1dkv4u6NSpk6//nnvuaceOHZvkSnkZAQTyVYCAXvYtp2fYQYMG+cEP1atXt1dccYVfxzn7krMvgYBe9oaUgAAC+SlAQC8/241aIxB7gUwDemvXrvXpIIrPost0Jt2GyKXN/DvggAP8CLUN9y3r3+qk6NWrl+9E2Gefffz6I2Udw+8RQAABBIIX0OeN1oDSzG7N1DjvvPPsDz/8EOiJwg7oKYXcSy+95Nf/00CRU0891aoTiy19gRdffNHuuuuutl69enbo0KHpF8ARkReYOXOmD0Rp/bRu3boFliIy8hceYAU1w23UqFE+c0W1atXspZdeGngHb9gBPa2P/cQTT9jatWvbSpUq2XPPPTfwe3+A5BSFAAIZCBDQywCt2CEaiDx16lSr1MTqUzn88MOtBsJEZSOgF5WWoB4IIJBrAQJ6uRbnfAggkJJApgE9dcIOHjzYP3AWD+qdeOKJWY+0f/bZZ61SZBYvVwtCP/744yldU/GddH1K76bOpKpVq/rgnjpk2RBAAAEEciuwZMkSfw/WGlANGzb0s7zVgRHkFnZAT3VdunSp7d27t/+MatCggR0zZkyQl1AwZWnmlkagK/3qTTfdVDDXXUgXqvXTtIaxnufat2/v11QrpOsP4lo1q/nss8/2hon0a0GUW7yMsAN6OtfcuXN9IE/vhSZNmtgXXniheBX4GQEE8lyAgF52DagMEH379rWbbbaZH/yg7AUKokVlI6AXlZagHgggkGsBAnq5Fud8CCCQkkCmAb3ly5fbq6++er2gm/5IP+mkk6w6bbPZnn/+ef8gWzygV79+fXv//fdnVKxSFWkNPqV4a9mypZ0zZ05G5XAQAggggEDmAm+++abvyNW9WDPbwkiBnIuAngaFaK1XDTzZfPPN7YUXXhipTpfMWyi3RxLQy613eZyNgF726gp81a1b13fyamab0pgGveUioPfbb7/5tfSqVKniA/n6GyLoAR1Bu1AeAgikLkBAL3WrDffUc6UGNCtrgZ6RNUB6/vz5G+5Wrv8moFeu/JwcAQTKUYCAXjnic2oEEEgukGlATzMULr/88hIBvVatWvnZC8nPWPZv1Hmx4447rlf2zjvvbO+6666yDy5lj5UrV/p89AoQ7rLLLnbEiBGl7MVLCCCAAAJhCagjYPTo0T7VpmZk9e/f32ot1qC3XAT0VOcPP/zQnnLKKUUDRT7++OOgLyX25RHQi30TWwJ62bXx6tWrfTpapfdNPL+GEQTLRUBPEtOmTbMtWrTw629rUMeyZcuyA+JoBBCIjAABvcybYsGCBbZr165W93qlIb/nnnus+miitBHQi1JrUBcEEMilAAG9XGpzLgQQSFkg04CeZuH17NlzvaCbAmYnn3yyVcqIbDatq6PRyMVn6O200052+PDhGRWrTmMFCTXLT2kszjnnHPvjjz9mVBYHIYAAAgikL6CO2z59+vj7+n777edHIqdfStlH5Cqgt2LFCh+U1OfUXnvtZR999NGyK8ce6wkQ0FuPI5b/IKCXXbNqhkanTp38ffPQQw+17733XnYFJjk6VwE9dfj36NHDX0/Tpk3tK6+8kqRGvIwAAvkmQEAvsxbT7OUJEyb49OMVK1a07dq1s8qEFLWNgF7UWoT6IIBArgQI6OVKmvMggEBaApkG9BYvXmwvueSS9YJuiYBetmnUXnrpJT8SuXhATzP2hgwZkta1Fd953rx5tmPHjr6+zZo1oxOhOA4/I4AAAiELfPTRR7Z169b+Hnz88cfbL774IpQz5iqgp/RICuIpfdx2223ng3uhXFCMCyWgF+PG/f8vjYBedm2c8FMKttNPP92uWrUquwKTHJ2rgN7atWvtvffe62c2K7WcZqGwIYBAPAQI6GXWjsrw0LZtW39fbNSokX3sscdCyWCRWe3+7ygCev9nwU8IIFBYAgT0Cqu9uVoE8kYg04CeOmO7detWIqCnFGTZjipTQE8pNosH9GrXrm0HDx6cseuvv/5qH3jgAZ/ubdttt7XXX399xmVxIAIIIIBAegJvvPGG3X///X2qNc2SVsdAGFuuAnqqu2aXNGjQwM/8Pv/881kPKs0GJaCXJlge7p4ISOl5rn379laBcLbUBZRdok6dOrZq1aq2V69eod1jchXQU7pQ/X+v5/Ctt97aXnXVValjsCcCCERagIBe+s3z888/+0EOW265pR8gpmfJsAZupF+79Y8goLe+B/9CAIHCESCgVzhtzZUikFcCmQb0Fi1aZC+66KL1gm7qsFFAL9sZekq5qRSbxQN6O+ywg7311lsztlUnQvG1O1RP/eHBhgACCCAQvsDzzz/v10bdaqutbO/evUM7YS4Deu+//7498sgj/WfVP/7xD6v1rthSFyCgl7pVvu5JQC/zltNz68SJE22lSpVstoPayqpFrgJ6qsfUqVPt3nvvbZVarkuXLqEFKcu6Zn6PAALBCujv6u7du/tnoiOOOMLOmjUr2BPEsLTp06cXPUceeOCBdsqUKZG9JxLQi+EbkEtCAIGUBAjopcTETgggkGuBTAN6emhPrINRPPCmNfSyDehpRLJSbBYvVyOUhw4dmhWP6qXRwCq3YcOGdvz48VmVx8EIIIAAAqkJPP3001YjkGvWrGlvvvnm1A7KYK9cBvSUJqlNmzb+MyWI9WMzuNy8PoSAXl43X0qVJ6CXElOpO/3xxx/2oYce8veXevXq2ZEjR5a6XxAv5jKgp3UAtR6gnsXPPPNMqwwabAggkP8CBPTSa8PvvvvODho0yGcPql69ur3iiius0hJHdSOgF9WWoV4IIBC2QAWdwD24siGAAAKREnDpj4wLbBmX4sG4DgPjAl7m4osvLrOOS5cuNcOHDzd33333evu2atXKjBo1yrgZduu9ns4/XEDPXHjhheabb74pOqxu3brGzerwX0UvpvnDunXrzKRJk4wLRBqX4sK4NfV8/d3o5zRLyt3ubu0/M2LECPPaa6/l7qScCYEUBdwfoKZp06Zmr732SvEIditUgQ8//NCMGzfOuNRx5qijjjLHHXdcKBQrV67090sXSPDnOvzww40LtoVyrq+//tq8/PLLRtem/wfOOuss41LJhXKuOBbqAqLGrRVjNtlkE+NG85uTTjopjpe53jW5DjHzww8/GLcmmqlVq5b/vt4OMfuHW2/ZTJ482biOXuNmH/jnLrU3W9kCbsCdmTFjhnniiSfM9ttv7++ZBx98cNkHZrCHC+gZN4vazJ8/37hBF8atc2qaN2+eQUllH7JkyRLz3HPPmYULFxqXhtm4FMxm8803L/tA9ihYARf0Nfpsr1y5sv9/oWAhIn7h+n/72WefNW5ZDv+Zrn4C/Y2Q75v6StasWeO/1H+gn/U98bMLwvnnGJeBwujLDV4r+p742a237PdJWKhr2KWi9/0an3zyidGz6rBhw8xBBx2U2CVy390gEzN27Fjjllwxu+++u+nXr5/p2rVr5OpJhRBAAIGgBQjoBS1KeQggEIhApgE9N9vN3HHHHT6oV7wi6pC77777zC677FL85bR+1h/6CuitWLGi6DiV17dvX9OzZ8+i1zL5QR2I/fv3950JiYfnZs2aZVJU6MeoA+zOO+80o0eP9n88hH5CToBAmgKbbrqp0R+p6mRhQ2BjAgpkqBNEnfnqvNX7JoxNAzfU+afzKWii96aCiGFsxc+12Wab+fPo/wm21ATUOaT3hNopzPdEarXJzV7qxNP7RptLOZibk5bjWfSM+csvvxh91/+L6txkS01A7xXdx+QX9metgofqlFY76R6t+3NYQTadQ+fSOTWgTu8J3QPYEEgm4NLP+vum3ieFcN9M5hD11/X/tO5X+ozbb7/9zIABA8xpp50W9Wr7+um+pH4Ht6SIWeICk/obXF/6+dtvvzV6XtH7MPGla0z8rO96b+reWfxL9239W9/1HOqyDfnB0xpArfueWwrED9jQQDANNtag6igPMiaglxdvZSqJAAIhCBDQCwGVIhFAIHsBPcBmMkPPpTUz9957r7npppvWq8QJJ5zgX99tt93Wez2df2h03wUXXGB0jsTWoEEDc80115jOnTsnXsroe/FA5L777uuDe27to4zKCvsgjUZ1KZbMjTfeGPapKB8BBBBAAAEEEEAAAQQQQACBrAQ0WHbw4MHm2GOPzaqcsA7+7bffjGaQf/DBB2b27NlGA36//PJLP4hCgUkFr/Sln9VXkm2yNQX2FIxWwE5f+rcGnykAqqxGbdu29dkkGjdubNyaqZEc5EBAL6x3I+UigEDUBQjoRb2FqB8CBSqQaUBPo+rd2h4lUmAqjdo999xjFIDLdFN6JqVwUFqqxKYHXAUP9cCbzaaH9uuuu8688sorpmXLlj7l5t57751NkaEdqxF/Lr++/2NDqYnYEIiSgN6f+qNUqcCYdRGllolmXd5++20/o3vrrbf2I7bDGkixatUqnzpOaeqUqllpMI8++uhQUJR6+vHHHze6tgMOOMB0797d7LDDDqGcK46FurW0zF133eVHr59yyimmQ4cOcbzM9a5JnYJ67tLo/rBmQK13wnL+x+eff24efvhho/ThRx55pM+0oI5MtrIF1HmqdOsaPOfWlTZuvbnQUhVrsNtTTz1lXn31Vf/8rsFzmmETxrZgwQIzZswY34F+yCGH+L8jtthiizBORZkxEdDzpgIrmgUV5RlMMeHO+DKWLVtmnnzySTN16lRz2GGH+We+qKSQ1Ofu8uXLzfTp0827777rg3j6t4Jq+lKAT+8xbXqf6fNZz6vFv7TMQPF/J37W7Dt9pv/444/mp59+MqtXr/Y/69+lfSlVZ+JcOp8CfSpDX0rZqXSW8nNrjRr1f+g8UdgI6EWhFagDAgiUhwABvfJQ55wIIFCmQKYBveLHFT+JOk6VJlIPoJluTz/9tOnUqZNPyZMoQ38Q3HrrrT4Il3gt3e+qszosLrnkEp8mQ+sGDh061ChVWlQ3df7poV9pl9gQiJpAIv0RHbRRa5no1Ufrl2rmtVK56R6sgRVhbJrZrXVcb775Zt8hrRnOChaFsWndE51Ha08p3bQ63pVSiS01Ac3G11os6szSe+L6669P7cA830uf6/oqhPumgrbKrvD+++/7gJQCOaSlTe0NrGe/Rx991Fx00UVm1113NVdccYX/ObWj09tLa+gpjb5S5ivIdtttt4W2hp461PWe0Pd27dr5tPKk7U6vvQptb90vE5ueO9miKaD0lFo374EHHojEGnq6hyptpgZG6OvTTz/1ATfNilMAT/0C2nT/2Xnnnf3ALK35p/VeNWtOn1WJL31eb/hz4jV913tUgedEKk59L+1nBQ/1PKxnR9VPAyIVpFZWHpWRCFprkIMCfJqt16JFC/+Mqe/bbLNNuTU+Ab1yo+fECCBQ3gLuBs2GAAIIRE7APUxat0ab/lKyLqe7dX/Mp1xHNwrPugdOf6yO15cbUWZdx03KZWy4o3u4tq7Dx7oH2vXKdSO77Ycffrjh7mn92/2hYXv16uXLduk2rQscpnU8OyOAAAIIZCbwwgsvWDfLxLrOC3v55ZdnVkgKR7mAnnUdJf7zo0mTJlbnDWtzHdJWn0367Dv99NOtG5kd1qliWe4zzzxj3Yh362b5WjcDP5bXWOgX9c4779iDDz7Y/z/Svn17q2c8ttQEXOewnThxonWdzdZ16tpBgwaldmAGe7mAnr300kt9O+k5fsaMGRmUktohrmPdNmrUyLpAvu3SpYvVdbIhgED+C7jgmXWZCvx95IgjjrCzZs0ql4vSc6AbwGvPPvts65YAsW6NOutm3BX1Leie2rBhQ9uxY0frBmJZN2PPqo/gm2++sW5GnXWBq9Dq7VJ7WpdtyNdlr732si74ad1Mdv+s6gagWbd0ia1Vq1ZRXV0Q0T83u+wP1g1utm4wnHVpQsvls9QNLvb11TOvm0VoXaam0JwoGAEEEIiSgEZcsCGAAAKRE8gmoOdS8/gH4kQwT9+bN29uX3/99Yyv06XytG6Gn/9joHi5blFtqwf0bLY33njDupmD/iG5TZs2/sE9m/I4FgEEEEAgNYE333zT7r///taNZLYutaJ1o6NTOzDNvXIZ0Pv3v/9t99hjD+tGV1uXJtq60dhp1rawdyegF//2J6CXXRtrQIKbKeIHz/Xs2TO7wjZydC4Dem52iq1Ro4YP5l999dUbqRW/QgCBfBIoz4Cenr8WLVpkb7/9dj+4WEExlxHC/82vQcJuZps9/vjjrcv2Y/U8qgDeihUrrEt/adUXkotN51IAUQPbVDeXKci6NPF+UIOeifWzSwNqP/vsMz/oWPd89VvoGVN9IgruufSbPpimYKXLDpHTgWQE9HLxLuEcCCAQRQECelFsFeqEAAL+ITbTGXqaMedSma0XfMt2RoRbM84OGDBgvTI1qu7iiy/OqrNUD9F33323dek1i0Y60/nK/wAIIIBAbgTmzJljTz31VH9vV6eKW0cplBPnKqCnmUYTJkzwo76ZYZZZUxLQy8wtn44ioJdda2nmiEuB6TulNQvYpWXLrsAkR+cqoOdS3dkRI0b4gR0ujajv3E5SJV5GAIE8EyiPgJ5m02nW25VXXmn32WcfP1hAs38VAKtWrZo95phjrFur189qc2uFhj4Db2NNVjyrg0vraadMmVLqDGXNWnapOf1A5sWLF9uXX37Zz6Bu0KBBUYBSAUGX4t0HKdWP8+23327s1IH8joBeIIwUggACeShAQC8PG40qI1AIAtnM0Fu6dKlPnVZ8Jt2ee+5px40blzGdyuzdu/d6AT2lmRgyZEjGZepAlzffnnHGGb5cpX9SJxMbAggggEBuBNSRog4XfV5oxLFmaYSx5Sqgp86TG264wXeuKH3cY489FsblxLpMAnqxbl5/cQT0smvj+fPn286dO/v7pgJ7YT275iqgp85pt16mv55mzZpZZfpgQwCBeAjkMqCn4NLs2bOtZrEpU4KCd8oAodl4devW9UtsTJ061erZU+nQyzvdswYsK22y0n0q1bhbE9WuXbu2zIZXcE/XqmdbpeZ8+OGH7XHHHedn+Ol5WrP3atasaQ8//HA/QOLrr78us8xMdyCgl6kcxyGAQL4LENDL9xak/gjEVCCbgJ5G2t5zzz3+4TkR1FNqILcgdsZamrWR6LxIlKk0bc8991zGZephePLkyX5mnh6kleJCdWdDAAEEEMiNgDoCHnnkEd+ZofVMrr/++lBOnKuAntYwadWqle+Y1ghwDRphS0+AgF56Xvm4NwG97FpNHdF6plYn9c477+xT0mdXYulH5yqg9/bbb1sF8nQ9mrGtNavYEEAgHgK5COip30Iz8rTmp9ZxU/pK3U+UgUcz9AYPHmw/+ugjHwALcy28dFpM/RAKLmowm/o2FHzLZJ1SZRZS/4UGP7/44ov2vPPOs9ttt50vU9evn7V24ahRo7JepqS06yOgV5oKryGAQCEIENArhFbmGhHIQ4FsAnp6QNUaQlrUORF806izfv36ZSyhtGxaLy9Rnh7Ss13vTqPVtIi0Ru5pFJ9Gt7EhgAACCORWQOuWKM2Q7sWtW7e26kQOestFQE8jvZ988kmrwKTSHikltDo62NITIKCXnlc+7k1AL7tW03O21tGrV6+e77A+55xzfMq47EoteXQuAnpKIffAAw/4NMVaz+raa6/NKpV+yavgFQQQKE+BMAN6uheq/P79+/t+h6222soH8jRQV4MENMBYM5pXr15d7rPxNmyDL7/80vbt27do2Y+BAwdm9cwoC625pwERb731lu3Ro4dVNiP1nSiwpxl7J554ol+HL5VZgBvWN9m/Ceglk+F1BBCIuwABvbi3MNeHQJ4KZBPQ0yXr4bp79+5FATgt2KwOB/3hnsmmDl/NyEsE9PRQevPNN2f1R/97773nR8OpzBNOOMF+8cUXmVSNYxBAAAEEshAonqZZa4GMGTMmi9JKPzQXAb0lS5b40eEKTGabZrr0qyiMVwnoxb+dCehl38Zz5871z9V6hs12nepktclFQE/p4s4++2z/fH/AAQf49aOS1YfXEUAg/wSK9wloptisWbMCuYhVq1bZ8ePH20MPPdSnq9Szl1JNNm3a1I4cOdIuWrTI/vzzz6WuRxdIBbIoRAPAnn32Was1QzVIWYE2BR6D2jQLUek89Vmr9KO1a9f291gFOjWrW1mJlFEiiI2AXhCKlIEAAvkoQEAvH1uNOiNQAALZBvT0IKm1g2rUqFEUhGvZsqX9z3/+k7aeRpxp1oNG3SUCegcddJB9/fXX0y4rcYBGsGmx6C222MLX8eqrr7a6ZjYEEEAAgdwK6N771FNP2Vq1avnOGA3+UAAuyC3sgJ4+p1566SW72267+ZmGShu3bNmyIC+hYMoioBf/piagl30ba4DcQw895J9jlV5Og+gyHTSXrDZhB/T0t8LEiRPt9ttv7+/9ShX3448/JqsOryOAQB4KBB3QUzBMmXsUlNJzo2afKZjXsGFDO3ToUKtlOqIayEs0n+rYtWtXqwHPmmmtmYRh9EOoTAX21GfSsWNHv6agAohVq1b1mTHuvvtuP3sxUa9MvhPQy0SNYxBAIA4CBPTi0IpcAwIxFNADoAJeCqDpQfO+++5L+yqVq16dmokgnNJaqsx0N6XGVAoePYCqLAX2evXqldKi0cnOtXDhQv8grfI0slk559kQQAABBMpHYN68eX7dD92TNbtt7NixgVYk7IBeYnaeOmcSa1qp04ktfQECeumb5dsRBPSybzENIpg9e7Zfs1PPx0pbHPSzbNgBPc3O69Chg++MV5r+CRMmRHI2TfatRQkIFK5AkAE9zcrT86Fm4SkopWdGBfXUL/Dhhx/6AQG6N0Z506Bi3es0kKFixYq2Xbt2dvny5aFWWYMndA4Nnjv66KN9IFHn1sw9DaTQZ0mmGwG9TOU4DgEE8l2AgF6+tyD1RyCmAkEE9DRS+PHHH/edm3rgVpoHjQ5Ld/TttGnTrGbkqQx9HXzwwVavZbNpjT8tmq3O17POOsv+8MMP2RTHsQgggAACWQioQ0AzNdS5oNHWbdu2tYsXL86ixPUPDTOgp44SzSLfcccdi9YBVICPLTMBAnqZueXTUQT0gmmtNWvW2Pvvv99qhp7W7ezcuXOgs5vDDOip7lo7T2ts6++Dc889N9C6ByNMKQggkK1AEAE9Bek0q+2yyy7zz4kKRum+cdRRR9lJkyb5e0e+DKL6+OOP/TOuBmI0atTIZzRat25dtsxlHi9D9c1oIMWAAQNsnTp1/GBpZStq3ry5H3Sdydp6BPTKpGcHBBCIqQABvZg2LJeFQL4LBBHQk8GKFSvsLbfc4he7VzCufv36Pq99qg+u+iPg0ksv9al4dLxyzd95551+0edMjRW8GzJkiB8VV7duXfvPf/6TEcGZYnIcAgggEJCAAniJtVc14lrrpOqzKIgtzICeZqO3bt3aB/M0E/3hhx+2+dKxFIRt0GUQ0AtaNHrlEdALpk3UQatU9hqYpmfkROq2oGaohBnQ03vgkEMO8R3KWiNb60kFVe9gdCkFAQSCENDf8olnu0zW0NOMNg3EPfbYY4uW39hhhx3slVde6dedCzrVcBDXnKwMpQK99957iwZhKG2oZh3mctPzqfpCXnjhBXvCCSf4Z1cNpNtll13sFVdcYXXfT2cjoJeOFvsigECcBAjoxak1uRYEYiQQVEBPgTuNBNOoYXU2aESdRoE9//zzZWqtXr3a55TfZptt/LHbbbedf3hfuXJlmcdubAel5GjVqpUv88gjjwxsUeiNnZPfIYAAAghsXECfO+q0Ueeu1kNRSiV18gaxhRXQU0ro/v37+9kxGuWsNVGy/YwK4nrzuQwCevnceqnVnYBeak6p7KXOVKVRU2esnrE1YyXbLBaJ84YV0NPgjZ49e/rBenrG79u3r9WMPTYEEIifQDYBPT1PadkPrY9XqVKlon4EZXTQ71IdIBwV1enTp1v1PahPRGmSp0yZUm4DGRQo/eyzz/yyJupj0XP31ltvbdu0aWP1GZ3qRkAvVSn2QwCBuAkQ0Itbi3I9CMREIKiAnjhUlmYwdOrUyc/U0wO5RuhprQ+lKittUyepFrbWjD6lpNCo42HDhvkZf9mM4NWoNP0RUKNGDZ97XyMG9UDLhgACCCBQ/gIayKFZ2EpkVXL7AAAWWUlEQVQhp3RKp512mh8Ukm3NwgjoKTXR+PHji9IWHX744VadNdl8RmV7nXE4noBeHFpx49dAQG/jPun+9ptvvvEDCzTLQgMLtCbSl19+mW4xJfYPI6Cne/yIESOsAnlKe3/SSScFco8vUXleQACBSAhkGtDTcVdddZVfIy8RbNK9TQNzM0kNWd4Y3333nR00aJB/tlWqYc2GK+/rUL+IsilpTb8DDjjABxo333xz26JFC/+a+nDK2gjolSXE7xFAIK4CBPTi2rJcFwJ5LhBkQE8UCtxpTSGlt1TaTHXUKkinVBManaZOA6V/UF55ramhP/D1x746JzSjTx186a69V1oTLF261Pbu3dsHCffaay+ft760/XgNAQQQQCD3AgqGLVy40Hbr1s3fpzVa+JJLLrHqCMlmCzqgp06QV1991Y+wVkeT1mQdNWqUVccGW3YCBPSy88uHownoBdtKmqWigXPt2rXzHbLbb7+9veaaa6zSu2WzBR3Q0wC6f/3rX1apiTVYr3Hjxv7fqXQaZ3MdHIsAAuUnkG5AT8+Bc+bMsR06dPAzxjSbbeedd/ZLeHz11VeBpWLPpYiuaerUqf6ep+vRALAZM2bksgpJz6W6/fLLL35m95lnnulnQar/Zc899/SDq8v6HCGgl5SWXyCAQMwFCOjFvIG5PATyVSDogJ4c1OGgoNy7775rr7vuOt8Rqs5a5cFXcG+33XbzD+xK+1CzZk2f1/3++++38+bNC2wE25tvvulHoKkj4ZRTTrHLli3L1yai3ggggEAsBfT5o5RxxxxzjO/01WfEjTfe6DscMr3gIAN66vyYOXOmPfHEE/2gk2233dang9bME7bsBQjoZW8Y9RII6AXfQho499JLL9kmTZr41Gl6rr7jjjuy6vwOMqCnvwFef/11P/NDM/Pq1Kljb7311qzu68ErUiICCAQt8N801tDTYCk9/x1//PF+trEGTOme9thjj1k9Y+n5Kx83zZhWamEFymrXrm0HDhwYuQFg+gyZO3eunxVZrVo1P4N6p5128oNDNjaojoBePr4jqTMCCAQhQEAvCEXKQACBwAXCCOglKqmytQC01tBQgG306NH+j/r+bh0ipVp74okn/Ki15cuX+zU1gsqPr/U5tBC1Un4qYHjTTTdZ/eHAhgACCCAQLYFff/3Vz9zQTGp16Ozi1ofKpvM3qICeOpOU7un000/3KaSV3u6cc87xM9CjJZi/tSGgl79tl2rNCeilKpXefppJ8cgjj1h1wipopvun1p/Sc3cmW1ABvUQnfcuWLf0zuNLN9ejRw6d6y6ReHIMAAvkjkGpATwElraN8yCGH+Ew++nv9uOOOs2+88UZeB/51/9N60MpQpAHFGgw2f/78SDag6qr+Fw0G0eeInr/VZ9KrV6+kg6AJ6EWyKakUAgjkQICAXg6QOQUCCKQvEGZAL1EbdYzqPErzoJl7CvL99NNPVh25YQTatPBz+/btfToipfHUSGE2BBBAAIFoCuhzQSmYd9xxR985XbduXT9SWOtFpbsFEdBTZ5MGoWjkeJUqVfxI61atWvnUUEENPEn3uuK4PwG9OLbq+tdEQG99j6D+pedqzaTQGtQKmlWsWNGnt7ztttv87JZ0zxNEQE/P9M8//7w9+OCDfSe97p16Fl+0aFHezrZJ15H9EShkgVQCegoKvfDCC7Zp06b+2UqDpc444wz/fKXf5fO2YMEC27VrV/8cq5nT99xzT8aDLHLhoM8RLYMyduxY27BhQx+E1DIoF198calrsxLQy0WrcA4EEIiiAAG9KLYKdUIAAf+gqZlzyvOuh0+N8M3nTQ+nzz33nE/xoxF/HTt2zHptkXz2oO4IIIBA1AV031YgbsSIET41s0YKq1NB60QpIKDfp7plG9BTJ/nIkSPtPvvs4zullTZJgb3p06dHumMmVZ8o7UdAL0qtEU5dCOiF46pSdV/UDItbbrnFB/U0U69WrVq2S5cuvnM8nTNnG9DTeleaWa01RnXPVDBP9+9PP/00lIF76Vwb+yKAQG4E/ltGyk0NiNL6cgceeKC/T2y11Va2c+fOVoGwTGcX5+bKyj6L1g2dMGGC1bqmGmCh+5/uz1Hf9DmiGd9PPfWUT3mqmYVa+/TBBx8sUXUCeiVIeAEBBApEoIKu03WYsyGAAAKREnAz5Mz48ePN+eefb1xAz1x11VXGjcyKVB3TqcyKFSuMS7dpBg0aZFzqNnPllVeaiy66yLgH1HSKYV8EEEAAgRwK6DHZzd42bkCGuf32241bU9VsvvnmxnUQmzPPPNO4Th/j0gKVWaOVK1caF5Azbi0+49ZjMW79EnPyySeXeZzrjDEzZszwx7pZ3b4uOr+Oveaaa8zee+9tXEd1meWwQ+oCkyZN8s8eLhDh27dPnz6pH5yjPfXsoPeBWwc4ss8RbkapcVkPjOsQzZFK6qeZNWuW/39w9uzZxs3WMq7D06i92YIRcJ2xxg1CMC6FvRk+fLhx6zcZN+PFuBSc5rzzzjMdOnQwbr3qMk+2dOlSf/zdd99tDjvsMP/zQQcdVOZxLvOGcbOZ/X3TDXowbra1cWsyGdeZ7Z+/3ZrZtHeZiuyAQDwElixZYtysYX8/OOKII/x9xM3EK7o4FxDyfQ7du3f39yk921133XXGZWUwbiBX0X75+MMnn3xi3BIfZvLkyf7+e/3115uzzjorb65r7dq1xqU8NcOGDTN6Hlb9N3x21rOGm81nunXr5p/N+/XrZ9yMxHxsLuqMAAIIpCVAQC8tLnZGAIFcCcQtoKcOWT1gqoPh2GOPNeqcUMcGGwIIIIBAtAUU1FMH8cyZM42brWdcWiZluPAdxG7GnHFr2Bm3pp1xI6CTXki6AT0FQf7zn/+Yhx9+2EyZMsW4NJ/GpY7zHUzqqOjsAol16tQxbsR10nPyi8wEnn76adOpUyejTj4FAWrUqJFZQSEfpffbueeeay644AIf3Av5dGkV79YoNi6zglFwNIpjR9Ux6FJ6+Q5CAnppNW3KO6vdFdB96623zF133eWff9U57lJx+kEN+n/slFNO8UHpZIWmG9BTuypYq/umm3Hjg4rq7NUADHXWq631/w3B22TivI5A/ATKCujpXqXnrccff9zfHxT410CtfA/mrVmzxowbN85cffXVxs1CNGeffbYPZuoenE+b7ut6htY1aCCIBocU3wjoFdfgZwQQKCgB9wHGhgACCEROQCku4pJyU6kgxowZY6tWrWrdaHrrRvtb9/AZOXMqhAACCCCQXED38oULF1o348Q2aNDAp4RWGjelMjr88MPtkCFDfCo3pW/acEs15abWcn3xxRetC9L49EJbbrmlXz9Enx+tW7e2L7/8sl/vNZ10nxvWhX9vXGDixIlWqbHdH4SR/lL6rLZt21oX9Nj4BZXDb1955ZWi/0ei7qj11MJYN7kc2CN5Sq1hpzWk+/fvb7UOqd4P+v+rdu3a1g1w8ymNdV8t7Z6WSspNHeeyYPjUbG5whd11112t1r/SebSOn5sNaKdNm+bXyC7tHJFEo1IIIBCYQFkpN3Ui/V2uddu0dnJpz3CBVSaHBSkl+5FHHunvhUon6gaHlXqfzWGVQjmVns213rXu+Uqv/NBDD4VyHgpFAAEEoibADD1352dDAIHoCcRphp5GqruOXuPyvpvGjRubAQMGmNNOOy166NQIAQQQQGCjAq5D2M/Wmzt3rh/N7YI/fvac0l664Jtxa+wZpXNr0aKFUWo4zeDTTDqlfNsw5WarVq2MRlB/8cUX5qOPPjJKDTdnzhzj1n3yM1uUash1fPvZLBdeeKFxa+b50eOVK1feaB35ZXYCSg+oUe0uCOC9ozoLsmbNmubEE0/0qQijlnbVBbDNq6++6mdnaaZj1Db3B7n/f0z/z2q2a8uWLaNWxVjVRzMr3HpIRunf9P+WW6fSpw/W/c2tV+VnXbhBEubggw82zZo1M40aNTJu3T1/L1TKzuIpN5UqTzP/5s+fbz788EN/3/z444/Nt99+61/XbA63Vp6/Byu1vevQ9vflqP0/EqsG5mIQiLBAWTP0Ilz1jKumz2AX5DI333yzvx9qCRO3rqn/OeNCI3ogM/Qi2jBUCwEEQhcgoBc6MSdAAIFMBOIU0HvttddMz549jRuBbNq0aWNGjRqV0tohmbhxDAIIIIBA+AL6jFKQzs088etEaX2S5cuX+/XM1HGsDmWlBdI6Z/pZ37UWnxsp7juwtTaLAnNK5alUmuqEVgBP39X5rd/tv//+PvWjAnluNosvj3VXw29b+SvQqrZRMC+q5qqb3mNRDPAq8J14Tyt4FsVN7ayUalqHMIqGUTTLtk5KJaxUpwrAPfroo8bNRvap1PT/mIJ7ej8n7pf6WfdSrcW3bNky305ag1ptpv8/9f5KvMf0Xe85HdO8eXMfpD3qqKN8QF7lsSGAQOEKFFpAT5+5Wneud+/efhCFyyDh16BLZf3RfHyXENDLx1ajzgggEIQAAb0gFCkDAQQCF4hLQE8dvi71g18/T6PpL7vsMtO3b9+8z8sfeINTIAIIIJCHAuqg1mwRdThrrVSt2/Tuu+/64F4ikKHOanVC69/qdN7w34nLVsez1lY95phjjDqj9957b7Ptttsal24zskGlRN35jgACCKQqoA7Y1atXG62Rp5nJGvj2/vvvG5c6s6iIDe+TG/47saNmWSr7hdanVsd1w4YN/Yw83U91DBsCCBS2QKEF9DRITDOhe/Xq5Z8he/ToYa666io/aCKO7wQCenFsVa4JAQRSESCgl4oS+yCAQM4F4hLQ0yjkG2+80Tz33HM+LdawYcP86OGcg3JCBBBAAIHQBBSoUyeKZo5oJt6iRYvMvHnzfDpOdVLrS53XSqepjub69ev7WXca6KEvzTxRMG+nnXbyqTujOvMqNEAKRgCBghPQLMnEfXPlypU+k4VSaSp9pu6Z+q4UuF9//bWf2bzhfdOtl+fvmzvssEPRfVMz/dgQQACBhEChBfT0PPrmm2+aO++806cvvuSSS/wzZsIjbt8J6MWtRbkeBBBIVYCAXqpS7IcAAjkViENATw/UWifk4osv9qnUzj33XL8OiFKvsSGAAAIIxFNAM/E0c09rh+m7Oq31maaf9aVZI+p0VsrExJdSyyntn/7NhgACCBSagJ6ZE/dN3S8TX3pNP2uWc7L75qabblpoXFwvAgikKFBoAT2xaKCEsgTpnlm9evVYZwYioJfi/wjshgACsRMgoBe7JuWCEIiHgP54Hz9+vNEizvXq1fOpIhQYy6dNMzE0Ou6f//yn2WOPPcy1115rOnbsmE+XQF0RQAABBBBAAAEEEEAAAQQQyDuBQgzo5V0jZVFhAnpZ4HEoAgjktQABvbxuPiqPQHwF4hDQmzZtmunTp4+ZNWuWOemkk8zIkSON0gOxIYAAAggggAACCCCAAAIIIIBAeAIE9MKzjULJBPSi0ArUAQEEykOAgF55qHNOBBAoU0CpdyZMmGA6depkdtttN9OvXz9zwQUXlHlcVHZYu3atX5D68ssv9+t6aHbhgAEDDGmBotJC1AMBBBBAAAEEEEAAAQQQQCCuAgT04tqy/++6COjFu325OgQQSC5AQC+5Db9BAIFyFnjqqadM586dfcrN/v37mzPOOKOca5T66b///ns/I0/1Puigg8ytt95qWrZsmXoB7IkAAggggAACCCCAAAIIIIAAAhkJENDLiC1vDiKglzdNRUURQCBgAQJ6AYNSHAIIBCcwb948M3bsWL+gs2bn1a1bN7jCQy5p3bp1ZubMmebJJ580jRs3Nu3btzdVqlQJ+awUjwACCCCAAAIIIIAAAggggAACBPTi/R4goBfv9uXqEEAguQABveQ2/AYBBMpZ4M8//zRr1qzxtahWrVrepav8/fffzS+//OIDkltuuWU5a3J6BBBAAAEEEEAAAQQQQAABBApDgIBevNuZgF6825erQwCB5AIE9JLb8BsEEEAAAQQQQAABBBBAAAEEEEAAAQQQyDMBAnp51mBpVpeAXppg7I4AArERIKAXm6bkQhBAAAEEEEAAAQQQQAABBBBAAAEEEECAgF683wME9OLdvlwdAggkFyCgl9yG3yCAAAIIIIAAAggggAACCCCAAAIIIIBAngkQ0MuzBkuzugT00gRjdwQQiI0AAb3YNCUXggACCCCAAAIIIIAAAggggAACCCCAAAIE9OL9HiCgF+/25eoQQCC5AAG95Db8BgEEEEAAAQQQQAABBBBAAAEEEEAAAQTyTICAXp41WJrVJaCXJhi7I4BAbAQI6MWmKbkQBBBAAAEEEEAAAQQQQAABBBBAAAEEECCgF+/3AAG9eLcvV4cAAskFCOglt+E3CCCAAAIIIIAAAggggAACCCCAAAIIIJBnAgT08qzB0qwuAb00wdgdAQRiI0BALzZNyYUggAACCCCAAAIIIIAAAggggAACCCCAAAG9eL8HCOjFu325OgQQSC5AQC+5Db9BAAEEEEAAAQQQQAABBBBAAAEEEEAAgTwTIKCXZw2WZnUJ6KUJxu4IIBAbAQJ6sWlKLgQBBBBAAAEEEEAAAQQQQAABBBBAAAEECOjF+z1AQC/e7cvVIYBAcgECeslt+A0CCCCAAAIIIIAAAggggAACCCCAAAII5JnA4sWLzZAhQ8wDDzxgqlSpYho1amQaN26cZ1dBdZMJKKA3f/58M3v2bFO3bl3Tp08fc9lllyXbndcRQACB2AgQ0ItNU3IhCCCAAAIIIIAAAggggAACCCCAAAIIIDBt2jQf5Jk1a5bHqFixoqlUqRIwMRGw1pq//vrL/Pnnn0Zte95555nRo0fH5Oq4DAQQQCC5AAG95Db8BgEEEEAAAQQQQAABBBBAAAEEEEAAAQTyTOD77783I0eONP379/c132yzzUzlypXz7CqobjKBREDv999/N82aNTODBw82xx57bLLdeR0BBBCIjQABvdg0JReCAAIIIIAAAggggAACCCCAAAIIIIAAAn///bf56aefzIoVKzxGhQoVjL7Y4iOgoJ6+lFJ1++23N5tvvnl8Lo4rQQABBJIIENBLAsPLCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCERBgIBeFFqBOiCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCQRICAXhIYXkYAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgCgIE9KLQCtQBAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAgSQCBPSSwPAyAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAlEQIKAXhVagDggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggkESCglwSGlxFAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBCIggABvSi0AnVAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAIIkAAb0kMLyMAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAQBQECOhFoRWoAwIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAJJBAjoJYHhZQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQSiIPD/AVza0bFxotnRAAAAAElFTkSuQmCC" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Superdense Coding" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this tutorial, we construct an implementation of the superdense coding protocol via Amazon Braket's SDK. Superdense coding is a method of transmitting two classical bits by sending only one qubit. Starting with a pair of entanged qubits, the sender (aka Alice) applies a certain quantum gate to their qubit and sends the result to the receiver (aka Bob), who is then able to decode the full two-bit message.\n", + "\n", + "If Alice wants to send a two-bit message to Bob using only classical channels, she would need to send two classical bits. However, with the help of quantum entanglement, Alice can do this by sending just one qubit. By ensuring that Alice and Bob initially share an entangled state of two qubits, they can devise a strategy such that Alice can transmit her two-bit message by sending her single qubit.\n", + "\n", + "To implement superdense coding, Alice and Bob need to share or otherwise prepare a maximally entangled pair of qubits (i.e., a Bell pair). Alice then selects one of the four possible messages to send with two classical bits: 00, 01, 10, or 11. Depending on which two-bit string she wants to send, Alice applies a corresponding quantum gate to encode her desired message. Finally, Alice sends her own qubit to Bob, which Bob then uses to decode the message by undoing the initial entangling operation.\n", + "\n", + "Note that superdense coding is closely related to quantum teleportation. In teleportation, one uses an entangled pair (an e-bit) and two uses of a classical channel to simulate a single use of a quantum channel. In superdense coding, one uses an e-bit and a single use of a quantum channel to simulate two uses of a classical channel.\n", + "\n", + "\n", + "## Detailed Steps\n", + "1. Alice and Bob initially share a Bell pair. This can be prepared by starting with two qubits in the |0⟩ state, then applying the Hadamard gate (𝐻) to the first qubit to create an equal superposition, and finally applying a CNOT gate (𝐶𝑋) between the two qubits to produce a Bell pair. Alice holds one of these two qubits, while Bob holds the other.\n", + "2. Alice selects one of the four possible messages to send Bob. Each message corresponds to a unique set of quantum gate(s) to apply to her own qubit, illustrated in the table below. For example, if Alice wants to send the message \"01\", she would apply the Pauli X gate.\n", + "3. Alice sends her qubit to Bob through the quantum channel.\n", + "4. Bob decodes Alice's two-bit message by first applying a CNOT gate using Alice's qubit as the control and his own qubit as the target, and then a Hadamard gate on Alice's qubit to restore the classical message.\n", + "\n", + "| Message | Alice's encoding | State Bob receives
(non-normalized) | After 𝐶𝑋 gate
(non-normalized) | After 𝐻 gate |\n", + "| :---: | :---: | :---: | :---: | :---: |\n", + "| 00 | 𝐼 | \\|00⟩ + \\|11⟩ | \\|00⟩ + \\|10⟩ | \\|00⟩\n", + "| 01 | 𝑋 | \\|10⟩ + \\|01⟩ | \\|11⟩ + \\|01⟩ | \\|01⟩\n", + "| 10 | 𝑍 | \\|00⟩ - \\|11⟩ | \\|00⟩ - \\|10⟩ | \\|10⟩\n", + "| 11 | 𝑍𝑋 | \\|01⟩ - \\|10⟩ | \\|01⟩ - \\|11⟩ | \\|11⟩\n", + "\n", + "\n", + "## Circuit Diagram\n", + "\n", + "Circuit used to send the message \"00\". To send other messages, swap out the identity (𝐼) gate.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Version: 1.0.0.post1\r\n" + ] + } + ], + "source": [ + "# Print version of SDK\n", + "!pip show amazon-braket-sdk | grep Version\n", + "\n", + "# Import Braket libraries\n", + "from braket.circuits import Circuit, Gate, Moments\n", + "from braket.circuits.instruction import Instruction\n", + "from braket.aws import AwsDevice\n", + "from braket.devices import LocalSimulator\n", + "import matplotlib.pyplot as plt\n", + "import time" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Typically, we recommend running circuits with fewer than 25 qubits on the local simulator to avoid latency bottlenecks. The on-demand, high-performance simulator SV1 is better suited for larger circuits up to 34 qubits. For demonstration purposes, we are going to continue this example with the local simulator, but it is easy to switch over to SV1 by commenting out the LocalSimulator line below and uncommenting the sv1 line.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Set up device: local simulator or the on-demand simulator\n", + "device = LocalSimulator()\n", + "# device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Function to run quantum task, check the status thereof and collect results\n", + "def get_result(device, circ):\n", + " \n", + " # get number of qubits\n", + " num_qubits = circ.qubit_count\n", + "\n", + " # specify desired results_types\n", + " circ.probability()\n", + "\n", + " # submit task: define task (asynchronous)\n", + " if device.name == 'StateVectorSimulator':\n", + " task = device.run(circ, shots=1000)\n", + " else:\n", + " task = device.run(circ, shots=1000)\n", + "\n", + " # Get ID of submitted task\n", + " task_id = task.id\n", + "# print('Task ID :', task_id)\n", + "\n", + " # Wait for job to complete\n", + " status_list = []\n", + " status = task.state()\n", + " status_list += [status]\n", + " print('Status:', status)\n", + "\n", + " # Only notify the user when there's a status change\n", + " while status != 'COMPLETED':\n", + " status = task.state()\n", + " if status != status_list[-1]:\n", + " print('Status:', status)\n", + " status_list += [status]\n", + "\n", + " # get result\n", + " result = task.result()\n", + "\n", + " # get metadata\n", + " metadata = result.task_metadata\n", + "\n", + " # get output probabilities\n", + " probs_values = result.values[0]\n", + "\n", + " # get measurement results\n", + " measurement_counts = result.measurement_counts\n", + "\n", + " # print measurement results\n", + " print('measurement_counts:', measurement_counts)\n", + "\n", + " # bitstrings\n", + " format_bitstring = '{0:0' + str(num_qubits) + 'b}'\n", + " bitstring_keys = [format_bitstring.format(ii) for ii in range(2**num_qubits)]\n", + "\n", + " # plot probabalities\n", + " plt.bar(bitstring_keys, probs_values)\n", + " plt.xlabel('bitstrings')\n", + " plt.ylabel('probability')\n", + " plt.xticks(rotation=90)\n", + " plt.show() \n", + " \n", + " return measurement_counts" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alice and Bob initially share a Bell pair. Let's create this now:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)]))])\n" + ] + } + ], + "source": [ + "circ = Circuit()\n", + "circ.h([0])\n", + "circ.cnot(0,1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define Alice's encoding scheme according to the table above. Alice selects one of these messages to send." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# Four possible messages and their corresponding gates\n", + "message = {\"00\": Circuit().i(0),\n", + " \"01\": Circuit().x(0),\n", + " \"10\": Circuit().z(0),\n", + " \"11\": Circuit().x(0).z(0)\n", + " }" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Select message to send. Let's start with '01' for now\n", + "m = \"01\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alice encodes her message by applying the gates defined above" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)])), Instruction('operator': X('qubit_count': 1), 'target': QubitSet([Qubit(0)]))])\n" + ] + } + ], + "source": [ + "# Encode the message\n", + "circ.add_circuit(message[m])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alice then sends her qubit to Bob so that Bob has both qubits in his lab. Bob decodes Alice's message by disentangling the two qubits:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)])), Instruction('operator': X('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)])), Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)]))])\n" + ] + } + ], + "source": [ + "circ.cnot(0,1)\n", + "circ.h([0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The full circuit now looks like" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4|\n", + " \n", + "q0 : -H-C-X-C-H-\n", + " | | \n", + "q1 : ---X---X---\n", + "\n", + "T : |0|1|2|3|4|\n" + ] + } + ], + "source": [ + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By measuring the two qubits in the computational basis, Bob can read off Alice's two qubit message" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status: COMPLETED\n", + "measurement_counts: Counter({'01': 1000})\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'01': 1000})\n" + ] + } + ], + "source": [ + "counts = get_result(device, circ)\n", + "print(counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can check that this scheme works for the other possible messages too:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status: COMPLETED\n", + "measurement_counts: Counter({'00': 1000})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Message: 00. Results:\n", + "Counter({'00': 1000})\n", + "Status: COMPLETED\n", + "measurement_counts: Counter({'01': 1000})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Message: 01. Results:\n", + "Counter({'01': 1000})\n", + "Status: COMPLETED\n", + "measurement_counts: Counter({'10': 1000})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Message: 10. Results:\n", + "Counter({'10': 1000})\n", + "Status: COMPLETED\n", + "measurement_counts: Counter({'11': 1000})\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Message: 11. Results:\n", + "Counter({'11': 1000})\n" + ] + } + ], + "source": [ + "for m in message:\n", + " \n", + " # Reproduce the full circuit above by concatenating all of the gates:\n", + " newcirc = Circuit().h([0]).cnot(0,1).add_circuit(message[m]).cnot(0,1).h([0])\n", + " \n", + " # Run the circuit:\n", + " counts = get_result(device, newcirc)\n", + " \n", + " print(\"Message: \" + m + \". Results:\")\n", + " print(counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.00 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.10 ('venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/0_TO_ORGANIZE/4_Superdense_coding/circuit.png b/0_TO_ORGANIZE/4_Superdense_coding/circuit.png new file mode 100644 index 0000000000000000000000000000000000000000..0b7409fedd0acb47a825e2d50716d6b59d0fecfe GIT binary patch literal 48954 zcma%i1z1&Gw=S`zr9%W^(xru3aaYrWNBk>fq?KVIz<~*N4<|Y`-PgEbqLxs^wwzVXQ}v-u~4XH zC0?SqWHcvL)YKc9dy{O`#$RI?n~B9IVp<=^w2D10EG><_N5<@=Ca&Fnws1ClHq;t4 zoOzs+*mO3GkgGnFB=4qbfZ$5!Q{8xAJTaB5LA-@7j)d6_r}_?Rxu;=>~m-eL&eoJPz8$ibWUPbSolKgtVJm?D!Z z;+huWTNS%h;TM#+MD){By+%G%M(BM)q4E|z*ppza=IA0lLH3Hcs~kT>2PqhvbQz&7 ziXoUEX_>02DJkW_3}Pf~-<#{MGhMW!Z^Z)J*n^dsDl%&A2l+znUCpDr7p`uEH=H|5 zxzXl$F8%LJ79A~AUTc^>>@rA%Z9a%Pp}K_<7w%9!Euxl@em_IOvo;`5X%&oKRT4~s zk6y*pWs;b=$rvXpB1Qf!;z2oXt$1dS(&#xGZokwDPv&@ap9|*=ztlGqJOAH4T$=j% zH*zwb)GxjUDbTK-9=Ed+($SWLQ z&4`Ypb!GQ&~rbcLzYY3<_hp^-2YhwT}U7zOK4 ztdi9G!ivCNUEoWEONiX>`s z<9o-UMl7*Mg^P-UPR`&j)hk==_OMY&$L^3qyYkc;M@(cy?PB6~A9Zy`)&p>t* z6%^C+vrEHMZBK7wX6sT{B$eT@Y8xe@Rkiy&#Z0Dtv#MViM!n1O=TecCbNci8h^m3I zV--bwisNU9CfRqNGB)l72e}v-E#^5j_p&1FC?E#=?q&?%()g3SKz8aj~uC|)5aN5A7!%BpwU;b19SBLLWm(m;u+c_6X>_7d#17cG>%bx_`%`S z&!3SehJK_vigtSmk%cwvlqA!Fi*+%5#L?t@_Y5_+6go zCdU|=#fLZ6NP>t%(gnE@)||}`%EawPv#gPQ$y*AcypSTUJqN`!${<+*W z^DXZFw|4wZh`%hPx$g^YvE<#$l>Y-Hrvq8H2Beq??t|2ipDW@JzjQS zre4-tc3kE(B|GG-ij<}%P0EzJ{rCVsK3SHTs*Gxv_7R-{l}CbTLR~MhIiKqTft1Ho zByR@#gnDIrwR=Z;TL}$fSi4j4rSMcgJ%6jptNxBDmGM!sVKK#c_O^;ruI2L$HI~AY zG4(OOF+M##JuN*^J+s;_J-1rs+EeSSao@s|H=k78-n&?@*kH_<&hXA~&N$4F31&IU z;=C{Tal9G3RR<%0p~7%xuy*ri^c_M@?RS}XQFd8o*gY5p>jmwzq6H%a*95QJ*|yxb z)ZBO71)7EDb(=MtQ9YctPd7PXFMoG$u5Gjan9cK2-ft3>TT~X)Fv>M5ZI`$tA z;7@yqYXGX&lxW7?8oh?i z?UPS}&)W<6W196WVysvM%&Knr*bl@()mXarTG%C_9*N@)HnyZDMU`{b)3(!g7EUSF zn&x%0+ig7KGqZwUee*qHJsRR7hO9G4c|CZ&?3wBp>ZxbP>#gh;XQyZBW``Q=YW*CY z%tz|jYb$EnH^jZr+|!m-SDc65Y;NwR?KVyvRugQm{-Sj)c5PmLCFmy@n>8ueaGwh6 zkd&HKjeGSI=1|0L;=bC(ku#&4_1Nh9yf`T%>>ARyg7(vu++W+8eH+&s9X(rx^n=a| zf608!h-~+Cb6siCY%*{wXo+kZ@pN(x;`!ne?%dUk*C70W;)BS#U#++QA?zsGXTs0Z zciKDON7HW}#(VJk#BeoWB65jfhkJG-VMNwQWl?yswJqqX>D=OK_rOo|N8m^2)%7>= zH)Yp8w`4c7$U2BNh-64J$gIddAv_`Rp`~FEi5FqnRgb21cd~X;JIgz(mykR61==#x zGtH=Uo_RmBd1hA_Xl-h3u^GluQaM=JT)F2Qf3WqdhZ+s<4c-8?qw7$kzawjdU-D#O z`UmBwKd4t|SZF9^1Z4W&zmxs&K{n2i^U|=^p_aCp6Q#@9Osi`yzAios|LW?&a@rK9 zrdjs4`|%lgUi8^`VoZUu*Dc{o;dJO;1ds5EqFLnx824Z_WE-2l3oRK%Z5rjWWSV*hoYN4n}mc4~2h>ZR5Lj zr7Uaf;_3dbS+MFccN*9mkQ<)PQW#bm5MlhDYObKH%$uXn(WJEfnDtG)%3)Tut$f2{ zwR+9hy$rn>M_5ZQZ{B~AIE-C32^0_1yp1f9Q$HixBzlIyrtJ2v-g&0xOXU~VpNCu5 zTddrVtp>9Wo$3A7zv=dt!gN_{%B)C6_RA4t;ftLVzjQOWq9g?7xewYDDqD4&~9=0 zRd<fM2pwv$k-_>sGUql_9loXW^mCUld zXMQ&^RjS*(?v`J8zv|e1FI)W>OCX3UekG4XT2|X+c?ik^@`ZB zE%qu}Y|LnCvB#PEFm=4)WYa!BMb^|{k#p8|c~gH?g2REG%nQB$^I?3=dQ#;XvtI@@VN7cd_9#aPgi8Nz0-LjXji79pk=tU+xgpbcx-pa9hsk{<#*j{i!uMTtaLq)^lrVk}A-#3)3vbVMu8wq}%yYm`dBx&jK^!l9Gy6xAx8F!fB;3WImVJmvq=YZ|Z zVE^g|&Ns^XAlR+5p&T%*j{aUWqZs#GMJIq*Bbou>x!Y^RN>uC?fnpkTRmX9HP=xJ0 zQI03nBhFsxZr_)pBM@
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"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Allocating Qubits on QPU Devices" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook demonstrates how you can specify explicitly which qubits to use when you run a quantum circuit on QPU devices from Rigetti.\n", + "\n", + "When you submit a circuit for execution on a QPU, Amazon Braket performs a series of compilation steps: it maps the _abstract qubits_ in your circuit to _physical qubits_ in the device; it synthesizes gates into the native gate set of the device; it optimizes the circuit to reduce the number of gates; and finally, it translates the gates into executable pulses.\n", + "\n", + "This section shows how the first step, called qubit allocation, works for the Rigetti Aspen-M-3 device." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "from braket.aws import AwsDevice\n", + "from braket.circuits import Circuit\n", + "import numpy as np\n", + "import random" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## Automatic qubit allocation\n", + "\n", + "Qubit allocation for Rigetti devices on Amazon Braket utilizes [the Quil Compilers](https://pyquil-docs.rigetti.com/en/latest/compiler.html#the-quil-compiler)'s _rewiring_ strategies. By default, when you submit a circuit on Amazon Braket to a Rigetti device, the circuit is rewired according to the [PARTIAL](https://pyquil-docs.rigetti.com/en/latest/compiler.html#partial) rewiring strategy. Specifically, the compiler starts with an empty mapping from logical to physical qubits. Taking into account the latest calibration data of the device, the compiler fills in the mapping with the goal, sequentially, to maximize the overall fidelity of the circuit.\n", + "\n", + "The example that follows shows how to create a GHZ state on qubits that are not physically connected. After the task is completed, you can obtain a list of the actual gates executed on the device, by viewing the result metadata.\n", + "\n", + "First, instantiate the Rigetti Aspen-M-3 device and retrieve its connectivity graph, which shows the qubits that are directly connected on the chip." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the connectivity of Aspen-M-3 is: {'0': ['1', '7'], '1': ['0', '16', '2'], '10': ['11', '113', '17'], '100': ['101', '107'], '101': ['100', '102', '116'], '102': ['101', '103', '115'], '103': ['102', '104'], '104': ['103', '105', '7'], '105': ['104', '106'], '106': ['105', '107'], '107': ['100', '106'], '11': ['10', '12', '26'], '110': ['111', '117'], '111': ['110', '112', '126'], '112': ['111', '113'], '113': ['10', '112', '114'], '114': ['113', '115', '17'], '115': ['102', '114', '116'], '116': ['101', '115', '117'], '117': ['110', '116'], '12': ['11', '13', '25'], '120': ['121', '127'], '121': ['120', '122', '136'], '122': ['121', '123', '135'], '123': ['122', '124', '20'], '124': ['123', '125', '27'], '125': ['124', '126'], '126': ['111', '125', '127'], '127': ['120', '126'], '13': ['12', '14'], '130': ['131', '137'], '131': ['130', '132', '146'], '132': ['131', '133', '145'], '133': ['132', '134', '30'], '134': ['133', '135', '37'], '135': ['122', '134', '136'], '136': ['121', '135', '137'], '137': ['130', '136'], '14': ['13', '15'], '140': ['141', '147'], '141': ['140', '142'], '142': ['141', '143'], '143': ['142', '144', '40'], '144': ['143', '145', '47'], '145': ['132', '144', '146'], '146': ['131', '145', '147'], '147': ['140', '146'], '15': ['14', '16', '2'], '16': ['1', '15', '17'], '17': ['10', '16', '114'], '2': ['1', '15', '3'], '20': ['123', '21', '27'], '21': ['20', '22', '36'], '22': ['21', '23', '35'], '23': ['22', '24'], '24': ['23', '25'], '25': ['12', '24', '26'], '26': ['11', '25', '27'], '27': ['20', '26', '124'], '3': ['2', '4'], '30': ['133', '31', '37'], '31': ['30', '32', '46'], '32': ['31', '33', '45'], '33': ['32', '34'], '34': ['33', '35'], '35': ['22', '34', '36'], '36': ['21', '35', '37'], '37': ['30', '36', '134'], '4': ['3', '5'], '40': ['143', '41', '47'], '41': ['40', '42'], '42': ['41', '43'], '43': ['42', '44'], '44': ['43', '45'], '45': ['32', '44', '46'], '46': ['31', '45', '47'], '47': ['40', '46', '144'], '5': ['4', '6'], '6': ['5', '7'], '7': ['0', '6', '104']}\n" + ] + } + ], + "source": [ + "device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "\n", + "connectivity_graph = device.properties.paradigm.connectivity.connectivityGraph\n", + "print(f\"the connectivity of {device.name} is: {connectivity_graph}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "Next, create a GHZ circuit with three qubits 0, 2, 4, and run it on the Aspen-M-3 device. Notice that none of these qubits are connected on the Aspen-M-3 connectivity graph." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|\n", + " \n", + "q0 : -H-C-C-\n", + " | | \n", + "q2 : ---X-|-\n", + " | \n", + "q4 : -----X-\n", + "\n", + "T : |0|1|2|\n" + ] + } + ], + "source": [ + "# create a GHZ state with non-neighboring qubits\n", + "circuit = Circuit()\n", + "circuit.h(0).cnot(0,2).cnot(0,4)\n", + "print(circuit)\n", + "\n", + "rigetti_rewiring = device.run(circuit, shots=10)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: CREATED\n" + ] + } + ], + "source": [ + "print(\"Status of task:\", rigetti_rewiring.state())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "To verify the final qubit allocation, retrieve the compiled program that was executed:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'001': 4, '111': 3, '000': 2, '101': 1})\n", + "The compiled circuit is:\n", + " DECLARE ro BIT[3]\n", + "PRAGMA INITIAL_REWIRING \"PARTIAL\"\n", + "RESET\n", + "RZ(-pi/2) 12\n", + "RX(-pi/2) 12\n", + "RZ(pi) 13\n", + "XY(pi) 12 13\n", + "RZ(pi/2) 12\n", + "RX(pi/2) 12\n", + "RZ(-pi/2) 12\n", + "XY(pi) 12 13\n", + "RZ(pi/2) 25\n", + "RX(-pi/2) 25\n", + "CZ 25 12\n", + "RZ(pi) 12\n", + "RX(-pi/2) 13\n", + "RX(pi/2) 25\n", + "RZ(-pi/2) 25\n", + "MEASURE 25 ro[2]\n", + "MEASURE 13 ro[1]\n", + "MEASURE 12 ro[0]\n", + "\n" + ] + } + ], + "source": [ + "result = rigetti_rewiring.result()\n", + "counts = result.measurement_counts\n", + "print(\"Measurement counts:\", counts)\n", + "print(\"The compiled circuit is:\\n\", result.additional_metadata.rigettiMetadata.compiledProgram)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "Notice that the PARTIAL rewiring was applied. The qubits 0, 2, 4 in the original circuit were mapped to three other qubits in the Rigetti device, and the gates were compiled into native gates." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## User-defined qubit allocation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In Amazon Braket, you can choose to prescribe a qubit mapping manually, and prevent further rewiring for Rigetti devices. To enable manual mapping, set `disable_qubit_rewiring=True` when submitting the task to run.\n", + "\n", + "If all the gates in the circuit satisfy the topological constraints of the device, Amazon Braket maps abstract qubit $i$ in the circuit to the physical qubit $i$ in the device, and maps qubit pair $(i, j)$ to the connection $(i, j)$ in the device. On the other hand, Amazon Braket raises an exception if a specified qubit or qubit pair do not exist in the device connectivity graph." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 |1|\n", + " \n", + "q0 : -Rz(1.57)-C-\n", + " | \n", + "q1 : ----------X-\n", + " \n", + "q3 : -X----------\n", + "\n", + "T : | 0 |1|\n" + ] + } + ], + "source": [ + "# create a random state with neighboring qubits\n", + "q1=random.choice(list(connectivity_graph))\n", + "q2=int(connectivity_graph[q1][0])\n", + "q1=int(q1)\n", + "\n", + "circuit = Circuit()\n", + "circuit.rz(0,np.pi/2).cnot(q1,q2).x(7)\n", + "print(circuit)\n", + "rigetti_task = device.run(circuit, shots=10, disable_qubit_rewiring=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: COMPLETED\n" + ] + } + ], + "source": [ + "print(\"Status of task:\", rigetti_task.state())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'011': 6, '001': 2, '101': 1, '000': 1})\n", + "The compiled circuit is:\n", + " DECLARE ro BIT[3]\n", + "PRAGMA INITIAL_REWIRING \"NAIVE\"\n", + "RESET\n", + "RZ(pi) 1\n", + "RX(-pi/2) 1\n", + "XY(pi) 0 1\n", + "RZ(-pi/2) 0\n", + "RX(pi/2) 0\n", + "RZ(pi/2) 0\n", + "XY(pi) 0 1\n", + "RX(pi) 3\n", + "MEASURE 3 ro[2]\n", + "MEASURE 1 ro[1]\n", + "MEASURE 0 ro[0]\n", + "\n" + ] + } + ], + "source": [ + "result = rigetti_task.result()\n", + "counts = result.measurement_counts\n", + "print(\"Measurement counts:\", counts)\n", + "print(\"The compiled circuit is:\\n\", result.additional_metadata.rigettiMetadata.compiledProgram)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "The qubits in the original circuit followed a one-to-one mapping to the physical qubits in the device. Other compilation steps, such as gate synthesis and circuit optimization, are still performed. These steps allow the circuit to run successfully and improve the overall fidelity." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using the qubits with the highest two-qubit gate fidelity\n", + "\n", + "Additionally, the device properties include calibration data, which you can use to find the qubits and qubit pairs with the highest fidelities for particular gates.\n", + "\n", + "The following function finds the qubit pair that has the highest two-qubit fidelity of an input gate, which can be any of the gates native to the Rigetti device, namely CPHASE, XY or CZ." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "def find_qubit_pair(gate):\n", + " \"Function to find the qubit pair that has the highest gate fidelity of a particular gate\"\n", + " \n", + " # check whether the input gate is a string\n", + " if not isinstance(gate, str):\n", + " raise ValueError('The input gate must be a string type.') \n", + " \n", + " # check whether the input gate is a native gate\n", + " gate_list = ['CPHASE', 'CZ', 'XY']\n", + " if gate not in gate_list:\n", + " raise ValueError('The input gate must be either CPHASE, CZ or XY.')\n", + " \n", + " # load all calibration data from device.properties\n", + " calibration_2Q = device.properties.provider.specs['2Q']\n", + " highest_fidelity = 0\n", + "\n", + " # iterate through all calibration data to find the highest fidelity\n", + " for pair in calibration_2Q.keys():\n", + " \n", + " # if the particular gate type is supported by the qubit pair\n", + " if ('f'+ gate) in calibration_2Q[pair].keys(): \n", + " \n", + " if calibration_2Q[pair]['f'+ gate] > highest_fidelity:\n", + " \n", + " # update the highest_fidelity and the best_pair\n", + " highest_fidelity = calibration_2Q[pair]['f'+ gate]\n", + " best_pair = pair\n", + "\n", + " # generate the two qubits as integers \n", + " q1 = best_pair[0]\n", + " i = 1\n", + " while best_pair[i] is not '-':\n", + " q1 += best_pair[i]\n", + " i += 1\n", + "\n", + " q1 = int(q1)\n", + " q2 = int(best_pair[i+1:])\n", + " \n", + " return q1, q2, highest_fidelity" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "The example in the following code applies a native two-qubit gate on the qubit pair that has the highest fidelity of that gate. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The highest fidelity for CZ gate is: 0.9794230141816626\n", + "And the corresponding qubit pair is: qubit 21 and qubit 36\n", + "T : |0|\n", + " \n", + "q21 : -C-\n", + " | \n", + "q36 : -Z-\n", + "\n", + "T : |0|\n" + ] + } + ], + "source": [ + "# the gate must be either 'CZ', 'CPHASE' or 'XY'\n", + "gate = 'CZ'\n", + "# find the qubit pair with the highest gate fidelity\n", + "q1, q2, highest_fidelity = find_qubit_pair(gate)\n", + "print('The highest fidelity for '+gate+' gate is:', highest_fidelity)\n", + "print(f'And the corresponding qubit pair is: qubit {q1} and qubit {q2}')\n", + "\n", + "# create a circuit with the gate applied to the discovered qubit pair.\n", + "# note that CPHASE in Rigetti corresponds to cphaseshift in Braket\n", + "circuit = Circuit()\n", + "circuit.cz(q1,q2)\n", + "print(circuit)\n", + "rigetti_task = device.run(circuit, shots=1000, disable_qubit_rewiring=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'00': 910, '01': 55, '10': 33, '11': 2})\n", + "The compiled circuit is:\n", + " DECLARE ro BIT[2]\n", + "PRAGMA INITIAL_REWIRING \"NAIVE\"\n", + "RESET\n", + "CZ 21 36\n", + "MEASURE 21 ro[1]\n", + "MEASURE 36 ro[0]\n", + "\n" + ] + } + ], + "source": [ + "print(\"Status of task:\", rigetti_task.state())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The qubits in the original circuit followed a one-to-one mapping to the physical qubits in the device. Since only native gates were used, the actual gates executed are the same as the gates in the original circuit." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "
    \n", + "Note: The IonQ device does not support manual allocation. For circuits submitted to the IonQ device, qubits are allocated automatically.\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 1020, 'tasks': {'QUEUED': 1, 'CREATED': 2}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 1.26 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.10 ('venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} \ No newline at end of file diff --git a/0_TO_ORGANIZE/Error_Mitigation_on_Amazon_Braket.ipynb b/0_TO_ORGANIZE/Error_Mitigation_on_Amazon_Braket.ipynb new file mode 100644 index 000000000..ba5125676 --- /dev/null +++ b/0_TO_ORGANIZE/Error_Mitigation_on_Amazon_Braket.ipynb @@ -0,0 +1,467 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Error mitigation on Amazon Braket \n", + "\n", + "In this example notebook, you will learn how to get started with using IonQ's Aria QPU on Amazon Braket. You’ll learn how Aria's two built-in error mitigation techniques work, how to switch between them, and the performance difference you can expect to see with and without these techniques for toy problems. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum phase estimation \n", + "\n", + "Quantum phase estimation (QPE) is a fundamental algorithm in quantum computing that plays a crucial role in many applications. The QPE algorithm is designed to estimate the eigenvalues of a unitary operator. Below, we provide an example implementation in the Braket SDK. " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "from braket.aws import AwsDevice\n", + "from braket.circuits import Circuit\n", + "from braket.devices import LocalSimulator\n", + "from braket.tracking import Tracker\n", + "from phase_estimation import phase_estimation_circuit\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "cost_tracker = Tracker().start()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# device = LocalSimulator()\n", + "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Aria-1\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0| 1 |2| 3 |4| 5 |6| 7 |8| 9 |10| 11 |12| 13 |14| 15 |16| 17 |18| 19 |20| 21 |22| 23 |24 | 25 |26| 27 |28 | 29 |30 | 31 |32 | 33 |34| 35 |36| 37 |38| 39 |40|\n", + " \n", + "q0 : -H-Rz(6.28)------------------------------------------------------------------------C------------C--SWAP------------------------------------------------------------------------X-Rz(0.20)---X-Rz(-0.20)---X-Rz(0.39)--X--Rz(-0.39)-X--Rz(0.79)-X--Rz(-0.79)-H--\n", + " | | | | | | | | | \n", + "q1 : -H-Rz(3.14)-----------------------------------------------C------------C--SWAP-----|------------|--|------------------------------------------------X-Rz(0.39)--X--Rz(-0.39)-X-|-Rz(0.79)-X-|-Rz(-0.79)-H-|-Rz(-0.79)-|------------C-----------C---------------\n", + " | | | | | | | | | | | | | | \n", + "q2 : -H-Rz(1.57)------------------------C-----------C----------|------------|--SWAP-----|------------|--|---------------------X--Rz(0.79)-X--Rz(-0.79)-H-|-Rz(-0.79)-|------------C-|----------C-|-Rz(-0.39)---C-----------C----------------------------------------\n", + " | | | | | | | | | | | | | \n", + "q3 : -H-Rz(0.79)-C-----------C----------|-----------|----------|------------|-----------|------------|--SWAP-----H--Rz(-0.79)-C-----------C--Rz(-0.39)---C-----------C--Rz(-0.20)---C------------C------------------------------------------------------------------\n", + " | | | | | | | | \n", + "q4 : -X----------X-Rz(-0.79)-X-Rz(0.79)-X-Rz(-1.57)-X-Rz(1.57)-X--Rz(-3.14)-X--Rz(3.14)-X--Rz(-6.28)-X--Rz(6.28)----------------------------------------------------------------------------------------------------------------------------------------------------\n", + "\n", + "T : |0| 1 |2| 3 |4| 5 |6| 7 |8| 9 |10| 11 |12| 13 |14| 15 |16| 17 |18| 19 |20| 21 |22| 23 |24 | 25 |26| 27 |28 | 29 |30 | 31 |32 | 33 |34| 35 |36| 37 |38| 39 |40|\n" + ] + } + ], + "source": [ + "circ = phase_estimation_circuit(n_qubits=4, phase=np.pi / 4)\n", + "print(circ)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aria \n", + "\n", + "First, we run the QPE circuit on the Aria device with the maximum number of shots per task (2,500). " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AwsQuantumTask('id/taskArn':'arn:aws:braket:us-east-1::quantum-task/6bd86be9-2811-49b2-a62e-86cd328d444f')\n" + ] + } + ], + "source": [ + "task = device.run(circ, shots=2500)\n", + "print(task)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'00000': 0.0028,\n", + " '10000': 0.0038,\n", + " '01000': 0.0102,\n", + " '11000': 0.0002,\n", + " '00100': 0.0002,\n", + " '01100': 0.0002,\n", + " '10010': 0.0002,\n", + " '01010': 0.0002,\n", + " '11010': 0.0004,\n", + " '00110': 0.0002,\n", + " '00001': 0.015,\n", + " '10001': 0.0084,\n", + " '01001': 0.8792,\n", + " '11001': 0.03,\n", + " '00101': 0.0046,\n", + " '10101': 0.0006,\n", + " '01101': 0.0128,\n", + " '11101': 0.0026,\n", + " '00011': 0.0004,\n", + " '10011': 0.002,\n", + " '01011': 0.0074,\n", + " '11011': 0.011,\n", + " '00111': 0.0018,\n", + " '10111': 0.004,\n", + " '01111': 0.001,\n", + " '11111': 0.0008}" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "probs = task.result().measurement_probabilities" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Error Mitigation with debiasing\n", + "\n", + "Debiasing aims to reduce the accumulation of coherent errors by using different physical implementations of the same circuit and using classical compute to combine the results and extract the clearest possible signal from a noisy source [1]. \n", + "\n", + "IonQ's debiasing method uses different implementations of a circuit through various qubit permutations and/or gate decompositions. The implementations can be chosen to reduce the effects of certain types of noise. Aggregating the results from all implementations reduces the effect of systematic errors and can improve the accuracy of your results. \n", + "\n", + "To use debiasing, a minimum of 2500 shots is required. In the Braket SDK, you can enable debiasing with a single line of code." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AwsQuantumTask('id/taskArn':'arn:aws:braket:us-east-1::quantum-task/522e8472-78ff-4997-850e-5d9d9a8f5474')\n" + ] + } + ], + "source": [ + "from braket.error_mitigation import Debias\n", + "\n", + "task_em = device.run(circ, shots=2500, device_parameters={\"errorMitigation\": Debias()})\n", + "print(task_em)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results from debiasing are returned like normal measurement probabilities. Any expecation value or result type will be computed from these probabilities. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "result = task_em.result()\n", + "debias_probs = result.measurement_probabilities" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Sharpening\n", + "\n", + "For quantum algorithms where the expected output distribution consists of few high-probability bitstrings, we can use IonQ’s sharpening strategy to post-process the results of a debiased run. Sharpening is a non-linear aggregation strategy that compares the results of each variant and discards inconsistent shots, favoring the most likely measurement outcome across variants. \n", + "This is in contrast the the default aggregation for debiasing, which averages all the measurements together. Since sharpening is a post-processing technique, it can be applied at no additional cost to a debiased run. It’s important to keep in mind that because there is a minimum probability threshold for a shot to be considered consistent, sharpening can distort the correct probability distribution if applied to a non-sparse output distribution.\n", + "\n", + "The sharpened probabilities are available in the task result via a single line of code:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "sharp_probs = result.additional_metadata.ionqMetadata.sharpenedProbabilities" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sharpening your results will return a renormalized probability distribution rather than the full distribution of measurements counts, and is available at no additional cost when you run with the Debias() strategy. Note that expectation values will be computed using the debiased probabilities, **not** the sharpened probabilities. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compare results from error mitigation" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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    " + ], + "text/plain": [ + " debias off debias on debias on, sharpened\n", + "10111 0.0040 0.0028 NaN\n", + "00101 0.0046 0.0076 NaN\n", + "01011 0.0074 0.0112 NaN\n", + "10001 0.0084 0.0068 NaN\n", + "01000 0.0102 0.0088 NaN\n", + "11011 0.0110 0.0120 NaN\n", + "01101 0.0128 0.0108 NaN\n", + "00001 0.0150 0.0088 NaN\n", + "11001 0.0300 0.0316 NaN\n", + "01001 0.8792 0.8852 1.0" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "debias_off = pd.DataFrame.from_dict(probs, orient=\"index\").rename(columns={0: \"debias off\"})\n", + "debias_on = pd.DataFrame.from_dict(debias_probs, orient=\"index\").rename(columns={0: \"debias on\"})\n", + "sharpen_on = pd.DataFrame.from_dict(sharp_probs, orient=\"index\").rename(\n", + " columns={0: \"debias on, sharpened\"}\n", + ")\n", + "df = debias_off.join(debias_on).join(sharpen_on)\n", + "df2 = df.sort_values(by=\"debias off\").tail(10)\n", + "df2" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df2.plot.bar(logy=False, ylabel=\"Probability\", xlabel=\"Bitstring\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 150.6 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(\n", + " \"Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\"\n", + ")\n", + "print(\n", + " f\"Estimated cost to run this example: {cost_tracker.qpu_tasks_cost() + cost_tracker.simulator_tasks_cost():.3f} USD\"\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References \n", + "\n", + "[1] “Enhancing quantum computer performance via symmetrization”, https://arxiv.org/abs/2301.07233" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "tket", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.5" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/0_TO_ORGANIZE/Getting_Devices_and_Checking_Device_Properties.ipynb b/0_TO_ORGANIZE/Getting_Devices_and_Checking_Device_Properties.ipynb new file mode 100644 index 000000000..0b656eb8e --- /dev/null +++ b/0_TO_ORGANIZE/Getting_Devices_and_Checking_Device_Properties.ipynb @@ -0,0 +1,1993 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Getting Devices and Checking Device Properties\n", + "\n", + "This tutorial demonstrates how to use the `get_devices()` method to search and instantiate devices available on Amazon Braket. It also shows how to obtain access to properties for simulator and QPU devices." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "import json\n", + "from braket.aws import AwsDevice\n", + "from braket.devices import LocalSimulator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using get_devices\n", + "You can get a device, including the on-demand simulators and the QPUs, by calling the `get_devices()` method. Search for devices with one or more of the following filtering criteria:\n", + "* device arn \n", + "* name \n", + "* type \n", + "* status \n", + "* provider_name. \n", + "\n", + "The following cells give examples for each of the cases." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Getting the device by type" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': SV1, 'arn': arn:aws:braket:::device/quantum-simulator/amazon/sv1),\n Device('name': TN1, 'arn': arn:aws:braket:::device/quantum-simulator/amazon/tn1),\n Device('name': dm1, 'arn': arn:aws:braket:::device/quantum-simulator/amazon/dm1)]" + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# to get the on-demand simulators\n", + "AwsDevice.get_devices(types=['SIMULATOR'])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': Aspen-10, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-10),\n Device('name': Aspen-11, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-11),\n Device('name': Aspen-8, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-8),\n Device('name': Aspen-9, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-9),\n Device('name': Aspen-M-1, 'arn': arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-1),\n Device('name': IonQ Device, 'arn': arn:aws:braket:us-east-1::device/qpu/ionq/Harmony)]" + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# to get the list of QPUs\n", + "AwsDevice.get_devices(types=['QPU'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Getting the device by ARN\n", + "For every type of device available in Amazon Braket, you can find the associated ARN in the Amazon Braket [Developer Guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html). You also can view the device ARN on the `Devices` section in the Amazon Braket console." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': IonQ Device, 'arn': arn:aws:braket:us-east-1::device/qpu/ionq/Harmony)]" + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# for example, the following ARN refers to the IonQ device.\n", + "AwsDevice.get_devices(arns=['arn:aws:braket:us-east-1::device/qpu/ionq/Harmony'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Getting the device by name" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': Aspen-M-3, 'arn': arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3)]" + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# for example, the following name refers to a Rigetti Aspen system.\n", + "AwsDevice.get_devices(names=['Aspen-M-3'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Getting the device by status" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': Aspen-11, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-11),\n Device('name': Aspen-8, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-8),\n Device('name': Aspen-M-3, 'arn': arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3),\n Device('name': IonQ Device, 'arn': arn:aws:braket:us-east-1::device/qpu/ionq/Harmony),\n Device('name': SV1, 'arn': arn:aws:braket:::device/quantum-simulator/amazon/sv1),\n Device('name': dm1, 'arn': arn:aws:braket:::device/quantum-simulator/amazon/dm1)]" + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# retrieve all devices that are currently online\n", + "AwsDevice.get_devices(statuses=['ONLINE'])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': Aspen-M-1, 'arn': arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-1)]" + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# retrieve all devices that are currently offline\n", + "AwsDevice.get_devices(statuses=['OFFLINE'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Getting the device by provider_name" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': IonQ Device, 'arn': arn:aws:braket:us-east-1::device/qpu/ionq/Harmony)]" + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# for example, the following ARN retrieves the IonQ device.\n", + "AwsDevice.get_devices(provider_names=['IonQ'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Retrieve devices in order" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': SV1, 'arn': arn:aws:braket:::device/quantum-simulator/amazon/sv1),\n Device('name': dm1, 'arn': arn:aws:braket:::device/quantum-simulator/amazon/dm1),\n Device('name': IonQ Device, 'arn': arn:aws:braket:us-east-1::device/qpu/ionq/Harmony),\n Device('name': Aspen-10, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-10),\n Device('name': Aspen-8, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-8),\n Device('name': Aspen-9, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-9),\n Device('name': Aspen-M-1, 'arn': arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-1),\n Device('name': Aspen-11, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-11)]" + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# retrieve the list of devices, ordered by provider name\n", + "AwsDevice.get_devices(order_by='provider_name')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Getting the device with multiple criteria" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": "[Device('name': Aspen-11, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-11),\n Device('name': Aspen-8, 'arn': arn:aws:braket:::device/qpu/rigetti/Aspen-8),\n Device('name': Aspen-M-1, 'arn': arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-1),\n Device('name': IonQ Device, 'arn': arn:aws:braket:us-east-1::device/qpu/ionq/Harmony)]" + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# multiple criteria can be applied\n", + "AwsDevice.get_devices(types=['QPU'],statuses=['ONLINE'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Getting a device directly\n", + "You can specify a device directly, with the device ARN." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# specify a device directly by device ARN\n", + "# Rigetti\n", + "device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "# IonQ\n", + "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")\n", + "# the on-demand simulator SV1\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n", + "# the on-demand simulator TN1\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/tn1\")\n", + "# the local simulator\n", + "device = LocalSimulator()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Properties of devices\n", + "\n", + "You can check properties of a device with the `device.properties` call. The following examples show some useful properties of each device." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The supported operations of SV1 are ['ccnot', 'cnot', 'cphaseshift', 'cphaseshift00', 'cphaseshift01', 'cphaseshift10', 'cswap', 'cy', 'cz', 'h', 'i', 'iswap', 'pswap', 'phaseshift', 'rx', 'ry', 'rz', 's', 'si', 'swap', 't', 'ti', 'unitary', 'v', 'vi', 'x', 'xx', 'xy', 'y', 'yy', 'z', 'zz']\n", + "\n", + "The supported result types are [ResultType(name='Sample', observables=['x', 'y', 'z', 'h', 'i', 'hermitian'], minShots=1, maxShots=100000), ResultType(name='Expectation', observables=['x', 'y', 'z', 'h', 'i', 'hermitian'], minShots=0, maxShots=100000), ResultType(name='Variance', observables=['x', 'y', 'z', 'h', 'i', 'hermitian'], minShots=0, maxShots=100000), ResultType(name='Probability', observables=None, minShots=1, maxShots=100000), ResultType(name='Amplitude', observables=None, minShots=0, maxShots=0)]\n", + "\n", + "The maximum number of qubits supported by this device is 34\n", + "The shots range of this device is (0, 100000)\n", + "The price of running tasks on this device: price=0.075 unit='minute'\n" + ] + } + ], + "source": [ + "# the on-demand simulator SV1\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n", + "\n", + "support_gates = device.properties.action['braket.ir.jaqcd.program'].supportedOperations\n", + "support_result_types = device.properties.action['braket.ir.jaqcd.program'].supportedResultTypes\n", + "qubit_count = device.properties.paradigm.qubitCount\n", + "shots_range = device.properties.service.shotsRange\n", + "device_cost = device.properties.service.deviceCost\n", + "\n", + "print(f'The supported operations of {device.name} are {support_gates}\\n')\n", + "print(f'The supported result types are {support_result_types}\\n')\n", + "print('The maximum number of qubits supported by this device is', qubit_count)\n", + "print('The shots range of this device is', shots_range)\n", + "print('The price of running tasks on this device:', device_cost)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the IonQ and Rigetti devices, you can get information about the properties shown previously. You also can get information about the availability windows and the device calibration data." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The availability windows for Aspen-M-3:\n", + "[DeviceExecutionWindow(executionDay=, windowStartHour=datetime.time(15, 0), windowEndHour=datetime.time(20, 0))]\n", + "\n", + "The connectivity graph of the qubits for this device:\n", + " fullyConnected=False connectivityGraph={'0': ['1', '7'], '1': ['0', '16', '2'], '10': ['11', '113', '17'], '100': ['101', '107'], '101': ['100', '102', '116'], '102': ['101', '103', '115'], '103': ['102', '104'], '104': ['103', '105', '7'], '105': ['104', '106'], '106': ['105', '107'], '107': ['100', '106'], '11': ['10', '12', '26'], '110': ['111', '117'], '111': ['110', '112', '126'], '112': ['111', '113'], '113': ['10', '112', '114'], '114': ['113', '115', '17'], '115': ['102', '114', '116'], '116': ['101', '115', '117'], '117': ['110', '116'], '12': ['11', '13', '25'], '120': ['121', '127'], '121': ['120', '122', '136'], '122': ['121', '123', '135'], '123': ['122', '124', '20'], '124': ['123', '125', '27'], '125': ['124', '126'], '126': ['111', '125', '127'], '127': ['120', '126'], '13': ['12', '14'], '130': ['131', '137'], '131': ['130', '132', '146'], '132': ['131', '133', '145'], '133': ['132', '134', '30'], '134': ['133', '135', '37'], '135': ['122', '134', '136'], '136': ['121', '135', '137'], '137': ['130', '136'], '14': ['13', '15'], '140': ['141', '147'], '141': ['140', '142'], '142': ['141', '143'], '143': ['142', '144', '40'], '144': ['143', '145', '47'], '145': ['132', '144', '146'], '146': ['131', '145', '147'], '147': ['140', '146'], '15': ['14', '16', '2'], '16': ['1', '15', '17'], '17': ['10', '16', '114'], '2': ['1', '15', '3'], '20': ['123', '21', '27'], '21': ['20', '22', '36'], '22': ['21', '23', '35'], '23': ['22', '24'], '24': ['23', '25'], '25': ['12', '24', '26'], '26': ['11', '25', '27'], '27': ['20', '26', '124'], '3': ['2', '4'], '30': ['133', '31', '37'], '31': ['30', '32', '46'], '32': ['31', '33', '45'], '33': ['32', '34'], '34': ['33', '35'], '35': ['22', '34', '36'], '36': ['21', '35', '37'], '37': ['30', '36', '134'], '4': ['3', '5'], '40': ['143', '41', '47'], '41': ['40', '42'], '42': ['41', '43'], '43': ['42', '44'], '44': ['43', '45'], '45': ['32', '44', '46'], '46': ['31', '45', '47'], '47': ['40', '46', '144'], '5': ['4', '6'], '6': ['5', '7'], '7': ['0', '6', '104']}\n", + "\n", + "Calibration data:\n", + " {\n", + " \"1Q\": {\n", + " \"0\": {\n", + " \"T1\": 8.777348365240911e-06,\n", + " \"T2\": 1.4387746662680443e-05,\n", + " \"f1QRB\": 0.998504263416883,\n", + " \"f1QRB_std_err\": 0.000200939668822899,\n", + " \"f1Q_simultaneous_RB\": 0.9303976571661898,\n", + " \"f1Q_simultaneous_RB_std_err\": 0.01832843535640074,\n", + " \"fActiveReset\": 0.983,\n", + " \"fRO\": 0.7455\n", + " },\n", + " \"1\": {\n", + " \"T1\": 5.6366506444582853e-05,\n", + " \"T2\": 2.6242615804514876e-06,\n", + " \"f1QRB\": 0.998504263416883,\n", + " \"f1QRB_std_err\": 0.000200939668822899,\n", + " \"f1Q_simultaneous_RB\": 0.9460049849871673,\n", + " \"f1Q_simultaneous_RB_std_err\": 0.015573861338627268,\n", + " \"fActiveReset\": 0.985,\n", + " \"fRO\": 0.8540000000000001\n", + " },\n", + " \"10\": {\n", + " \"T1\": 2.4649825183020724e-05,\n", + " \"T2\": 2.112458278475246e-05,\n", + " \"f1QRB\": 0.998567587494012,\n", + " \"f1QRB_std_err\": 0.000207675573751291,\n", + " \"f1Q_simultaneous_RB\": 0.9979683963345315,\n", + " \"f1Q_simultaneous_RB_std_err\": 0.00020991123805034803,\n", + " \"fActiveReset\": 0.9995,\n", + " \"fRO\": 0.97\n", + " },\n", + " \"100\": {\n", + " \"T1\": 1.4605161566150215e-05,\n", + " \"T2\": 8.902523025740775e-06,\n", + " \"f1QRB\": 0.997775892122462,\n", + " \"f1QRB_std_err\": 0.000374351563384802,\n", + " \"f1Q_simultaneous_RB\": 0.9961567026311122,\n", + " \"f1Q_simultaneous_RB_std_err\": 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0.012153685231816464,\n", + " \"fXY\": 0.928899043563923,\n", + " \"fXY_std_err\": 0.013782460855314657\n", + " },\n", + " \"144-145\": {\n", + " \"fCPHASE\": 0.9395760087297282,\n", + " \"fCPHASE_std_err\": 0.009408591391284958,\n", + " \"fCZ\": 0.8797440089127171,\n", + " \"fCZ_std_err\": 0.009596281960738503,\n", + " \"fXY\": 0.8929118950612976,\n", + " \"fXY_std_err\": 0.006623673522961696\n", + " },\n", + " \"145-146\": {\n", + " \"fCPHASE\": 0.9248967242677248,\n", + " \"fCPHASE_std_err\": 0.012372216008812402,\n", + " \"fCZ\": 0.9250826853297689,\n", + " \"fCZ_std_err\": 0.01184069809947199,\n", + " \"fXY\": 0.8247601945398406,\n", + " \"fXY_std_err\": 0.00957548802252057\n", + " },\n", + " \"146-147\": {\n", + " \"fCPHASE\": 0.8274787219159552,\n", + " \"fCPHASE_std_err\": 0.012916145303183676,\n", + " \"fCZ\": 0.8069355268652384,\n", + " \"fCZ_std_err\": 0.011974372157029201,\n", + " \"fXY\": 0.8526092049762855,\n", + " \"fXY_std_err\": 0.006987348271687152\n", + " },\n", + " 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" \"fCPHASE\": 0.8779216546510856,\n", + " \"fCPHASE_std_err\": 0.008984824164987791,\n", + " \"fCZ\": 0.9480866054086365,\n", + " \"fCZ_std_err\": 0.010319346614322746,\n", + " \"fXY\": 0.9795288135184532,\n", + " \"fXY_std_err\": 0.003958747950871068\n", + " },\n", + " \"20-123\": {\n", + " \"fCPHASE\": 0.8431036186470358,\n", + " \"fCPHASE_std_err\": 0.006169724764577705,\n", + " \"fCZ\": 0.8933816092239404,\n", + " \"fCZ_std_err\": 0.0046623328964517175,\n", + " \"fXY\": 0.8252419892398489,\n", + " \"fXY_std_err\": 0.009394429704878264\n", + " },\n", + " \"20-21\": {\n", + " \"fCPHASE\": 0.7899019718604859,\n", + " \"fCPHASE_std_err\": 0.009411264368555643,\n", + " \"fCZ\": 0.8703538536793619,\n", + " \"fCZ_std_err\": 0.007022811723452874,\n", + " \"fXY\": 0.8158581549695172,\n", + " \"fXY_std_err\": 0.006946473176179534\n", + " },\n", + " \"20-27\": {\n", + " \"fCPHASE\": 0.8763753230954336,\n", + " \"fCPHASE_std_err\": 0.00625207371316308,\n", + " \"fCZ\": 0.799166480232074,\n", 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0.006241995575404114\n", + " },\n", + " \"22-35\": {\n", + " \"fCPHASE\": 0.9080011737139104,\n", + " \"fCPHASE_std_err\": 0.004355936765447585,\n", + " \"fCZ\": 0.9112749783878215,\n", + " \"fCZ_std_err\": 0.006986762028397102,\n", + " \"fXY\": 0.9806907358502073,\n", + " \"fXY_std_err\": 0.004704057188026671\n", + " },\n", + " \"23-24\": {\n", + " \"fCPHASE\": 0.9569750181774397,\n", + " \"fCPHASE_std_err\": 0.007574992417364864,\n", + " \"fCZ\": 0.9681453299247146,\n", + " \"fCZ_std_err\": 0.00508749895754165,\n", + " \"fXY\": 0.8416917105635126,\n", + " \"fXY_std_err\": 0.006732002502778592\n", + " },\n", + " \"24-25\": {\n", + " \"fCPHASE\": 0.8658350938592758,\n", + " \"fCPHASE_std_err\": 0.021909272442443176,\n", + " \"fCZ\": 0.984128639829115,\n", + " \"fCZ_std_err\": 0.0026998808555934325,\n", + " \"fXY\": 0.9827905160840157,\n", + " \"fXY_std_err\": 0.0034710695867806503\n", + " },\n", + " \"25-26\": {\n", + " \"fCPHASE\": 0.8374713018133112,\n", + " \"fCPHASE_std_err\": 0.010468040876200317,\n", + " \"fCZ\": 0.8018425294114914,\n", + " \"fCZ_std_err\": 0.014235856445919192,\n", + " \"fXY\": 0.9052719848120904,\n", + " \"fXY_std_err\": 0.005569411999606964\n", + " },\n", + " \"26-27\": {\n", + " \"fCPHASE\": 0.9484835812485717,\n", + " \"fCPHASE_std_err\": 0.007829961706098426,\n", + " \"fCZ\": 0.9012630325528697,\n", + " \"fCZ_std_err\": 0.004691716240046407,\n", + " \"fXY\": 0.953585694103604,\n", + " \"fXY_std_err\": 0.010932206430380766\n", + " },\n", + " \"27-124\": {\n", + " \"fCPHASE\": 0.8638133235975534,\n", + " \"fCPHASE_std_err\": 0.021794684669212708,\n", + " \"fCZ\": 0.8787593624565879,\n", + " \"fCZ_std_err\": 0.023267015943500925,\n", + " \"fXY\": 0.8732572235376224,\n", + " \"fXY_std_err\": 0.04702368958531526\n", + " },\n", + " \"3-4\": {\n", + " \"fCPHASE\": 0.8236032034332953,\n", + " \"fCPHASE_std_err\": 0.009637889740194503,\n", + " \"fCZ\": 0.9631654556896767,\n", + " \"fCZ_std_err\": 0.006883806965521097,\n", + " \"fXY\": 0.8160515267766147,\n", + " \"fXY_std_err\": 0.012395715402937168\n", + " },\n", + " \"30-133\": {\n", + " \"fCPHASE\": 0.850145462488844,\n", + " \"fCPHASE_std_err\": 0.01168941595728125,\n", + " \"fCZ\": 0.835269201359459,\n", + " \"fCZ_std_err\": 0.011802776547716056,\n", + " \"fXY\": 0.8451511697574544,\n", + " \"fXY_std_err\": 0.007428569073776654\n", + " },\n", + " \"30-31\": {\n", + " \"fCPHASE\": 0.7959482238289587,\n", + " \"fCPHASE_std_err\": 0.009599101830901808,\n", + " \"fCZ\": 0.8347314059950581,\n", + " \"fCZ_std_err\": 0.007943197234786764,\n", + " \"fXY\": 0.8741391749172258,\n", + " \"fXY_std_err\": 0.005827549306131333\n", + " },\n", + " \"30-37\": {\n", + " \"fCPHASE\": 0.8145099941776652,\n", + " \"fCPHASE_std_err\": 0.009368198118349361,\n", + " \"fCZ\": 0.8635580585784683,\n", + " \"fCZ_std_err\": 0.00810366449996026,\n", + " \"fXY\": 0.90240849694021,\n", + " \"fXY_std_err\": 0.005049518848030976\n", + " },\n", + " \"31-32\": {\n", + " \"fCPHASE\": 0.8122877362351132,\n", + " \"fCPHASE_std_err\": 0.012044800753909436,\n", + " \"fCZ\": 0.8399060477451475,\n", + " \"fCZ_std_err\": 0.014714830688181652,\n", + " \"fXY\": 0.8302699874100965,\n", + " \"fXY_std_err\": 0.013009830172898642\n", + " },\n", + " \"31-46\": {\n", + " \"fCPHASE\": 0.9639175020002607,\n", + " \"fCPHASE_std_err\": 0.00556452031578792,\n", + " \"fCZ\": 0.9899490016021413,\n", + " \"fCZ_std_err\": 0.002117361396498773,\n", + " \"fXY\": 0.9893403896755063,\n", + " \"fXY_std_err\": 0.0022178340508080896\n", + " },\n", + " \"32-33\": {\n", + " \"fCPHASE\": 0.8902505914708183,\n", + " \"fCPHASE_std_err\": 0.006294531513856973,\n", + " \"fCZ\": 0.9358403617020014,\n", + " \"fCZ_std_err\": 0.009388054807090016,\n", + " \"fXY\": 0.9546362970029817,\n", + " \"fXY_std_err\": 0.007553442226022641\n", + " },\n", + " \"32-45\": {\n", + " \"fCPHASE\": 0.872231361471259,\n", + " \"fCPHASE_std_err\": 0.01121985823707833,\n", + " \"fCZ\": 0.9738444794692535,\n", + " \"fCZ_std_err\": 0.0043942654522665485\n", + " },\n", + " \"33-34\": {\n", + " \"fCPHASE\": 0.7958929831240406,\n", + " \"fCPHASE_std_err\": 0.015425462116718731,\n", + " \"fCZ\": 0.8651742677416149,\n", + " \"fCZ_std_err\": 0.007592588486357907,\n", + " \"fXY\": 0.8835390987642395,\n", + " \"fXY_std_err\": 0.0043867947035354325\n", + " },\n", + " \"34-35\": {\n", + " \"fCPHASE\": 0.859602533039039,\n", + " \"fCPHASE_std_err\": 0.009138076035450015,\n", + " \"fCZ\": 0.9715705945287438,\n", + " \"fCZ_std_err\": 0.006301031003720571\n", + " },\n", + " \"35-36\": {\n", + " \"fXY\": 0.9774969885122631,\n", + " \"fXY_std_err\": 0.0033829465454611072\n", + " },\n", + " \"36-37\": {\n", + " \"fCPHASE\": 0.9092561183890484,\n", + " \"fCPHASE_std_err\": 0.0058376807088631735,\n", + " \"fCZ\": 0.9784518885903303,\n", + " \"fCZ_std_err\": 0.003029130589787604,\n", + " \"fXY\": 0.9875603191593725,\n", + " \"fXY_std_err\": 0.002358423302265576\n", + " },\n", + " \"37-134\": {\n", + " \"fCPHASE\": 0.9146399454060954,\n", + " \"fCPHASE_std_err\": 0.004337076992693843,\n", + " \"fCZ\": 0.934092256502296,\n", + " \"fCZ_std_err\": 0.008770591000249005,\n", + " \"fXY\": 0.8682740375243889,\n", + " \"fXY_std_err\": 0.006471746052616916\n", + " },\n", + " \"4-5\": {\n", + " \"fCPHASE\": 0.8552743505131355,\n", + " \"fCPHASE_std_err\": 0.007608179558157967,\n", + " \"fCZ\": 0.9706519855005057,\n", + " \"fCZ_std_err\": 0.005554291023953174,\n", + " \"fXY\": 0.8624177383174734,\n", + " \"fXY_std_err\": 0.006925013192967286\n", + " },\n", + " \"40-143\": {\n", + " \"fCPHASE\": 0.7600839684763812,\n", + " \"fCPHASE_std_err\": 0.01455730512726115,\n", + " \"fCZ\": 0.8104453814594197,\n", + " \"fCZ_std_err\": 0.00992447081179879,\n", + " \"fXY\": 0.905776157678926,\n", + " \"fXY_std_err\": 0.005978628164178389\n", + " },\n", + " \"40-41\": {\n", + " \"fCPHASE\": 0.7616214479970531,\n", + " \"fCPHASE_std_err\": 0.0153397409764428,\n", + " \"fCZ\": 0.7990943294436262,\n", + " \"fCZ_std_err\": 0.010747152786691874,\n", + " \"fXY\": 0.8988201697808387,\n", + " \"fXY_std_err\": 0.0052605650112824524\n", + " },\n", + " \"40-47\": {\n", + " \"fCPHASE\": 0.7168934897637623,\n", + " \"fCPHASE_std_err\": 0.02194610037601451,\n", + " \"fCZ\": 0.9032407469051222,\n", + " \"fCZ_std_err\": 0.02019307343891585,\n", + " \"fXY\": 0.9786320871734574,\n", + " \"fXY_std_err\": 0.005267238871515598\n", + " },\n", + " \"41-42\": {\n", + " \"fCPHASE\": 0.8604180987325472,\n", + " \"fCPHASE_std_err\": 0.00925843597058478,\n", + " \"fCZ\": 0.9533150920640057,\n", + " \"fCZ_std_err\": 0.01097766567033766,\n", + " \"fXY\": 0.9586422965574871,\n", + " \"fXY_std_err\": 0.007132225169109244\n", + " },\n", + " \"42-43\": {\n", + " \"fCPHASE\": 0.8423849056255256,\n", + " \"fCPHASE_std_err\": 0.010008919179737015,\n", + " \"fCZ\": 0.917858001758817,\n", + " \"fCZ_std_err\": 0.012413160703071257,\n", + " \"fXY\": 0.8141502882786736,\n", + " \"fXY_std_err\": 0.01184872526534798\n", + " },\n", + " \"43-44\": {\n", + " \"fCPHASE\": 0.7537923626609487,\n", + " \"fCPHASE_std_err\": 0.015080828085127,\n", + " \"fCZ\": 0.8611710085628796,\n", + " \"fCZ_std_err\": 0.008865627688122714,\n", + " \"fXY\": 0.942283542329304,\n", + " \"fXY_std_err\": 0.009503765439193682\n", + " },\n", + " \"44-45\": {\n", + " \"fCPHASE\": 0.8299030141719563,\n", + " \"fCPHASE_std_err\": 0.009857478899323988,\n", + " \"fCZ\": 0.9557288578270758,\n", + " \"fCZ_std_err\": 0.006702511019316729,\n", + " \"fXY\": 0.8996048966729704,\n", + " \"fXY_std_err\": 0.004152212435951456\n", + " },\n", + " \"45-46\": {\n", + " \"fCPHASE\": 0.9675162959658308,\n", + " \"fCPHASE_std_err\": 0.008914968542324951,\n", + " \"fCZ\": 0.965380988480898,\n", + " \"fCZ_std_err\": 0.00600956773698424,\n", + " \"fXY\": 0.9811754888501525,\n", + " \"fXY_std_err\": 0.002809467046863083\n", + " },\n", + " \"46-47\": {\n", + " \"fCPHASE\": 0.9550132096198518,\n", + " \"fCPHASE_std_err\": 0.011101139047072738,\n", + " \"fCZ\": 0.9334902005702788,\n", + " \"fCZ_std_err\": 0.013121527876568584,\n", + " \"fXY\": 0.9598039171384231,\n", + " \"fXY_std_err\": 0.008923248606730105\n", + " },\n", + " \"47-144\": {\n", + " \"fCPHASE\": 0.8982407044055271,\n", + " \"fCPHASE_std_err\": 0.00621785488733503,\n", + " \"fCZ\": 0.9394007045007381,\n", + " \"fCZ_std_err\": 0.010877234167113965,\n", + " \"fXY\": 0.7767641365585107,\n", + " \"fXY_std_err\": 0.0173400113341025\n", + " },\n", + " \"5-6\": {\n", + " \"fCPHASE\": 0.8856589225078974,\n", + " \"fCPHASE_std_err\": 0.007252911389298091,\n", + " \"fCZ\": 0.9548890325016192,\n", + " \"fCZ_std_err\": 0.0053040819246874624,\n", + " \"fXY\": 0.9708587201438419,\n", + " \"fXY_std_err\": 0.004633224705448535\n", + " },\n", + " \"6-7\": {\n", + " \"fCPHASE\": 0.8390933924372902,\n", + " \"fCPHASE_std_err\": 0.009445019626481147,\n", + " \"fCZ\": 0.9418483009558972,\n", + " \"fCZ_std_err\": 0.01218466822075986,\n", + " \"fXY\": 0.9661361224326979,\n", + " \"fXY_std_err\": 0.009003517168496214\n", + " },\n", + " \"7-104\": {\n", + " \"fXY\": 0.6631486133799958,\n", + " \"fXY_std_err\": 0.010365519549584151\n", + " }\n", + " }\n", + "}\n" + ] + } + ], + "source": [ + "# the IonQ device\n", + "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")\n", + "\n", + "# the Rigetti device\n", + "device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "\n", + "execution_windows = device.properties.service.executionWindows\n", + "connectivity_graph = device.properties.paradigm.connectivity\n", + "calibration = device.properties.provider.specs\n", + "\n", + "print(f'The availability windows for {device.name}:\\n{execution_windows}\\n')\n", + "print(f'The connectivity graph of the qubits for this device:\\n {connectivity_graph}\\n')\n", + "print('Calibration data:\\n', json.dumps(calibration,sort_keys=True,indent=2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each device has more properties to explore. To learn more, view the [Amazon Braket schemas documentation](https://amazon-braket-schemas-python.readthedocs.io/en/latest/_apidoc/braket.device_schema.html)." + ] + } + ], + "metadata": { + "kernelspec": { + "name": "python3", + "language": "python", + "display_name": "Python 3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.7" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} \ No newline at end of file diff --git a/0_TO_ORGANIZE/Getting_notifications_when_a_task_completes/Getting_notifications_when_a_task_completes.ipynb b/0_TO_ORGANIZE/Getting_notifications_when_a_task_completes/Getting_notifications_when_a_task_completes.ipynb new file mode 100644 index 000000000..7ab69ee49 --- /dev/null +++ b/0_TO_ORGANIZE/Getting_notifications_when_a_task_completes/Getting_notifications_when_a_task_completes.ipynb @@ -0,0 +1,253 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Getting notifications when a task completes" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook walks you through how to set up notifications for completion of Amazon Braket tasks through the Amazon Simple Notification Service (SNS). Active notifications may be useful in situations where a large wait time is expected, such as when a submitted task is large and takes a while to complete, or when a task is submitted to a device outside of its availability window. In such a setting, a user may not want to wait for the task to complete, and would prefer to move forward and receive an alert once the task is complete.\n", + "\n", + "## The workflow\n", + "\n", + "Amazon Braket tasks leverage Amazon S3 as an intermediate storage device. This allows you to leverage the built-in event architecture of S3 to generate active push notifications. All you need to do is subscribe an SMS capable endpoint (for example, an email address or a cell phone number) to an SNS Topic, and tie that SNS Topic to the S3 bucket of interest.\n", + "\n", + "See the architecture diagram for a full picture of the sequence of events:\n", + "\n", + "
    \n", + "\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Instructions\n", + "\n", + "### Optional Step: Create a KMS customer master key (CMK)\n", + "\n", + "Security is a priority at AWS. Therefore, nearly all AWS Services integrate with AWS Key Management Service (KMS) to allow data to be encrypted in transmission and at rest. In particular, Amazon S3 and SNS are integrated with KMS. To leverage this capability, follow the quick summary provided here. First, create a custom key through the KMS console, by following these instructions:\n", + "\n", + "https://docs.aws.amazon.com/kms/latest/developerguide/create-keys.html#create-symmetric-cmk\n", + "\n", + "**NOTE: When creating the key, you don't need to explicitly allow any IAM users, roles, or services to have access to the key.**\n", + "\n", + "After the key is created, you must edit the default Key Policy to include S3 and SNS services as Principals that can encrypt and decrypt data. Add the following permission within the \"Statement\" list (remember to replace the <CMK ARN> into the ARN of the key)\n", + " \n", + "``` \n", + "{\n", + " \"Sid\": \"Allow access for S3 and SNS (as Service Principals)\",\n", + " \"Effect\": \"Allow\",\n", + " \"Principal\": {\n", + " \"Service\": [\n", + " \"s3.amazonaws.com\",\n", + " \"sns.amazonaws.com\"\n", + " ]\n", + " },\n", + " \"Action\": [\n", + " \"kms:GenerateDataKey*\",\n", + " \"kms:Decrypt\"\n", + " ],\n", + " \"Resource\": \"\"\n", + "}\n", + "```\n", + "\n", + "### Step 1: Create an Appropriate S3 Bucket\n", + "\n", + "You can create an S3 bucket to receive the Amazon Braket task results. To accommodate certain IAM permissions, Amazon Braket expects your bucket name to begin with \"amazon-braket-\" and generally follow this naming convention:\n", + "\n", + "`amazon-braket-`\n", + "\n", + "If you don't specify the S3 location, default S3 folder, where all inputs and outputs for your tasks are saved, follows the convention `amazon-braket--`. \n", + "\n", + "### Step 2: Create an SNS Topic\n", + "\n", + "Amazon Simple Notification Service (SNS) acts as the event broker that receives notifications from S3 (along a given Topic) and routes them out to any subscriber, for example, an email address. You must create that SNS Topic to serve as the central communications channel. See the following instructions:\n", + "\n", + "https://docs.aws.amazon.com/sns/latest/dg/sns-tutorial-create-topic.html#create-topic-aws-console\n", + "\n", + "**NOTE: If you created a CMK in the optional step, make sure you enable encryption on the SNS Topic, and select the CMK you created from the dropdown menu.**\n", + "\n", + "You should already have created an S3 bucket \"amazon-braket-<bucket name>\" for this workflow. Now you must add permissions to the SNS Topic so it can receive events from the bucket. To do so, edit the Topic's \"Access Policy\" to paste the following permission (under the \"Statement\" list). Replace the contents in <>. \n", + " \n", + "```\n", + "{\n", + " \"Sid\": \"allow-S3-access\",\n", + " \"Effect\": \"Allow\",\n", + " \"Principal\": {\n", + " \"AWS\": \"*\"\n", + " },\n", + " \"Action\": \"SNS:Publish\",\n", + " \"Resource\": \"arn:aws:sns:::\",\n", + " \"Condition\": {\n", + " \"StringEquals\": {\n", + " \"aws:SourceAccount\": \"\"\n", + " },\n", + " \"ArnLike\": {\n", + " \"aws:SourceArn\": \"arn:aws:s3:*:*:amazon-braket-\"\n", + " }\n", + " }\n", + "}\n", + "```\n", + "\n", + "### Step 3: Subscribe an endpoint to the SNS Topic\n", + "\n", + "Follow the instructions here to subscribe an endpoint to an SNS Topic:\n", + "\n", + "https://docs.aws.amazon.com/sns/latest/dg/sns-create-subscribe-endpoint-to-topic.html\n", + "\n", + "SNS > Subscriptions > Create subscription > choose the Topic ARN from the dropdown menu > choose the protocol from the dropdown menu (SMS for cell phone number and Email for email address) > fill in the details of the endpoint\n", + "\n", + "**NOTE: SNS is not a free service. Check the pricing [here](https://aws.amazon.com/sns/pricing/). Sending text messages to non-US cell phone numbers might be expensive. On the other hand, the default spending limit for SMS messages is 1.00 USD per month. You can [request](https://aws.amazon.com/premiumsupport/knowledge-center/sns-sms-spending-limit-increase/) a limit increase through the support center.**\n", + "\n", + "After this step is completed, you should see the endpoint listed under the SNS > Subscriptions tab in the console. To test functionality, go to the subscribed Topic and publish a test message by choosing \"Publish message\". If the endpoint is subscribed properly, you will receive a message immediately, containing the message title and text you provided. If you do not receive a text, double check the instructions in this step\n", + "\n", + "### Step 4: Create an S3 Event and tie it to the SNS Topic\n", + "\n", + "Follow the instructions provided here to create a new S3 Event:\n", + "\n", + "https://docs.aws.amazon.com/AmazonS3/latest/user-guide/enable-event-notifications.html#enable-event-notifications-how-to\n", + "\n", + "Open the Amazon S3 console > choose the bucket `amazon-braket-` > Properties > choose Create event notification under Event notifications > Enter event name, prefix, and suffix > choose event type > choose SNS topic as the destination > select the SNS topic created in Step 2 from the dropdown menu.\n", + "\n", + "**NOTE 1: AWS recommends that you filter the S3 events by prefix to prevent unnecessary notifications. For the purpose of this tutorial, you can add a prefix filter on `sns-testing/` , which is used as the destination in the following cell for Braket task outputs.**\n", + "\n", + "**NOTE 2: If the SNS Topic ARN does not appear in the dropdown menu, it is likely that the appropriate permissions were not added to the Topic Access Policy - review Step 2.**\n", + "\n", + "### Step 5: Test the setup with a Braket task\n", + "\n", + "Now the pipeline is configured and ready to test. To test it, run the following code to kick off an Amazon Braket task. After the task state registers as \"COMPLETED\", within a few seconds you should receive a message stating that a file has been added to the S3 bucket. Your task is done." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from braket.circuits import Circuit\n", + "from braket.aws import AwsDevice\n", + "\n", + "n_qubits = 10\n", + "n_shots = 100\n", + "\n", + "device = AwsDevice('arn:aws:braket:::device/quantum-simulator/amazon/sv1')\n", + "# ##\n", + "\n", + "def ghz_circuit(n_qubits: int) -> Circuit:\n", + " \"\"\"\n", + " Function to return simple GHZ circuit ansatz. Assumes all qubits in range(0, n_qubits-1)\n", + " are entangled.\n", + "\n", + " :param int n_qubits: number of qubits\n", + " :return: Constructed GHZ circuit\n", + " :rtype: Circuit\n", + " \"\"\"\n", + "\n", + " circuit = Circuit() # instantiate circuit object\n", + " circuit.h(0) # add Hadamard gate on first qubit\n", + "\n", + " for ii in range(0, n_qubits-1):\n", + " circuit.cnot(control=ii, target=ii+1) # apply series of CNOT gates\n", + " return circuit\n", + "\n", + "\n", + "# Define circuit\n", + "ghz = ghz_circuit(n_qubits)\n", + "\n", + "# Kick off single task execution\n", + "task = device.run(ghz, shots=n_shots)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'QUEUED'" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "task.state()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 100, 'tasks': {'COMPLETED': 1}, 'execution_duration': datetime.timedelta(microseconds=112000), 'billed_execution_duration': datetime.timedelta(seconds=3)}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.004 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.10 ('venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/0_TO_ORGANIZE/Getting_notifications_when_a_task_completes/sns_task_notification.png 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"74154c03-d48f-4f41-867b-5e30254ce31a", + "metadata": {}, + "source": [ + "# Noise models on Amazon Braket\n", + "\n", + "\n", + "This notebook introduces noise models on Amazon Braket. We show how to create noise models containing different types of noise and instructions for how to apply the noise to a circuit.\n", + "In the next notebooks, we will show how to construct a noise model from device calibration data for real quantum processing units (QPUs). \n", + "\n", + "**Before you begin**: We recommend being familiar with noise channels in Braket. For an introduction see [Simulating Noise On Amazon Braket](https://github.com/aws/amazon-braket-examples/blob/main/examples/braket_features/Simulating_Noise_On_Amazon_Braket.ipynb).\n", + "Additionally, users should be familiar with [Running quantum circuits on QPU devices](https://github.com/aws/amazon-braket-examples/blob/main/examples/getting_started/2_Running_quantum_circuits_on_QPU_devices/2_Running_quantum_circuits_on_QPU_devices.ipynb)\n", + "\n", + "### Table of Contents\n", + "- What is a noise model?\n", + "- Introduction to Noise Models\n", + " - Adding noise to a noise model\n", + " - Applying noise models to circuits\n", + " - Qubit noise\n", + " - Readout noise\n", + " - Filtering noise models\n", + " - Saving and loading noise models" + ] + }, + { + "cell_type": "markdown", + "id": "0c874b33-fa75-4d0f-80d4-46de40a14aa5", + "metadata": {}, + "source": [ + "## What is a noise model? \n", + "\n", + "Quantum devices and QPUs are subject noise on qubits and gate operations due to imperfect control.\n", + "The presence of noise deteriorates the quality of a quantum computation, especially when creating highly-entangled states. \n", + "Understanding the source and magnitude of this noise is essential to debugging and improving quantum computers. \n", + "\n", + "\n", + "The general noise on a quantum device is modelled as a noise channel (see [Simulating Noise On Amazon Braket](https://github.com/aws/amazon-braket-examples/blob/main/examples/braket_features/Simulating_Noise_On_Amazon_Braket.ipynb)). The size of the full noise channel for a QPU scales exponentially with the number of qubits. Accordingly, it is essential to place assumptions on the noise channel to make it practical to simulate and debug circuits of interest.\n", + "\n", + "\n", + "A noise model encapsulates the assumptions on quantum noise channels and how they act on a given circuit. \n", + "Simulating this noisy circuit gives information about much the noise impacts the results of the quantum computation. \n", + "By incrementally adjusting the noise model, the impact of noise can be understood on a variety of quantum algorithms. \n", + "\n", + "Finding realistic and accurate noise models for quantum devices is a active field of research. \n", + "While simple models that treat each qubit or gate independently are useful, the effects of non-local crosstalk are often the most important when using multi-qubit devices. " + ] + }, + { + "cell_type": "markdown", + "id": "4d832c58-4505-4dc4-9ebc-239dd3c203da", + "metadata": {}, + "source": [ + "## Introduction to noise models\n", + "\n", + "Noise models are contained in the Amazon Braket SDK, within the circuits module. The following lines of code import the required features:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e5e15fcd-55a2-4168-acc6-a38100f94511", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "from braket.aws import AwsDevice\n", + "from braket.circuits import Circuit, Gate, Noise, Observable\n", + "from braket.circuits.noise_model import (GateCriteria, NoiseModel,\n", + " ObservableCriteria)\n", + "from braket.circuits.noises import (AmplitudeDamping, BitFlip, Depolarizing,\n", + " PauliChannel, PhaseDamping, PhaseFlip,\n", + " TwoQubitDepolarizing)\n", + "from braket.devices import LocalSimulator" + ] + }, + { + "cell_type": "markdown", + "id": "f3489d3f-672a-42a2-a852-1a2f7a2631d2", + "metadata": {}, + "source": [ + "### Adding noise to a noise model\n", + "\n", + "A noise model consists of a list of noise model instructions. Similar to circuits, we can add `NoiseModelInstructions` to model. First, we start we an empty noise model:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "901c7adc-8924-451d-8120-4ec7cb2c8ba8", + "metadata": {}, + "outputs": [], + "source": [ + "noise_model = NoiseModel()" + ] + }, + { + "cell_type": "markdown", + "id": "3b0a0113-c368-4073-9d5e-65280c5c2379", + "metadata": {}, + "source": [ + "A `NoiseModelInstruction` consists of two pieces of information: (1) what noise channel to apply, and (2) when to apply it. Common noise channels are available in the Braket noise module (see [**Simulating Noise On Amazon Braket**](https://github.com/aws/amazon-braket-examples/blob/main/examples/braket_features/Simulating_Noise_On_Amazon_Braket.ipynb)). The information about when to apply the noise is contained a `Criteria` object. Criteria can depend on qubits, gates, or measured observables.\n", + "\n", + "For example, consider applying depolarizing noise with probability $p=0.1$ noise after every Hadamard gate (`Gate.H`). \n", + "The depolarizing channel maps a state $\\rho$ to the maximal mixed state $I/d$ with probability $p$, i.e. $\\rho \\rightarrow (1-p)\\rho + \\frac{p}{3}\\left(X\\rho X + Y\\rho Y + Z\\rho Z\\right)$. In Braket, we denote this as `Depolarizing(0.1)`. \n", + "The condition to apply the noise only depends on the gate, so it is created with `GateCriteria(Gate.H)`.\n", + "The default behavior for gate criteria is to apply to all qubits, which is specified by setting `qubits=None`. \n", + "We can specify only a subset of qubits with `GateCriteria(gates=Gate.H, qubits=[0,1])` which will only apply noise to qubits 0 and 1. \n", + "Similarly, we can apply the same noise channel to a set of gates with `GateCriteria(gates=[Gate.H, Gate.S], qubits=[0])` which applies noise to both the Hadamard and phase gate on qubit 0. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "92a8f43c-94c9-4987-bef1-3f28d8c533c3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n" + ] + } + ], + "source": [ + "noise_model = NoiseModel()\n", + "noise_model.add_noise(Depolarizing(0.1), GateCriteria(Gate.H))\n", + "print(noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "4afee7ff-30fa-4101-870e-f4fac4beea1e", + "metadata": {}, + "source": [ + "Great! We added depolarizing noise on gate $H$ to the noise model.\n", + "\n", + "**Note**: Be careful adding noise to the model. If we repeat the `noise_model.add_noise()` twice with the same noise and criteria, we will get two entries in the noise model!\n", + "\n", + "Similar to a circuit with instructions, we can see the list of noise model instructions with:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d04178e2-5074-4519-be0e-21819517ef76", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[NoiseModelInstruction(noise=Depolarizing(0.1), criteria=GateCriteria({'H'}, None))]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "noise_model.instructions" + ] + }, + { + "cell_type": "markdown", + "id": "00d55a98-320c-4eab-9011-c4186c611596", + "metadata": {}, + "source": [ + "Here, we only have one instruction which applies depolarizing noise after every $H$ gate." + ] + }, + { + "cell_type": "markdown", + "id": "134c59eb-617f-4230-8a6d-c1f8e715d6bb", + "metadata": {}, + "source": [ + "### Applying noise models to circuits\n", + "\n", + "Noise models encapsulate all the information about the noise we wish to apply to circuits. \n", + "This lets us apply noise channels across different circuits with minimal repetition.\n", + "\n", + "For example, consider the circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "07513636-a747-4c67-935c-4640f38a7dc9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|\n", + " \n", + "q0 : -H-Y-\n", + " \n", + "q1 : -S-X-\n", + " \n", + "q2 : -H-Z-\n", + "\n", + "T : |0|1|\n" + ] + } + ], + "source": [ + "circ = Circuit().h(0).s(1).h(2).y(0).x(1).z(2)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "id": "46f9c503-a8f3-4daa-be2c-907900af61aa", + "metadata": {}, + "source": [ + "We can apply the noise model to the circuit with `noise_model.apply(circ)` to produce the noisy circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "d94f3908-6e96-4878-9566-6d04ba5feaab", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 |1|\n", + " \n", + "q0 : -H-DEPO(0.1)-Y-\n", + " \n", + "q1 : -S-----------X-\n", + " \n", + "q2 : -H-DEPO(0.1)-Z-\n", + "\n", + "T : | 0 |1|\n" + ] + } + ], + "source": [ + "noisy_circ = noise_model.apply(circ)\n", + "print(noisy_circ)" + ] + }, + { + "cell_type": "markdown", + "id": "85424a62-4ec0-420b-ac2a-ba5e3ccfd81d", + "metadata": {}, + "source": [ + "Notice how depolarizing noise is applied after every Hadamard gate, just like it was specified in the noise model.\n", + "\n", + "We can also apply multiple noise models to a circuit. For example," + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "9def4229", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 |1|\n", + " \n", + "q0 : -H-BF(0.2)---DEPO(0.1)-Y-\n", + " \n", + "q1 : -S---------------------X-\n", + " \n", + "q2 : -H-DEPO(0.1)-----------Z-\n", + "\n", + "T : | 0 |1|\n" + ] + } + ], + "source": [ + "noise_model_2 = NoiseModel().add_noise(BitFlip(0.2), criteria=GateCriteria(Gate.H, 0))\n", + "\n", + "noisy_circ_2 = noise_model_2.apply(noisy_circ)\n", + "\n", + "print(noisy_circ_2)" + ] + }, + { + "cell_type": "markdown", + "id": "beab4c73", + "metadata": {}, + "source": [ + "Notice that the most recently applied noise model inserts noise directly after the target gate(s)." + ] + }, + { + "cell_type": "markdown", + "id": "f1058f37-b3f5-48b6-b28f-fad69f1c988a", + "metadata": {}, + "source": [ + "### Modeling qubit decoherence by gate noise\n", + "\n", + "Let's add a few more types of noise to the model.\n", + "This time we will add amplitude dampening noise after every single-qubit gate, but only on qubit $0$.\n", + "This is intended to mimic the effect of the |1⟩ state decaying into the ground state |0⟩." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f2325d73-b9dc-4014-b34f-5886dae4968f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n", + " AmplitudeDamping(0.1), GateCriteria(None, {0})\n" + ] + } + ], + "source": [ + "noise_model.add_noise(AmplitudeDamping(0.1), GateCriteria(qubits=0))\n", + "print(noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "79acfb26-8e71-485b-8c9e-9ff2c1411696", + "metadata": {}, + "source": [ + "Let's also add a highly-specific type of noise.\n", + "Consider adding a Pauli channel noise after the `X` gate only on qubit `1`." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "65b88f6d-66e6-4000-8578-441fc213a70e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n", + " AmplitudeDamping(0.1), GateCriteria(None, {0})\n", + " PauliChannel(0.1, 0.2, 0.3), GateCriteria({'X'}, {1})\n" + ] + } + ], + "source": [ + "noise_model.add_noise(PauliChannel(0.1, 0.2, 0.3), GateCriteria(gates=Gate.X, qubits=1))\n", + "print(noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "7e220eca-f370-45b3-8cd1-6fa0aa2a32d8", + "metadata": {}, + "source": [ + "Now we have a noise model containing three terms.\n", + "\n", + "- depolarizing(0.1) after every Hadamard gate\n", + "- amplitude dampening(0.1) after every gate on qubit 0.\n", + "- Pauli channel(0.1, 0.2, 0.3) after an $X$-gate on qubit 1.\n", + "\n", + "Let' apply it to previous circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "40ff7893-f45d-45d7-a77e-c247c5932559", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |\n", + " \n", + "q0 : -H-DEPO(0.1)-AD(0.1)-Y-AD(0.1)---------\n", + " \n", + "q1 : -S-------------------X-PC(0.1,0.2,0.3)-\n", + " \n", + "q2 : -H-DEPO(0.1)---------Z-----------------\n", + "\n", + "T : | 0 | 1 |\n" + ] + } + ], + "source": [ + "print(noise_model.apply(circ))" + ] + }, + { + "cell_type": "markdown", + "id": "685f8ed8-fcac-4cc2-8e57-411dde73dbb9", + "metadata": {}, + "source": [ + "Take a minute to double check that this is correct.\n", + "\n", + "**Note**: If two or more criteria apply to the same gate and target qubits, then the order of the noise instructions in the noise model matters. In the above example, the Hadamard gate on qubit 0 has two types of noise applied after the gate. Since depolarizing noise appeared first in the noise model, it was applied first. The next criteria had amplitude dampening, so it was applied *after* the depolarizing noise. " + ] + }, + { + "cell_type": "markdown", + "id": "38445cb5-dec1-4980-a213-603697ae9bf3", + "metadata": {}, + "source": [ + "### Readout noise\n", + "\n", + "Similarly, we can also add readout noise to circuits. By default, circuits at the end of a Braket circuit are measured in the $Z$-basis.\n", + "\n", + "Let's add a bit flip readout noise with probability $0.01$ on qubits 0 and 1." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "aa01c6db-1fb3-4d4f-bae0-155a6b28e518", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Readout Noise:\n", + " BitFlip(0.01), ObservableCriteria(None, {1, 2})\n" + ] + } + ], + "source": [ + "noise_model = NoiseModel()\n", + "noise_model.add_noise(BitFlip(0.01), ObservableCriteria(qubits=[1, 2]))\n", + "print(noise_model)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "833d5002-88ac-476b-9a60-614ae26c07b7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|\n", + " \n", + "q0 : -H-Y-\n", + " \n", + "q1 : -S-X-\n", + " \n", + "q2 : -H-Z-\n", + "\n", + "T : |0|1|\n" + ] + } + ], + "source": [ + "print(noise_model.apply(circ))" + ] + }, + { + "cell_type": "markdown", + "id": "d2b98157-ad3a-4b34-9831-85abc09f19e7", + "metadata": {}, + "source": [ + "### Observable Criteria\n", + "\n", + "Readout noise can also depend on the measurement basis. For single-qubit measurements, those would be measuring the in $X$, $Y$, or $Z$ basis. In Braket, measurements in other basis are defined with observables at the end of a circuit (see [Braket result types](https://docs.aws.amazon.com/braket/latest/developerguide/braket-result-types.html)).\n", + "\n", + "For example, lets' measure $X$ on qubit 0, and $Z$ on qubit 1." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "a4fba08d-947c-4703-872c-f2600f0100af", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|Result Types|\n", + " \n", + "q0 : -H-Y-Sample(X)----\n", + " \n", + "q1 : -S-X-Sample(Z)----\n", + " \n", + "q2 : -H-Z--------------\n", + "\n", + "T : |0|1|Result Types|\n" + ] + } + ], + "source": [ + "circ.sample(Observable.X(), target=0)\n", + "circ.sample(Observable.Z(), target=1)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "id": "b3f66148-38db-4a65-9545-ba30e366c30b", + "metadata": {}, + "source": [ + "Noise models can also contain instructions based on which observable is present.\n", + "\n", + "For example, let's add a phase flip error on qubit 0 when we measure in the $X$-basis. Let's also add a bit flip channel when measuring in the $Z$-basis." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "d04ce147-f881-41f2-94b9-fa6ccfdfcdea", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Readout Noise:\n", + " PhaseFlip(0.02), ObservableCriteria({'X'}, {0})\n", + " BitFlip(0.01), ObservableCriteria({'Z'}, {1})\n" + ] + } + ], + "source": [ + "noise_model = NoiseModel()\n", + "noise_model.add_noise(PhaseFlip(0.02), ObservableCriteria(Observable.X, 0))\n", + "noise_model.add_noise(BitFlip(0.01), ObservableCriteria(Observable.Z, 1))\n", + "print(noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "82153657-56b2-4c24-bdb7-dd2dd79a6b61", + "metadata": {}, + "source": [ + "Let's apply this noise model to a circuit.\n", + "The circuit is the same as above, but this time we measure `Observable.X` on qubit 0." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "d0e9a783-558e-4e86-abe0-4dc095c4b25d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0| 1 |Result Types|\n", + " \n", + "q0 : -H-Y-PF(0.02)-Sample(X)----\n", + " \n", + "q1 : -S-X-BF(0.01)-Sample(Z)----\n", + " \n", + "q2 : -H-Z-----------------------\n", + "\n", + "T : |0| 1 |Result Types|\n" + ] + } + ], + "source": [ + "noisy_circ = noise_model.apply(circ)\n", + "print(noisy_circ)" + ] + }, + { + "cell_type": "markdown", + "id": "dd08b5d3-f87d-4155-9721-cc9145b05035", + "metadata": {}, + "source": [ + "Take a minute to double check that all the terms in the noise model are applied in the correct place in the circuit." + ] + }, + { + "cell_type": "markdown", + "id": "ce8555fe-f8f1-49e6-ac9d-5f9a8a7a410e", + "metadata": {}, + "source": [ + "### Filtering noise models\n", + "\n", + "We can reduce the size of the noise model by selecting only noise and criteria relevant to our interest.\n", + "For instance, we might only care about noise affecting qubit 0.\n", + "\n", + "Let's start with a large noise model:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "bf87cb71-0a83-46c0-9d7e-13402dff3cf0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n", + " Depolarizing(0.1), GateCriteria(None, None)\n", + " AmplitudeDamping(0.1), GateCriteria(None, {0})\n", + " PauliChannel(0.1, 0.2, 0.3), GateCriteria({'X'}, {0})\n", + "Readout Noise:\n", + " PhaseFlip(0.02), ObservableCriteria({'X'}, {0})\n", + " BitFlip(0.01), ObservableCriteria({'Z'}, {1})\n" + ] + } + ], + "source": [ + "noise_model = NoiseModel()\n", + "noise_model.add_noise(Depolarizing(0.1), GateCriteria(Gate.H))\n", + "noise_model.add_noise(Depolarizing(0.1), GateCriteria())\n", + "\n", + "noise_model.add_noise(AmplitudeDamping(0.1), GateCriteria(qubits=0))\n", + "noise_model.add_noise(PauliChannel(0.1, 0.2, 0.3), GateCriteria(Gate.X, qubits=0))\n", + "noise_model.add_noise(PhaseFlip(0.02), ObservableCriteria(Observable.X, 0))\n", + "noise_model.add_noise(BitFlip(0.01), ObservableCriteria(Observable.Z, 1))\n", + "print(noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "47619c82-60dc-4000-9886-865dc043213c", + "metadata": {}, + "source": [ + "Now we filter the noise model by `qubit=0` which returns a *new* noise model with only the noise affecting qubit 0. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "9b15f5fb-f1d7-4fb5-aadf-c6e85e2cb291", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n", + " Depolarizing(0.1), GateCriteria(None, None)\n", + " AmplitudeDamping(0.1), GateCriteria(None, {0})\n", + " PauliChannel(0.1, 0.2, 0.3), GateCriteria({'X'}, {0})\n", + "Readout Noise:\n", + " PhaseFlip(0.02), ObservableCriteria({'X'}, {0})\n" + ] + } + ], + "source": [ + "reduced_noise_model = noise_model.from_filter(qubit=0)\n", + "print(reduced_noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "925c0e6d-598b-4428-a254-b1d26ed2f3e6", + "metadata": {}, + "source": [ + "Likewise, we can scope the noise model to only include noise that references a specific gate.\n", + "Below, we filter by gate = `Gate.H`. Notice that qubit criteria, which doesn't depend on gate, is also included." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "11e6967a-37b7-499a-98c4-81c13535d484", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n", + " Depolarizing(0.1), GateCriteria(None, None)\n", + " AmplitudeDamping(0.1), GateCriteria(None, {0})\n" + ] + } + ], + "source": [ + "reduced_noise_model = noise_model.from_filter(gate=Gate.H)\n", + "print(reduced_noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "f79279ba-634c-4f26-a698-1796a75912d6", + "metadata": {}, + "source": [ + "Similarly we can also filter by the type of noise, for instance to get only bit flip channels, we do:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "12a0ffb0-3217-45a3-84e7-562d8378b350", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Readout Noise:\n", + " BitFlip(0.01), ObservableCriteria({'Z'}, {1})\n" + ] + } + ], + "source": [ + "reduced_noise_model = noise_model.from_filter(noise=BitFlip)\n", + "print(reduced_noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "c414a99d-1a7a-4761-839a-0a60d239d664", + "metadata": {}, + "source": [ + "We can also combine filters to get more specific reductions." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "bfe264f4-12fb-4b16-bd6a-093c7b80a22a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n", + " Depolarizing(0.1), GateCriteria(None, None)\n" + ] + } + ], + "source": [ + "reduced_noise_model = noise_model.from_filter(gate=Gate.H, qubit=1)\n", + "print(reduced_noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "1b9ed8de-e9aa-4ca1-b2c0-fda6892c4dbd", + "metadata": {}, + "source": [ + "If we don't filter by anything, the returned model will be the same as the original." + ] + }, + { + "cell_type": "markdown", + "id": "16e40060-d791-4b0d-88e1-c8912c3192f1", + "metadata": {}, + "source": [ + "### Saving and loading noise models\n", + "\n", + "Noise models can be converted to Python dictionaries. This makes it easy to save and load models." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "25865b8e-68f2-4d55-a225-275ec0d16978", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'instructions': [{'noise': {'__class__': 'Depolarizing',\n", + " 'probability': 0.1,\n", + " 'qubit_count': 1,\n", + " 'ascii_symbols': ('DEPO(0.1)',)},\n", + " 'criteria': {'__class__': 'GateCriteria', 'gates': ['H'], 'qubits': None}},\n", + " {'noise': {'__class__': 'Depolarizing',\n", + " 'probability': 0.1,\n", + " 'qubit_count': 1,\n", + " 'ascii_symbols': ('DEPO(0.1)',)},\n", + " 'criteria': {'__class__': 'GateCriteria', 'gates': None, 'qubits': None}},\n", + " {'noise': {'__class__': 'AmplitudeDamping',\n", + " 'gamma': 0.1,\n", + " 'qubit_count': 1,\n", + " 'ascii_symbols': ('AD(0.1)',)},\n", + " 'criteria': {'__class__': 'GateCriteria', 'gates': None, 'qubits': [0]}},\n", + " {'noise': {'__class__': 'PauliChannel',\n", + " 'probX': 0.1,\n", + " 'probY': 0.2,\n", + " 'probZ': 0.3,\n", + " 'qubit_count': 1,\n", + " 'ascii_symbols': ('PC(0.1,0.2,0.3)',)},\n", + " 'criteria': {'__class__': 'GateCriteria', 'gates': ['X'], 'qubits': [0]}},\n", + " {'noise': {'__class__': 'PhaseFlip',\n", + " 'probability': 0.02,\n", + " 'qubit_count': 1,\n", + " 'ascii_symbols': ('PF(0.02)',)},\n", + " 'criteria': {'__class__': 'ObservableCriteria',\n", + " 'observables': ['X'],\n", + " 'qubits': [0]}},\n", + " {'noise': {'__class__': 'BitFlip',\n", + " 'probability': 0.01,\n", + " 'qubit_count': 1,\n", + " 'ascii_symbols': ('BF(0.01)',)},\n", + " 'criteria': {'__class__': 'ObservableCriteria',\n", + " 'observables': ['Z'],\n", + " 'qubits': [1]}}]}" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "noise_model.to_dict()" + ] + }, + { + "cell_type": "markdown", + "id": "57170712", + "metadata": {}, + "source": [ + "To save the Python dictionary as a json file in a local directory, we use the json package." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "b9564451-7ab5-415b-8fa3-beb79b2aeb33", + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "\n", + "# save to local file\n", + "json.dump(noise_model.to_dict(), open(\"model_dict.json\", \"w\"))\n", + "\n", + "# Load from local file:\n", + "model_dict = json.load(open(\"model_dict.json\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "340c6010-0e8e-45c0-8a08-5956860c7a48", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " Depolarizing(0.1), GateCriteria({'H'}, None)\n", + " Depolarizing(0.1), GateCriteria(None, None)\n", + " AmplitudeDamping(0.1), GateCriteria(None, {0})\n", + " PauliChannel(0.1, 0.2, 0.3), GateCriteria({'X'}, {0})\n", + "Readout Noise:\n", + " PhaseFlip(0.02), ObservableCriteria({'X'}, {0})\n", + " BitFlip(0.01), ObservableCriteria({'Z'}, {1})\n" + ] + } + ], + "source": [ + "print(NoiseModel().from_dict(model_dict))" + ] + }, + { + "cell_type": "markdown", + "id": "87aec0e3", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "In this section, we showed how to construct custom noise models in Braket containing qubit, gate, and readout noise. We showed how to apply noise models to circuits, construct smaller noise models by filtering, and how to save/load models." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.5" + }, + "toc-autonumbering": false, + "toc-showcode": false, + "toc-showmarkdowntxt": false, + "toc-showtags": true + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0_TO_ORGANIZE/Noise_models/Noise_models_on_Rigetti.ipynb b/0_TO_ORGANIZE/Noise_models/Noise_models_on_Rigetti.ipynb new file mode 100644 index 000000000..abdabc763 --- /dev/null +++ b/0_TO_ORGANIZE/Noise_models/Noise_models_on_Rigetti.ipynb @@ -0,0 +1,1058 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "74154c03-d48f-4f41-867b-5e30254ce31a", + "metadata": {}, + "source": [ + "# Noise models on Rigetti\n", + "\n", + "This notebook shows how to construct a noise model from device calibration data for Rigetti Aspen-M-3. We compare the measurement outcomes of circuits run on a noisy simulator with the same circuits run on quantum processing units (QPUs), to show that simulating circuits with noise models more closely mimics QPUs.\n", + "\n", + "**Before you begin**: We recommend being familiar with [Noise models on Amazon Braket.](https://github.com/aws/amazon-braket-examples/blob/main/examples/braket_features/Noise_models/Noise_models_on_Amazon_Braket.ipynb)\n", + "Additionally, users should be familiar with [Running quantum circuits on QPU devices](https://github.com/aws/amazon-braket-examples/blob/main/examples/getting_started/2_Running_quantum_circuits_on_QPU_devices/2_Running_quantum_circuits_on_QPU_devices.ipynb). \n", + "\n", + "### Table of Contents\n", + "\n", + "- Noise model for Rigetti\n", + " - Loading device calibration data\n", + " - Comparing noisy simulator results to QPU results\n", + " - Smaller noise models compared to QPU results" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e5e15fcd-55a2-4168-acc6-a38100f94511", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "from braket.aws import AwsDevice\n", + "from braket.circuits import Circuit, Gate, Noise, Observable\n", + "from braket.circuits.noise_model import (GateCriteria, NoiseModel,\n", + " ObservableCriteria)\n", + "from braket.circuits.noises import (AmplitudeDamping, BitFlip, Depolarizing,\n", + " PauliChannel, PhaseDamping, PhaseFlip,\n", + " TwoQubitDepolarizing)\n", + "from braket.devices import LocalSimulator" + ] + }, + { + "cell_type": "markdown", + "id": "d4da3e37-e93c-4273-98bc-d67b26b8c822", + "metadata": {}, + "source": [ + "Braket provides access to hardware providers' reported calibration data. \n", + "This can be used to construct noise models to approximate the behavior of the QPU when running circuits on a noisy simulator.\n", + "In this tutorial, we focus on local noise models with no crosstalk interactions. Real devices can have crosstalk and unexpected effects that can further degrade the results.\n", + "\n", + "The Aspen-M-3 calibration data is available on the Braket devices page. Under qubit specs, the calibration data include the qubit index, with corresponding values for the $T_1$, $T_2$, fidelity from randomized benchmarking (fRB), fidelity from simultaneous randomized benchmarking (fsRB), readout fidelity (fRO), and active reset fidelity.\n", + "Under \"edge specs\", the data includes the RB fidelity for C-Phase, XY, and CZ gates for each connected edge in the device topology." + ] + }, + { + "cell_type": "markdown", + "id": "38001b96-faf7-49f0-b5a5-2d52820fcfc9", + "metadata": {}, + "source": [ + "**One-qubit calibration data (Qubit specs)**\n", + "

    \n", + "\n", + "\n", + "**Two-qubit calibration data (Edge specs)**\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "id": "276d680f-887d-4929-bcaa-e276a6303496", + "metadata": {}, + "source": [ + "We can programmatically access all the calibration data with the Braket SDK. First we load the AwsDevice using the ARN for Rigetti Aspen-M-3." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a55ea9d5-05f3-4da5-a305-a391e914d012", + "metadata": {}, + "outputs": [], + "source": [ + "aspen_m = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")" + ] + }, + { + "cell_type": "markdown", + "id": "a8a42ae1-51ac-4bf1-bd6a-81ffd982b5f8", + "metadata": {}, + "source": [ + "The properties dictionary contains keys \"provider\" and \"specs\", with \"1Q\" and \"2Q\" keys for the one- and two-qubit calibration data. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "153b5b63-8205-4a7e-bb18-0305ef428f36", + "metadata": {}, + "outputs": [], + "source": [ + "aspen_m_specs = aspen_m.properties.dict()[\"provider\"][\"specs\"]\n", + "\n", + "one_qubit_data = aspen_m_specs[\"1Q\"]\n", + "two_qubit_data = aspen_m_specs[\"2Q\"]" + ] + }, + { + "cell_type": "markdown", + "id": "661cca17-01fa-40be-bd3e-741bacc74ce4", + "metadata": {}, + "source": [ + "The keys of the \"1Q\" dictionary is the qubit number. \n", + "For Aspen-M-3, there are 79 qubits indexed by the first digit representing the octagon (0 to 4, and 10 to 14)\n", + "and the second representing the qubit in that octagon (0 to 7). We can get all qubit indices with `one_qubit_data.keys()` or with `aspen_m.topology_graph.nodes`.\n", + "\n", + "The keys of the \"2Q\" dictionary are the connected qubit pairs separated by a hyphen. \n", + "For example, if qubit 0 and 1 are connected the key is \"0-1\".\n", + "\n", + "\n", + "#### One-qubit noise \n", + "\n", + "Let's look at the one qubit calibration data for qubit 0." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "8d4ecc35-f4dc-49d8-b6ff-adaee560ac4b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'T1': 2.4443429874176914e-05,\n", + " 'T2': 1.627681336532139e-05,\n", + " 'f1QRB': 0.9985669301541129,\n", + " 'f1QRB_std_err': 0.0004092835114091019,\n", + " 'f1Q_simultaneous_RB': 0.9977676229871197,\n", + " 'f1Q_simultaneous_RB_std_err': 0.00021522363993495725,\n", + " 'fActiveReset': 0.9905000000000002,\n", + " 'fRO': 0.9795}" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "one_qubit_data[\"0\"]" + ] + }, + { + "cell_type": "markdown", + "id": "4b676762-e642-4a98-89e3-86d79367071a", + "metadata": {}, + "source": [ + "For each qubit, there are various metrics of the quality:\n", + "\n", + "- **T1**: Thermal relaxation time is related to the time it takes for the excited state, |1⟩, to decay into the ground state, |0⟩. The probability of remaining in the excited state is $p(|1⟩)\\sim e^{-t/T_1}$\n", + "\n", + "- **T2**: The dephasing time, is the decay constant for the scale for a |+⟩ state to decohere into the completely mixed state. $p(|+⟩)\\sim e^{-t/T_2}$ \n", + "\n", + "- **Fidelity (RB)**: Single-qubit randomized benchmarking fidelities. RB fidelity quantifies the average gate fidelity where the average is over all Clifford gates. RB describes an *effective* noise model with gate-independent depolarizing noise on each Clifford gate.\n", + "\n", + "- **Fidelity (sRB)**: Single-qubit simultaneous randomized benchmarking fidelities. These are extracted by running single-qubit RB on all qubits simultaneously. Note that we expect the sRB fidelity to be lower than standard RB fidelity due to non-local crosstalk type noise on the device. \n", + "\n", + "- **Active reset fidelity**: Single-qubit active reset fidelities represents the accuracy to which qubits are reinitalized into the ground state |0⟩.\n", + "\n", + "- **Readout fidelity**: Single-qubit readout fidelities describes the probability of a bit flip error before readout in the computational basis. The readout fidelity is related to the probability of correctly measuring the ground state and excited states respectively, e.g. $f_{RO} =\\frac{p(0|0)+p(1|1)}{2}$" + ] + }, + { + "cell_type": "markdown", + "id": "296708a3-771e-42b4-9ba8-f3db1a02970b", + "metadata": {}, + "source": [ + "Now that we know how to extract and use the calibration data, we can build a simple noise model. For every qubit we will add:\n", + "- amplitude dampening noise with probability $p= 1-e^{-t/T_1}$ for every gate\n", + "- phase dampening noise with probability $p= 0.5(1-e^{-t/T_2})$ for every gate\n", + "- depolarizing noise with probability $p=1-f_{sRB}$ (from simultaneous RB fidelity) for every gate\n", + "- readout bit flip noise with probability $p=1-f_{RO}$ to measurements \n", + "\n", + "Technically, the sRB fidelity already includes effects from $T_1$/$T_2$, however to be explicit we add these as separate terms. In a sense, this model might overestimate the noise on the QPU. \n", + "\n", + "For the dampening noises, we first need the gate times to model $T_1$ and $T_2$ errors.\n", + "From the Braket Aspen-M-3 device page: \"These gates offer fast (40ns and 180ns) 1Q and 2Q gate times.\"" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "cd27adfb-f7d6-4583-b854-794e38152c90", + "metadata": {}, + "outputs": [], + "source": [ + "# median 1q and 2q gate times\n", + "gate_time_1_qubit = 40e-9\n", + "gate_time_2_qubit = 240e-09" + ] + }, + { + "cell_type": "markdown", + "id": "5769f2f4-de1c-4b47-9e4e-fd8d39b9e975", + "metadata": {}, + "source": [ + "To create the noise model, we iterate over all qubits keys in `one_qubit_data`" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "508070bc-b1d2-4737-a2fc-d7711e419996", + "metadata": {}, + "outputs": [], + "source": [ + "noise_model = NoiseModel()\n", + "\n", + "# Single-qubit noise\n", + "for q, data in one_qubit_data.items(): # iterate over qubits\n", + "\n", + " # T1 dampening\n", + " t1 = data[\"T1\"]\n", + " damping_prob = 1 - np.exp(-(gate_time_1_qubit / t1))\n", + " noise_model.add_noise(AmplitudeDamping(damping_prob), GateCriteria(qubits=int(q)))\n", + "\n", + " # T2 phase flip\n", + " t2 = data[\"T2\"]\n", + " dephasing_prob = 0.5 * (1 - np.exp(-(gate_time_1_qubit / t2)))\n", + " noise_model.add_noise(PhaseDamping(dephasing_prob), GateCriteria(qubits=int(q)))\n", + "\n", + " # 1q RB depolarizing rate from simultaneous RB\n", + " depolar_rate = 1 - data[\"f1Q_simultaneous_RB\"]\n", + " noise_model.add_noise(Depolarizing(depolar_rate), GateCriteria(qubits=int(q)))\n", + "\n", + " # 1q RB readout\n", + " readout_value = 1 - data[\"fRO\"]\n", + " noise_model.add_noise(BitFlip(readout_value), ObservableCriteria(qubits=int(q)))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "9d20d24c-17e2-4bba-b317-fb2d156bedb0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of terms in noise model is: 320\n", + "Number of parameters in noise model is: 320\n" + ] + } + ], + "source": [ + "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n", + "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n", + "print(f\"Number of parameters in noise model is: {num_params}\")" + ] + }, + { + "cell_type": "markdown", + "id": "790c62f7-776a-4e4c-9405-7b7a14eee5b0", + "metadata": {}, + "source": [ + "#### Two-qubit noise \n", + "Next we consider adding two-qubit noise to the model. \n", + "\n", + "Let's first look at the data provided in the Aspen-M-3 device calibration data. On the first connect, \"0-1\", the properties are:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "626cbe56-3649-48eb-a2a1-f669eb790b47", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'fCPHASE': 0.8991973184700036,\n", + " 'fCPHASE_std_err': 0.019391126441846068,\n", + " 'fCZ': 0.9406104552003762,\n", + " 'fCZ_std_err': 0.011069113247524152,\n", + " 'fXY': 0.8365560014004874,\n", + " 'fXY_std_err': 0.014585224789608713}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "two_qubit_data[\"0-1\"]" + ] + }, + { + "cell_type": "markdown", + "id": "4bcd3be4-a6e4-4cf3-841e-1a451e01803a", + "metadata": {}, + "source": [ + "Here, we see the fidelity per gate (CPhase, CZ, or XY) and the associated standard error. \n", + "\n", + "Next we loop over the entries in the `two_qubit_data` dictionary and add two-qubit depolarizing noise to the model. Notice that Aspen-M-3 has symmetric connections (\"0-1\" and \"1-0\") so we need to add noise in both directions." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "80f57550-6549-46b6-9a6d-ff7f0f03e90d", + "metadata": {}, + "outputs": [], + "source": [ + "# Two-qubit noise\n", + "for pair, data in two_qubit_data.items(): # iterate over qubit connections\n", + "\n", + " # parse strings \"0-1\" to integers [0, 1]\n", + " q0, q1 = (int(s) for s in pair.split(\"-\"))\n", + "\n", + " if \"fCPHASE\" in data:\n", + " phase_rate = 1 - data[\"fCPHASE\"]\n", + " noise_model.add_noise(\n", + " TwoQubitDepolarizing(phase_rate),\n", + " GateCriteria(\n", + " Gate.CPhaseShift, [(q0, q1), (q1, q0)]\n", + " ), # symmetric connections\n", + " )\n", + "\n", + " if \"fXY\" in data:\n", + " xy_rate = 1 - data[\"fXY\"]\n", + " noise_model.add_noise(\n", + " TwoQubitDepolarizing(xy_rate), GateCriteria(Gate.XY, [(q0, q1), (q1, q0)])\n", + " )\n", + "\n", + " if \"fCZ\" in data:\n", + " cz_rate = 1 - data[\"fCZ\"]\n", + " noise_model.add_noise(\n", + " TwoQubitDepolarizing(cz_rate), GateCriteria(Gate.CZ, [(q0, q1), (q1, q0)])\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "82376d08-84bc-4249-9c8d-d7aacdb73113", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of terms in noise model is: 612\n", + "Number of parameters in noise model is: 612\n" + ] + } + ], + "source": [ + "num_params = sum(len(item.noise.parameters) for item in noise_model.instructions)\n", + "print(f\"Number of terms in noise model is: {len(noise_model.instructions)}\")\n", + "print(f\"Number of parameters in noise model is: {num_params}\")" + ] + }, + { + "cell_type": "markdown", + "id": "5913a8a2-a9de-4e32-a35d-c48191891b1f", + "metadata": {}, + "source": [ + "### Compare circuits run on device vs simulator with a noise model\n", + "\n", + "Let's just look at the first 5 qubits. Note that to ensure the noise model applied T1 and T2 noise during the time between gate, we manually add identity gates to each moment." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "6fabbd05-b480-43c6-b43a-d396d81bd687", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -Rx(0.50)-Rx(3.14)-C-\n", + " | \n", + "q1 : -Rz(0.50)-Rx(3.14)-Z-\n", + " \n", + "q2 : -Rz(0.50)-Rx(3.14)---\n", + "\n", + "T : | 0 | 1 |2|\n" + ] + } + ], + "source": [ + "from braket.circuits import Circuit, Noise\n", + "\n", + "np.random.seed(42)\n", + "\n", + "circ = Circuit().rx(0, 0.5).rz(1, 0.5).rz(2, 0.5).rx(0, np.pi).rx(1, np.pi).rx(2, np.pi).cz(0, 1)\n", + "print(circ)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e2af07ed-33de-4709-9e7c-5e3c3caaa751", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 |\n", + " \n", + "q0 : -Rx(0.50)-AD(0.0016)--PD(0.0012)-DEPO(0.0022)-Rx(3.14)-AD(0.0016)--PD(0.0012)-DEPO(0.0022)-C-DEPO(0.059)-\n", + " | | \n", + "q1 : -Rz(0.50)-AD(0.00086)-PD(0.0015)-DEPO(0.025)--Rx(3.14)-AD(0.00086)-PD(0.0015)-DEPO(0.025)--Z-DEPO(0.059)-\n", + " \n", + "q2 : -Rz(0.50)-AD(0.0018)--PD(0.0011)-DEPO(0.0041)-Rx(3.14)-AD(0.0018)--PD(0.0011)-DEPO(0.0041)---------------\n", + "\n", + "T : | 0 | 1 | 2 |\n" + ] + } + ], + "source": [ + "noisy_circ = noise_model.apply(circ)\n", + "\n", + "print(noisy_circ)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "9304dcf1-a1e8-4e41-a6b5-769841f4eefe", + "metadata": {}, + "outputs": [], + "source": [ + "simulator = LocalSimulator() # noise free simulator\n", + "task = simulator.run(circ, shots=100_000)\n", + "free_probs = task.result().measurement_probabilities" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "0e1d9cfe-03d6-406b-b4ab-89166a907681", + "metadata": {}, + "outputs": [], + "source": [ + "noisy_simulator = LocalSimulator(\"braket_dm\")\n", + "noisy_task = noisy_simulator.run(noisy_circ, shots=100_000)\n", + "noisy_probs = noisy_task.result().measurement_probabilities" + ] + }, + { + "cell_type": "markdown", + "id": "b3f370bd-a8b3-4d5b-a724-da549fc4c81f", + "metadata": {}, + "source": [ + "
    \n", + "Note: The below section runs tasks on the Rigetti Aspen-M-3 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console.\n", + "
    \n", + "\n", + "
    \n", + "Note: Running the circuit below will result in charges on your AWS account.\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "c8f4664a-0527-46fb-87f2-2a0c85f0bd79", + "metadata": {}, + "outputs": [], + "source": [ + "aspen_m_task = aspen_m.run(circ, shots=100_000, disable_qubit_rewiring=True)\n", + "aspen_m_result = aspen_m_task.result()\n", + "aspen_m_probs = aspen_m_result.measurement_probabilities" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "1676a45c-5ef8-49cc-b227-69f69fa2004a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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    aspen-mnoisy_simfree_sim
    0000.001360.00016NaN
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    \n", + "
    " + ], + "text/plain": [ + " aspen-m noisy_sim free_sim\n", + "000 0.00136 0.00016 NaN\n", + "111 0.68340 0.85721 0.93927\n", + "110 0.07619 0.00635 NaN\n", + "011 0.12967 0.07411 0.06073\n", + "101 0.07366 0.04401 NaN\n", + "100 0.00777 0.00023 NaN\n", + "010 0.01303 0.00045 NaN\n", + "001 0.01492 0.01748 NaN" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "free_sim = pd.DataFrame.from_dict(free_probs, orient=\"index\").rename(\n", + " columns={0: \"free_sim\"}\n", + ")\n", + "noisy_sim = pd.DataFrame.from_dict(noisy_probs, orient=\"index\").rename(\n", + " columns={0: \"noisy_sim\"}\n", + ")\n", + "aspenm = pd.DataFrame.from_dict(aspen_m_probs, orient=\"index\").rename(\n", + " columns={0: \"aspen-m\"}\n", + ")\n", + "df = aspenm.join(noisy_sim).join(free_sim)\n", + "df" + ] + }, + { + "cell_type": "markdown", + "id": "472e6850-2603-4174-bf92-b04eb0c38c2f", + "metadata": {}, + "source": [ + "We can compute the fidelity between the free simulation and Rigetti, as well as the noisy simulation and Rigetti. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "5b7d1740-cb46-433e-8c2b-7e8b7c10fb4e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Total fidelity between Aspen-M and noise-free simulator is 0.8899252242353248\n", + "\n", + "Total fidelity between Aspen-M and noisy simulator is 0.9627231692802513\n" + ] + } + ], + "source": [ + "def fidelity(p, q):\n", + " return np.sum(np.sqrt(p * q))\n", + "\n", + "\n", + "f_free_aspen = fidelity(df[\"free_sim\"], df[\"aspen-m\"])\n", + "f_noisy_aspen = fidelity(df[\"noisy_sim\"], df[\"aspen-m\"])\n", + "\n", + "print(f\"\\nTotal fidelity between Aspen-M and noise-free simulator is {f_free_aspen}\")\n", + "print(f\"\\nTotal fidelity between Aspen-M and noisy simulator is {f_noisy_aspen}\")" + ] + }, + { + "cell_type": "markdown", + "id": "fd4d88b7-015e-445b-ba26-1bdbc6a2bd16", + "metadata": {}, + "source": [ + "To better visualize, we can also plot the output probability distributions from each circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "9329ed72-2f30-4383-b48f-0d50e1a5dd11", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "\n", + "df.plot.bar(\n", + " title=\"Comparing noise-free simulator, noisy simulator, and Aspen-M\",\n", + " figsize=(12, 6),\n", + ")\n", + "\n", + "text = f\"f_free_aspen = {f_free_aspen:.3f} \\nf_noise_model_aspen = {f_noisy_aspen:.3f}\"\n", + "plt.text(1, 0.5, text, fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "aa8ffab8-e062-4c33-9c9d-4a312cd76b63", + "metadata": {}, + "source": [ + "We confirm that the simulator with a noise model is closer to the distribution produced by Aspen-M-3." + ] + }, + { + "cell_type": "markdown", + "id": "c4571a5e-2f8d-4767-b28e-a527d2490830", + "metadata": {}, + "source": [ + "### Smaller, reduced noise models\n", + "\n", + "The full Rigetti Aspen-M-3 noise model contains due to non-uniform qubit noise. We can obtain simpler, smaller noise models by coarse graining the model above.\n", + "\n", + "Here, we consider taking the average over all qubits for the $T_1$, $T_2$, depolarizing, and readout depolarizing rates. This is a substantially smaller noise model, but may be less accurate. \n", + "\n", + "We use the `from_filter` function to extract all instructions with amplitude dampening noise in the model. We then compute the mean of the error probabilities. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "eac8479f-4b29-42d8-a15a-ba10aae82d3f", + "metadata": {}, + "outputs": [], + "source": [ + "avg_t1 = np.mean(\n", + " [\n", + " n.noise.parameters\n", + " for n in noise_model.from_filter(noise=AmplitudeDamping).instructions\n", + " ]\n", + ")\n", + "avg_t2 = np.mean(\n", + " [\n", + " n.noise.parameters\n", + " for n in noise_model.from_filter(noise=PhaseDamping).instructions\n", + " ]\n", + ")\n", + "avg_depo = np.mean(\n", + " [\n", + " n.noise.parameters\n", + " for n in noise_model.from_filter(noise=Depolarizing).instructions\n", + " ]\n", + ")\n", + "avg_readout = np.mean(\n", + " [n.noise.parameters for n in noise_model.from_filter(noise=BitFlip).instructions]\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "d1a64cae-226c-45d2-9af3-4b5b7a36c7a4", + "metadata": {}, + "source": [ + "Now we construct a new noise model with the mean values above:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "e49eb24c-5f24-4084-9d4c-c2e7e82fc259", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate Noise:\n", + " AmplitudeDamping(0.0019483910859341453), GateCriteria(None, None)\n", + " PhaseDamping(0.0018677309884621795), GateCriteria(None, None)\n", + " Depolarizing(0.007153677053977023), GateCriteria(None, None)\n", + "Readout Noise:\n", + " BitFlip(0.053481250000000015), ObservableCriteria(None, None)\n" + ] + } + ], + "source": [ + "simple_noise_model = NoiseModel()\n", + "simple_noise_model.add_noise(AmplitudeDamping(avg_t1), GateCriteria())\n", + "simple_noise_model.add_noise(PhaseDamping(avg_t2), GateCriteria())\n", + "simple_noise_model.add_noise(Depolarizing(avg_depo), GateCriteria())\n", + "simple_noise_model.add_noise(BitFlip(avg_readout), ObservableCriteria())\n", + "\n", + "print(simple_noise_model)" + ] + }, + { + "cell_type": "markdown", + "id": "b44bbbd1-fb65-4b8f-8dfa-0ea5aa7979b2", + "metadata": {}, + "source": [ + "We can see the resultant circuits contain qubit-independent noise:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "c83e96f6-54b0-445b-bcdd-8a7a16691b62", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 |\n", + " \n", + "q0 : -Rx(0.75)-AD(0.0019)-PD(0.0019)-DEPO(0.0072)-C-AD(0.0019)-PD(0.0019)-DEPO(0.0072)-I--------AD(0.0019)-PD(0.0019)-DEPO(0.0072)-\n", + " | \n", + "q1 : -I--------AD(0.0019)-PD(0.0019)-DEPO(0.0072)-Z-AD(0.0019)-PD(0.0019)-DEPO(0.0072)-Rx(0.50)-AD(0.0019)-PD(0.0019)-DEPO(0.0072)-\n", + " \n", + "q2 : -Rz(0.50)-AD(0.0019)-PD(0.0019)-DEPO(0.0072)-I-AD(0.0019)-PD(0.0019)-DEPO(0.0072)-I--------AD(0.0019)-PD(0.0019)-DEPO(0.0072)-\n", + "\n", + "T : | 0 | 1 | 2 |\n" + ] + } + ], + "source": [ + "simple_noisy_circ = simple_noise_model.apply(circ)\n", + "print(simple_noisy_circ)" + ] + }, + { + "cell_type": "markdown", + "id": "e2c20b79-cbf2-4897-80b3-452c78d56a03", + "metadata": {}, + "source": [ + "We run the circuit on a noisy simulator below" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a1bb19e8-6824-4a50-b9fb-ae06c14359b6", + "metadata": {}, + "outputs": [], + "source": [ + "simple_noisy_task = noisy_simulator.run(simple_noisy_circ, shots=100_000)\n", + "simple_noisy_probs = simple_noisy_task.result().measurement_probabilities" + ] + }, + { + "cell_type": "markdown", + "id": "76418e5c-be5b-4b3a-8916-c0f56f003cd7", + "metadata": {}, + "source": [ + "and add it to the previous dataframe" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "b4d27a95-612d-4dea-9f6a-98d4525b0a70", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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    " + ], + "text/plain": [ + " aspen-m noisy_sim free_sim simple_noisy_sim\n", + "000 0.53302 0.74544 0.81380 0.78149\n", + "100 0.11748 0.13151 0.12486 0.13176\n", + "010 0.24681 0.08706 0.05338 0.06130\n", + "110 0.05687 0.02742 0.00796 0.01061\n", + "011 0.01819 0.00055 NaN 0.00096\n", + "111 0.00477 0.00021 NaN 0.00015\n", + "001 0.01892 0.00650 NaN 0.01179\n", + "101 0.00394 0.00131 NaN 0.00194" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simple_noisy_sim = pd.DataFrame.from_dict(simple_noisy_probs, orient=\"index\").rename(\n", + " columns={0: \"simple_noisy_sim\"}\n", + ")\n", + "df = df.join(simple_noisy_sim)\n", + "df" + ] + }, + { + "cell_type": "markdown", + "id": "b1699bc2-712f-4a99-b9d6-0a0920114a13", + "metadata": {}, + "source": [ + "We compute the fidelity between the simple noise model and the QPU:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "d7710e0b-29ac-4968-aa00-e23cb8b32269", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Total fidelity between Aspen-M and full noise model is: 0.9582415634979304\n", + "\n", + "Total fidelity between Aspen-M and simple noise model is: 0.9401126418474742\n", + "\n", + "Total fidelity between Aspen-M and noise-free is: 0.915784824249657\n" + ] + } + ], + "source": [ + "f_simple = fidelity(df[\"simple_noisy_sim\"], df[\"aspen-m\"])\n", + "\n", + "print(f\"\\nTotal fidelity between Aspen-M and full noise model is: {f_noisy_aspen}\")\n", + "print(f\"\\nTotal fidelity between Aspen-M and simple noise model is: {f_simple}\")\n", + "print(f\"\\nTotal fidelity between Aspen-M and noise-free is: {f_free_aspen}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "e36e19d0-664a-4cb4-a2e3-0061cd60a6c1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "df.plot.bar(title=\"Comparing simulators and Aspen-M\", figsize=(12, 6))\n", + "text = f\"f_free = {f_free_aspen:.3f} \\nf_simple_noise_model = {f_simple:.3f} \\nf_noise_model = {f_noisy_aspen:.3f}\"\n", + "plt.text(1, 0.5, text, fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "6da72e22-a594-41e7-a4e2-cb82cfe0726a", + "metadata": {}, + "source": [ + "We see that compared to the full noise model, the simple model is less accurate, however, it is still a significant improvement over the noise-free case and has far fewer parameters in the model. " + ] + }, + { + "cell_type": "markdown", + "id": "b2c6b2ba-cb54-43f6-9a89-e29066b5192a", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "In this notebook, we showed how to construct a noise model for Rigetti Aspen-M-3 based only on the available calibration data.\n", + "We used a coarse assumption of gate-independent single-qubit depolarizing noise and gate-dependant two-qubit noise. Our qubit-dependent model could be improved in many ways. We could add gate-dependence noise, or change the depolarizing channel to Pauli channels. " + ] + } + ], + "metadata": { + "interpreter": { + "hash": "a86a9ff96c3b20b9c94872c880ce00e370ced2a9959f9303c435918fb220e358" + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.5" + }, + "toc-autonumbering": false, + "toc-showcode": false, + "toc-showmarkdowntxt": false, + "toc-showtags": true + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/0_TO_ORGANIZE/Noise_models/aspenm_edge_specs.png b/0_TO_ORGANIZE/Noise_models/aspenm_edge_specs.png new file mode 100644 index 0000000000000000000000000000000000000000..e8b1e15dc21c61cbd9d6d6d41913b546c8ad42a3 GIT binary patch literal 46592 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zw)j@>YdQ*oGLj%q-d;@tt1Yk+Q;z%CWJC|(EAYQiO~~*mtp~~Y0;%S?Uf+3x9#54S zz98|cnpctb@l)7|;Oz11nrN@JR5((M+zW~2o`afVDlgeqoTGOr&KC2=)|wQ7z1WpR7(c0fZXJ%-r>O*7`5{7yaW_62|=*5I7wA8e-pwU<7DYY`mrH<_+SV>-g%XsApGJxqG# zQsme2@k_0}DU$ESJENK=PQf+iO?Z9FdY}V;4s_t|zCwzlx_+=aP<9TYpHokE$HR-a zG6`a$HGxYA#r@(U;^7|tj;&1cq`NoJZ3lHr?oy$_uNHTO$Q%d^n*I1U2zlzt>^4Il z;(ZrfmC~9TKC}`DER0dyWwCUrf8$S8bDpqbY|@I~99|B_Svy4FB#|=-{Wf21QciYe z=Cqt^L^5c8u09O1!JxRc-en6KjvJ!#wK-MiGKeVx^~IkF53(h1-nMx9ulq7zEzOHO`5ug@Uqf&tXE4%Aw?iHTeWoir|XW< z0b**?=fZ6G!L8TOz#V5S*R2NEi$+EFr&iaC7J!=MXu##VSIdVjhAMLD}7A05v2@8uzOh3xd47(Tk7ojgfc zXoW*?o!m%HwhBI>+P>Le2<0&+M zYNYQ2b=MW#Qk5EbTHQG^JKNd&uZLIn&mCU(oT z_mk;rk&bVI>mD;$^DB^8L9*S~&tR7on{hrqOftBk?s>@1#g{ZEzrs|hJy6S&pJo|`XSsLnL{ zy%(8ln|}Om#Md%H^@d1~YXrKW#(UQq4rk)bx;5Od49dn$q4M9 zTie Circuit: + """Phase estimation circuit. + + Args: + n_qubits (int): Number of total qubits in the circuit. + phase (float): Phase in radians. + + Returns: + Circuit: Circuit for phase estimation. + """ + n_precision_qubits = n_qubits - 1 + + q_precision = range(n_precision_qubits) + q_query = [n_precision_qubits] + + circ = Circuit() + circ.h(q_precision) + circ.x(q_query) + + for i, qubit in enumerate(reversed(q_precision)): + circ.add(_custom_control_phase(qubit, q_query, phase * 2**i)) + + iqft_circuit = _inverse_quantum_fourier_transform_circuit(n_precision_qubits) + circ.add(iqft_circuit) + + return circ + + +def _custom_control_phase(control: int, target: int, angle: float) -> Circuit: + """Custom control phase shift using CNots and Rz rotations. + + Args: + control (int): Control qubit + target (int): Target qubit + angle (float): Angle of controlled-phaseshift. + + Returns: + Circuit: Circuit for control phase shift. + """ + circuit = Circuit() + circuit.rz(control, angle / 2).cnot(control, target) + circuit.rz(target, -angle / 2).cnot(control, target).rz(target, angle / 2) + return circuit + + +def _inverse_quantum_fourier_transform_circuit(n_qubits: int) -> Circuit: + """Inverse quanutm Fourier transform (iQFT). + + Args: + n_qubits (int): Number of qubits. + + Returns: + Circuit: inverse QFT circuit. + """ + qft_circ = Circuit() + qubits = list(range(n_qubits)) + + for i in range(n_qubits // 2): + qft_circ.swap(qubits[i], qubits[-i - 1]) + + for k in reversed(range(n_qubits)): + for j in reversed(range(1, n_qubits - k)): + angle = -2 * np.pi / (2 ** (j + 1)) + qft_circ.add(_custom_control_phase(qubits[k + j], qubits[k], angle)) + + qft_circ.h(qubits[k]) + + return qft_circ diff --git a/0_TO_ORGANIZE/utils_qaoa.py b/0_TO_ORGANIZE/utils_qaoa.py new file mode 100644 index 000000000..344ba2c7c --- /dev/null +++ b/0_TO_ORGANIZE/utils_qaoa.py @@ -0,0 +1,315 @@ +# IMPORTS +import numpy as np +from braket.aws import AwsDevice +from braket.circuits import Circuit, Observable, circuit, FreeParameter, QubitSet +from braket.devices import LocalSimulator +from scipy.optimize import minimize + + +# function to implement evolution with driver Hamiltonian +@circuit.subroutine(register=True) +def driver(beta, n_qubits): + """ + Returns circuit for driver Hamiltonian U(Hb, beta) + """ + # instantiate circuit object + circ = Circuit() + + # apply parametrized rotation around x to every qubit + for qubit in range(n_qubits): + gate = Circuit().rx(qubit, beta) + circ.add(gate) + + return circ + +# helper function for evolution with cost Hamiltonian +@circuit.subroutine(register=True) +def cost_circuit(gammas, n_qubits, ising, device): + """ + returns circuit for evolution with cost Hamiltonian + """ + # instantiate circuit object + circ = Circuit() + + # get all non-zero entries (edges) from Ising matrix + idx = ising.nonzero() + edges = list(zip(idx[0], idx[1])) + + # apply ZZ gate for every edge (with corresponding interaction strength) + for (ii, qubit_pair) in enumerate(edges): + circ.zz(qubit_pair[0], qubit_pair[1], angle=gammas[ii]) + + return circ + + +# function to build the QAOA circuit with depth p +def circuit(params, device, n_qubits, ising): + """ + function to return full QAOA circuit; depends on device as ZZ implementation depends on gate set of backend + """ + + # initialize qaoa circuit with first Hadamard layer: for minimization start in |-> + circ = Circuit() + H_on_all = Circuit().h(range(0, n_qubits)) + circ.add(H_on_all) + + # setup two parameter families + circuit_length = int(len(params) / 2) + gammas = params[:circuit_length] + betas = params[circuit_length:] + + # add QAOA circuit layer blocks + for mm in range(circuit_length): + circ.cost_circuit(gammas[mm], n_qubits, ising, device) + circ.driver(betas[mm], n_qubits) + return circ + +def cost_H(ising): + idx = ising.nonzero() + edges = list(zip(idx[0], idx[1])) + + H = [] + # apply ZZ gate for every edge (with corresponding interaction strength) + for qubit_pair in edges[1:]: + # get interaction strength from Ising matrix + int_strength = ising[qubit_pair[0], qubit_pair[1]] + H.append(2*ising[qubit_pair[0], qubit_pair[1]] * Observable.Z() @ Observable.Z()) + targets = [QubitSet([edge[0], edge[1]]) for edge in edges] + return sum(H, 2*ising[edges[0][0], edges[0][1]] * Observable.Z() @ Observable.Z()), targets + +def form_inputs_dict(params, ising): + n_params = len(params) + params_dict = {} + idx = ising.nonzero() + edges = list(zip(idx[0], idx[1])) + split = int(n_params/2) + for i in range(split): + params_dict[f'beta_{i}'] = 2 * params[split + i] + for j in range(len(edges)): + params_dict[f'gamma_{i}_{j}'] = 2 * ising[edges[j][0], edges[j][1]] * params[i] + + return params_dict + +def form_jacobian(n_params, gradient, ising): + # fix jacobian + jac = [0.0] * n_params + idx = ising.nonzero() + edges = list(zip(idx[0], idx[1])) + split = int(n_params/2) + for i in range(split): + # handle betas + jac[split + i] += 2 * gradient[f'beta_{i}'] + # handle gammas + for j in range(len(edges)): + jac[i] += 2 * ising[edges[j][0], edges[j][1]] * gradient[f'gamma_{i}_{j}'] + + return jac + +# function that computes cost function for given params +def objective_function(params, qaoa_circuit, ising, device, tracker, verbose): + """ + objective function takes a list of variational parameters as input, + and returns the cost associated with those parameters + """ + + if verbose: + print("==================================" * 2) + print("Calling the quantum circuit. Cycle:", tracker["count"]) + + # create parameter dict + params_dict = form_inputs_dict(params, ising) + # classically simulate the circuit + # set the parameter values using the inputs argument + # execute the correct device.run call depending on whether the backend is local or cloud based + task = device.run( + qaoa_circuit(**params_dict), shots=0, poll_timeout_seconds=3 * 24 * 60 * 60 + ) + + # get result for this task + result = task.result() + energy = 0.0 + idx = ising.nonzero() + edges = list(zip(idx[0], idx[1])) + for (term, edge) in zip(result.values, edges): + energy += 2*ising[edge[0], edge[1]]*term + + # get metadata + metadata = result.task_metadata + + tracker["opt_energies"].append(energy) + + # store optimal (classical) result/bitstring + if energy < tracker["optimal_energy"]: + tracker.update({"optimal_energy": energy}) + + # store global minimum + tracker["global_energies"].append(tracker["optimal_energy"]) + + if verbose: + print("Energy expectation value (cost):", energy) + + # update tracker + tracker.update({"count": tracker["count"] + 1, "res": result}) + tracker["costs"].append(energy) + tracker["params"].append(params) + + return energy + +# The function to execute the training: run classical minimization. +def train( + device, options, p, ising, n_qubits, opt_method, tracker, params0, verbose=True +): + """ + function to run QAOA algorithm for given ising matrix, fixed circuit depth p + """ + print("Starting the training.") + + print("==================================" * 2) + print(f"OPTIMIZATION for circuit depth p={p}") + + if not verbose: + print('Param "verbose" set to False. Will not print intermediate steps.') + print("==================================" * 2) + + # initialize + cost_energy = [] + + # set bounds for search space + bnds_gamma = [(0, 2 * np.pi) for _ in range(int(len(params0) / 2))] + bnds_beta = [(0, np.pi) for _ in range(int(len(params0) / 2))] + bnds = bnds_gamma + bnds_beta + + tracker["params"].append(params0) + + gamma_params = [[FreeParameter(f"gamma_{i}_{j}") for j in range(len(ising.nonzero()[0]))] for i in range(p)] + beta_params = [FreeParameter(f"beta_{i}") for i in range(p)] + params = gamma_params + beta_params + H, targets = cost_H(ising) + qaoa_circ = circuit(params, device, n_qubits, ising) + for (term, target) in zip(H.summands, targets): + qaoa_circ.expectation(observable=term._unscaled(), target=target) + + print('Initial energy: ', objective_function(params0, qaoa_circ, ising, device, tracker, False)) + # run classical optimization (example: method='Nelder-Mead') + result = minimize( + objective_function, + params0, + jac=False, + args=(qaoa_circ, ising, device, tracker, verbose), + options=options, + method=opt_method, + bounds=bnds, + ) + + # store result of classical optimization + result_energy = result.fun + cost_energy.append(result_energy) + print("Final average energy (cost):", result_energy) + result_angle = result.x + print("Final angles:", result_angle) + print("Training complete.") + + return result_energy, result_angle, tracker + +# function that computes cost function and gradient for given params +def objective_function_adjoint(params, qaoa_circuit, ising, device, tracker, verbose): + """ + objective function takes a list of variational parameters as input, + and returns the cost associated with those parameters + """ + + if verbose: + print("==================================" * 2) + print("Calling the quantum circuit. Cycle:", tracker["count"]) + + # create parameter dict + params_dict = form_inputs_dict(params, ising) + # classically simulate the circuit + # set the parameter values using the inputs argument + # execute the correct device.run call depending on whether the backend is local or cloud based + task = device.run( + qaoa_circuit, shots=0, inputs=params_dict, poll_timeout_seconds=3 * 24 * 60 * 60 + ) + + # get result for this task + result = task.result() + gradient = result.values[0] + energy = gradient['expectation'] + # get metadata + metadata = result.task_metadata + + tracker["opt_energies"].append(energy) + + # store optimal energy + if energy < tracker["optimal_energy"]: + tracker.update({"optimal_energy": energy}) + + # store global minimum + tracker["global_energies"].append(tracker["optimal_energy"]) + + if verbose: + print("Energy expectation value (cost):", energy) + + # update tracker + tracker.update({"count": tracker["count"] + 1, "res": result}) + tracker["costs"].append(energy) + tracker["params"].append(params) + jac = form_jacobian(len(params), gradient["gradient"], ising) + return energy, jac + + +# The function to execute the training: run classical minimization. +def train_adjoint( + device, options, p, ising, n_qubits, opt_method, tracker, params0, verbose=True +): + """ + function to run QAOA algorithm for given, fixed circuit depth p + """ + print("Starting the training.") + + print("==================================" * 2) + print(f"OPTIMIZATION for circuit depth p={p}") + + if not verbose: + print('Param "verbose" set to False. Will not print intermediate steps.') + print("==================================" * 2) + + # initialize + cost_energy = [] + + # set bounds for search space + bnds_gamma = [(0, 2 * np.pi) for _ in range(int(len(params0) / 2))] + bnds_beta = [(0, np.pi) for _ in range(int(len(params0) / 2))] + bnds = bnds_gamma + bnds_beta + + tracker["params"].append(params0) + + gamma_params = [[FreeParameter(f"gamma_{i}_{j}") for j in range(len(ising.nonzero()[0]))] for i in range(p)] + beta_params = [FreeParameter(f"beta_{i}") for i in range(p)] + params = gamma_params + beta_params + qaoa_circ = circuit(params, device, n_qubits, ising) + + H, targets = cost_H(ising) + qaoa_circ.adjoint_gradient(observable=H, target=targets, parameters=[]) + + print('Initial energy: ', objective_function_adjoint(params0, qaoa_circ, ising, device, tracker, False)[0]) + # run classical optimization (example: method='Nelder-Mead') + result = minimize( + objective_function_adjoint, + params0, + jac=True, # objective function will return both f and its jacobian + args=(qaoa_circ, ising, device, tracker, verbose), + options=options, + method=opt_method, + bounds=bnds, + ) + + # store result of classical optimization + result_energy = result.fun + cost_energy.append(result_energy) + print("Final average energy (cost):", result_energy) + result_angle = result.x + print("Final angles:", result_angle) + print("Training complete.") + + return result_energy, result_angle, tracker diff --git a/modules/0_Getting_Started/0_Getting_started/0_Getting_started.ipynb b/modules/0_Getting_Started/0_Getting_started/0_Getting_started.ipynb new file mode 100644 index 000000000..22fe34775 --- /dev/null +++ b/modules/0_Getting_Started/0_Getting_started/0_Getting_started.ipynb @@ -0,0 +1,127 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Getting started with Amazon Braket\n", + "\n", + "In this hello-world tutorial we prepare a maximally entangled Bell state between two qubits. We then run our circuit on a local simulator and obtain the results." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "# AWS imports: Import Braket SDK modules\n", + "from braket.circuits import Circuit\n", + "from braket.devices import LocalSimulator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Build a circuit\n", + "\n", + "Let's build a Bell state with two qubits. By calling `Circuit()` we create an empty circuit, and we can just add gates to the circuit. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# build a Bell state with two qubits. Here 'cnot(control=0, target=1)' can be simplified as 'cnot(0,1)'\n", + "bell = Circuit().h(0).cnot(control=0, target=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Submit the circuit to the local simulator and obtain the results\n", + "\n", + "Here we submit our circuit to the local simulator and obtain the results." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'00': 502, '11': 498})\n" + ] + } + ], + "source": [ + "# set up device\n", + "device = LocalSimulator()\n", + "\n", + "# run circuit\n", + "result = device.run(bell, shots=1000).result()\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "# print counts\n", + "print(counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values());\n", + "plt.xlabel('bitstrings');\n", + "plt.ylabel('counts');" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "conda_braket", + "language": "python", + "name": "conda_braket" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.7" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/0_Getting_Started/1_Running_quantum_circuits_on_simulators/1_Running_quantum_circuits_on_simulators.ipynb b/modules/0_Getting_Started/1_Running_quantum_circuits_on_simulators/1_Running_quantum_circuits_on_simulators.ipynb new file mode 100644 index 000000000..044bcb0c9 --- /dev/null +++ b/modules/0_Getting_Started/1_Running_quantum_circuits_on_simulators/1_Running_quantum_circuits_on_simulators.ipynb @@ -0,0 +1,537 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Preparing a GHZ state and running the circuit on simulators" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This hello-world tutorial prepares a paradigmatic example for a multi-qubit entangled state, the so-called [GHZ state](https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state) (named after the three physicists Greenberger, Horne and Zeilinger). The GHZ state is extremely non-classical, and therefore very sensitive to decoherence. Therefore, it is often used as a performance benchmark for today's hardware. Moreover, in many quantum information protocols it is used as a resource for quantum error correction, quantum communication and quantum metrology. \n", + "\n", + "Amazon Braket offers several classical simulators including a local simulator and three on-demand simulators: a full state-vector simulator SV1, a density matrix simulator DM1, and a tensor-network simulator TN1. You can seamlessly swap between different devices without any modifications to the circuit definition, as shown below, by just re-defining the device object. For additional information about simulators, see the [Amazon Braket Dev Guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#choose-a-simulator)." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "import matplotlib.pyplot as plt\n", + "# magic word for producing visualizations in notebook\n", + "%matplotlib inline\n", + "import time\n", + "import numpy as np\n", + "\n", + "# AWS imports: Import Braket SDK modules\n", + "from braket.circuits import Circuit, Observable\n", + "from braket.devices import LocalSimulator\n", + "from braket.aws import AwsDevice" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Problem: Prepare a GHZ State" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Goal: Prepare an $N$-qubit GHZ state: \n", + "$$\\left|0,0, ...\\right> \\rightarrow \\left|\\mathrm{GHZ}\\right> = \\frac{1}{\\sqrt{2}}\\left(\\left|0,0, ...\\right> + \\left|1,1, ...\\right>\\right).$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The GHZ state is a quantum superposition of all subsystems being in state 0 with all of them being in state 1 (as often discussed in the famous Gedanken experiment of a cat being dead and alive at the same time). The GHZ state is a maximally entangled quantum state. \n", + "\n", + "To prepare this state, build and run the following circuit using a single-qubit Hadamard gate (denoted as H) acting on the first qubit followed by a series of two-qubit CNOT gates: " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + "\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setup Circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# function to build a GHZ state\n", + "def ghz_circuit(n_qubits):\n", + " \"\"\"\n", + " function to return a GHZ circuit ansatz\n", + " input: number of qubits\n", + " \"\"\"\n", + "\n", + " # instantiate circuit object\n", + " circuit = Circuit()\n", + " \n", + " # add Hadamard gate on first qubit\n", + " circuit.h(0)\n", + "\n", + " # apply series of CNOT gates\n", + " for ii in range(0, n_qubits-1):\n", + " circuit.cnot(control=ii, target=ii+1)\n", + "\n", + " return circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# define circuit\n", + "n_qubits = 10\n", + "ghz = ghz_circuit(n_qubits)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4|5|6|7|8|9|\n", + " \n", + "q0 : -H-C-----------------\n", + " | \n", + "q1 : ---X-C---------------\n", + " | \n", + "q2 : -----X-C-------------\n", + " | \n", + "q3 : -------X-C-----------\n", + " | \n", + "q4 : ---------X-C---------\n", + " | \n", + "q5 : -----------X-C-------\n", + " | \n", + "q6 : -------------X-C-----\n", + " | \n", + "q7 : ---------------X-C---\n", + " | \n", + "q8 : -----------------X-C-\n", + " | \n", + "q9 : -------------------X-\n", + "\n", + "T : |0|1|2|3|4|5|6|7|8|9|\n" + ] + } + ], + "source": [ + "# print circuit\n", + "print(ghz)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Local Simulator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, the circuit is run locally using the local simulator." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# set up device: Local Simulator\n", + "device = LocalSimulator()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'1111111111': 505, '0000000000': 495})\n" + ] + } + ], + "source": [ + "# run circuit\n", + "result = device.run(ghz, shots=1000).result()\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "# print counts\n", + "print(counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values())\n", + "plt.xlabel('bitstrings')\n", + "plt.ylabel('counts')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As opposed to quantum hardware where only measurement shots can be obtained, with a classical simulator you can access the full state vector, amplitudes and expectation values of certain observables by assigning the corresponding result types. To do so, append the result types to the circuit before submitting it to run. This can be very useful for debugging. \n", + "\n", + "The example code below outputs the state vector, the expectation value of $Z\\otimes Z\\otimes Z$, and the amplitude of the $|111\\rangle$ state of a three-qubit GHZ state. \n", + "\n", + "To reiterate, the following output is expected:\n", + "$$\\left|\\mathrm{GHZ}\\right> = \\frac{1}{\\sqrt{2}}\\left(\\left|0,0,0\\right> + \\left|1,1,1\\right>\\right) = \\left[\\frac{1}{\\sqrt{2}},0,0,0,0,0,0,\\frac{1}{\\sqrt{2}}\\right],$$\n", + "\n", + "for which $\\left=0$ and $\\left<111|\\mathrm{GHZ}\\right>=\\frac{1}{\\sqrt{2}}$." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2| Result Types |\n", + " \n", + "q0 : -H-C---Expectation(Z@Z@Z)-\n", + " | | \n", + "q1 : ---X-C-Expectation(Z@Z@Z)-\n", + " | | \n", + "q2 : -----X-Expectation(Z@Z@Z)-\n", + "\n", + "T : |0|1|2| Result Types |\n", + "\n", + "Additional result types: StateVector, Amplitude(111)\n" + ] + } + ], + "source": [ + "# define circuit\n", + "n_qubits = 3\n", + "ghz = ghz_circuit(n_qubits) \n", + "\n", + "# add the state_vector ResultType\n", + "ghz.state_vector()\n", + "# add the Z \\otimes Z \\otimes Z expectation value\n", + "ghz.expectation(Observable.Z() @ Observable.Z() @ Observable.Z(), target=[0,1,2])\n", + "# add the amplitude for |111>\n", + "ghz.amplitude(state=[\"111\"])\n", + "# print circuit including requested result types\n", + "print(ghz)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final EXACT state vector:\n", + " [0.70710678+0.j 0. +0.j 0. +0.j 0. +0.j\n", + " 0. +0.j 0. +0.j 0. +0.j 0.70710678+0.j]\n", + "Expectation value : 0.0\n", + "Amplitude <111|Final state>: {'111': (0.7071067811865475+0j)}\n" + ] + } + ], + "source": [ + "# run the circuit and output the results\n", + "task = device.run(ghz, shots=0)\n", + "result = task.result()\n", + "\n", + "# print results\n", + "print(\"Final EXACT state vector:\\n\", result.values[0])\n", + "print(\"Expectation value :\", np.round(result.values[1], 5))\n", + "print(\"Amplitude <111|Final state>:\", result.values[2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Clearly the expected results with perfect correlations between the three qubits making up the GHZ state are obtained.\n", + "\n", + "Note that you can only request state vector and amplitude when shots = 0 for a classical simulator. When shots = 0 for a simulator, you get the exact values of probability, expectation values, and variance, as derived from the full wave function. When shots > 0, you cannot access the full state vector, but you can get approximate expectation values as taken from measurement samples. Note that Amazon Braket also supports probability, sample, expectation, and variance as result types for QPU devices." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The On-Demand Simulators" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apart from the local simulator, you can also run your circuit on an on-demand simulator. This approach adds some latency overhead, but is beneficial for larger circuits by leveraging the optimized cloud hardware infrastructure. Moreover, all your results will be stored reliably in S3.\n", + "\n", + "Amazon Braket provides three on-demand simulators:\n", + "* SV1\n", + "\n", + " State vector simulator supports simulations of circuits with up to 34 qubits, calculates and keeps track of the full state vector evolution.\n", + "* TN1\n", + "\n", + " Tensor-network simulator represents each gate in a circuit as a tensor. TN1 can simulate a larger number of qubits for circuits with local gates or other special structure as compared with SV1 and DM1, but typically is slower for circuits with long-range or all-to-all gate structure.\n", + "* DM1\n", + "\n", + " Density matrix simulator stores the full density matrix of the system and sequentially applies gates and noise operations of the circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# set up the on-demand simulator SV1\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'111111111111111': 506, '000000000000000': 494})\n", + "Counts for all-zero bitstring: 494\n", + "Counts for all-one bitstring: 506\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# define a 15-qubit GHZ circuit\n", + "n_qubits = 15\n", + "ghz = ghz_circuit(n_qubits)\n", + "\n", + "# run GHZ circuit on SV1\n", + "result = device.run(ghz, shots=1000).result()\n", + "counts = result.measurement_counts\n", + "print(counts)\n", + "\n", + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values())\n", + "plt.xlabel('bitstrings')\n", + "plt.ylabel('counts')\n", + "\n", + "# print counts of all-zero-string\n", + "print('Counts for all-zero bitstring:', counts['0'*n_qubits])\n", + "# print counts of all-one-string\n", + "print('Counts for all-one bitstring:', counts['1'*n_qubits])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following example demonstrates that TN1 can easily simulate GHZ circuits with up to 50 qubits due to the sparse, nearest neighbor gate structure." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# set up the on-demand simulator TN1\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/tn1\")" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'00000000000000000000000000000000000000000000000000': 510, '11111111111111111111111111111111111111111111111111': 490})\n", + "Counts for all-zero bitstring: 510\n", + "Counts for all-one bitstring: 490\n" + ] + } + ], + "source": [ + "# define a larger GHZ circuit\n", + "n_qubits = 50\n", + "ghz = ghz_circuit(n_qubits)\n", + "\n", + "# run the same circuit on TN1\n", + "result = device.run(ghz, shots=1000).result()\n", + "counts = result.measurement_counts\n", + "print(counts)\n", + "\n", + "# print counts of all-zero-string\n", + "print('Counts for all-zero bitstring:', counts['0'*n_qubits])\n", + "# print counts of all-one-string\n", + "print('Counts for all-one bitstring:', counts['1'*n_qubits])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__NOTE__: Use unique task ID to look up task details in AWS console." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of qubits: 50\n" + ] + } + ], + "source": [ + "# print unique TASK ID (task = execution of individual circuit)\n", + "task_id = result.task_metadata.id\n", + "# recover other metadata information such as number of qubits\n", + "n = result.task_metadata.deviceParameters.paradigmParameters.qubitCount\n", + "# print('Task ID:', task_id)\n", + "print('Number of qubits:', n)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 1000, 'tasks': {'COMPLETED': 1}, 'execution_duration': datetime.timedelta(microseconds=37000), 'billed_execution_duration': datetime.timedelta(seconds=3)}, 'arn:aws:braket:::device/quantum-simulator/amazon/tn1': {'shots': 1000, 'tasks': {'COMPLETED': 1}, 'execution_duration': datetime.timedelta(seconds=5, microseconds=317000), 'billed_execution_duration': datetime.timedelta(seconds=5, microseconds=317000)}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.03 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.15" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/0_Getting_Started/1_Running_quantum_circuits_on_simulators/circuit.png 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\\left|\\mathrm{Bell}\\right> = \\frac{1}{\\sqrt{2}}\\left(\\left|0,0\\right> + \\left|1,1\\right>\\right).$$" + ] + }, + { + "attachments": { + "image-2.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To this end, we build and run the following circuit using a single-qubit Hadamard gate (denoted as ```H```) acting on the first qubit followed by a two-qubit ```CNOT``` gate: \n", + "

    \n", + "\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setup Circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "# define circuit\n", + "bell = Circuit().h(0).cnot(0, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|\n", + " \n", + "q0 : -H-C-\n", + " | \n", + "q1 : ---X-\n", + "\n", + "T : |0|1|\n" + ] + } + ], + "source": [ + "# print circuit\n", + "print(bell)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "### Local Simulator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we run our circuit locally, using an exact state-vector simulator. This local simulator is the preferred choice for fast experiments with low to intermediate qubit numbers ($N<20-25$) and essentially unlimited circuit depth. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "# set up device: Local Simulator\n", + "device = LocalSimulator()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'11': 506, '00': 494})\n" + ] + } + ], + "source": [ + "# run circuit (execute single TASK)\n", + "result = device.run(bell, shots=1000).result()\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "# print counts\n", + "print(counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values())\n", + "plt.xlabel('bitstrings')\n", + "plt.ylabel('counts')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "### Quantum Hardware: Rigetti" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we submit our circuit to the superconducting quantum chip provided by Rigetti. Depending on our position in the queue, we may have to wait for some time till our circuit is actually run. However, thanks to asynchronous execution, we can always come back and recover the results by providing the unique ID associated with every task. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: CREATED\n" + ] + } + ], + "source": [ + "# set up device\n", + "rigetti = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "\n", + "# create a clean circuit with no result type attached.(This is because some result types are only supported when shots=0)\n", + "bell = Circuit().h(0).cnot(0, 1) \n", + "\n", + "# add the Z \\otimes Z expectation value\n", + "bell.expectation(Observable.Z() @ Observable.Z(), target=[0,1])\n", + "\n", + "# run circuit \n", + "rigetti_task = rigetti.run(bell, shots=1000)\n", + "\n", + "# get id and status of submitted task\n", + "rigetti_task_id = rigetti_task.id\n", + "rigetti_status = rigetti_task.state()\n", + "# print('ID of task:', rigetti_task_id)\n", + "print('Status of task:', rigetti_status)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "The task is submitted and we can regularly (or irregularly) check the status of this task by executing the following cell. You may easily build logic around this query to wait for this task to complete before your code proceeds. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: COMPLETED\n" + ] + } + ], + "source": [ + "# print status\n", + "status = rigetti_task.state()\n", + "print('Status of (reconstructed) task:', status)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "### Quantum Hardware: IonQ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we submit our example Bell state circuit to IonQ. We set the device as AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\"). This task may not readily be executed but enter a queue for this specific machine. While we can interrupt our kernel (and work on something else), we can always recover our results using the unique ID of this task." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: CREATED\n" + ] + } + ], + "source": [ + "# set up device\n", + "ionq = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")\n", + "\n", + "# run circuit\n", + "ionq_task = ionq.run(bell, shots=1000)\n", + "\n", + "# get id and status of submitted task\n", + "ionq_task_id = ionq_task.id\n", + "ionq_status = ionq_task.state()\n", + "# print('ID of task:', ionq_task_id)\n", + "print('Status of task:', ionq_status)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: COMPLETED\n" + ] + } + ], + "source": [ + "# print status\n", + "status = ionq_task.state()\n", + "print('Status of (reconstructed) task:', status)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Quantum Hardware: Oxford Quantum Circuits" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we submit our circuit to the superconducting quantum computer provided by Oxford Quantum Circuits (OQC). The task runs asynchronously. We can retrieve the result when the task is completed." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: COMPLETED\n" + ] + } + ], + "source": [ + "# set up device\n", + "oqc = AwsDevice(\"arn:aws:braket:eu-west-2::device/qpu/oqc/Lucy\")\n", + "\n", + "# run circuit\n", + "oqc_task = oqc.run(bell, shots=1000)\n", + "\n", + "# get id and status of submitted task\n", + "oqc_task_id = oqc_task.id\n", + "oqc_status = oqc_task.state()\n", + "# print('ID of task:', oqc_task_id)\n", + "print('Status of task:', oqc_status)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "### Task Recovery" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By simply grabbing the unique task ID associated with the quantum tasks we have submitted above, we can recover this task at any point in time and (once the status is completed) visualize and analyze the corresponding results. Note that apart from other metadata, you can retrieve the compiled circuit that was actually run on the Rigetti device. More information about the compiling process can be found [here](https://pyquil-docs.rigetti.com/en/v2.22.0/compiler.html#partial). " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: COMPLETED\n", + "\n", + "\n", + "1000 shots taken on machine arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3.\n", + "\n", + "The compiled circuit is:\n", + " DECLARE ro BIT[2]\n", + "PRAGMA INITIAL_REWIRING \"PARTIAL\"\n", + "RESET\n", + "RZ(pi) 12\n", + "RZ(-pi/2) 13\n", + "RX(-pi/2) 13\n", + "XY(pi) 13 12\n", + "RZ(pi/2) 13\n", + "RX(pi/2) 13\n", + "RZ(-pi/2) 13\n", + "XY(pi) 13 12\n", + "RX(-pi/2) 12\n", + "MEASURE 12 ro[1]\n", + "MEASURE 13 ro[0]\n", + "\n", + "Measurement counts: Counter({'11': 458, '00': 421, '10': 81, '01': 40})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# recover task\n", + "task_load = AwsQuantumTask(arn=rigetti_task_id)\n", + "\n", + "# print status\n", + "status = task_load.state()\n", + "print('Status of (reconstructed) task:', status)\n", + "print('\\n')\n", + "# wait for job to complete\n", + "# terminal_states = ['COMPLETED', 'FAILED', 'CANCELLED']\n", + "if status == 'COMPLETED':\n", + " # get results\n", + " rigetti_results = task_load.result()\n", + " # print(rigetti_results)\n", + " \n", + " # get all metadata of submitted task\n", + " metadata = task_load.metadata()\n", + " # example for metadata\n", + " shots = metadata['shots']\n", + " machine = metadata['deviceArn']\n", + " # print example metadata\n", + " print(\"{} shots taken on machine {}.\\n\".format(shots, machine))\n", + " \n", + " # get the compiled circuit\n", + " print(\"The compiled circuit is:\\n\", rigetti_results.additional_metadata.rigettiMetadata.compiledProgram)\n", + " \n", + " # get measurement counts\n", + " rigetti_counts = rigetti_results.measurement_counts\n", + " print('Measurement counts:', rigetti_counts)\n", + "\n", + " # plot results: see effects of noise\n", + " plt.bar(rigetti_counts.keys(), rigetti_counts.values())\n", + " plt.xlabel('bitstrings')\n", + " plt.ylabel('counts')\n", + " plt.tight_layout()\n", + " plt.savefig('rigetti.png', dpi=700)\n", + " \n", + "elif status in ['FAILED', 'CANCELLED']:\n", + " # print terminal message \n", + " print('Your task is in terminal status, but has not completed.')\n", + "\n", + "else:\n", + " # print current status\n", + " print('Sorry, your task is still being processed and has not been finalized yet.')" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: COMPLETED\n", + "1000 shots taken on machine arn:aws:braket:us-east-1::device/qpu/ionq/Harmony.\n", + "Measurement counts: Counter({'11': 501, '00': 456, '01': 25, '10': 18})\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# recover task\n", + "task_load = AwsQuantumTask(arn=ionq_task_id)\n", + "\n", + "# print status\n", + "status = task_load.state()\n", + "print('Status of (reconstructed) task:', status)\n", + "\n", + "# wait for job to complete\n", + "# terminal_states = ['COMPLETED', 'FAILED', 'CANCELLED']\n", + "if status == 'COMPLETED':\n", + " # get results\n", + " results = task_load.result()\n", + " # print(rigetti_results)\n", + " \n", + " # get all metadata of submitted task\n", + " metadata = task_load.metadata()\n", + " # example for metadata\n", + " shots = metadata['shots']\n", + " machine = metadata['deviceArn']\n", + " # print example metadata\n", + " print(\"{} shots taken on machine {}.\".format(shots, machine))\n", + " \n", + " # get measurement counts\n", + " counts = results.measurement_counts\n", + " print('Measurement counts:', counts)\n", + "\n", + " # plot results: see effects of noise\n", + " plt.bar(counts.keys(), counts.values())\n", + " plt.xlabel('bitstrings')\n", + " plt.ylabel('counts')\n", + " plt.tight_layout()\n", + " plt.savefig('bell_ionq.png', dpi=700)\n", + " \n", + "elif status in ['FAILED', 'CANCELLED']:\n", + " # print terminal message \n", + " print('Your task is in terminal status, but has not completed.')\n", + "\n", + "else:\n", + " # print current status\n", + " print('Sorry, your task is still being processed and has not been finalized yet.')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "We have successfully recovered the results associated with the tasks that were queued up for the quantum hardware providers. Because of noise (decoherence) and other imperfections we cannot fully recover the exact results we have seen when using the classical simulator. To deal with that, in the fullness of time we will be able to use error correction techniques. As long as error correction is not available, it is important to benchmark our quantum results using classical simulators, whenever possible. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "# APPENDIX" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "# set up device\n", + "rigetti = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "\n", + "# run circuit\n", + "task = rigetti.run(bell, shots=1000)\n", + "print('Information on task:\\n', task)\n", + "print('==================================' * 2)\n", + "\n", + "# get status of submitted task\n", + "status = task.state()\n", + "\n", + "# wait for job to complete\n", + "terminal_states = ['COMPLETED', 'FAILED', 'CANCELLED']\n", + "while status not in terminal_states:\n", + " status = task.state()\n", + " print('Status:', status)\n", + " # time.sleep(60)\n", + "\n", + "print('Status:', status)\n", + "\n", + "# get results\n", + "rigetti_results = task.result()\n", + "print(rigetti_results)\n", + "\n", + "# get measurement counts\n", + "rigetti_counts = rigetti_results.measurement_counts\n", + "print(rigetti_counts)\n", + "\n", + "# plot results: see effects of noise\n", + "plt.bar(rigetti_counts.keys(), rigetti_counts.values())\n", + "plt.xlabel('bitstrings')\n", + "plt.ylabel('counts')\n", + "plt.tight_layout()\n", + "plt.savefig('rigetti2.png', dpi=700)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 2000, 'tasks': {'COMPLETED': 2}}, 'arn:aws:braket:us-east-1::device/qpu/ionq/Harmony': {'shots': 1000, 'tasks': {'QUEUED': 1}}, 'arn:aws:braket:eu-west-2::device/qpu/oqc/Lucy': {'shots': 1000, 'tasks': {'CREATED': 1}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 12.25 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.10 ('venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} \ No newline at end of file diff --git a/modules/0_Getting_Started/2_Running_quantum_circuits_on_QPU_devices/bell_circuit.png 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Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this tutorial we discuss in detail the anatomy of quantum circuits in Amazon Braket's SDK. Specifically, we learn how to build (parametrized) circuits and display them graphically, how to append circuits to each other, and discuss the associated circuit depth and circuit size. Finally we show how to execute our circuit on a device of our choice (defining a quantum task). We then learn how to efficiently track, log, recover or cancel such a _quantum task_. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## IMPORT STATEMENTS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we import some modules we will need." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "import asyncio\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "# magic word for producing visualizations in notebook\n", + "%matplotlib inline\n", + "import string\n", + "from datetime import datetime\n", + "import logging\n", + "\n", + "# AWS imports: Import Braket SDK modules\n", + "from braket.circuits import Circuit, Gate, Instruction, circuit, Observable, FreeParameter\n", + "from braket.circuits.serialization import IRType\n", + "from braket.aws import AwsDevice, AwsQuantumTask\n", + "from braket.devices import LocalSimulator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## CIRCUIT DEFINITION" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us get started a sample circuit for four qubits (labelled q0, q1, q2 and q3) consisting of standard single-qubit ```Hadamard``` gates and two-qubit ```CNOT``` gates; for a full list of available gates see below. We can then visualize our circuit by simply calling the ```print``` function. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0| 1 |\n", + " \n", + "q0 : -H-C---\n", + " | \n", + "q1 : -H-|-C-\n", + " | | \n", + "q2 : -H-X-|-\n", + " | \n", + "q3 : -H---X-\n", + "\n", + "T : |0| 1 |\n" + ] + } + ], + "source": [ + "# define circuit with 4 qubits\n", + "my_circuit = Circuit().h(range(4)).cnot(control=0, target=2).cnot(control=1, target=3)\n", + "print(my_circuit)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, time is sliced up into moments. The circuit above consists of just two moments. First, we apply a ```Hadamard``` gate to every qubit in moment 0 and then we apply two ```CNOT``` gates. Since the latter can be run in parallel as they involve different sets of qubits, they only use up one moment of time. For better readability they are displayed next to each other with some small offset. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MomentsKey(time=0, qubits=QubitSet([Qubit(0)]), moment_type=, noise_index=0)\n", + "MomentsKey(time=0, qubits=QubitSet([Qubit(1)]), moment_type=, noise_index=0)\n", + "MomentsKey(time=0, qubits=QubitSet([Qubit(2)]), moment_type=, noise_index=0)\n", + "MomentsKey(time=0, qubits=QubitSet([Qubit(3)]), moment_type=, noise_index=0)\n", + "MomentsKey(time=1, qubits=QubitSet([Qubit(0), Qubit(2)]), moment_type=, noise_index=0)\n", + "MomentsKey(time=1, qubits=QubitSet([Qubit(1), Qubit(3)]), moment_type=, noise_index=0)\n" + ] + } + ], + "source": [ + "# show moments of our quantum circuit\n", + "my_moments = my_circuit.moments\n", + "for moment in my_moments:\n", + " print(moment)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)]))\n", + "Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(1)]))\n", + "Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(2)]))\n", + "Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(3)]))\n", + "Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(2)]))\n", + "Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(1), Qubit(3)]))\n" + ] + } + ], + "source": [ + "# list all instructions/gates making up our circuit\n", + "my_instructions = my_circuit.instructions\n", + "for instruction in my_instructions:\n", + " print(instruction)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, let us build a parametrized circuit where we have to supply numerical parameter values to fully define the circuit, as is the case for example for single-qubit rotations (as described [here](https://github.com/aws/amazon-braket-sdk-python/blob/main/src/braket/circuits/gates.py#L578)) and the two-qubit ```cnot``` as described in the source code [here](https://github.com/aws/amazon-braket-sdk-python/blob/main/src/braket/circuits/gates.py#L701). The specific parameter values are shown in circuit diagram. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -Rx(0.15)-C-----\n", + " | \n", + "q1 : -Ry(0.20)-|-C-X-\n", + " | | \n", + "q2 : -Rz(0.25)-X-|---\n", + " | \n", + "q3 : -H----------X-X-\n", + "\n", + "T : | 0 | 1 |2|\n" + ] + } + ], + "source": [ + "# define circuit with some parametrized gates \n", + "my_circuit = Circuit().rx(0, 0.15).ry(1, 0.2).rz(2, 0.25).h(3).cnot(control=0, target=2).cnot(1, 3).x([1,3])\n", + "print(my_circuit)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also create a `Circuit` with gates which depend on a `FreeParameter`, the value of which can be set later, either by fixing it in the circuit itself, or when the circuit is run on a device." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -Rx(alpha)-C-----\n", + " | \n", + "q1 : -Ry(beta)--|-C-X-\n", + " | | \n", + "q2 : -Rz(gamma)-X-|---\n", + " | \n", + "q3 : -H-----------X-X-\n", + "\n", + "T : | 0 | 1 |2|\n", + "\n", + "Unassigned parameters: [alpha, beta, gamma].\n" + ] + } + ], + "source": [ + "# define circuit with some parametrized gates and free parameters\n", + "alpha = FreeParameter('alpha')\n", + "beta = FreeParameter('beta')\n", + "gamma = FreeParameter('gamma')\n", + "my_circuit = Circuit().rx(0, alpha).ry(1, beta).rz(2, gamma).h(3).cnot(control=0, target=2).cnot(1, 3).x([1,3])\n", + "print(my_circuit)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__GATE SET__: Below we list all gates currently available in our SDK. Moreover, we can build custom gates as shown below for a general single-qubit rotation. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['CCNot', 'CNot', 'CPhaseShift', 'CPhaseShift00', 'CPhaseShift01', 'CPhaseShift10', 'CSwap', 'CV', 'CY', 'CZ', 'ECR', 'GPi', 'GPi2', 'H', 'I', 'ISwap', 'MS', 'PSwap', 'PhaseShift', 'PulseGate', 'Rx', 'Ry', 'Rz', 'S', 'Si', 'Swap', 'T', 'Ti', 'Unitary', 'V', 'Vi', 'X', 'XX', 'XY', 'Y', 'YY', 'Z', 'ZZ']\n" + ] + } + ], + "source": [ + "# print all available gates currently available within SDK\n", + "gate_set = [attr for attr in dir(Gate) if attr[0] in string.ascii_uppercase]\n", + "print(gate_set)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# helper function to build custom gate \n", + "def u3(alpha, theta, phi):\n", + " \"\"\"\n", + " function to return matrix for general single qubit rotation\n", + " rotation is given by exp(-i sigma*n/2*alpha) where alpha is rotation angle\n", + " and n defines rotation axis as n=(sin(theta)cos(phi), sin(theta)sin(phi), cos(theta))\n", + " sigma is vector of Pauli matrices\n", + " \"\"\"\n", + " u11 = np.cos(alpha/2)-1j*np.sin(alpha/2)*np.cos(theta)\n", + " u12 = -1j*(np.exp(-1j*phi))*np.sin(theta)*np.sin(alpha/2)\n", + " u21 = -1j*(np.exp(1j*phi))*np.sin(theta)*np.sin(alpha/2)\n", + " u22 = np.cos(alpha/2)+1j*np.sin(alpha/2)*np.cos(theta)\n", + " \n", + " return np.array([[u11, u12], [u21, u22]])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|\n", + " \n", + "q0 : -U-C-\n", + " | \n", + "q1 : -H-X-\n", + "\n", + "T : |0|1|\n" + ] + } + ], + "source": [ + "# define and print custom unitary\n", + "my_u3 = u3(np.pi/2, 0, 0)\n", + "# print(my_u3)\n", + "# define example circuit applying custom U to the first qubit\n", + "circ = Circuit().unitary(matrix=my_u3, targets=[0]).h(1).cnot(control=0, target=1)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, in the circuit diagram our custom unitary is depicted with the general symbol ```U```. \n", + "In addition, we can use Braket's `circuit.subroutine` functionality, which allows us to use custom-built gates as any other built-in gates. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# helper function to build custom gate\n", + "@circuit.subroutine(register=True)\n", + "def u3(target, angles):\n", + " \"\"\"\n", + " Function to return the matrix for a general single qubit rotation,\n", + " given by exp(-i sigma*n/2*alpha), where alpha is the rotation angle,\n", + " n defines the rotation axis via n=(sin(theta)cos(phi), sin(theta)sin(phi), cos(theta)),\n", + " and sigma is the vector of Pauli matrices\n", + " \"\"\"\n", + " \n", + " # get angles\n", + " alpha = angles[0]\n", + " theta = angles[1]\n", + " phi = angles[2]\n", + " \n", + " # set 2x2 matrix entries\n", + " u11 = np.cos(alpha/2)-1j*np.sin(alpha/2)*np.cos(theta)\n", + " u12 = -1j*(np.exp(-1j*phi))*np.sin(theta)*np.sin(alpha/2)\n", + " u21 = -1j*(np.exp(1j*phi))*np.sin(theta)*np.sin(alpha/2)\n", + " u22 = np.cos(alpha/2)+1j*np.sin(alpha/2)*np.cos(theta)\n", + " \n", + " # define unitary as numpy matrix\n", + " u = np.array([[u11, u12], [u21, u22]])\n", + " # print('Unitary:', u)\n", + " \n", + " # define custom Braket gate\n", + " circ = Circuit()\n", + " circ.unitary(matrix=u, targets=target)\n", + " \n", + " return circ" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|\n", + " \n", + "q0 : -U-C-\n", + " | \n", + "q1 : ---X-\n", + "\n", + "T : |0|1|\n" + ] + } + ], + "source": [ + "# define example circuit applying custom single-qubit gate U to the first qubit\n", + "angles = [np.pi/2, np.pi/2, np.pi/2]\n", + "angles = [np.pi/4, 0, 0]\n", + "\n", + "# build circuit using custom u3 gate\n", + "circ2 = Circuit().u3([0], angles).cnot(control=0, target=1)\n", + "print(circ2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## CIRCUIT DEPTH AND CIRCUIT SIZE" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can get the circuit depth (the number of moments defining our circuit) with ```circuit.depth``` as shown below. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -Rx(0.15)-C---X-\n", + " | \n", + "q1 : -Ry(0.20)-|-C---\n", + " | | \n", + "q2 : -Rz(0.25)-X-|---\n", + " | \n", + "q3 : -H----------X---\n", + "\n", + "T : | 0 | 1 |2|\n", + "\n", + "Total circuit depth: 3\n" + ] + } + ], + "source": [ + "# define circuit with parametrized gates \n", + "my_circuit = Circuit().rx(0, 0.15).ry(1, 0.2).rz(2, 0.25).h(3).cnot(control=0, target=2).cnot(1, 3).x(0)\n", + "circuit_depth = my_circuit.depth\n", + "print(my_circuit)\n", + "print()\n", + "print('Total circuit depth:', circuit_depth)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The total circuit depth of the circuit above is three (moments 0, 1, 2). It is three because we have added a single qubit ```X``` gate applied to qubit 0 in the final layer. However, note that gates are applied as early as possible in time, provided that this is not in conflict with any other gate that has to be applied before. See below an example where we add one qubit to which we only apply one single qubit ```X``` gate. This circuit is shallower as its circuit depth is only two. The ```X``` gate is applied to qubit 4 as early as possible even though we have applied the corresponding command at the end of our circuit definition. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |\n", + " \n", + "q0 : -Rx(0.15)-C---\n", + " | \n", + "q1 : -Ry(0.20)-|-C-\n", + " | | \n", + "q2 : -Rz(0.25)-X-|-\n", + " | \n", + "q3 : -H----------X-\n", + " \n", + "q4 : -X------------\n", + "\n", + "T : | 0 | 1 |\n", + "\n", + "Total circuit depth: 2\n", + "Number of qubits: 5\n", + "Circuit size: 10\n" + ] + } + ], + "source": [ + "# define circuit with parameterized gates \n", + "my_circuit = Circuit().rx(0, 0.15).ry(1, 0.2).rz(2, 0.25).h(3).cnot(control=0, target=2).cnot(1, 3).x(4)\n", + "# get circuit depth\n", + "circuit_depth = my_circuit.depth\n", + "# get qubit number\n", + "qubit_count = my_circuit.qubit_count\n", + "# get approx. estimate of circuit size\n", + "circuit_size = circuit_depth*qubit_count\n", + "# print circuit\n", + "print(my_circuit)\n", + "print()\n", + "# print characteristics of our circuit\n", + "print('Total circuit depth:', circuit_depth)\n", + "print('Number of qubits:', qubit_count)\n", + "print('Circuit size:', circuit_size)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the example above we have also introduced the concept of __circuit size__. Intuitively, the circuit size is a metric that reflects the complexity of our circuit. The circuit size accounts for both quantity (the number of qubits) and quality (as captured by the depth of the circuit); here we have used a very simple definition multiplying the qubit number with the circuit depth (that is the area of our diagram). In practice, in the absence of quantum error correction, on real quantum machines the depth is limited by noise so we can only faithfully run circuits whose depth is within the quality bounds of our machine. Simply speaking, this means: The larger the circuit size, the harder it is to simulate on a classical device and the more powerful the quantum machine is that is able to faithfully execute this circuit. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## APPENDING CIRCUITS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can extend existing circuits by adding instructions or just appending circuits to each other, as shown below. In the most simple and straightforward fashion we can just append gates to existing circuits (for example, ```my_circuit.y(4)```). " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |\n", + " \n", + "q0 : -Rx(0.15)-C---\n", + " | \n", + "q1 : -Ry(0.20)-|-C-\n", + " | | \n", + "q2 : -Rz(0.25)-X-|-\n", + " | \n", + "q3 : -H----------X-\n", + " \n", + "q4 : -X--------Y---\n", + "\n", + "T : | 0 | 1 |\n", + "\n", + "Total circuit depth: 2\n", + "Number of qubits: 5\n", + "Circuit size: 10\n" + ] + } + ], + "source": [ + "# simple circuit extension by appending gates (here Y on qubit 4)\n", + "my_circuit = my_circuit.y(4)\n", + "# get circuit depth\n", + "circuit_depth = my_circuit.depth\n", + "# get qubit number\n", + "qubit_count = my_circuit.qubit_count\n", + "# get circuit size\n", + "circuit_size = circuit_depth*qubit_count\n", + "# print circuit\n", + "print(my_circuit)\n", + "print()\n", + "print('Total circuit depth:', circuit_depth)\n", + "print('Number of qubits:', qubit_count)\n", + "print('Circuit size:', circuit_size)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, we can define a gate as an ```Instruction``` and use the ```add_instruction(...)``` method to add this gate to an existing circuit object." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -Rx(0.15)-C---C-\n", + " | | \n", + "q1 : -Ry(0.20)-|-C-X-\n", + " | | \n", + "q2 : -Rz(0.25)-X-|---\n", + " | \n", + "q3 : -H----------X---\n", + " \n", + "q4 : -X--------Y-----\n", + "\n", + "T : | 0 | 1 |2|\n", + "\n", + "Total circuit depth: 3\n", + "Number of qubits: 5\n", + "Circuit size: 15\n" + ] + } + ], + "source": [ + "# add instruction to circuit\n", + "gate_instr = Instruction(Gate.CNot(), [0, 1])\n", + "my_circuit = my_circuit.add_instruction(gate_instr)\n", + "# get circuit depth\n", + "circuit_depth = my_circuit.depth\n", + "# get qubit number\n", + "qubit_count = my_circuit.qubit_count\n", + "# get circuit size\n", + "circuit_size = circuit_depth*qubit_count\n", + "# print circuit\n", + "print(my_circuit)\n", + "print()\n", + "print('Total circuit depth:', circuit_depth)\n", + "print('Number of qubits:', qubit_count)\n", + "print('Circuit size:', circuit_size)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can append entire circuits to each other with ```add_circuit()```. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | 3 |\n", + " \n", + "q0 : -Rx(0.15)-C---C--------Rz(0.10)-\n", + " | | \n", + "q1 : -Ry(0.20)-|-C-X--------Rz(0.20)-\n", + " | | \n", + "q2 : -Rz(0.25)-X-|-------------------\n", + " | \n", + "q3 : -H----------X-Rz(0.30)----------\n", + " \n", + "q4 : -X--------Y---Rz(0.40)----------\n", + "\n", + "T : | 0 | 1 | 2 | 3 |\n", + "\n", + "Total circuit depth: 4\n", + "Number of qubits: 5\n", + "Circuit size: 20\n" + ] + } + ], + "source": [ + "# append two circuits with add_circuit() functionality\n", + "my_circuit2 = Circuit().rz(0, 0.1).rz(1, 0.2).rz(3, 0.3).rz(4, 0.4)\n", + "my_circuit.add_circuit(my_circuit2)\n", + "\n", + "# get circuit depth\n", + "circuit_depth = my_circuit.depth\n", + "# get qubit number\n", + "qubit_count = my_circuit.qubit_count\n", + "# get circuit size\n", + "circuit_size = circuit_depth*qubit_count\n", + "# print circuit\n", + "print(my_circuit)\n", + "print()\n", + "# print characteristics of our circuit\n", + "print('Total circuit depth:', circuit_depth)\n", + "print('Number of qubits:', qubit_count)\n", + "print('Circuit size:', circuit_size)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, note that the single qubit rotations we have appended to our circuit are applied as early as possible. This helps keeping the circuit as short as possible, as required in the presence of decoherence. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## CIRCUIT EXECUTION AND TASK TRACKING" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, let us run our circuit on a device of our choice. We do so by defining a classical ```device``` object below and calling the method ```device.run(my_circuit)```. Additional _task creation_ arguments can be provided to the ```run()``` method of the device object; in particular the optional “shots” argument refers to the number of desired measurement shots (default = 1000).\n", + "\n", + "The command ```device.run(...)``` defines a task (with a unique task ID), the status of which can be queried and tracked with ```task.state()``` as shown below. Once the task completes (which may take some time, specifically for the QPU devices, depending on the length of the queue), one can retrieve the results from the S3 bucket as specified below; you can check for \"Task Status” under Tasks within your Braket console. Note that ```task = device.run()``` is an _asynchronous_ operation. This means you can keep working while the system in the background polls for the results. You can always check the task status with ```task.state()```. When you call ```task.result()```, this becomes a blocking call that will throw an error if within the timeout period you will not get a result. We show below how to set this timeout period. \n", + "\n", + "By calling ```result()``` on a task, you get the quantum task result by polling Amazon Braket to see if the task is completed. Once the task is completed, the result is retrieved from S3 and returned as a ```QuantumTaskResult```. As opposed to ```async_result()```, this method is a blocking thread call and synchronously returns a result." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "# Create the device. The experiment value must be unique among any devices in use at the tim\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n", + "\n", + "# set up the device to be the Rigetti quantum computer\n", + "# device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "\n", + "# set up the device to be the IonQ quantum computer\n", + "# device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")\n", + "\n", + "# set up the device to be the Oxford Quantum Circuits (OQC) quantum computer\n", + "# device = AwsDevice(\"arn:aws:braket:eu-west-2::device/qpu/oqc/Lucy\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can check out the set of gates this device supports as follows: " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum Gates supported by this device:\n", + " ['ccnot', 'cnot', 'cphaseshift', 'cphaseshift00', 'cphaseshift01', 'cphaseshift10', 'cswap', 'cy', 'cz', 'ecr', 'h', 'i', 'iswap', 'pswap', 'phaseshift', 'rx', 'ry', 'rz', 's', 'si', 'swap', 't', 'ti', 'unitary', 'v', 'vi', 'x', 'xx', 'xy', 'y', 'yy', 'z', 'zz']\n" + ] + } + ], + "source": [ + "# show the properties of the device\n", + "device_properties = device.properties\n", + "# show supportedQuantumOperations (supported gates for a device)\n", + "device_operations = device_properties.dict()['action']['braket.ir.jaqcd.program']['supportedOperations']\n", + "# Note: This field also exists for other devices like the QPUs\n", + "print('Quantum Gates supported by this device:\\n',device_operations)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__POLLING PARAMETERS__: With the ```run(...)``` method we can set two important parameters: \n", + "* ```poll_timeout_seconds``` is the number of seconds you want to wait and poll the task before it times out; the default value is 5 days (that is $\\sim 5*60*60*24$ seconds). \n", + "* ```poll_interval_seconds``` is the frequency how often the task is polled, e.g., how often you call the Braket API to get the status; the default value is 1 second. " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: CREATED\n", + "Status: CREATED\n", + "Status: CREATED\n", + "Status: QUEUED\n", + "Status: QUEUED\n", + "Status: QUEUED\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: COMPLETED\n", + "Counter({'00010': 503, '00000': 488, '11100': 5, '01010': 2, '01000': 2})\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# define task (asynchronous)\n", + "task = device.run(my_circuit, \n", + " poll_timeout_seconds = 100, \n", + " shots=1000)\n", + "\n", + "# get id and status of submitted task\n", + "task_id = task.id\n", + "status = task.state()\n", + "# print('ID of task:', task_id)\n", + "print('Status of task:', status)\n", + "\n", + "# wait for job to complete\n", + "while status != 'COMPLETED':\n", + " status = task.state()\n", + " print('Status:', status)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "\n", + "# print counts\n", + "print(counts)\n", + "\n", + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values());\n", + "plt.xlabel('bitstrings');\n", + "plt.ylabel('counts');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The on-demand simulators SV1 and DM1 also support running parametrized tasks. The value of any free parameters can be fixed when the circuit is run using the optional `inputs` argument to `run`. `inputs` should be a `dict` of `string`-`float` pairs." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -Rx(alpha)-C-----\n", + " | \n", + "q1 : -Ry(beta)--|-C-X-\n", + " | | \n", + "q2 : -Rz(gamma)-X-|---\n", + " | \n", + "q3 : -H-----------X-X-\n", + "\n", + "T : | 0 | 1 |2|\n", + "\n", + "Unassigned parameters: [alpha, beta, gamma].\n", + "Status of task: CREATED\n", + "Status: CREATED\n", + "Status: CREATED\n", + "Status: CREATED\n", + "Status: QUEUED\n", + "Status: QUEUED\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: COMPLETED\n", + "Counter({'0101': 501, '0100': 485, '0000': 7, '0001': 4, '1110': 2, '1111': 1})\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# define circuit with some parametrized gates and free parameters\n", + "alpha = FreeParameter('alpha')\n", + "beta = FreeParameter('beta')\n", + "gamma = FreeParameter('gamma')\n", + "my_circuit = Circuit().rx(0, alpha).ry(1, beta).rz(2, gamma).h(3).cnot(control=0, target=2).cnot(1, 3).x([1,3])\n", + "print(my_circuit)\n", + "# define task (asynchronous)\n", + "task = device.run(my_circuit, \n", + " poll_timeout_seconds = 100, \n", + " shots=1000, inputs={'alpha': 0.1, 'beta': 0.2, 'gamma': 0.3})\n", + "\n", + "# get id and status of submitted task\n", + "task_id = task.id\n", + "status = task.state()\n", + "# print('ID of task:', task_id)\n", + "print('Status of task:', status)\n", + "\n", + "# wait for job to complete\n", + "while status != 'COMPLETED':\n", + " status = task.state()\n", + " print('Status:', status)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "\n", + "# print counts\n", + "print(counts)\n", + "\n", + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values());\n", + "plt.xlabel('bitstrings');\n", + "plt.ylabel('counts');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__TASK METADATA__: You can access a range of metadata associated with your ```task``` object, as shown below. " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1000 shots taken on Thu, 10 Nov 2022 17:19:03 GMT.\n" + ] + } + ], + "source": [ + "# get all metadata of submitted task\n", + "metadata = task.metadata()\n", + "# example for metadata\n", + "shots = metadata['shots']\n", + "date = metadata['ResponseMetadata']['HTTPHeaders']['date']\n", + "# print example metadata\n", + "print(\"{} shots taken on {}.\".format(shots, date))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__TASK RECONSTRUCTION__: Imagine your kernel dies after you have submitted the task, or you simply close your notebook. As recovery method, here is how you can reconstruct the ```task``` object (given the corresponding unique arn). You can reconstruct the ```task``` object using `task = AwsQuantumTask(arn=...)`; then you can simply call `task.result()` to get the result from S3. " + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: COMPLETED\n" + ] + } + ], + "source": [ + "# restore task from unique arn\n", + "task_load = AwsQuantumTask(arn=task_id)\n", + "# print status\n", + "status = task_load.state()\n", + "print('Status of (reconstructed) task:', status)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'0101': 501, '0100': 485, '0000': 7, '0001': 4, '1110': 2, '1111': 1})\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# get results of task\n", + "result = task_load.result()\n", + "\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "\n", + "# print counts\n", + "print(counts)\n", + "\n", + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values(), color='g');\n", + "plt.xlabel('bitstrings');\n", + "plt.ylabel('counts');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__TASK CANCELLATION__: Finally, we can also cancel existing tasks by calling the ```cancel()``` method." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: CREATED\n", + "Status of task: CANCELLING\n" + ] + } + ], + "source": [ + "# define task\n", + "task = device.run(my_circuit, shots=1000, inputs={'alpha': 0.1, 'beta': 0.2, 'gamma': 0.3})\n", + "\n", + "# get id and status of submitted task\n", + "task_id = task.id\n", + "status = task.state()\n", + "# print('ID of task:', task_id)\n", + "print('Status of task:', status)\n", + "\n", + "# cancel task \n", + "task.cancel()\n", + "status = task.state()\n", + "print('Status of task:', status)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## DEMONSTRATION OF RESULT TYPES: Expectation Values and Observables " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far, we have only taken measurements in the computational basis. However, it is also possible to measure in other bases, as well as estimate important statistics like expectation value and variance. We do this by adding `ResultType`s to our circuit; in the following example, we will make measurements in the basis of the observable $X_{0}Y_{1}$ (this is the tensor product $X(0) \\otimes Y(1)$):" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | Result Types |\n", + " \n", + "q0 : -Rx(0.15)-C---Expectation(X@Y)-Variance(X@Y)-Sample(X@Y)-\n", + " | | | | \n", + "q1 : -Ry(0.20)-|-C-Expectation(X@Y)-Variance(X@Y)-Sample(X@Y)-\n", + " | | \n", + "q2 : -Rz(0.25)-X-|--------------------------------------------\n", + " | \n", + "q3 : -H----------X--------------------------------------------\n", + " \n", + "q4 : -X-------------------------------------------------------\n", + "\n", + "T : | 0 | 1 | Result Types |\n" + ] + } + ], + "source": [ + "# define example circuit\n", + "circ = Circuit().rx(0, 0.15).ry(1, 0.2).rz(2, 0.25).h(3).cnot(control=0, target=2).cnot(1, 3).x(4)\n", + "# add expectation value\n", + "obs = Observable.X() @ Observable.Y()\n", + "target_qubits = [0, 1]\n", + "circ.expectation(obs, target=target_qubits)\n", + "# add variance\n", + "circ.variance(obs, target=target_qubits) \n", + "# add samples\n", + "\n", + "circ.sample(obs, target=target_qubits)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "_Note_: `sample` is only valid when `shots>0`.\n", + "\n", + "As shown above, results types are part of the `print` information. We now run this circuit on the local simulator above and output these results. " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Expectation value for : 0.08\n", + "Variance for : 0.9936\n", + "Measurement samples for X0*Y1: [-1. 1. -1. 1. 1. 1. -1. -1. -1. 1. 1. 1. 1. -1. 1. 1. -1. -1.\n", + " -1. -1. -1. -1. 1. 1. 1. -1. -1. -1. 1. -1. 1. 1. -1. 1. -1. 1.\n", + " -1. 1. 1. -1. -1. -1. 1. 1. 1. -1. 1. 1. -1. 1. 1. -1. 1. 1.\n", + " 1. 1. -1. -1. 1. 1. 1. -1. 1. -1. 1. 1. 1. -1. -1. 1. -1. -1.\n", + " -1. -1. 1. 1. -1. -1. 1. 1. 1. -1. 1. -1. -1. -1. -1. 1. 1. -1.\n", + " 1. 1. -1. 1. -1. -1. 1. 1. 1. 1.]\n" + ] + } + ], + "source": [ + "# set up device\n", + "device = LocalSimulator()\n", + "# run the circuit and output the results specified above\n", + "task = device.run(circ, shots=100)\n", + "result = task.result()\n", + "print(\"Expectation value for :\", result.values[0])\n", + "print(\"Variance for :\", result.values[1])\n", + "print(\"Measurement samples for X0*Y1:\", result.values[2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can verify that we get the same estimate for the expectation value if we compute it by hand from the samples:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Expectation value from samples: 0.08\n" + ] + } + ], + "source": [ + "samples = result.values[2]\n", + "sum_of_samples = samples.sum()\n", + "total_counts = len(samples)\n", + "expect_from_samples = sum_of_samples/total_counts\n", + "print('Expectation value from samples:', expect_from_samples)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far, we have measured only one observable, namely $X_{0}Y_{1}$. However, it is possible to measure multiple observables at once, provided that any observables with overlapping qubits have the same factor acting on each qubit:\n", + "\n", + "
    \n", + "Note The following code requires amazon-braket-sdk>=1.5.0 and amazon-braket-default-simulator>=1.1.0\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Expectation value for : -0.022\n", + "Expectation value for : -0.668\n", + "Expectation value for :: -0.024\n" + ] + } + ], + "source": [ + "circ = Circuit().rx(0, 0.15).ry(1, 0.2).rz(2, 0.25).h(3).cnot(control=0, target=2).cnot(1, 3).x(4)\n", + "circ.expectation(Observable.X() @ Observable.Y(), target=[0, 1])\n", + "circ.expectation(Observable.Z() @ Observable.H(), target=[2, 4])\n", + "# Overlaps on qubits 1 and 4, but Y and H are the same factors that have been applied to each, respectively\n", + "circ.expectation(Observable.Y() @ Observable.X() @ Observable.H(), target=[1, 3, 4])\n", + "\n", + "# run circuit\n", + "task = device.run(circ, shots=1000)\n", + "result = task.result()\n", + "print(\"Expectation value for :\", result.values[0])\n", + "print(\"Expectation value for :\", result.values[1])\n", + "print(\"Expectation value for ::\", result.values[2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is possible because we only need to measure in at most one basis for each qubit. For instance in the example above, on qubit 1 we only measure in the Y basis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### RESULT TYPES FOR ```shots=0```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + "Note This section requires amazon-braket-sdk>=1.8.0 and amazon-braket-default-simulator>=1.3.0\n", + "
    \n", + "\n", + "In all examples discussed so far we have set the parameter `shots>0`, thereby mimicking the behavior of actual quantum hardware. However, on a classical simulator we do have access to the full state vector when `shots=0`. We will illustrate this functionality in more detail in this section. \n", + "\n", + "Note that the full state vector and amplitudes can only be requested when `shots=0` for a classical simulator. \n", + "When `shots=0` for a simulator, probability and expectation values are the exact values, as derived from the full wavefunction. \n", + "When `shots>0` we cannot access the full state vector, but we can still get approximate expectation values as taken from measurement samples. Note that probability, sample, expectation, and variance are also supported for QPU devices.\n", + "\n", + "In the following example we output the state vector, the exact expectation values of $Y_{1}X_{2}$ and $Z_{0}Z_{1}$, the amplitude of the state $|00000\\rangle$, and the marginal probability of qubit $3$. Notice in particular that the two observables share qubit $1$ but don't have the same factor acting on it; this is allowed because simulators can directly compute expectation values using the state vector, and don't have to measure in a common basis." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |2| Result Types |\n", + " \n", + "q0 : -Rx(alpha)-C----------------------Expectation(Z@Z)-\n", + " | | \n", + "q1 : -Ry(beta)--|-C-X-Expectation(Y@X)-Expectation(Z@Z)-\n", + " | | | \n", + "q2 : -Rz(gamma)-X-|---Expectation(Y@X)------------------\n", + " | \n", + "q3 : -H-----------X-X-Probability-----------------------\n", + "\n", + "T : | 0 | 1 |2| Result Types |\n", + "\n", + "Additional result types: StateVector, Amplitude(0000)\n", + "\n", + "Unassigned parameters: [alpha, beta, gamma].\n" + ] + } + ], + "source": [ + "# add result types\n", + "circ = my_circuit\n", + "# add the state_vector ResultType available for shots=0\n", + "circ.state_vector() \n", + "# add single qubit expectation value\n", + "obs1 = Observable.Y() @ Observable.X()\n", + "circ.expectation(obs1, target=[1, 2])\n", + "# add the two-qubit Z0*Z1 expectation value\n", + "obs2 = Observable.Z() @ Observable.Z()\n", + "circ.expectation(obs2, target=[0,1]) \n", + "# add the amplitude for |0...0>\n", + "bitstring = '0'*circ.qubit_count\n", + "circ.amplitude(state=[bitstring]) \n", + "# add marginal probability \n", + "circ.probability(target=[3])\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As shown above, results types are part of the `print` information. We now run this circuit on the local simulator above and output these results. " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final state vector:\n", + " [ 6.97129718e-02-0.01053609j 6.97129718e-02-0.01053609j\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j\n", + " 6.94804402e-01-0.10500941j 6.94804402e-01-0.10500941j\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j\n", + " -5.27243703e-04-0.00348856j -5.27243703e-04-0.00348856j\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j\n", + " -5.25485051e-03-0.0347692j -5.25485051e-03-0.0347692j ]\n", + "Expectation value 0.0\n", + "Expectation value : -0.9751703272018153\n", + "Amplitude <00000|Final state>: {'0000': (0.06971297180671754-0.010536085195500033j)}\n", + "Marginal probability for target qubit 3 in computational basis: [0.5 0.5]\n" + ] + } + ], + "source": [ + "# set up device\n", + "device = LocalSimulator()\n", + "# run the circuit and output the results specified above\n", + "task = device.run(circ, shots=0, inputs={'alpha': 0.1, 'beta': 0.2, 'gamma': 0.3})\n", + "result = task.result()\n", + "print(\"Final state vector:\\n\", result.values[0])\n", + "print(\"Expectation value \", result.values[1])\n", + "print(\"Expectation value :\", result.values[2])\n", + "print(\"Amplitude <00000|Final state>:\", result.values[3])\n", + "print(\"Marginal probability for target qubit 3 in computational basis:\", result.values[4])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ADVANCED LOGGING" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we provide an example for advanced logging. Here, we change the ```poll_timeout_seconds``` and ```poll_interval_seconds``` parameters, such that a task can be long-running and the task status will be continuously logged to a file. You can also transfer this code to a python script instead of a Jupyter notebook, and the script can run as a process in the background so that your laptop can go to sleep and the script will still run. These advanced logging techniques allow you to see the background polling and create a record for later debugging. " + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task info will be logged in: device_logs-20221110121905.txt\n" + ] + } + ], + "source": [ + "# set filename for logs\n", + "log_file = 'device_logs-'+datetime.strftime(datetime.now(), '%Y%m%d%H%M%S')+'.txt'\n", + "print('Task info will be logged in:', log_file)\n", + "\n", + "# create new logger object\n", + "logger = logging.getLogger(\"newLogger\") \n", + "# configure to log to file device_logs.txt in the appending mode\n", + "logger.addHandler(logging.FileHandler(filename=log_file, mode='a'))\n", + "# add to file all log messages with level DEBUG or above\n", + "logger.setLevel(logging.DEBUG) " + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 |\n", + " \n", + "q0 : -Rx(0.15)-C---\n", + " | \n", + "q1 : -Ry(0.20)-|-C-\n", + " | | \n", + "q2 : -Rz(0.25)-X-|-\n", + " | \n", + "q3 : -H----------X-\n", + " \n", + "q4 : -X------------\n", + "\n", + "T : | 0 | 1 |\n" + ] + } + ], + "source": [ + "# define circuit\n", + "circ_log = Circuit().rx(0, 0.15).ry(1, 0.2).rz(2, 0.25).h(3).cnot(control=0, target=2).cnot(1, 3).x(4)\n", + "print(circ_log)\n", + "# define device\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n", + "# define what info to log\n", + "logger.info(\n", + " device.run(circ_log, \n", + " poll_timeout_seconds=1200, poll_interval_seconds=0.25, logger=logger, shots=1000)\n", + " .result().measurement_counts\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task arn:aws:braket:us-west-2:746192259860:quantum-task/b03f8639-b1f3-458e-89e3-0fb47e292e14: start polling for completion\r\n", + "Task arn:aws:braket:us-west-2:746192259860:quantum-task/b03f8639-b1f3-458e-89e3-0fb47e292e14: task status CREATED\r\n", + "Task arn:aws:braket:us-west-2:746192259860:quantum-task/b03f8639-b1f3-458e-89e3-0fb47e292e14: task status QUEUED\r\n", + "Task arn:aws:braket:us-west-2:746192259860:quantum-task/b03f8639-b1f3-458e-89e3-0fb47e292e14: task status RUNNING\r\n", + "Task arn:aws:braket:us-west-2:746192259860:quantum-task/b03f8639-b1f3-458e-89e3-0fb47e292e14: task status RUNNING\r\n", + "Task arn:aws:braket:us-west-2:746192259860:quantum-task/b03f8639-b1f3-458e-89e3-0fb47e292e14: task status COMPLETED\r\n", + "Counter({'00001': 496, '00011': 495, '01001': 3, '10111': 3, '01011': 2, '10101': 1})\r\n" + ] + } + ], + "source": [ + "# print logs\n", + "! cat {log_file}" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# parse log file for arn\n", + "with open(log_file) as openfile:\n", + " for line in openfile:\n", + " for part in line.split():\n", + " if \"arn:\" in part:\n", + " arn = part\n", + " break\n", + "# remove final semicolon in logs\n", + "arn = arn[:-1]\n", + "# print(arn)\n", + "\n", + "# with this arn we can restore again task from unique arn\n", + "task_load = AwsQuantumTask(arn=arn)\n", + "\n", + "# get results of task\n", + "result = task_load.result()\n", + "\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "\n", + "# plot using Counter\n", + "plt.bar(counts.keys(), counts.values(), color='tab:orange');\n", + "plt.xlabel('bitstrings');\n", + "plt.ylabel('counts');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "--- \n", + "## APPENDIX" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### APPENDIX: SDK version" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Version: 1.33.2.dev0\r\n" + ] + } + ], + "source": [ + "# print version of SDK\n", + "! pip show amazon-braket-sdk | grep Version" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### APPENDIX: ADVANCED FUNCTIONALITY WITH ASYNCHRONOUS EXECUTION" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__ASYNCHRONOUS EXECUTION__: When replacing the ```result()``` call on the task object above with ```async_result()```, we can get the quantum task result asynchronously. Consecutive calls to this method return the result cached from the most recent request. See [here](https://github.com/aws/braket-python-sdk/blob/master/src/braket/aws/aws_quantum_task.py#L206) for source code implementation. \n", + "\n", + "While ```result()``` is a blocking call that waits for the result, ```async_result()``` is a non-blocking call. For example, in Jupyter as shown here, if you run ```result()```, the notebook will stop and wait at this cell for a certain polling time (set as ```poll_timeout_seconds``` with default of 5 days) till the polling returns the result object or times out. If you run ```async_result()```, the notebook immediately goes to the next cell, _not_ waiting for polling to complete. Calling `result()` on the `async_result` object before it has completed, an `asyncio.exceptions.InvalidStateError` will be raised. This is expected behavior. Later, you can call ```result()``` and get the actual result from the task. \n", + "\n", + "Alternatively, we have provided a basic `asyncio` waiter function `wait_on_result()`, which will create a blocking call, wait for the result, and then return that result for downstream use. We have defaulted the notebook to leverage this call in favor of avoiding the `InvalidStateError`, but we have left the non-blocking `async_result.result()` call example as an option." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "# asyncio waiter function to leverage Task.async_result() object\n", + "async def wait_on_result(async_result):\n", + " print('Waiting on task.')\n", + " await async_result\n", + "\n", + " print(f'Final task state: {async_result._state}')\n", + " res = async_result.result()\n", + " \n", + " return res" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "# example with async_result - immediately returns asyncio Future object\n", + "async_result = device.run(circ2, shots=100).async_result()" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Waiting on task.\n", + "Final task state: FINISHED\n", + "Counter({'00': 100})\n" + ] + } + ], + "source": [ + "# async_result.result() then returns the actual result (once completed)\n", + "# Non-blocking call. Will raise an InvalidStateError if this is run before async task is complete:\n", + "# async_res = async_result.result()\n", + "# Blocking call, leveraging asyncio.run and await\n", + "async_res = asyncio.run(wait_on_result(async_result))\n", + "# get measurement shots\n", + "counts = async_res.measurement_counts\n", + "print(counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One can also define custom callbacks to be invoked when the Future is completed. " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [], + "source": [ + "# async_result returns back a Future. \n", + "# Details on Future: https://docs.python.org/3.8/library/asyncio-future.html#asyncio.Future\n", + "future = device.run(circ2, shots=100).async_result()\n", + "\n", + "# this is invoked when the Future is done. i.e. task is in a terminal state.\n", + "# This will print out to STDOUT when its done.\n", + "def call_back_function(future):\n", + " print(f\"Custom task Result: {future.result().measurement_probabilities}\")\n", + "\n", + "# attached the callback function to the future.\n", + "future.add_done_callback(call_back_function)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 4200, 'tasks': {'COMPLETED': 4, 'CANCELLING': 1, 'CREATED': 1}, 'execution_duration': datetime.timedelta(microseconds=175000), 'billed_execution_duration': datetime.timedelta(seconds=12)}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.02 USD\n", + "Custom task Result: {'00': 1.0}\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.15" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} \ No newline at end of file diff --git a/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb new file mode 100644 index 000000000..d85066581 --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb @@ -0,0 +1,575 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "47503455", + "metadata": {}, + "source": [ + "# Introduction of analog Hamiltonian simulation\n", + "\n", + "Analog Hamiltonian Simulation (AHS) is a quantum computing paradigm different from gate-based computing. AHS uses a well-controlled quantum system and tunes its parameters to mimic the dynamics of another quantum system, the one we aim to study. \n", + "\n", + "In the gate-based quantum computation, the program is a quantum circuit consisting of a series of quantum gates, each of which acts only a small subset of qubits. In contrast, an AHS program is a sequence of time-dependent Hamiltonians that govern the quantum dynamics of all qubits. The comparison can be seen in the following figure, where the left side shows a typical quantum circuit, and the right side illustrates that, during AHS, the effect of the evolution under a Hamiltonian can be understood as a unitary acting simultaneously on all qubits.\n", + "\n", + "Digital quantum circuit | Analog Hamiltonian Simulation\n", + ":-------------------------:|:-------------------------:\n", + "\"digital | \"analog\n", + "\n", + "(\"Digital quantum circuit\" and \"Analog Hamiltonian Simulation\" figures by [QuEra Computing Inc.](https://www.quera.com/) are licensed under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/))\n", + "\n", + "In this notebook, we focus on running Analog Hamiltonian Simulations with Rydberg atoms. Also, we will use `matplotlib` package and `ahs_utils.py` module in the current working directory for visualization purposes." + ] + }, + { + "cell_type": "markdown", + "id": "b327221a-aee8-4621-b657-ea85c750a09f", + "metadata": {}, + "source": [ + "# AHS with Rydberg atoms\n", + "\n", + "An Analog Hamiltonian Simulation **program** is fully specified by its quantum register and (time-dependent) Hamiltonian." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8a93745e-02b0-4cd8-9926-c1d4aae14aa2", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.ahs.hamiltonian import Hamiltonian\n", + "from braket.ahs.atom_arrangement import AtomArrangement\n", + "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n", + "\n", + "register = AtomArrangement()\n", + "H = Hamiltonian()\n", + "\n", + "ahs_program = AnalogHamiltonianSimulation(\n", + " hamiltonian=H,\n", + " register=register\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "2871eb36-e6ef-4519-84f6-a40d492c4987", + "metadata": {}, + "source": [ + "In order to run AHS program with Rydberg atoms, we will first have to understand what type of Hamiltonian can Rydberg atoms simulate." + ] + }, + { + "cell_type": "markdown", + "id": "65319098-d1b9-4bb5-8777-878938c51018", + "metadata": {}, + "source": [ + "## Introduction to Rydberg Hamiltonian\n", + "\n", + "Depending on the atomic states we use for the Rydberg system, its Hamiltonian could take different forms. Here we shall focus on the following type of Hamiltonian\n", + "\n", + "\\begin{align}\n", + "H(t) = \\sum_{k=1}^N H_{\\text{drive}, k}(t) + \\sum_{k=1}^N H_{\\text{shift}, k}(t) + \\sum_{j=1}^{N-1}\\sum_{k = j+1}^N H_{\\text{vdW}, j, k},\n", + "\\end{align}\n", + "\n", + "where $j, k=1,2,\\ldots N$ index the atoms (qubits) in the program register. We describe the nature and effect of each term in the Hamiltonian in the following sections, using a triangular array as an example." + ] + }, + { + "cell_type": "markdown", + "id": "bdc99a17-a873-4b80-a41b-a8fb3df46ba9", + "metadata": {}, + "source": [ + "### Register\n", + "\n", + "First, we need to define a quantum **register**, 2-dimensional layout of neutral atoms, on which this Hamiltonian will act." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "cf3738c1-38a4-4b54-8537-33f16d3acba2", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "# e.g. three atoms in an equilateral triangle, with pairwise\n", + "# separation equal to 5.5 micrometers\n", + "a = 5.5e-6 # meters\n", + "\n", + "register.add([0, 0])\n", + "register.add([a, 0.0])\n", + "register.add([0.5 * a, np.sqrt(3)/2 * a]);" + ] + }, + { + "cell_type": "markdown", + "id": "b549d2ca", + "metadata": {}, + "source": [ + "The atom arrangement can be visualized in the following way" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "70fcb4f0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from ahs_utils import show_register\n", + "\n", + "show_register(register)" + ] + }, + { + "cell_type": "markdown", + "id": "8096aa7e-4925-4317-ba85-d69d97b9150f", + "metadata": {}, + "source": [ + "### Driving field\n", + "\n", + "The first term of the Hamiltonian represents the effect of a **driving field** that addresses the atoms simultaneously and uniformly\n", + "\n", + "\\begin{align}\n", + "H_{\\text{drive}, k}(t) = \\frac{\\Omega(t)}{2}\\left(e^{i\\phi(t)}|g_k\\rangle\\langle r_k| + e^{-i\\phi(t)}|r_k\\rangle\\langle g_k|\\right) - \\Delta_\\text{global}(t)n_k,\n", + "\\end{align}\n", + "\n", + "where $\\Omega$, $\\phi$, and $\\Delta_\\text{global}$ to denote the **amplitude** (Rabi frequency), laser **phase**, and the **detuning** of the driving laser field. Here $n_k = |r_k\\rangle\\langle r_k|$ is the number operator of atom $k$; the kets $|g_k\\rangle$ and $|r_k\\rangle$ denote the ground and Rydberg states, respectively. The $\\Omega$ part of the driving term is identical to a uniform (time-dependent) _transverse_ magnetic field, whereas the $\\Delta_\\text{global}$ part implements the effect of a _longitudinal_ magnetic field, in a spin-model representation.\n", + "\n", + "For the purpose of this example, we choose a constant Rabi frequency equal to $\\Omega_\\text{max}=2.5\\times10^6$ rad/s, with the phase and global detuning set to zero. The duration of the program is set to $\\frac{\\pi}{\\sqrt{2}\\Omega_\\text{max}}$, which will be explained in the next section. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "784fd2a4-7bd7-4f67-90c1-4b3664515cfb", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.timings.time_series import TimeSeries\n", + "from braket.ahs.driving_field import DrivingField\n", + "\n", + "# e.g. trapzoid amplitude time series\n", + "Omega_max = 2.5e6 # rad / seconds\n", + "\n", + "# e.g. the duration of the program\n", + "t_max = np.pi/(np.sqrt(2)*Omega_max) # seconds\n", + "\n", + "# e.g. constant Rabi frequency\n", + "Omega = TimeSeries()\n", + "Omega.put(0.0, Omega_max)\n", + "Omega.put(t_max, Omega_max)\n", + "\n", + "# e.g. all-zero phase and detuning\n", + "phi = TimeSeries().put(0.0, 0.0).put(t_max, 0.0) # (time [s], value [rad])\n", + "Delta_global = TimeSeries().put(0.0, 0.0).put(t_max, 0.0) # (time [s], value [rad/s])\n", + "\n", + "drive = DrivingField(\n", + " amplitude=Omega,\n", + " phase=phi,\n", + " detuning=Delta_global\n", + ")\n", + "\n", + "H += drive" + ] + }, + { + "cell_type": "markdown", + "id": "613d27bb-c88e-4325-8263-c6e935eab0cf", + "metadata": {}, + "source": [ + "### Shifting field\n", + "\n", + "The second term in $H(t)$ represents the effect of a **shifting field** that detunes atoms according to a non-uniform pattern.\n", + "\n", + "\\begin{align}\n", + "H_{\\text{shift}, k}(t) = -\\Delta_\\text{local}(t)h_k \\,n_k,\n", + "\\end{align}\n", + "\n", + "where $\\Delta_\\text{local}(t)$ is the time-dependent **magnitude** of the frequency shift, and $h_k$ is the atom-dependent **pattern**, which is a dimensionless number between 0 and 1. This shifting term is identical to a non-uniform (and time-dependent) _longitudinal_ magnetic field in a spin-model representation.\n", + "\n", + "For the purpose of this example, we choose a shifting field that strongly detunes the top atom in the triangular lattice." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "4783bb48-31f4-4213-873b-879ad641b092", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.ahs.field import Field\n", + "from braket.ahs.pattern import Pattern\n", + "from braket.ahs.shifting_field import ShiftingField\n", + "\n", + "# e.g. constant strong shifting field\n", + "Delta_local = TimeSeries()\n", + "Delta_local.put(0.0, -Omega_max*20) # (time [s], value [rad/s])\n", + "Delta_local.put(t_max, -Omega_max*20)\n", + "\n", + "\n", + "# e.g. the shifting field only acts on the third atom, \n", + "# which is the top atom in the triangular array.\n", + "h = Pattern([0, 0, 0.5])\n", + "\n", + "shift = ShiftingField(\n", + " magnitude=Field(\n", + " time_series=Delta_local,\n", + " pattern=h\n", + " )\n", + ")\n", + "\n", + "H += shift" + ] + }, + { + "cell_type": "markdown", + "id": "3c2f1d9a", + "metadata": {}, + "source": [ + "The driving field and the shifting field can be inspected with the following utility function" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "4cfd6e37", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from ahs_utils import show_drive_and_shift\n", + "\n", + "show_drive_and_shift(drive, shift)" + ] + }, + { + "cell_type": "markdown", + "id": "e0cff122-476f-45fd-bafe-c86b63f22deb", + "metadata": {}, + "source": [ + "### Rydberg-Rydberg interaction\n", + "\n", + "Finally, the third term in $H(t)$ is the van der Waals interaction between all pairs of Rydberg atoms,\n", + "\n", + "\\begin{align}\n", + "H_{\\text{vdW}, j, k} =V_{j,k} \\,n_j\\, n_k = \\frac{C_6}{R_{j,k}^6} \\,n_j\\, n_k,\n", + "\\end{align}\n", + "\n", + "where $C_6$ is a fixed interaction coefficient, and $R_{j,k}=|{\\bf x}_j-{\\bf x}_k|$ is the distance between atoms $j$ and $k$. This interaction shifts the frequency of the Rydberg level of all atoms that are close to an atom that is already in its Rydberg state. While the overall coefficient, $C_6$ is a fixed value (determined by the nature of the ground and Rydberg states), the strength of this interaction can be tuned by adjusting the pairwise distance $R_{j,k}$ between atoms." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "12529050-720f-450a-84e8-d266d1c9ac48", + "metadata": {}, + "outputs": [], + "source": [ + "# Note:\n", + "# The van der Waals interaction term is implicitly assumed in the current version of the AHS module,\n", + "# its strength (C6 / R_{j,k}^6) is calculated (if using the local simulator) from the atomic positions \n", + "# of the register, hence there is no need to specify it explicitly." + ] + }, + { + "cell_type": "markdown", + "id": "9de2469a-7326-4cce-9382-45668759ecc6", + "metadata": {}, + "source": [ + "**Introduction to Rydberg blockade**\n", + "\n", + "For the interaction coefficient, the value of $C_6$ depends on the atom species, and the states used in the simulation. Here we shall take the value \n", + "\n", + "\\begin{align}\n", + "C_6 = 5.42\\times 10^{-24} ~\\text{rad}~ \\text{m}^6/\\text{s}\n", + "\\end{align}\n", + "\n", + "for $|r\\rangle = |70S_{1/2}\\rangle$ of the $^{87}$Rb atoms. For the typical scenario, where atoms are separated by $4\\times10^{-6}$ meters, the van der Waals interaction strength is $V_{jk}=1.32\\times10^9 \\text{rad}/\\text{s}$, which is much larger than the typical scale of the Rabi frequency (around $6\\times10^6 \\text{rad}/\\text{s}$). As a result, when the separation of two atoms is within certain distance, it is nearly impossible to drive them to the Rydberg state simultaneously. \n", + "\n", + "This is called the Rydberg blockade phenomena, illustrated in the figure below (Source: [Browaeys and Lahaye](https://arxiv.org/abs/2002.07413)), where $R$ is the separation between the atoms, and $E$ indicates the energies or frequencies of the different two-atom states as $R$ changes. The vertical arrows indicate the effect of a uniform driving field (with Rabi frequency $\\Omega$) that successfully transitions the atoms from the $|gg\\rangle$ ground state to the 1-atom excited state $|\\psi_+\\rangle = (|gr\\rangle + |rg\\rangle)/\\sqrt{2}$ (independent of $R$), but fails to get from there to the doubly-excited state $|rr\\rangle$, if $R$ is smaller than $R_b = (C_6 / \\Omega)^{1/6}$, the blockade radius.\n", + "\n", + "Note: In the presence of both global Rabi frequency and detuning, it is more accurate to estimate the blockade radius with $R_b = (C_6 / \\sqrt{\\Omega^2+\\Delta^2})^{1/6}$, see [Pichler, et. al.](https://arxiv.org/abs/1808.10816).\n", + "\n", + "\"drawing\"" + ] + }, + { + "cell_type": "markdown", + "id": "8eae4fdd-9b85-42fd-b7ae-aad65f6fb30b", + "metadata": { + "tags": [] + }, + "source": [ + "### Full program\n", + "\n", + "The fully-specified program can be inspected with the following command." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "98489138-a878-4514-8d3b-b36f19337eda", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'braketSchemaHeader': {'name': 'braket.ir.ahs.program', 'version': '1'},\n", + " 'setup': {'ahs_register': {'sites': [[Decimal('0'), Decimal('0')],\n", + " [Decimal('0.0000055'), Decimal('0.0')],\n", + " [Decimal('0.00000275'), Decimal('0.000004763139720814412')]],\n", + " 'filling': [1, 1, 1]}},\n", + " 'hamiltonian': {'drivingFields': [{'amplitude': {'time_series': {'values': [Decimal('2500000.0'),\n", + " Decimal('2500000.0')],\n", + " 'times': [Decimal('0.0'), Decimal('8.885765876316732E-7')]},\n", + " 'pattern': 'uniform'},\n", + " 'phase': {'time_series': {'values': [Decimal('0.0'), Decimal('0.0')],\n", + " 'times': [Decimal('0.0'), Decimal('8.885765876316732E-7')]},\n", + " 'pattern': 'uniform'},\n", + " 'detuning': {'time_series': {'values': [Decimal('0.0'), Decimal('0.0')],\n", + " 'times': [Decimal('0.0'), Decimal('8.885765876316732E-7')]},\n", + " 'pattern': 'uniform'}}],\n", + " 'shiftingFields': [{'magnitude': {'time_series': {'values': [Decimal('-50000000.0'),\n", + " Decimal('-50000000.0')],\n", + " 'times': [Decimal('0.0'), Decimal('8.885765876316732E-7')]},\n", + " 'pattern': [Decimal('0'), Decimal('0'), Decimal('0.5')]}}]}}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ahs_program.to_ir().dict()" + ] + }, + { + "cell_type": "markdown", + "id": "bf450c2f", + "metadata": {}, + "source": [ + "# Running AHS program with local simulator" + ] + }, + { + "cell_type": "markdown", + "id": "ecfcc7bc", + "metadata": {}, + "source": [ + "The AHS program defined above realizes the maximally entangled state for a pair of atoms, out of the three atoms in the triangular array. To see that, recall that we have subjected the top atom in the triangular array (labeled as atom 2) with a strong detuning $H_{\\text{shift}, 2}(t) = -\\frac{1}{2}\\Delta_\\text{local}n_2$ where $\\Delta_\\text{local}=-10\\Omega_\\text{max}=-2.5\\times10^7$ rad/s. Since $\\Delta_\\text{local}$ is much bigger than any other energy scales in the system, including the Rabi frequency, it is energy unfavorable for atom 2 to be excited to the Rydberg state (note the minus sign in $H_{\\text{shift}, 2}(t)$). Hence atom 2 remains in the ground state throughout the evolution, and can be neglected in the following analysis.\n", + "\n", + "Since the other two atoms are subjected with only the driving field with zero detuning and phase, the constant Hamiltonian reads\n", + "\\begin{align}\n", + "H = \\frac{\\Omega}{2}\\sum_{k=0}^1\\left(|g_k\\rangle\\langle r_k| + |r_k\\rangle\\langle g_k|\\right) + V_{0,1}{n}_0{n}_1,\n", + "\\end{align}\n", + "where $k=0,1$ are the indices for the two lower atoms in the triangular array. More concretely, in the basis of $\\left\\{|gg\\rangle, |gr\\rangle, |rg\\rangle, |rr\\rangle\\right\\}$, the Hamiltonian takes the following matrix representation\n", + "\\begin{align}\n", + "H = \n", + "\\begin{bmatrix}\n", + "0 & \\frac{\\Omega}{2} & \\frac{\\Omega}{2} & 0 \\\\\n", + "\\frac{\\Omega}{2} & 0 & 0 & \\frac{\\Omega}{2}\\\\\n", + "\\frac{\\Omega}{2} & 0 & 0 & \\frac{\\Omega}{2}\\\\\n", + "0 & \\frac{\\Omega}{2} & \\frac{\\Omega}{2} & V_{0,1}\n", + "\\end{bmatrix}.\n", + "\\end{align}\n", + "Since the two atoms are separated by $d_{0,1} = 5.5\\times10^{-6}$ meters, the interaction strength between them reads\n", + "\\begin{align}\n", + "V_{0,1}=\\frac{C_6}{(d_{0,1})^6} = \\frac{5.42\\times10^{-24}}{(5.5\\times10^{-6})^6}\\approx1.96\\times10^8 \\text{ rad/s},\n", + "\\end{align}\n", + "which is much greater than the Rabi frequency. Hence the two atoms are in the Rydberg blockade regime, and the state $|rr\\rangle$ is very unlikely to be excited (assuming the initial state is $|gg\\rangle$). Hence we can neglect the $|rr\\rangle$ state, and the Hamiltonian is simplified to be\n", + "\\begin{align}\n", + "H = \n", + "\\begin{bmatrix}\n", + "0 & \\frac{\\Omega}{2} & \\frac{\\Omega}{2} \\\\\n", + "\\frac{\\Omega}{2} & 0 & 0 \\\\\n", + "\\frac{\\Omega}{2} & 0 & 0 \n", + "\\end{bmatrix},\n", + "\\end{align}\n", + "and the final state of the evolution can be solved to be\n", + "\\begin{align}\n", + "|\\psi\\rangle = e^{-iHt}|gg\\rangle = \n", + "\\begin{bmatrix}\n", + "\\cos\\frac{\\Omega t}{\\sqrt{2}}\\\\\n", + "\\frac{i}{\\sqrt{2}}\\sin\\frac{\\Omega t}{\\sqrt{2}}\\\\\n", + "\\frac{i}{\\sqrt{2}}\\sin\\frac{\\Omega t}{\\sqrt{2}}\n", + "\\end{bmatrix}.\n", + "\\end{align}\n", + "Hence if the system evolves for a duration $T=\\frac{\\pi}{\\sqrt{2}\\Omega}$, which is indeed the duration of the AHS program defined in the previous section, we will arrive at a maximally entangled state between the two atoms\n", + "\\begin{align}\n", + "|\\psi\\rangle = \\frac{1}{\\sqrt{2}}(|gr\\rangle+|rg\\rangle).\n", + "\\end{align}\n", + "\n", + "Before submitting the AHS program to a QPU, it is useful to run the program on the local simulator to check if the simulation result meets one's expectation. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "9967419e", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.devices import LocalSimulator\n", + "device = LocalSimulator(\"braket_ahs\")" + ] + }, + { + "cell_type": "markdown", + "id": "da67bcf1", + "metadata": {}, + "source": [ + "We can run the AHS program just like running a quantum circuit on other Braket devices. Below we have explicitly specified the values of `steps` and `shots`, which are the number of time steps in the simulation and the number of sampling for the final stats, respectively. One could increase the accuracy of the result by increasing the values of these arguments, at the expense of longer runtime. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "6a510997", + "metadata": {}, + "outputs": [], + "source": [ + "result = device.run(ahs_program, shots=1000, steps=100).result()" + ] + }, + { + "cell_type": "markdown", + "id": "85747c3e", + "metadata": {}, + "source": [ + "To confirm that we indeed arrive at a maximally entangled state, we first collect the measurement results, followed by counting the number of occurrence of $|gr\\rangle$ and $|rg\\rangle$ respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "7a906e64", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'ggr': 1, 'grg': 484, 'rgg': 515}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def get_counters_from_result(result):\n", + " post_sequences = [list(measurement.post_sequence) for measurement in result.measurements]\n", + " post_sequences = [\"\".join(['r' if site==0 else 'g' for site in post_sequence]) for post_sequence in post_sequences]\n", + "\n", + " counters = {}\n", + " for post_sequence in post_sequences:\n", + " if post_sequence in counters:\n", + " counters[post_sequence] += 1\n", + " else:\n", + " counters[post_sequence] = 1\n", + " return counters\n", + "\n", + "get_counters_from_result(result)" + ] + }, + { + "cell_type": "markdown", + "id": "7143ac6b", + "metadata": {}, + "source": [ + "The simulation outcome indeed confirms our expectations\n", + "1. It is very unlikely to excite the 3rd atom to the Rydberg state because of the strong local detuning. \n", + "2. Due to the Rydberg blockade, it is very unlikely to excite the 1st and 2nd atoms to the Rydberg states simultaneously.\n", + "3. By appropriately tuning the Rabi frequency and the duration of the AHS program, we can arrive at a maximally entangled state for the 1st and 2nd atoms. Since our simulation is noiseless, the discrepancy from ideal 50%-50% split is attributed to statistical sampling (aka \"shot noise\").\n", + "\n", + "In summary, in this notebook, we have introduced Analog Hamiltonian Simulation (AHS), a different quantum computing paradigm, and showed how to run an AHS program with Rydberg atoms using Braket's local AHS simulator." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1e9f5dac", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb new file mode 100644 index 000000000..ffd85f996 --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb @@ -0,0 +1,888 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "92c948f0-6dd3-4955-b4eb-2926a79ecf7e", + "metadata": { + "tags": [] + }, + "source": [ + "# Introduction to Aquila\n", + "\n", + "In the previous notebook, we have introduced the concept of Analog Hamiltonian Simulation (AHS) and how to run an AHS program on the neutral atom local simulator. In this notebook, we illustrate how to run an AHS program on QuEra's Aquila, a Rydberg based QPU, via Amazon Braket. \n" + ] + }, + { + "cell_type": "markdown", + "id": "f4df5b53", + "metadata": {}, + "source": [ + "## QuEra's Aquila\n", + "\n", + "In order to use the Aquila device, let us first connect to it, and query its parameters with its unique Amazon Resource Number (ARN)." + ] + }, + { + "cell_type": "markdown", + "id": "57ac4e1c", + "metadata": {}, + "source": [ + "
    \n", + "Note: You need to pip install the Braket SDK. If you are new to Amazon Braket, make sure you have completed the necessary Get Started steps. If you are using a Braket hosted notebook instance, this SDK comes pre-installed with the notebooks.\n", + "
    \n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "6f3c3385", + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "tracker = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "id": "7175daec", + "metadata": {}, + "source": [ + "In this notebook, we will use `matplotlib` package and `ahs_utils.py` module in the current working directory for visualization purposes and other functionalities." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3cd780d0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'braketSchemaHeader': {'name': 'braket.device_schema.quera.quera_ahs_paradigm_properties',\n", + " 'version': '1'},\n", + " 'lattice': {'area': {'height': Decimal('0.000076'),\n", + " 'width': Decimal('0.000075')},\n", + " 'geometry': {'numberSitesMax': 256,\n", + " 'positionResolution': Decimal('1E-7'),\n", + " 'spacingRadialMin': Decimal('0.000004'),\n", + " 'spacingVerticalMin': Decimal('0.000004')}},\n", + " 'performance': {'lattice': {'positionErrorAbs': Decimal('1E-7')},\n", + " 'rydberg': {'rydbergGlobal': {'rabiFrequencyErrorRel': Decimal('0.02')}}},\n", + " 'qubitCount': 256,\n", + " 'rydberg': {'c6Coefficient': Decimal('5.42E-24'),\n", + " 'rydbergGlobal': {'detuningRange': (Decimal('-125000000.0'),\n", + " Decimal('125000000.0')),\n", + " 'detuningResolution': Decimal('0.2'),\n", + " 'detuningSlewRateMax': Decimal('2500000000000000.0'),\n", + " 'phaseRange': (Decimal('-99.0'),\n", + " Decimal('99.0')),\n", + " 'phaseResolution': Decimal('5E-7'),\n", + " 'rabiFrequencyRange': (Decimal('0.0'),\n", + " Decimal('15800000.0')),\n", + " 'rabiFrequencyResolution': Decimal('400.0'),\n", + " 'rabiFrequencySlewRateMax': Decimal('250000000000000.0'),\n", + " 'timeDeltaMin': Decimal('5E-8'),\n", + " 'timeMax': Decimal('0.000004'),\n", + " 'timeMin': Decimal('0.0'),\n", + " 'timeResolution': Decimal('1E-9')}}}\n" + ] + } + ], + "source": [ + "from braket.aws import AwsDevice \n", + "from pprint import pprint as pp\n", + "\n", + "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")\n", + "capabilities = device.properties.paradigm\n", + "pp(capabilities.dict())" + ] + }, + { + "cell_type": "markdown", + "id": "ea413e47", + "metadata": {}, + "source": [ + "The preceding numbers represent numerical capabilities and constraints for which AHS programs can be run on Aquila. In the following sections, we will go through these device capabilities and build an AHS program that complies with these constraints." + ] + }, + { + "cell_type": "markdown", + "id": "a0b5f568", + "metadata": {}, + "source": [ + "## Building an AHS program for Aquila\n", + "\n", + "We have seen the basic components of an AHS program in the previous example, including the register, the driving and shifting fields. In order to run an AHS program on Aquila, however, these components have to meet certain requirements. Particularly, the first version of Aquila does not support shifting field. In this section, we introduce other constraints via building up a valid program for Aquila step by step. " + ] + }, + { + "cell_type": "markdown", + "id": "6535a209", + "metadata": {}, + "source": [ + "### Register\n", + "In contrast to the local simulator which can only simulate a handful of atoms (qubits), Aquila can simulate systems with a few hundred. The coordinates of the atoms (qubits), however, have to meet certain constraints. We can check the requirements as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "edf0d67c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'area': {'height': Decimal('0.000076'), 'width': Decimal('0.000075')},\n", + " 'geometry': {'numberSitesMax': 256,\n", + " 'positionResolution': Decimal('1E-7'),\n", + " 'spacingRadialMin': Decimal('0.000004'),\n", + " 'spacingVerticalMin': Decimal('0.000004')}}\n" + ] + } + ], + "source": [ + "lattice_constraints = capabilities.lattice\n", + "pp(lattice_constraints.dict())" + ] + }, + { + "cell_type": "markdown", + "id": "7dadd661", + "metadata": {}, + "source": [ + "The detailed description of these sections can be inspected as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "409362f9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " The area of the FOV\n", + " Attributes:\n", + " width (Decimal): Largest allowed difference between x\n", + " coordinates of any two sites (measured in meters)\n", + " height (Decimal): Largest allowed difference between y\n", + " coordinates of any two sites (measured in meters)\n", + " \n", + "\n", + " Spacing or number of sites or rows\n", + " Attributes:\n", + " spacingRadialMin (Decimal): Minimum radial spacing between any\n", + " two sites in the lattice (measured in meters)\n", + " spacingVerticalMin (Decimal): Minimum spacing between any two\n", + " rows in the lattice (measured in meters)\n", + " positionResolution (Decimal): Resolution with which site positions\n", + " can be specified (measured in meters)\n", + " numberSitesMax (int): Maximum number of sites that can be placed\n", + " in the lattice\n", + " \n" + ] + } + ], + "source": [ + "print(lattice_constraints.area.__doc__)\n", + "print(lattice_constraints.geometry.__doc__)" + ] + }, + { + "cell_type": "markdown", + "id": "b15d2f13", + "metadata": {}, + "source": [ + "As we can see, the requirements for the setup in an AHS program can be summarized as follows\n", + "1. The number of sites in the setup cannot be greater than `capabilities.lattice.geometry.numberSitesMax`\n", + "2. The atoms have to be separated by at least `capabilities.lattice.geometry.spacingRadialMin` meters\n", + "3. The rows in the setup have to be separated by at least `capabilities.lattice.geometry.spacingVerticalMin` meters\n", + "4. The resolution for the coordinates of the atoms cannot be greater than `capabilities.lattice.geometry.positionResolution` meters\n", + "5. The setup cannot be wider than `capabilities.lattice.area.width` meters\n", + "6. The setup cannot be taller than `capabilities.lattice.area.height` meters\n", + "\n", + "Below, we demonstrate a valid setup that meets these requirements, which has 105 atoms grouped as 35 equilateral triangles that are well separated from each other." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "487a6b5e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from braket.ahs.atom_arrangement import AtomArrangement\n", + "from ahs_utils import show_register\n", + "\n", + "separation = 5e-6\n", + "block_separation = 15e-6\n", + "k_max = 5\n", + "m_max = 5\n", + "\n", + "register = AtomArrangement()\n", + "for k in range(k_max):\n", + " for m in range(m_max):\n", + " register.add((block_separation*m, block_separation*k + separation/np.sqrt(3)))\n", + " register.add((block_separation*m-separation/2, block_separation*k - separation/(2*np.sqrt(3))))\n", + " register.add((block_separation*m+separation/2, block_separation*k - separation/(2*np.sqrt(3)))) \n", + "\n", + "show_register(register, show_atom_index=False, blockade_radius= 1.5 * separation)" + ] + }, + { + "cell_type": "markdown", + "id": "62acf66e", + "metadata": {}, + "source": [ + "In the above figure, each blue link connects a pair of atoms that blockade each other. Since the triangles are well separated from each other, and the driving field (see below) is acting on all atoms uniformly, effectively we are repeating the same experiment on the same setup (an equilateral triangle) 35 times in one shot. If the setup of interest is small and contains only a few atoms, we could try to fit in a few identical copies of the setup in the bounding box while avoiding the interference between them. In this way, we are effectively taking more shots for the AHS program of interest." + ] + }, + { + "cell_type": "markdown", + "id": "75e18060", + "metadata": {}, + "source": [ + "### Driving field\n", + "\n", + "Recall that Aquila can simulate the following Hamiltonian \n", + "\n", + "\\begin{align}\n", + "H(t) = \\sum_{k=1}^N H_{\\text{drive}, k}(t) + \\sum_{j=1}^{N-1}\\sum_{k = j+1}^N H_{\\text{vdW}, j, k}.\n", + "\\end{align}\n", + "Here the second term is the van der Waals interaction term which is fixed once the setup is defined. The first term is the driving field,\n", + "\\begin{align}\n", + "H_{\\text{drive}, k}(t) = \\frac{\\Omega(t)}{2}\\left(e^{i\\phi(t)}|g_k\\rangle\\langle r_k| + e^{-i\\phi(t)}|r_k\\rangle\\langle g_k|\\right) - \\Delta_\\text{global}(t)n_k,\n", + "\\end{align}\n", + "which act on all the atoms in the setup. Here $n_k = |r_k\\rangle\\langle r_k|$ is the number operator of atom $k$. The specification of the driving field has to satisfy several conditions, which can be queried as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "91e004b1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'c6Coefficient': Decimal('5.42E-24'),\n", + " 'rydbergGlobal': {'detuningRange': (Decimal('-125000000.0'),\n", + " Decimal('125000000.0')),\n", + " 'detuningResolution': Decimal('0.2'),\n", + " 'detuningSlewRateMax': Decimal('2500000000000000.0'),\n", + " 'phaseRange': (Decimal('-99.0'), Decimal('99.0')),\n", + " 'phaseResolution': Decimal('5E-7'),\n", + " 'rabiFrequencyRange': (Decimal('0.0'),\n", + " Decimal('15800000.0')),\n", + " 'rabiFrequencyResolution': Decimal('400.0'),\n", + " 'rabiFrequencySlewRateMax': Decimal('250000000000000.0'),\n", + " 'timeDeltaMin': Decimal('5E-8'),\n", + " 'timeMax': Decimal('0.000004'),\n", + " 'timeMin': Decimal('0.0'),\n", + " 'timeResolution': Decimal('1E-9')}}\n" + ] + } + ], + "source": [ + "rydberg = capabilities.rydberg\n", + "pp(rydberg.dict())" + ] + }, + { + "cell_type": "markdown", + "id": "4b67aec2", + "metadata": {}, + "source": [ + "`c6Coefficient` is the constant for the interaction strength between two Rydberg atoms. The detailed description for the `rydbergGlobal` section can be inspected as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "d0bca3f4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Parameters determining the limitations on the driving field that drives the\n", + " ground-to-Rydberg transition uniformly on all atoms\n", + " Attributes:\n", + " rabiFrequencyRange (Tuple[Decimal,Decimal]): Achievable Rabi frequency\n", + " range for the global Rydberg drive waveform (measured in rad/s)\n", + " rabiFrequencyResolution (Decimal): Resolution with which global Rabi\n", + " frequency amplitude can be specified (measured in rad/s)\n", + " rabiFrequencySlewRateMax (Decimal): Maximum slew rate for changing the\n", + " global Rabi frequency (measured in (rad/s)/s)\n", + " detuningRange(Tuple[Decimal,Decimal]): Achievable detuning range for\n", + " the global Rydberg pulse (measured in rad/s)\n", + " detuningResolution(Decimal): Resolution with which global detuning can\n", + " be specified (measured in rad/s)\n", + " detuningSlewRateMax (Decimal): Maximum slew rate for detuning (measured in (rad/s)/s)\n", + " phaseRange(Tuple[Decimal,Decimal]): Achievable phase range for the global\n", + " Rydberg pulse (measured in rad)\n", + " phaseResolution(Decimal): Resolution with which global Rabi frequency phase\n", + " can be specified (measured in rad)\n", + " timeResolution(Decimal): Resolution with which times for global Rydberg drive\n", + " parameters can be specified (measured in s)\n", + " timeDeltaMin(Decimal): Minimum time step with which times for global Rydberg\n", + " drive parameters can be specified (measured in s)\n", + " timeMin (Decimal): Minimum duration of Rydberg drive (measured in s)\n", + " timeMax (Decimal): Maximum duration of Rydberg drive (measured in s)\n", + " \n" + ] + } + ], + "source": [ + "print(rydberg.rydbergGlobal.__doc__)" + ] + }, + { + "cell_type": "markdown", + "id": "a0f2d5a4", + "metadata": {}, + "source": [ + "As we can see, the requirements for the driving field in the AHS program can be summarized as follows\n", + "\n", + "1. The Rabi frequency $\\Omega(t)$ has to be within the range `rydberg.rydbergGlobal.rabiFrequencyRange`, in the unit of rad/s\n", + "2. The resolution for the Rabi frequency cannot be greater than `rydberg.rydbergGlobal.rabiFrequencyResolution` rad/s\n", + "3. The slew rate for the Rabi frequency cannot be greater than `rydberg.rydbergGlobal.rabiFrequencySlewRateMax` (rad/s)/s\n", + "\n", + "4. The phase $\\phi(t)$ has to be within the range `rydberg.rydbergGlobal.phaseRange`, in the unit of rad\n", + "5. The resolution for the phase cannot be greater than `rydberg.rydbergGlobal.phaseResolution` rad\n", + "\n", + "6. The detuning $\\Delta(t)$ has to be within the range `rydberg.rydbergGlobal.detuningRange`, in the unit of rad\n", + "7. The resolution for the detuning cannot be greater than `rydberg.rydbergGlobal.detuningResolution` rad\n", + "8. The slew rate for the detuning cannot be greater than `rydberg.rydbergGlobal.detuningSlewRateMax` rad/s\n", + "\n", + "9. The duration of the driving field cannot be less than `rydberg.rydbergGlobal.timeMin` seconds\n", + "10. The duration of the driving field cannot be more than `rydberg.rydbergGlobal.timeMax` seconds\n", + "11. The time points have to be separated by at least `rydberg.rydbergGlobal.timeDeltaMin` seconds\n", + "12. The resolution for the time points cannot be greater than `rydberg.rydbergGlobal.timeResolution` seconds\n", + "\n", + "Besides, there are a few additional requirements\n", + "1. The Rabi frequency $\\Omega(t)$ has to start with 0 rad/s\n", + "2. The Rabi frequency $\\Omega(t)$ has to end with 0 rad/s\n", + "3. The phase $\\phi(t)$ has to start with 0 rad\n", + "4. All the fields in the driving field have to have the same duration" + ] + }, + { + "cell_type": "markdown", + "id": "cbf846fd", + "metadata": {}, + "source": [ + "In this example, we are interested in driving the atoms with constant Rabi frequency $\\Omega_\\text{const}=1.5\\times10^7$ rad/s for a duration of $T_\\text{const}=\\frac{\\pi}{\\sqrt{3}\\Omega}\\approx2.09\\times10^{-7}$ seconds such that each atom has average Rydberg density equal to 1/3. Since the Rabi frequency corresponds to blockade radius $R_b\\approx8.44\\times10^{-6}$ meters, which is greater than the sides of the equilateral triangles ($5\\times10^{-6}$ meters), the atoms of the same triangle blockade one another. On the other hand, $R_b$ is smaller than the distance between nearest atoms of neighboring triangles, which is around $10\\times10^{-6}$ meters, hence the neighboring triangles are not interacting with each other, as desired. \n", + "\n", + "However, for the AHS program submitted to Aquila, the Rabi frequency cannot be a constant because of the constraint that it has to start and end with 0 rad/s. Hence we will need to create a time series $\\Omega(t)$ such that $\\int_0^T\\Omega(t)dt=\\Omega_\\text{const}T_\\text{const}=\\frac{\\pi}{\\sqrt{3}}$, while satisfying $\\Omega(0)=\\Omega(T)=0$. This could be achieved via the utility function `rabi_pulse` below where we demonstrate how to create the desired driving field for Aquila." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "11bd0f7e", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.timings.time_series import TimeSeries\n", + "from braket.ahs.driving_field import DrivingField\n", + "from ahs_utils import rabi_pulse, constant_time_series\n", + "\n", + "omega_const = 1.5e7 # rad / s\n", + "rabi_pulse_area = np.pi/np.sqrt(3) # rad\n", + "omega_slew_rate_max = float(rydberg.rydbergGlobal.rabiFrequencySlewRateMax) # rad/s^2\n", + "\n", + "time_points, amplitude_values = rabi_pulse(rabi_pulse_area, omega_const, 0.99 * omega_slew_rate_max)\n", + "\n", + "amplitude = TimeSeries()\n", + "for t, v in zip(time_points, amplitude_values):\n", + " amplitude.put(t, v)\n", + "\n", + "detuning = constant_time_series(amplitude, 0.0) \n", + "phase = constant_time_series(amplitude, 0.0) \n", + "\n", + " \n", + "drive = DrivingField(\n", + " amplitude=amplitude, \n", + " detuning=detuning, \n", + " phase=phase\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "3efaeb42", + "metadata": {}, + "source": [ + "We can inspect the driving field in the following way " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5db7e231", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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cNBBx7LKm/TP14BE8fOUSxh04lAtuXcf6rbt8W1dXtp2C59dr1Hek/3ko8E7gH+nr7wOeUdVPeL7SDNgetZsqXmvk3NVraUskueeyRRw7+aCwh2RMZOxsaOHc1WvZsbuFWy9awLuOivZngk3PwniN+hJVvQRQYI6qflJVPwkc48f6wlBcXBz2EDwXxaaXX93DOavW0pFUHly5ZL8n6Sg2eSGOXdaUnQmjh/PgyiVMHTeCS+7cwNMv1/q6PttOwfP7c9QvquqxXa7nAC90/V6QvNyjbm1tZdiwYZ4sKyqi1vRi9RtccNs6hubmcN+KxRx16Mj9XkbUmrwSxy5rGphde9u44LZ1bN65hxvPnceHjznMl/XYdvJH4HvUXTwjIk+KyMUichGpo5M97fM6A1FVVRX2EDwXpaaNr+zm3NVrGTE0l4evWJLVJA3RavJSHLusaWDGHTiU+1csZs6kg/jMfYU8+sIOX9Zj2yl4vk7Uqno1sIrU56lPAG5R1c/29zgRuV1EakXkxV5uFxG5QUTKReQFEZnn6cAzMGHChKBX6buoNOVX7uL8W9cxZsRQHrpiMdMOzv4ITFFp8locu6xp4A4akce9ly3kxKlj+NwDz/OH570/NKZtp+D5fhJOVf29qn4xfflDhg+7k9QBU3pzKjAzfVkJ3DSwUe6/3bt3B71K30Wh6T8VdVx4+3oOHTWMh65YzJSxIwa0vCg0+SGOXdbkjVHD87jr0oUsPuJgvvRwEQ9t8HZv0bZT8HydqEVksYhsEJFGEWkTkQ4Raejvcar6LNDXZw3OBO7WlLXAGBHp+RiSPhk+fHiQqwtE2E3/3Pwal9yxgSljD+DBKxYz8aADBrzMsJv8Escua/LOiKG53H7xSbxn5iF89XfF3LOm0rNl23YKnt971L8ClgNlwAHACuCXHix3MvBKl+vb0997GxFZKSL5IpJfU1NDXV0dNTU1VFdXU19fT0VFBc3NzZSUlJBMJiksLATe+lxdYWEhyWSSkpISmpubqaiooL6+/s3l1NXVUVlZSWNjI6WlpSQSCYqKivZZRufX4uJiWltbKSsro6GhgaqqKmpra6mtraWqqoqGhgbKyspobW19812I3ZdRVFREIpGgtLSUxsZGKisrY9H01xd3sOLO9cw4eAQ/XDqZnNZG55v82k7V1dXs2rXLmqypz6bKijJ+9onZvHPaKP7fnzbx08c2Ot8Ux+3U2dQXv9/1na+qC0TkBVU9Pv29/6jqOzN47HTg0Z7eIS4ijwHfV9Xn0tefAq5R1T4/te7lu76rqqqYOnWqJ8uKirCa/lJcw2cfeJ5jJo3mrksXMmbEUM+WHcftBPHssiZ/tCWSfOGh53m8+FX++5Sjuep9Rw1oeVFo8loUmvp617ff5/VqEpGhwEYR+SFQA3hxbrbtQNcTD08B/HmLYy/GjBkT5OoCEUbTnzZW86WHizjh8DHccclJjB6e5+ny47idIJ5d1uSPobk53LDsRPKGFPGjJ1+mtb2DL35oFiKS1fKi0OS1qDf5/dT3Bel1XA3sJTW5ftKD5T4CXJh+9/di4A1VrfFguRnbuXNnkKsLRNBND+e/whce2shJ08dy96ULPZ+kIZ7bCeLZZU3+yR2Sw0/PPoGzF0zhhn+Uc/0TpWT7bGpUmrwU9Sbf9qhFZAjwXVU9H2gBvr0fj30AOBkYLyLbgW8BeQCqejPwOHAaUA40AZd4OvgMhP00iR+CbLpv3Ta+/ocX+a+Z47nlggUcMHSIL+uJ43aCeHZZk7+G5AjXf+J4hubmsOqfW2htT/Ktj87Z7z3rKDV5JepNvu1Rq2oHcEj6qe/9fexyVZ2oqnmqOkVVb1PVm9OTNOl3e1+lqkeq6nGqGvgBvDdv3hz0Kn0XVNPtz23l6394kQ/MPpTVF/o3SUM8txPEs8ua/JeTI/zvmcdy6btmcOd/Kvn6H18kmdy/PeuoNXkh6k1+v5lsFTCP1FPVezu/r6o/9W2lfbCTcoTv5n9WcP1fSll6zGHcsPxEhub6/lF+Y0w3qsoPn3yZm56p4Kz5U/jBJ49nSE52r1kbb4R5CNEdwKPp9YzqcnFe1E+Llg0/m1SVX/y9jOv/UsoZcyfxq3ODmaTjuJ0gnl3WFBwR4ZpTjuYLH5zJbwu288WHNtLekczosVFtGoioN/m6Rx01tkcdDlXlR0++zK/tr3djIuemZyr4wRP2LFfYAt+jFpHrvLhPlEX9L7Bs+NGkqvzfYy/x62cqWL5wKj8MeJKO43aCeHZZUzg+ffKRfPP0OTyx6VWuvLeAlvaOPu/vQtP+inqTL3vU6Xdq9/U6tACXq+psz1feB9ujDlYyqXzzkRe5d20VF79zelbvMDXGBOPetdv4xh/9/ySG6VkYr1GvZt/XpLtfRqbv46zOQ8vFiZdNHUnl2t8Xc+/aKq547xGhTdJx3E4Qzy5rCtf5i6fxw7OO57nyOi65cz17WxM93s+lpkxFvcleo85SIpEgN9fvA7sFy6umREeSr/ymiD9u3MHnPjCTL35wZmh70nHcThDPLmuKhv6OFuhiU3+i0BTmu75jq7y8POwheM6LpvaOJJ978Hn+uHEH/33K0XxpAIcq9EIctxPEs8uaouHMEybzq+UnUvTKbs6/dR27m9r2ud3Fpv5Evckm6ixNmTIl7CF4bqBNrYkOPn1vIY8Xv8o3PvKOAR/83wtx3E4Qzy5rio5Tj5vIzefPp7RmD+euXsfrja1v3uZqU1+i3mQTdZbq6urCHoLnBtLU0t7ByrsL+PtLO/nOmcew4r+O8HBk2YvjdoJ4dllTtHxwzgRWX7SAitcaWb56LbV7WgC3m3oT9SZfJ2oRmSUiT4nIi+nrx4vIN/xcZ1BGjhwZ9hA8l21TU1uCS+/cwLNlr/GDTx7HhUumezuwAYjjdoJ4dllT9Lx31iHccclJvLKrmWWr1vLqGy3ON/Uk6k1+71GvBq4F2gFU9QVgmc/rDER7e3vYQ/BcNk17Wtq56Pb1rN3yOj89ey7nnBStg9vHcTtBPLusKZreeeR47r5sIbV7Wjl71RqqXm8Me0iei/p28nuiHqGq67t9r+f3/DsmmczscHsu2d+mN5rbueC29TxftZtfLp/Hx0+M3us8cdxOEM8ua4quk6aP494Vi9jd1Manf7uZyrq9/T/IIVHfTn5P1HUiciSgACJyFhDoeaP9MmLEiLCH4Ln9aarf28a5q9eyaccb/Pq8eXzk+Ik+jix7cdxOEM8ua4q2Ew4fw/2XL6Y1oZxzyxrKa+OzZx317eT3RH0VsAqYLSLVwBeAT/u8zkDs2rUr7CF4LtOm1/a0snz1WspqG7nlwgV8+JjDfB5Z9uK4nSCeXdYUfcdOPogfn3Y4HUll2S1rePnVPWEPyRNR306BHPBERA4EclQ11K3q5QFPmpubOeCAAzxZVlRk0rSzoYVzV6+lenczt110Eu86anxAo8tOHLcTxLPLmtzQ3NxM9Z4Ozrt1LW2JJPdctohjJx8U9rAGJArbKYyTcnyp6wW4Ari8y3Xnbd26NewheK6/purdzZy9ag2vvtHC3ZcuivwkDfHcThDPLmtyw9atWznq0JE8fMUSRgzN5dzVa9n4yu6whzUgUd9Ofp2U41vpfx4NnAQ8kr7+UeBZVV3h+Uoz4OUedTKZJCcnXh9D76up6vUmlq9eS0NLO3ddupB5U8cGPLrsxHE7QTy7rMkNXZu21zdx7up17Nrbxh2XnMRJ08eFPLrsRGE7Bb5HrarfVtVvA+OBear6ZVX9MjAfiN5bg7OwcePGsIfgud6atrzWyNmr1rC3LcH9KxY7M0lDPLcTxLPLmtzQtWnK2BE8fMUSDh01jAtvW89/yqN94JDeRH07+foatYiUAnNVtTV9fRhQFPTpLTvZaS733+adqUMIqir3rljEOyaODntIxpiIqd3Twvm3rmPb603ccuEC3jvrkLCH5JwwT8pxD7BeRK5LPx2+Drjb53UGIuonGs9G96aSHQ0su2UtOQIPXbHYyUk6jtsJ4tllTW7oqenQUcN5cOUSjjxkJJfflc/fS3aGMLLsRX07+f6ubxGZB/xX+uqzqvq8ryvsg+1RZ+6F7bu54Lb1HDh0CPddvpgZ4w8Me0jGmIjb3dTGRbevZ9OOBn65/EROPS6ax1eIotD2qEVkKlAH/CF9eT39PecVFhaGPQTPdTYVbKvnvNXrGH1ALg9dscTpSTqO2wni2WVNbuiracyIodyzYhFzDx/D1Q88z582Vgc4suxFfTv5/Rp1MemjkgEHADOAl1X1GN9W2gd713ffkskk6yvrufTODUwYPZz7Vixi0hi3PwMax+0E8eyyJjdk0rS3NcFld21g3dZd/OCTx3P2gsMDGl12orCdQtujVtXjVPX49GUmsBB4zs91BqW0tDTsIXju/n88z8V3rGfSmAN4aOVi5ydpiOd2gnh2WZMbMmk6cFgud1y8kHcfNZ5rfvsC967dFsDIshf17RTonxCqWkjqc9XOmzFjRthD8NQ/SnfynadrmX7wgTy4cjGHjh4e9pA8Ebft1CmOXdbkhkybDhg6hNUXLuADsw/lG398kduei+5BRaK+nfx+jbrrEcq+IiL3A6/5uc6g7NixI+wheOaJF1/linsKmD52KA9cvpjxI4eFPSTPxGk7dRXHLmtyw/40Dc8bwk3nz2fpMYfxv4+WcNMzFT6OLHtR305+71GP6nIZBjwGnOnzOgMxbpybR+Dp7s9FO7jq/kKOm3wQt553PGMPHBr2kDwVl+3UXRy7rMkN+9s0NDeHX517ImfMncQPnijl53/fTBDnmNgfUd9OuT4vv0RVf9P1GyLyKeA3vdzfGU1NTYwd684Runry24LtXPPbIhZMH8ftF5/EG3VuffYxE3HYTj2JY5c1uSGbptwhOfzsnBMYmpvDz/9eRmsiyTWnHI2I+DTK/RP17eT3HvW1GX7POWG/Q3Cg7l9XxX//toh3Hjmeuy5ZyMhhuc439SSOTRDPLmtyQ7ZNQ3KEH37yeM5dNJWbnqngfx99KTJ71lHfTr7sUYvIqcBpwGQRuaHLTaOBhB/rDFpeXl7YQ8janf/eynV/LuF9Rx/CTefPZ3jeEMDtpt7EsQni2WVNbhhIU06O8N2PHcuw3Bxu//dW2jo6+M4Zx5KTE+6eddS3k19/RuwA8oEWoKDL5RHgFJ/WGajGxsawh5CVW56t4Lo/l/DhORO4+YK3Jmlwt6kvcWyCeHZZkxsG2iQifPP0OVzx3iO4d20VX/v9C3Qkw92zjvp28mWPWlWLgCIRuU9VY7EH3d348dE/F3N3v3yqjJ/8bTOnHz+Rn51zAnlD9v07zcWm/sSxCeLZZU1u8KJJRPja0tkMyx3CDU+V0ZZI8uNPzSV3SDhPQUd9O/nyX0VEHk7/83kReaH7JcNlLBWRl0WkXES+1sPtJ4vIGyKyMX35pqcR/di+fXuQqxsQVeXHT77MT/62mU/Mm8wvlp34tkka3GrKVBybIJ5d1uQGr5pEhC99aBb/fcrR/HHjDj734PO0dyQ9Wfb+ivp28uUQoiIyUVVrRGRaT7erap+HqRGRIcBm4EPAdmADsFxVS7rc52TgK6p6eqbj8vIQoolEgtxcv980P3Cqyvcef4nV/9rKspMO53sfP67X14NcadofcWyCeHZZkxv8aLr1X1v4v8de4oPvmMCN553IsNwh/T/IQ1HYToEfQlRVa9Jft/V0yWARC4FyVd2iqm3Ag0Ts89ebNm0Kewj9SiaVbz2yidX/2spFS6b1OUmDG037K45NEM8ua3KDH00r/usI/vfMY/j7Szu5/O4CWto7PF9HX6K+nfx66nuPiDR0uezp+jWDRUwGXulyfXv6e90tEZEiEfmLiPR4og8RWSki+SKSX1NTQ11dHTU1NVRXV1NfX09FRQXNzc2UlJSQTCbfOoNU+vykhYWFJJNJSkpKaG5upqKigvr6esaPH0/n8iorK2lsbKS0tJREIkFRUdE+y+j8WlxcTGtrK2VlZTQ0NFBVVUVtbS21tbVUVVXR0NBAWVkZra2tFBcX97iMoqIiEokEpaWlNDY2UllZ2WPT3qYmPn37s9y9ZhtnzDqQ6844huefL3S6KY7bKZum6upqDj30UGuyplg1nT1vIp9dNI5/lb3GWTf8g6a2hPNN+7Od+qSqkbsAnwJu7XL9AuCX3e4zGhiZ/vdpQFl/y50/f756JT8/37Nlea090aFffPB5nfbVR/VHT5RqMpnM6HFRbspWHJtU49llTW7wu+n3ha/ojK89qmfd9G9taG7zdV2dorCdgHztZe7y9TSXACIyD3g3qdNdPqeqz2fwmCXAdap6Svr6tQCq+v0+HlMJLFDVut7u4+Vr1FHV3pHkiw9t5NEXavjyh2bx2Q/MDHtIxhizXx57oYbPP/g8x0w+iLsvWchBI6L9OWcvhHaay/Q7se8CDgbGA3eKyDcyeOgGYKaIzBCRocAyUp/B7rrswyR9/DkRWUiq5XUvx9+XzqcvoqQ10cFV9xXy6As1/M9ps/d7ko5i00DFsQni2WVNbgii6SPHT+TX582jZMcbnHvrWur3tvm6vqhvJ1/3qEXkJeBEVW1JXz8AKFTVd2Tw2NOAnwNDgNtV9bsiciWAqt4sIlcDnyZ1pLNm4Euq+p++lhnnPeqW9g4+fW8BT7/8Gt8+4xgueuf0sIdkjDED8vTLtVx5TwHTDz6Qe1cs4pBR8TmzX3eh7VEDlUDXExsPAzI6z5mqPq6qs1T1SFX9bvp7N6vqzel//0pVj1HVuaq6uL9J2mudbxCIgqa2BCvuyueZza/xvY8fl/UkHaUmr8SxCeLZZU1uCLLpfUcfyu0Xn0TVribOuWUNr77R4st6or6d/N6j/iNwEvA3Uq9Rfwh4DqgFUNXP+bbyHni5R93a2sqwYeH/ddfYmuDSOzeQX7mLH541l7PmT8l6WVFp8lIcmyCeXdbkhjCa1m/dxSV3rGf8qGHcf/liJo85wNPlR2E7hblH/Qfgf4CngWeArwN/4a1jfzurqqoq7CHwRnM7F9y2joJt9fx82YkDmqQhGk1ei2MTxLPLmtwQRtPCGeO4Z8Uidu1t4+yb11D1epOny4/6dvL9Xd9R4uUedUNDA6NHj/ZkWdnY3dTGBbetp/TVBn65fB5Ljz1swMsMu8kPcWyCeHZZkxvCbCre/gYX3L6O4blDuP/yRRxxyEhPlhuF7RTmu75PF5HnRWTXfh7wJPJ2794d2rrrGltZdstaXt65h1UXzPdkkoZwm/wSxyaIZ5c1uSHMpuOmHMQDly+mvSPJ2avWsnnnHk+WG/Xt5PdT3z8HLgIOVtXRqjpKVWPx5+Xw4cP7v5MPahtaWHbLWipf38ttFy3g/bMneLbssJr8FMcmiGeXNbkh7KZ3TBzNQ1csJkdg2S1r2bTjjQEvM+ym/vg9Ub8CvKiD6fl1H+3Y3czZq9awY3czd16ykP+aeUjYQzLGmMAddegoHr5iCcNzczh39TqKXtkd9pB85fdEfQ3wuIhcKyJf6rz4vM5AtLT48zGB3ryyq4mzV63h9cY27rlsIYuPONjzdQTdFIQ4NkE8u6zJDVFpmj7+QB66YgmjD8jl/FvXUbBtV9bLikpTb/yeqL8LNJH6LPWoLhfnjRkzJrB1ba3byzmr1rCnJcF9ly9i/rRxvqwnyKagxLEJ4tllTW6IUtPh40bw0MoljB81jAtuW8/aLdkdnDJKTT3xe6Iep6qfUNVvqeq3Oy8+rzMQO3fuDGQ95bV7OGfVGloSSR64fDHHTxnj27qCagpSHJsgnl3W5IaoNU0acwAPrVzMpDEHcPEd6/lX2Wv7vYyoNXXn90T9dxH5sM/rCMXUqVN9X8dLNQ2cs2otCjy0cjFzJvn7PrwgmoIWxyaIZ5c1uSGKTYeOHs6DKxcz/eADueyufJ56af8m3ig2deX3RH0V8ISINMft41mbN2/2dfnF299g+eq15A3J4aGVi5k5wf9XDPxuCkMcmyCeXdbkhqg2jR85jAdXLuboCaO48t4CnnixJuPHRrWpkx3wJIIKq+q56Pb1jB6exwOXL2bqwSPCHpIxxjihoaWdi29fT9H2N/jZOSdwxtxJYQ8pI2EeQhQRGSsiC0XkPZ0Xv9cZBL9Oi7Z+6y4uuHUd4w4cysNXLgl0ko76qd6yEccmiGeXNbkh6k2jh+dx92WLmD9tLF948Hl+W7C938dEvcnvk3KsAD4PTAE2AouBNar6ft9W2oeo71H/u7yOFXflM2nMcO6/fDETRkf7Q/jGGBNVzW0dXH53Pv+uqOO7HzuOcxdF+3XoMPeoP0/q7FnbVPV9wInA/r8lL4K8/gvs6ZdrueTODUw7eAQPXbEklEk66n9VZiOOTRDPLmtygytNBwwdwq0XLeDkWYfwP38o5s5/b+31vlFv8nuPeoOqniQiG4FFqtoqIhtV9QTfVtqHqO5R/3XTq1x1fyFHHzaKey5dxNgDh4Y9JGOMiYW2RJLPPlDIk5t2cu2ps7nivUeGPaQehblHvV1ExgB/BP4mIn8Cdvi8zkAUFRV5spxHX9jBZ+4r5JhJB3HfisWhTtJeNUVJHJsgnl3W5AbXmobm5vCrc+dx+vET+f5fSrnhqbK33SfqTYG961tE3gscBDyhqm2BrLQbL/eoE4kEubm5A1rGH57fzpcfLmL+tLHcfvFJjBqe58nYsuVFU9TEsQni2WVNbnC1qSOp/Pdvi/h9YTVXv+8ovvzhWYgIEI2mUN/13UlV/6mqj4Q1SXutvLx8QI9/aEMVX3q4iMVHHMxdly4MfZKGgTdFURybIJ5d1uQGV5uG5Ag/Pmsuy046nF89Xc73Hn+Jzh3VqDe592dRREyZMiXrx96zppL/96dNvHfWIay6YD7D84Z4OLLsDaQpquLYBPHssiY3uNyUkyN87+PHMSw3h9X/2kprIsl1Hz0m8k02UWeprq6OkSNH7vfjbv3XFv7vsZf44DsmcON5JzIsNxqTNGTfFGVxbIJ4dlmTG1xvyskRrjvjGIblDeGWZ7fQlkhy+YmjIt1kE3WWstmoNz5dzo+efJmPHDeRny87gbwhgb3ykJEo/6BmK45NEM8ua3JDHJpEhGtPnc2w3Bx++Y9yGvaO54Zp08iN2P+TO9lEnaX29vaM76uq/Oxvm7nhH+V87IRJ/PhTcyP5A7E/Ta6IYxPEs8ua3BCXJhHhyx8+mqFDcvjJ3zYjD23k5+dEbwcKbKLOWjKZzOh+qsr1T5Sy6p9bOHvBFL7/ieMZkiM+jy47mTa5JI5NEM8ua3JD3Jo++4GZtDQ1cuO/d9CWSPKrc6P1kiQE+K7vuBkxov9jcKsq3/5zCav+uYXzF0/l+ghP0pBZk2vi2ATx7LImN8SxacW7p/PtM47hbyU7ueKeAlraO8Ie0j5sos7Srl27+rw9mVS+/scXufM/lVz27hn875nHkhPhSRr6b3JRHJsgnl3W5Ia4Nl30zul8/xPH8c/Nr3HZXRtoakuEPaw32USdpUmTej91WuqD9S9w/7oqPnPykXzjI+9484P1UdZXk6vi2ATx7LImN8S5afnCqfz4rLmsqXidi2/fQGNrNCZrm6iztHVrzwd4b+9I8oWHNvK7wu188YOz+O9TjnZikobem1wWxyaIZ5c1uSHuTZ+cP4VfLDuRgqp6LrhtHW80h//mucAOIRoFXh5CNJlMkpOz7985bYkkn3vgeZ7Y9CpfXTqbT58czYO/96anJtfFsQni2WVNbhgsTU+8+CqffSC4kyVF4hCicbNx48Z9rre0d3DlvQU8selVvnn6HOcmaXh7UxzEsQni2WVNbhgsTUuPPYxVF8xn885Glq9eS11ja/ADS7M9ag80t3Ww8p58/lVWx/997FjOXzzN83UYY4wJ3nNlday4ewNTxo7g/hWLOHT0cF/WY3vUPug80fje1gSX3Lme58rr+NFZxzs9SUf95OnZiGMTxLPLmtww2JrePXM8d12ykJrdzZy9ag07djcHOLKUyO5Ri8hS4BfAEOBWVb2+2+2Svv00oAm4WFUL+1qm13vUDS3tXHLHBja+spufnj2XM0+Y7NmyjTHGREfBtnouvn09B43I44HLF3P4OG8/T+7cHrWIDAFuBE4F5gDLRWROt7udCsxMX1YCNwU1voJt9Xzlrn/y8Rv/TdEru/nV8hNjMUkXFvb5d46T4tgE8eyyJjcM1qb508Zy3+WL2NOS4OxVa3j0hR3c+HQ5BdvqfR9fJPeoRWQJcJ2qnpK+fi2Aqn6/y31WAc+o6gPp6y8DJ6tqTW/L9WKPumBbPeeuXktrInUYvWtPnc0V73XvjWM9GSzv5oyDOHZZkxsGe1PJjgbOuWUNe1oS5AgMzc3hvhWLmT9t7IDG4NweNTAZeKXL9e3p7+3vfRCRlSKSLyL5NTU11NXVUVNTQ3V1NfX19VRUVNDc3ExJSQnJZPLNv6w6X7MoLCwkmUxSUlJCc3Mzj+eXvTlJ5wANjY1UVlbS2NhIaWkpiUSCoqKifZbR+bW4uJjW1lbKyspoaGigqqqK2tpaamtrqaqqoqGhgbKyMlpbWykuLu5xGUVFRSQSCUpLS2lMr3ugTRUVFdTX17NhwwY6/xtZU3Sbqquryc/PtyZrsqYQmuZMGs37ph8AQFKhPZHkycKKATf1Jap71J8CTlHVFenrFwALVfWzXe7zGPB9VX0uff0p4BpV7fVdAV7tUZ+3ei1tHUnP/pKKiubmZg444ICwh+GpODZBPLusyQ3W9NYzq4mOJHmDeI96O3B4l+tTgB1Z3MdzqdcpFnPJgkNiNUkD7Njh+3++wMWxCeLZZU1usKbUPHD/5Yv50oePDmQeiOppLjcAM0VkBlANLAPO7XafR4CrReRBYBHwRl+vT3tp/rSxHDF6JmPHxmeSBhg3blzYQ/BcHJsgnl3W5AZrSpk/bWxgO2qR3KNW1QRwNfAk8BLwsKpuEpErReTK9N0eB7YA5cBq4DNBjrGpqSnI1QXCmtwRxy5rcoM1BS+qe9So6uOkJuOu37u5y78VuCrocXWK27sewZpcEscua3KDNQUv2qOLsLy8vLCH4Dlrckccu6zJDdYUvEi+69svIvIasM2jxY0H6jxaVlRYkzvi2GVNbrAmf0xT1UN6umFQTdReEpH83t5K7yprckccu6zJDdYUPHvq2xhjjIkwm6iNMcaYCLOJOnu3hD0AH1iTO+LYZU1usKaA2WvUxhhjTITZHrUxxhgTYTZRG2OMMRFmE7UxxhgTYTZRG2OMMRFmE7UxxhgTYTZRG2OMMRFmE7UxxhgTYTZRG2OMMREW2fNR+2H8+PE6ffr0sIdhjDHG7KOgoKCut7NnDaqJevr06eTn53uyrIKCAubPn+/JsqLCmtwRxy5rcoM1+UNEej0F86A6hOiCBQvUq4naGGOM8YqIFPR2qk17jTpLBQUFYQ/Bc9bkjjh2WZMbrCl4tkdtjDHGhMz2qH1QVFQU9hA8Z03uiGOXNbnBmoJne9RZSiQS5ObG67141uSOOHZZkxusyR+2R+2D8vLysIfgOWtyRxy7rMkN1hQ8m6izNGXKlLCH4Dlrckccu6zJDdYUPJuos1RXVxf2EDxnTe6IY5c1ucGagmcTdZZGjhwZ9hA8Z03uiGOXNbnBmoJnE3WW2tvbwx6C56zJHXHssiY3WFPwbKLOUjKZDHsInrMmd8Sxy5rcYE3Bs4k6SyNGjAh7CJ6zJnfEscua3GBNwbOJOku7du0KewiesyZ3xLHLmtxgTcELdaIWkaUi8rKIlIvI13q4XUTkhvTtL4jIvG63DxGR50Xk0eBGnTJp0qSgV+k7a3JHHLusyQ3WFLzQJmoRGQLcCJwKzAGWi8icbnc7FZiZvqwEbup2++eBl3weao+2bt0axmp9ZU3uiGOXNbnBmoIX5h71QqBcVbeoahvwIHBmt/ucCdytKWuBMSIyEUBEpgAfAW4NctCdZs+eHcZqfWVN7ohjlzW5wZqCF+ZEPRl4pcv17envZXqfnwPXAKG8XW/jxo1hrNZX1uSOOHZZkxusKXhhTtTSw/e6nyGkx/uIyOlArar2exJREVkpIvkikl9TU0NdXR01NTVUV1dTX19PRUUFzc3NlJSUkEwmKSwsBN46P2lhYSHJZJKSkhKam5upqKigvr6eCRMm0Lm8yspKGhsbKS0tJZFIvHkmls5ldH4tLi6mtbWVsrIyGhoaqKqqora2ltraWqqqqmhoaKCsrIzW1laKi4t7XEZRURGJRILS0lIaGxuprKy0pkHWVF1dzcSJE63JmqwpRk19Ce3sWSKyBLhOVU9JX78WQFW/3+U+q4BnVPWB9PWXgZOBzwEXAAlgODAa+L2qnt/XOr08e1ZBQQHz58/3ZFlRYU3uiGOXNbnBmvzR19mzwpyoc4HNwAeAamADcK6qbupyn48AVwOnAYuAG1R1YbflnAx8RVVP72+dXk7UxhhjjFcieZpLVU2QmoSfJPXO7YdVdZOIXCkiV6bv9jiwBSgHVgOfCWWwPeh8WiVOrMkdceyyJjdYU/BC26MOg5d71MlkkpyceB0vxprcEccua3KDNfkjknvUristLQ17CJ6zJnfEscua3GBNwbOJOkszZswIewiesyZ3xLHLmtxgTcGziTpLO3bsCHsInrMmd8Sxy5rcYE3Bs4k6S+PGjQt7CJ6zJnfEscua3GBNwbOJOktNTU1hD8Fz1uSOOHZZkxusKXg2UWcp7HcI+sGa3BHHLmtygzUFL7e3G7qfUrIX7apa7OF4nJGXlxf2EDxnTe6IY5c1ucGagtfrRA38k9TRwno63nanGcB0LwfkisbGRsaPHx/2MDxlTe6IY5c1ucGagtfXRL1BVd/f14NF5B8ej8cZUd6o2bImd8Sxy5rcYE3B6/WJ+f4m6UzvE1fbt28PewiesyZ3xLHLmtxgTcHr9xCiIvIuYKOq7hWR84F5wC9UdVsQA/SSl4cQTSQS5Ob29YSEe6zJHXHssiY3WJM/BnoI0ZuAJhGZC1wDbAPu9nB8Ttq0aVP/d3KMNbkjjl3W5AZrCl4me9SFqjpPRL4JVKvqbZ3fC2aI3rHTXBpjjImige5R7xGRa4HzgcdEZAgQ7feyB6CgoCDsIXjOmtwRxy5rcoM1BS+TPerDgHNJvQv8XyIyFThZVZ17+tv2qI0xxkRRVnvUIvKkiHwRGKOqP1XVfwGoapWLk7TXov4XWDasyR1x7LImN1hT8Hrdo07vSS9NX2YB64AngKdUtdGTlYssBX4BDAFuVdXru90u6dtPA5qAi1W1UEQOJ/WGtsOAJHCLqv6iv/XZHrUxxpgoymqPWlVfVdU7VXUZsIDUxDgfeFJE/i4i1wxwUEOAG4FTgTnAchGZ0+1upwIz05eVpN6BDpAAvqyq7wAWA1f18FhfFRfH78ip1uSOOHZZkxusKXgZHYlcVZOqukZVv6mq7wKWAdUDXPdCoFxVt6hqG/AgcGa3+5wJ3K0pa4ExIjJRVWtUtTA9tj3AS8DkAY5nv8yaNSvI1QXCmtwRxy5rcoM1Ba+v16h/KSI39HQBvqmq9w1w3ZOBV7pc387bJ9t+7yMi04ETST01H5iqqqogVxcIa3JHHLusyQ3WFLy+9qjzgQJgOKmjkZWlLycAHR6su6eTfXR/wbzP+4jISOB3wBdUtaHHlYisFJF8Ecmvqamhrq6Ompoaqqurqa+vp6KigubmZkpKSkgmkxQWFgJvvbmgsLCQZDJJSUkJzc3NVFRUUF9fD0Dn8iorK2lsbKS0tJREIkFRUdE+y+j8WlxcTGtrK2VlZTQ0NFBVVUVtbS21tbVUVVXR0NBAWVkZra2tbz4V030ZRUVFJBIJSktLaWxspLKy0poGWVN1dTVDhgyxJmuyphg19SWTj2c9DXxYVdvT1/OAv6rq+/p8YD9EZAlwnaqekr5+LYCqfr/LfVYBz6jqA+nrL5P6aFhNehyPAk+q6k8zWaeXbyarqqpi6tSpniwrKqzJHXHssiY3WJM/BnrAk0nAqC7XR6a/N1AbgJkiMkNEhpJ63fuRbvd5BLhQUhYDb6QnaQFuA17KdJL22vDhw8NYra+syR1x7LImN1hT8DI5Cvn1wPPpPWuA9wLXDXTFqpoQkauBJ0l9POt2Vd0kIlemb78ZeJzUR7PKSX0865L0w98FXAAUi8jG9Pf+R1UfH+i4jDHGmCjpd6JW1TtE5C/AovS3vqaqr3qx8vTE+ni3793c5d8KXNXD456j59evA9PS0hLm6n1hTe6IY5c1ucGagpfRx7OAVqAGqAdmich7/BuSG8aMGRP2EDxnTe6IY5c1ucGagtfvRC0iK4BnST1F/e301+v8HVb07dy5M+wheM6a3BHHLmtygzUFL5M96s8DJwHb0u/0PhF4zddROSDsdwj6wZrcEccua3KDNQUvk4m6RVVbAERkmKqWAkf7O6zo27x5c9hD8Jw1uSOOXdbkBmsKXiafo/4DqXdbfwF4P6nXqfNU9TTfR+cxOymHMcaYKBrQ56hV9eOqultVrwP+H6nPL3/M0xE6KOqnRcuGNbkjjl3W5AZrCl6fe9QikgO8oKrHBjck/9getTHGmCjKeo9aVZNAkYhE+5X2EET9L7BsWJM74thlTW6wpuBl8hr1P0i963s9sLfz+6p6hr9D857tURtjjImigR7r+9vA6cB3gJ90uQxqnWdViRNrckccu6zJDdYUvH73qOPEyz3qRCJBbm4mh0p3hzW5I45d1uQGa/JHVnvUIvJoBgvu9z5xVV5eHvYQPGdN7ohjlzW5wZqC19efEO8Wke6nnexKgDkej8cZU6ZMCXsInrMmd8Sxy5rcYE3B62uiPjODx7d5NRDX1NXVMXLkyLCH4Slrckccu6zJDdYUvF4nalX9Z5ADcU2UN2q2rMkdceyyJjdYU/AyPc2l6aa9vT3sIXjOmtwRxy5rcoM1BS/UiVpElorIyyJSLiJf6+F2EZEb0re/ICLzMn2s35LJZNCr9J01uSOOXdbkBmsKXmgTtYgMAW4ETiX1prTlItL9zWmnAjPTl5XATfvxWF+NGDEiyNUFwprcEccua3KDNQWv34laRIrTe7NdL/8SkZ+JyMEDWPdCoFxVt6hqG/Agb38D25nA3ZqyFhgjIhMzfKxvCrbV86t/lFGwrT6oVQZi165dYQ/Bc341FWyr58any0P7GbBtFa5Mt79LTZmyppQg/x+QySe8/wJ0APenry9Lf20A7gQ+muW6JwOvdLm+HViUwX0mZ/hYXxRsq+fsVWvoSCp35L/G7MNGMWp4XhCr9l0ymSQnpzbsYXjKj6Y9Le2UvrqHpEKOEMrPgG2r8OzP9nelaX9Y01s/A6owLC+H+1YsZv60sb6NL5Onvt+lqteqanH68nXgZFX9ATB9AOuWHr7X/TBpvd0nk8emFiCyUkTyRSS/pqaGuro6ampqqK6upr6+noqKCpqbmykpKSGZTFJYWAi8dZD2wsJCkskkJSUlNDc383h+GR3J1KqSCrv3ttLS0kJHRwdNTU2oKnv3NgLQ2Lhnn6979+5FNUlzczMdHR20trbS3t5Oe3s7ra2tdHR00NzcjGqSvXv39rKMRlSVpqYmOjo6aGlpob29nba2NtraWkkkErS0NJNMJmlqako/tvt4UtebmppIJpO0tDSTSCTYu7eRtrY22tvbramPpjea2kj/CJBUaGhJBNrU1tbK3r17Y7WdXGqqa2jaZ/vXNTQ53xTH7eRn0+vpnwEF2hNJniysoLa2ltraWqqqqmhoaKCsrIzW1laKi4uBt+aUzq9FRUUkEglKS0vfHFtvMtmjHikii1R1HYCILAQ638ueyODxvdkOHN7l+hRgR4b3GZrBYwFQ1VuAWyB1CNHx48fvc/vYsam/gubMSb3EPW9e6v1q8+fP3+d65+2nLZjJfRtfpz2RJC83h1+et8DXv6SClPqrMl4fBPCjqWBbPefduvbNn4FfLDsx8J8B21bh6b79b7pwUa/b35Wm/WFNb/8ZOGXekRx66L4/A6NHjwbguOOOA96aUzq/zp07F4DZs2f3v0JV7fNC6sxZxcBWoBJ4gdRrxAcCZ/f3+D6WmwtsAWaQmniLgGO63ecjpJ56F2AxsD7Tx/Z0mT9/vnohv3KX/s+9/9T8yl2eLC8qCgoKwh6C5/xqyq/cpb/6R1loPwO2rcKV6fZ3qSlT1pTi9f8DgHztZe7K+KQcInIQqZN47M7oAZkt8zTg58AQ4HZV/a6IXAmgqjeLiAC/ApYCTcAlqprf22P7W5+d5tIYY0wUDeg0lyIyTETOBa4CPici3xSRb3oxMFV9XFVnqeqRnROtqt6sqjen/62qelX69uM6J+neHhukqJ9oPBvW5I44dlmTG6wpeP3uUYvIE8AbQAGpd38DoKrOnZPa9qiNMcZE0YD2qIEpqnqOqv5QVX/SefF4jM7pfHd4nFiTO+LYZU1usKbgZbJHfQvwS1UtDmZI/vFyj9re+eiGODZBPLusyQ3W5I+B7lG/GyhIH1f7hc4jlXk7RPeUlpaGPQTPWZM74thlTW6wpuBl8jnqU30fhYNmzJgR9hA8Z03uiGOXNbnBmoLX6x61iIxO/3NPL5dBbceOHo+v4jRrckccu6zJDdYUvL72qO8HTif1bu/uh+1U4AgfxxV548aNC3sInrMmd8Sxy5rcYE3B63WPWlVPT3+doapHpL92Xgb1JA28eTzZOLEmd8Sxy5rcYE3By+Q1akRkMjCt6/1V9Vm/BuWCsN8h6Adrckccu6zJDdYUvH4nahH5AXAOUMJbBzxRYFBP1Hl58Ti1ZVfW5I44dlmTG6wpeJn8GfEx4GhVPU1VP5q+nOHzuCKvv9OSucia3BHHLmtygzUFL5OJegsQ7T83QtD9dJlxYE3uiGOXNbnBmoKXyUTdBGwUkVUickPnxe+BRd327dvDHoLnrMkdceyyJjdYU/AyOYToRT19X1Xv8mVEPvLyEKKJRILc3Izei+cMa3JHHLusyQ3W5I8BHUJUVe/q6eL9MN2yadOmsIfgOWtyRxy7rMkN1hS8TPaot5J6l/c+XPwstZ3m0hhjTBQN9KQcC4CT0pf/Am4A7h3ggMaJyN9EpCz9dWwv91uaPhlIuYh8rcv3fyQipemThPxBRMYMZDzZiPqJxrNhTe6IY5c1ucGagtfvHnWPDxJ5TlXfnfVKRX4I7FLV69MT8FhV/Wq3+wwBNgMfArYDG4DlqloiIh8G/qGqifTnvOn++J7YHrUxxpgoGtAetYjM63JZICJXAqMGOKYzgc7Xue8i9Vnt7hYC5aq6RVXbgAfTj0NV/6qqifT91gJTBjie/Rb1v8CyYU3uiGOXNbnBmoKXyWvUT3e5mgC2Aj9R1ZezXqnIblUd0+V6vaqO7Xafs4Clqroiff0CYJGqXt3tfn8GHlLVfp+Otz1qY4wxUTTQ16gvU9X3pS8fUtWVQFsGK/27iLzYw+XMTMfdw/f2+atCRL5O6o+H+/oYx0oRyReR/JqaGurq6qipqaG6upr6+noqKipobm6mpKSEZDJJYWEh8NZfWIWFhSSTSUpKSmhubqaiooL6+nrWrFlD5/IqKytpbGyktLSURCJBUVHRPsvo/FpcXExraytlZWU0NDRQVVVFbW0ttbW1VFVV0dDQQFlZGa2trRQXF/e4jKKiIhKJBKWlpTQ2NlJZWWlNg6ypurqatWvXWpM1WVOMmvqSyR51oarO6/a9AlWd3+cD+17my8DJqlojIhOBZ1T16G73WQJcp6qnpK9fC6Cq309fvwi4EviAqmZ06hMv96hbW1sZNmyYJ8uKCmtyRxy7rMkN1uSPrPaoRWS2iHwSOEhEPtHlcjEwfIBjegToPJDKRcCferjPBmCmiMwQkaHAsvTjEJGlwFeBMzKdpL1WVVUVxmp9ZU3uiGOXNbnBmoLX16FYjgZOB8YAH+3y/T3A5QNc7/XAwyJyGVAFfApARCYBt6ZPAJIQkauBJ4EhwO2q2vmp9F8Bw4C/iQjAWlW9coBj2i8TJkwIcnWBsCZ3xLHLmtxgTcHrdaJW1T8BfxKRJaq6xsuVqurrwAd6+P4O4LQu1x8HHu/hfkd5OZ5s7N69m9GjR4c9DE9Zkzvi2GVNbrCm4GXyZrLXReQpEXkRQESOF5Fv+DyuyBs+fKDP/kePNbkjjl3W5AZrCl4mE/Vq4FqgHUBVXyD1erExxhhjfJbJRD1CVdd3+16ix3sOIi0tLWEPwXPW5I44dlmTG6wpeJlM1HUiciTpzzCnD0RS4+uoHDBmzJiwh+A5a3JHHLusyQ3WFLxMJuqrgFXAbBGpBr4AfNrPQblg586dYQ/Bc9bkjjh2WZMbrCl4GZ+UQ0QOBHJUdY+/Q/KPHfCkb9bkjjh2WZMbrMkf2R7w5EtdL8AVwOVdrg9qmzdvDnsInrMmd8Sxy5rcYE3B63WPWkS+lf7n0aTORf1I+vpHgWc7T5bhEjsphzHGmCjKao9aVb+tqt8GxgPzVPXLqvplYD4hnFYyaqJ+WrRsWJM74thlTW6wpuBlclKOUmCuqramrw8DilR1dgDj85TtURtjjImigZ7m8h5gvYhcl346fB1wl5cDdFHU/wLLhjW5I45d1uQGawpeRu/6FpF5wH+lrz6rqs/7Oiqf2B61McaYKBroHjWqWqiqv0hfnJykvdZ5QvE4sSZ3xLHLmtxgTcHL+HPUceDlHnUikSA3t6+zhLrHmtwRxy5rcoM1+WPAe9Tm7crLy8MeguesyR1x7LImN1hT8GyiztKUKfH7hJo1uSOOXdbkBmsKXigTtYiME5G/iUhZ+uvYXu63VEReFpFyEflaD7d/RURURMb7P+p91dXVBb1K31mTO+LYZU1usKbghbVH/TXgKVWdCTyVvr4PERkC3AicCswBlovInC63Hw58CKgKZMTdjBw5MozV+sqa3BHHLmtygzUFL6yJ+kze+iz2XcDHerjPQqBcVbeoahvwYPpxnX4GXEP69JtBa29vD2O1vrImd8Sxy5rcYE3BC2uinqCqNQDpr4f2cJ/JwCtdrm9Pfw8ROQOoVtXQ3lOfTCbDWrVvrMkdceyyJjdYU/B8m6hF5O8i8mIPlzP7f3RqET18T0VkBPB14JsZjmOliOSLSH5NTQ11dXXU1NRQXV1NfX09FRUVNDc3U1JSQjKZpLCwEHjrSDWFhYUkk0lKSkpobm6moqKC+vp6Ghsb6VxeZWUljY2NlJaWkkgk3vxMXucyOr8WFxfT2tpKWVkZDQ0NVFVVUVtbS21tLVVVVTQ0NFBWVkZrayvFxcU9LqOoqIhEIkFpaSmNjY1UVlZa0yBrqq6uprm52ZqsyZpi1NSXUD5HLSIvAyerao2ITASeUdWju91nCXCdqp6Svn5t+qZHSb2u3ZS+PgXYASxU1Vf7Wq+Xn6OuqKjgyCOP9GRZUWFN7ohjlzW5wZr8EcXPUT8CXJT+90XAn3q4zwZgpojMEJGhwDLgEVUtVtVDVXW6qk4n9ZT4vP4maa9NmjQpyNUFwprcEccua3KDNQUvrIn6euBDIlJG6p3b1wOIyCQReRxAVRPA1cCTwEvAw6q6KaTxvs3WrVvDHoLnrMkdceyyJjdYU/DsEKJZSiaT5OTE63gx1uSOOHZZkxusyR9RfOrbeRs3bgx7CJ6zJnfEscua3GBNwbM9amOMMSZktkftg6ifaDwb1uSOOHZZkxusKXi2R22MMcaEzPaofdD5Yfo4sSZ3xLHLmtxgTcGzPeosReFdgl6zJnfEscua3GBN/rA9ah+UlpaGPQTPWZM74thlTW6wpuDZRJ2lGTNmhD0Ez1mTO+LYZU1usKbg2USdpR07doQ9BM9Zkzvi2GVNbrCm4NlEnaVx48aFPQTPWZM74thlTW6wpuDZRJ2lpqam/u/kGGtyRxy7rMkN1hQ8m6izFPY7BP1gTe6IY5c1ucGaghft0UVYXl5e2EPwnDW5I45d1uQGawreoPoctYi8BmzzaHHjgTqPlhUV1uSOOHZZkxusyR/TVPWQnm4YVBO1l0Qkv7cPp7vKmtwRxy5rcoM1Bc+e+jbGGGMizCZqY4wxJsJsos7eLWEPwAfW5I44dlmTG6wpYPYatTHGGBNhtkdtjDHGRJhN1MYYY0yE2URtjDHGRJhN1MYYY0yE2URtjDHGRJhN1MYYY0yE2URtjDHGRJhN1MYYY0yE2URtjDHGRFhu2AMI0vjx43X69OlhD8MYY4zZR0FBQV1vp7kcVBP19OnTyc/P92RZBQUFzJ8/35NlRYU1uSOOXdbkBmvyh4hs6/W2wXSs7wULFqhXE7UxxhjjFREp6O2c2PYadZYKCgrCHoLnrMkdceyyJjdYU/Bsj9oYY4wJme1R+6CoqCjsIXjOmtwRxy5rcoM1Bc/2qLOUSCTIzY3Xe/GsyR1x7LImN1iTP2yP2gfl5eVhD8Fz1uSOOHZZkxusKXg2UWdpypQpYQ/Bc9bkjjh2WZMbrCl4NlFnqa6uLuwheM6a3BHHLmtygzUFzybqLI0cOTLsIXjOmtwRxy5rcoM1Bc8m6iy1t7eHPQTPWZM74thlTW6wpuDZRJ2lZDIZ9hA8Z03uiGOXNbnBmoJnE3WWRowYEfYQPGdN7ohjlzW5wZqCZxN1lnbt2hX2EDxnTe6IY5c1ucGaghfqRC0iS0XkZREpF5Gv9XC7iMgN6dtfEJF53W4fIiLPi8ijwY06ZdKkSUGv0nfW5I44dlmTG6wpeKFN1CIyBLgROBWYAywXkTnd7nYqMDN9WQnc1O32zwMv+TzUHm3dujWM1frKmtwRxy5rcoM1BS/MPeqFQLmqblHVNuBB4Mxu9zkTuFtT1gJjRGQigIhMAT4C3BrkoDvNnj07jNX6yprcEccua3KDNQUvzIl6MvBKl+vb09/L9D4/B64B+ny7noisFJF8Ecmvqamhrq6Ompoaqqurqa+vp6KigubmZkpKSkgmkxQWFgJvnfassLCQZDJJSUkJzc3NVFRUUF9fz3/+8x86l1dZWUljYyOlpaUkEok3D/DeuYzOr8XFxbS2tlJWVkZDQwNVVVXU1tZSW1tLVVUVDQ0NlJWV0draSnFxcY/LKCoqIpFIUFpaSmNjI5WVldY0yJqqq6tZs2aNNVmTNcWoqS+hnZRDRD4FnKKqK9LXLwAWqupnu9znMeD7qvpc+vpTpCbnicBpqvoZETkZ+Iqqnt7fOu00l8YYY6Ioqifl2A4c3uX6FGBHhvd5F3CGiFSSesr8/SJyr39Dfbuon2g8G9bkjjh2WZMbrCl4Ye5R5wKbgQ8A1cAG4FxV3dTlPh8BrgZOAxYBN6jqwm7LORnbozbGGOOwSO5Rq2qC1CT8JKl3bj+sqptE5EoRuTJ9t8eBLUA5sBr4TCiD7UHn6x9xYk3uiGOXNbnBmoIX2h51GLzco04mk+TkxOt4Mdbkjjh2WZMbrMkfkdyjdl1paWnYQ/CcNbkjjl3W5AZrCp5N1FmaMWNG2EPwnDW5I45d1uQGawqeTdRZ2rGj+xvU3WdN7ohjlzW5wZqCZxN1lsaNGxf2EDxnTe6IY5c1ucGagmcTdZaamprCHoLnrMkdceyyJjdYU/Bsos5S2O8Q9IM1uSOOXdbkBmsKXrRHF2F5eXlhD8Fz1uSOOHZZkxusKXg2UWepv4Oou8ia3BHHLmtygzUFzybqLI0fPz7sIXjOmtwRxy5rcoM1Bc8m6ixt37497CF4zprcEccua3KDNQXPDiGapUQiQW5urifLigprckccu6zJDdbkDzuEqA82bdrU/50cY03uiGOXNbnBmoJne9TGGGNMyGyP2gdRP9F4NqzJHXHssiY3WFPwbI/aGGOMCZntUfsg6n+BZcOa3BHHLmtygzUFL9Q9ahFZCvwCGALcqqrXd7td0refBjQBF6tqoYgcDtwNHAYkgVtU9Rf9rc/2qI0xxkRRJPeoRWQIcCNwKjAHWC4ic7rd7VRgZvqyErgp/f0E8GVVfQewGLiqh8f6qri4OMjVBcKa3BHHLmtygzUFr9cPjolIQz+PFaBGVWdlue6FQLmqbkmv70HgTKCky33OBO7W1G7/WhEZIyITVbUGqAFQ1T0i8hIwudtjfTVrVrbZ0WVN7ohjlzW5wZqC19cedYWqju7jMgrYO4B1TwZe6XJ9e/p7+3UfEZkOnAis62klIrJSRPJFJL+mpoa6ujpqamqorq6mvr6eiooKmpubKSkpIZlMUlhYCLz1mkVhYSHJZJKSkhKam5upqKigvr6e4uJiOpdXWVlJY2MjpaWlJBIJioqK9llG59fi4mJaW1spKyujoaGBqqoqamtrqa2tpaqqioaGBsrKymhtbX3zL7zuyygqKiKRSFBaWkpjYyOVlZXWNMiaqqur2bRpkzVZkzXFqKkvvb5GLSJHdO7t9vrgDO7Tx2M/BZyiqivS1y8AFqrqZ7vc5zHg+6r6XPr6U8A1qlqQvj4S+CfwXVX9fX/r9PI16oaGBkaPHu3JsqLCmtwRxy5rcoM1+SOr16gzmYCznaTTtgOHd7k+BdiR6X1EJA/4HXBfJpO013bv3h30Kn1nTe6IY5c1ucGagtfrRC0ie0SkobeLB+veAMwUkRkiMhRYBjzS7T6PABdKymLgDVWtSb8b/DbgJVX9qQdj2W/Dhw8PY7W+siZ3xLHLmtxgTcHr9c1k6degEZHvAK8C95B6A9l5wKiBrlhVEyJyNfAkqY9n3a6qm0TkyvTtNwOPk/poVjmpj2ddkn74u4ALgGIR2Zj+3v+o6uMDHZcxxhgTJZmcLuQUVV3U5fpNIrIO+OFAV56eWB/v9r2bu/xbgat6eNxzpP5oCE1LS0uYq/eFNbkjjl3W5AZrCl4mn6PuEJHzRGSIiOSIyHlAh98Di7oxY8aEPQTPWZM74thlTW6wpuBlMlGfC5wN7ExfPpX+3qC2c+fOsIfgOWtyRxy7rMkN1hQ8OylHllpbWxk2bJgny4oKa3JHHLusyQ3W5I8BHUJURIaLyFUi8msRub3z4v0w3bJ58+awh+A5a3JHHLusyQ3WFLx+96hF5DdAKamnu79D6l3fL6nq5/0fnrfspBzGGGOiaKAn5ThKVf8fsFdV7wI+Ahzn5QBdFPXTomXDmtwRxy5rcoM1BS+TPer1qrpQRJ4FPkPqM9XrVfWIIAboJdujNsYYE0UD3aO+RUTGAt8gdaSwEuAHHo7PSVH/Cywb1uSOOHZZkxusKXh97lGLSA5wlqo+HNyQ/GN71MYYY6Io6z1qVU0CV/syKsd1nv4sTqzJHXHssiY3WFPwMnmN+v8BzcBDdDn/tKru8ndo3vNyjzqRSJCbm8kRWN1hTe6IY5c1ucGa/DHQ16gvJXW87WeBgvRl0D9/XF5eHvYQPGdN7ohjlzW5wZqC1++fEKo6I4iBuGbKlClhD8Fz1uSOOHZZkxusKXh9nY96Xn8PzuQ+cVVXVxf2EDxnTe6IY5c1ucGagtfXHvUdInIyfZ9O8jbgRC8H5IqRI0eGPQTPWZM74thlTW6wpuD1NVEfROr16L4m6te8HY472tvbwx6C56zJHXHssiY3WFPwen3qW1Wnq+oRqjqjj8vCgaxcRJaKyMsiUi4iX+vhdhGRG9K3v9D1qfb+Huu3ZDIZ9Cp9Z03uiGOXNbnBmoKXybu+fSEiQ4AbgVOBOcByEZnT7W6nAjPTl5XATfvxWN8UbKvngaJdFGyrD2qVgRgxYkTYQ/CcX00F2+q58eny0H4GbFuFK9Pt71JTpqwpJcj/B4T5wbGFQLmqbgEQkQeBM0kdorTTmcDdmvqw91oRGSMiE4HpGTzWFwXb6jl71Ro6ksqv/1XF7MNGMWp4nt+rDURLSzPDhx8Q9jA85UfTnpZ2Sl/dQ1IhRwjlZ8C2VXj2Z/u70rQ/rOmtnwFVGJaXw30rFjN/2ljfxhfaHjUwGXily/Xt6e9lcp9MHguAiKwUkXwRya+pqaGuro6amhqqq6upr6+noqKC5uZmSkpKSCaTFBYWAm8d+7WwsJBkMklJSQnNzc08nl9GRzJ1kJikwu69rbS0tNDR0UFTUxOqyt69jQA0Nu7Z5+vevXtRTdLc3ExHRwetra20t7fT3t5Oa2srHR0dNDc3o5pk7969vSyjEVWlqamJjo4OWlpaaG9vp62tjba2VhKJBC0tzSSTSZqamtKP7T6e1PWmpiaSySQtLc0kEglAaGtro7293Zr6aHqjqY30jwBJhYaWRKBNbW2tiEistpNLTXUNTfts/7qGJueb4rid/Gx6Pf0zoEB7IsmThRXU1tZSW1tLVVUVDQ0NlJWV0draSnFxMfDWnNL5taioiEQiQWlp6Ztj602/e9QiIqTOQX2Eqn5HRKYCh6nq+v4e29+ie/he98Ok9XafTB6b+qbqLcAtkDoy2fjx4/e5fezY1F9Bc+aknjmfNy/1Mvj8+fP3ud55+2kLZnLfxtdpSyQZmpvDL89b4OtfUkEqKSl5szMu/Ggq2FbPebeupT2RJC83h18sOzHwnwHbVuHpvv1vunBRr9vflab9YU1v/xk4Zd6RHHrovj8Do0ePBuC441Jnhe6cUzq/zp07F4DZs2f3u75MDiF6E5AE3q+q70ifSeuvqnpSxlU9L3cJcJ2qnpK+fi2Aqn6/y31WAc+o6gPp6y8DJ5N66rvPx/bEq0OIFmyrZ01FHUuOHB+bSRpSb6jIyQnzSRbv+dVUsK2etVteZ/ERB4fyM2DbKlyZbn+XmjJlTSle/z9goIcQXaSqVwEtAKpaDwwd8KhgAzBTRGaIyFBgGanTaHb1CHBh+t3fi4E3VLUmw8f6Zv60sbxzzJ5YTdIAGzduDHsInvOraf60sVz1vqNC+xmwbRWuTLe/S02ZsqaUIP8fkMke9TrgncAGVZ0nIoeQ2qMe8IFOROQ04OfAEOB2Vf2uiFwJoKo3p592/xWwFGgCLlHV/N4e29/67DSXxhhjomige9Q3AH8ADhWR7wLPAd/zYmCq+riqzlLVIzsnWlW9WVVvTv9bVfWq9O3HdU7SvT02SFE/0Xg2rMkdceyyJjdYU/D63aMGEJHZwAdIvYnrKVV9ye+B+cH2qI0xxkTRgPaoReRIYKuq3gi8CHxIRMZ4O0T3dH6MK06syR1x7LImN1hT8DJ5jXojsIDUO62fAP4MHK2qp/k9OK95uUdt73x0QxybIJ5d1uQGa/LHQF+jTqpqAvgE8AtV/SIw0csBuqi0tDTsIXjOmtwRxy5rcoM1BS+TibpdRJYDFwKPpr8Xj2NmDsCMGTPCHoLnrMkdceyyJjdYU/AymagvAZYA31XVrSIyA7jX32FF344dO8IeguesyR1x7LImN1hT8Po9hKiqlgCf63J9K3C9n4Nywbhx48IeguesyR1x7LImN1hT8DJ51/dMEfmtiJSIyJbOSxCDi7LOA7/HiTW5I45d1uQGawpeJk9930HqPNAJ4H3A3cA9fg7KBWG/Q9AP1uSOOHZZkxusKXiZjO4AVX2K1Ee5tqnqdcD7/R1W9OXlxe/9dNbkjjh2WZMbrCl4mUzULSKSA5SJyNUi8nHgUJ/HFXn9nT/URdbkjjh2WZMbrCl4mUzUXwBGkHpD2XzgAuAiH8fkhO7ntY4Da3JHHLusyQ3WFLx+J2pV3aCqjaq6XVUvUdVPqOraIAYXZdu3bw97CJ6zJnfEscua3GBNwcvkEKKzgP8GptHl41yq6tzr1F4eQjSRSJCb2++n25xiTe6IY5c1ucGa/DHQQ4j+BigEvkFqwu68DGqbNm0KewiesyZ3xLHLmtxgTcHLZI+6QFXnBzQeX9lpLo0xxkRRVnvUIjJORMYBfxaRz4jIxM7vpb8/kAGNE5G/iUhZ+uvYXu63VEReFpFyEflal+//SERKReQFEflDGKfdjPqJxrNhTe6IY5c1ucGagtfrHrWIbAUUkB5uVlU9IuuVivwQ2KWq16cn4LGq+tVu9xkCbAY+BGwHNgDLVbVERD4M/ENVEyLyg/SAvko/bI/aGGNMFGW1R62qM1T1iPTX7pesJ+m0M4G70v++C/hYD/dZCJSr6hZVbQMeTD8OVf1r+tSbAGuBKQMcz36L+l9g2bAmd8Sxy5rcYE3By+RY38NF5Esi8nsR+Z2IfEFEhg9wvRNUtQYg/bWnA6hMBl7pcn17+nvdXQr8pbcVichKEckXkfyamhrq6uqoqamhurqa+vp6KioqaG5upqSkhGQySWFhIfDWhissLCSZTFJSUkJzczMVFRXU19dz2GGH0bm8yspKGhsbKS0tJZFIUFRUtM8yOr8WFxfT2tpKWVkZDQ0NVFVVUVtbS21tLVVVVTQ0NFBWVkZrayvFxcU9LqOoqIhEIkFpaSmNjY1UVlZa0yBrqq6uZtKkSdZkTdYUo6a+ZPJmsoeBPbx1asvlpJ6q/lQ/j/s7cFgPN30duEtVx3S5b72q7vM6tYh8CjhFVVekr18ALFTVz3a5z9eBBcAntL8QvH3qu7i4mOOOO86TZUWFNbkjjl3W5AZr8kdfT31n8sGxo1V1bpfrT4tIUX8PUtUP9jGgnSIyUVVrRGQiUNvD3bYDh3e5PgV486ShInIRcDrwgUwmaa/NmjUr6FX6zprcEccua3KDNQUvk89RPy8iizuviMgi4N8DXO8jvHUY0ouAP/Vwnw3ATBGZISJDgWXpxyEiS4GvAmeoaijnJ6uqqgpjtb6yJnfEscua3GBNwctkol4E/EdEKkWkElgDvFdEikXkhSzXez3wIREpI/Wu7usBRGSSiDwOkH6z2NXAk8BLwMOq2vmp9F8Bo4C/ichGEbk5y3FkbcKECUGv0nfW5I44dlmTG6wpeJk89b3U65Wq6uvAB3r4/g7gtC7XHwce7+F+R3k9pv21e/duRo8eHfYwPGVN7ohjlzW5wZqC1+9ErarbghiIa4YPH+gb36PHmtwRxy5rcoM1BS+Tp76NMcYYExKbqLPU0tIS9hA8Z03uiGOXNbnBmoJnE3WWxowZE/YQPGdN7ohjlzW5wZqCZxN1lnbu3Bn2EDxnTe6IY5c1ucGagmcTdZamTp0a9hA8Z03uiGOXNbnBmoJnE3WWNm/eHPYQPGdN7ohjlzW5wZqC1++xvuPETnNpjDEmirI6zaXpW9RPi5YNa3JHHLusyQ3WFDzbozbGGGNCZnvUPoj6X2DZsCZ3xLHLmtxgTcGzPWpjjDEmZLZH7YOion5Pye0ca3JHHLusyQ3WFDzbo85SIpEgNzeTk4+5w5rcEccua3KDNfnD9qh9UF5eHvYQPGdN7ohjlzW5wZqCZxN1lqZMmRL2EDxnTe6IY5c1ucGaghfKRC0i40TkbyJSlv46tpf7LRWRl0WkXES+1sPtXxERFZHx/o96X3V1dUGv0nfW5I44dlmTG6wpeGHtUX8NeEpVZwJPpa/vQ0SGADcCpwJzgOUiMqfL7YcDHwKqAhlxNyNHjgxjtb6yJnfEscua3GBNwQtroj4TuCv977uAj/Vwn4VAuapuUdU24MH04zr9DLgGCOXdcO3t7WGs1lfW5I44dlmTG6wpeGFN1BNUtQYg/fXQHu4zGXily/Xt6e8hImcA1ara73vqRWSliOSLSH5NTQ11dXXU1NRQXV1NfX09FRUVNDc3U1JSQjKZpLCwEHjrA/CFhYUkk0lKSkpobm6moqKC+vr6N5dTV1dHZWUljY2NlJaWkkgk3nyrf+cyOr8WFxfT2tpKWVkZDQ0NVFVVUVtbS21tLVVVVTQ0NFBWVkZrayvFxcU9LqOoqIhEIkFpaSmNjY1UVlZa0yBrqq6uZteuXdZkTdYUo6a++PbxLBH5O3BYDzd9HbhLVcd0uW+9qu7zOrWIfAo4RVVXpK9fQGov+6vA08CHVfUNEakEFqhqvy8yePnxrPr6esaO7fGldWdZkzvi2GVNbrAmf4Ty8SxV/aCqHtvD5U/AThGZmB7cRKC2h0VsBw7vcn0KsAM4EpgBFKUn6SlAoYj09EeBb3bt2hXk6gJhTe6IY5c1ucGaghfWU9+PABel/30R8Kce7rMBmCkiM0RkKLAMeERVi1X1UFWdrqrTSU3o81T11SAG3mnSpElBri4Q1uSOOHZZkxusKXhhTdTXAx8SkTJS79y+HkBEJonI4wCqmgCuBp4EXgIeVtVNIY33bbZu3Rr2EDxnTe6IY5c1ucGagmeHEM1SMpkkJydex4uxJnfEscua3GBN/rBDiPpg48aNYQ/Bc9bkjjh2WZMbrCl4tkdtjDHGhMz2qH0Q9RONZ8Oa3BHHLmtygzUFz/aojTHGmJDZHrUPOo96EyfW5I44dlmTG6wpeLZHnaUovEvQa9bkjjh2WZMbrMkftkftg9LS0rCH4Dlrckccu6zJDdYUPJuoszRjxoywh+A5a3JHHLusyQ3WFDybqLO0Y8eOsIfgOWtyRxy7rMkN1hQ8m6izNG7cuLCH4Dlrckccu6zJDdYUPJuos9TU1BT2EDxnTe6IY5c1ucGagmcTdZbCfoegH6zJHXHssiY3WFPwoj26CMvLywt7CJ6zJnfEscua3GBNwRtUn6MWkdeAbR4tbjxQ59GyosKa3BHHLmtygzX5Y5qqHtLTDYNqovaSiOT39uF0V1mTO+LYZU1usKbg2VPfxhhjTITZRG2MMcZEmE3U2bsl7AH4wJrcEccua3KDNQXMXqM2xhhjIsz2qI0xxpgIs4naGGOMiTCbqHsgIktF5GURKReRr/Vwu4jIDenbXxCReZk+NiwZNJ2XbnlBRP4jInO73FYpIsUislFEvDmhtwcyaDpZRN5Ij3ujiHwz08eGJYOm/+7S86KIdIjIuPRtUd1Ot4tIrYi82MvtLv4+9dfk4u9Tf00u/j711+TG75Oq2qXLBRgCVABHAEOBImBOt/ucBvwFEGAxsC7Tx0a46Z3A2PS/T+1sSl+vBMaH3ZFF08nAo9k8NqpN3e7/UeAfUd5O6XG9B5gHvNjL7U79PmXY5NTvU4ZNTv0+ZdLU7b6R/X2yPeq3WwiUq+oWVW0DHgTO7HafM4G7NWUtMEZEJmb42DD0Oy5V/Y+q1qevrgWmBDzG/TWQ/9bObqdulgMPBDKyAVDVZ4FdfdzFtd+nfpsc/H3KZDv1xtnt1E1kf59son67ycArXa5vT38vk/tk8tgw7O+4LiO1h9NJgb+KSIGIrPRhfNnItGmJiBSJyF9E5Jj9fGzQMh6XiIwAlgK/6/LtKG6nTLj2+7S/XPh9ypRLv08Zi/rvU26YK48o6eF73T/D1tt9MnlsGDIel4i8j9T/WN7d5dvvUtUdInIo8DcRKU3/pRqmTJoKSR0/t1FETgP+CMzM8LFh2J9xfRT4t6p23VuI4nbKhGu/Txlz6PcpE679Pu2PSP8+2R71220HDu9yfQqwI8P7ZPLYMGQ0LhE5HrgVOFNVX+/8vqruSH+tBf5A6qmusPXbpKoNqtqY/vfjQJ6IjM/ksSHZn3Eto9vTdBHdTplw7fcpI479PvXLwd+n/RHt36ewXySP2oXUswxbgBm89caIY7rd5yPs++aX9Zk+NsJNU4Fy4J3dvn8gMKrLv/8DLHWk6TDeOqjPQqAqvc2c3U7p+x1E6nW3A6O+nbqMbzq9v0nJqd+nDJuc+n3KsMmp36dMmtK3R/73yZ767kZVEyJyNfAkqXcz3q6qm0TkyvTtNwOPk3qnajnQBFzS12NDyNhHhk3fBA4Gfi0iAAlNnU1mAvCH9PdygftV9YkQMvaRYdNZwKdFJAE0A8s09Zvn8nYC+DjwV1Xd2+XhkdxOACLyAKl3DI8Xke3At4A8cPP3CTJqcur3CTJqcur3CTJqAgd+n+wQosYYY0yE2WvUxhhjTITZRG2MMcZEmE3UxhhjTITZRG2MMcZEmE3UxhhjTC/6O7HHfi7rfV1OArJRRFpE5GP9Ps7e9W2MMcb0TETeAzSSOh79sR4udxypjyROUdWmvu5re9TGDCIiMkZEPtPl+iQR+a0P67lORKpF5Dt93OfI9F5Fo9frN8Yr2sOJPdI/u0+kjwP+LxGZncWizwL+0t8kDTZRGzPYjAHenKhVdYeqnuXTun6mqt/s7UZVrVDVE3xatzF+ugX4rKrOB74C/DqLZbztsKW9sSOTGTO4XA8cKSIbgb8BN5I6x/CxInIx8DFSR5c6FvgJqUNCXgC0Aqep6i4ROTL9uENIHUnsclUt7WulIvJe4Bfpqwq8R1X3eJtmjP9EZCSp843/Jn3kMoBh6ds+AfT0LFK1qp7SZRkTgeNIHc2tXzZRGzO4fA04tnNPVkSmd7v9WOBEYDip18++qqonisjPgAuBn5Pam7hSVctEZBGpvYn397PerwBXqeq/0/+ja/Emx5jA5QC7e3o2SFV/D/w+g2WcDfxBVdszXaExxnR6WlX3qOprwBvAn9PfLwamd9ub2AisAiZmsNx/Az8Vkc8BY1Q14f3QjfGfqjYAW0XkUwCSMnc/F7OcDJ/2BpuojTH7au3y72SX60lSz8C9uTfR5fKO/haqqtcDK4ADgLVZvvnGmMClT+yxBjhaRLaLyGXAecBlIlIEbALO3I/lTSd1WtB/ZvoYe+rbmMFlDzAq2weraoOIbBWRT6nqbyT1It3xqlrU1+NE5EhVLQaKRWQJMBvo83VtY6JAVZf3ctPSLJdXCUzen8fYHrUxg4iqvg78W0ReFJEfZbmYbPYmvpBeZxGpUyT+Jct1GzPo2AFPjDGeE5HrgEZV/XEG921U1ZH+j8oYN9ketTHGD43AykwOeALsDGxUxjjI9qiNMcaYCLM9amOMMSbCbKI2xhhjIswmamOMMSbCbKI2xhhjIuz/A4BVLhX0C/e1AAAAAElFTkSuQmCC\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from ahs_utils import show_global_drive\n", + "show_global_drive(drive);" + ] + }, + { + "cell_type": "markdown", + "id": "9c84b2ad", + "metadata": {}, + "source": [ + "Here we used constant-zero phase and detuning, but, for more involved programs, its time series can be customized similarly to how we set the amplitude of the Rabi frequency here." + ] + }, + { + "cell_type": "markdown", + "id": "7d37e943", + "metadata": {}, + "source": [ + "### AHS program\n", + "\n", + "We can assemble the register and Hamiltonian to an AHS program " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "4d5ab540", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.ahs.hamiltonian import Hamiltonian\n", + "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n", + "\n", + "ahs_program = AnalogHamiltonianSimulation(\n", + " register=register, \n", + " hamiltonian=drive\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "6bbedb27-3568-4803-a1ed-7b26dc60c946", + "metadata": {}, + "source": [ + "### Task \n", + "\n", + "Before submitting the AHS program to Aquila, we need to discretize the program to ensure that it complies with resolution-specific validation rules. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "59fb7f60", + "metadata": {}, + "outputs": [], + "source": [ + "discretized_ahs_program = ahs_program.discretize(device)" + ] + }, + { + "cell_type": "markdown", + "id": "09b11fc2", + "metadata": {}, + "source": [ + "We note that the number of shots has to be within the range specified by `device.properties.service.shotsRange`. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "46d2da98", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1, 1000)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "device.properties.service.shotsRange" + ] + }, + { + "cell_type": "markdown", + "id": "4895c99a", + "metadata": {}, + "source": [ + "The AHS program can be submitted to the device to create a quantum task on the Braket service." + ] + }, + { + "cell_type": "markdown", + "id": "825eda10", + "metadata": {}, + "source": [ + "
    \n", + "Note: Some atoms may be missing even if the shot was successful. We recommend comparing pre_sequence of each shot with the requested atom filling in the AHS program specification. \n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "0e6528d5", + "metadata": {}, + "outputs": [], + "source": [ + "n_shots = 100" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c395c2a1-8ce2-4521-8d92-16efad87ac9e", + "metadata": {}, + "outputs": [], + "source": [ + "task = device.run(discretized_ahs_program, shots=n_shots)" + ] + }, + { + "cell_type": "markdown", + "id": "60c6be46", + "metadata": {}, + "source": [ + "The task metadata can be inspected in the following way" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "158f1044-4cfa-4fc1-a26e-5581900f8783", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ARN: arn:aws:braket:us-east-1:545821822555:quantum-task/0f934b5d-fc5c-4b77-85c0-7ef0d2a8cf41\n", + "status: CREATED\n" + ] + } + ], + "source": [ + "metadata = task.metadata()\n", + "task_arn = metadata['quantumTaskArn']\n", + "task_status = metadata['status']\n", + "\n", + "print(f\"ARN: {task_arn}\")\n", + "print(f\"status: {task_status}\")" + ] + }, + { + "cell_type": "markdown", + "id": "54a39bff", + "metadata": {}, + "source": [ + "It is suggested to save the task ARN for retrieving the task result in a later time. For example if the saved task ARN reads `arn:aws:braket:us-east-1:545821822555:quantum-task/12345`, the task can be retrieved as follows.\n", + " \n", + "```\n", + "from braket.aws import AwsQuantumTask\n", + "task = AwsQuantumTask(arn=\"arn:aws:braket:us-east-1:545821822555:quantum-task/12345\") \n", + "```\n", + "\n", + "\n", + "\n", + "Alternatively, we can access the tasks through [the tasks page of Amazon Braket console](https://us-east-1.console.aws.amazon.com/braket/home?region=us-east-1#/tasks)." + ] + }, + { + "cell_type": "markdown", + "id": "d496c2bb-89ec-4475-bf7d-ae75ef13cdde", + "metadata": {}, + "source": [ + "## Analyzing the result from Aquila\n", + "\n", + "The results (once the task is completed) can be downloaded directly into an object in the python session." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "d8176e09-deeb-485d-96e9-5046f9d03fc5", + "metadata": {}, + "outputs": [], + "source": [ + "result = task.result()" + ] + }, + { + "cell_type": "markdown", + "id": "ae5eac68", + "metadata": {}, + "source": [ + "The call `task.result()` is blocking execution until the task is completed and results are loaded from Amazon Braket. After the task is completed, the measurement result is saved in `result.measurements` which is a list of `ShotResult`, as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "afb85bab", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "ShotResult(status=, pre_sequence=array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1]), post_sequence=array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1,\n", + " 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1,\n", + " 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0,\n", + " 1, 0, 1, 1, 1, 1, 1, 1, 0]))" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result.measurements[0]" + ] + }, + { + "cell_type": "markdown", + "id": "91a9823b", + "metadata": {}, + "source": [ + "`ShotResult` contains three pieces of information\n", + "\n", + "1. `status` indicates if the shot is successful\n", + "2. `pre_sequence` contains the measurement result *before* running the AHS program. Here `0` indicates an empty site, while `1` indicates a filled site with an atom in the ground state\n", + "3. `post_sequence` contains the measurement result *after* running the AHS program. Here `0` indicates an empty site, or an atom in the Rydberg state, while `1` indicates an atom in the ground state\n" + ] + }, + { + "cell_type": "markdown", + "id": "88687ac9", + "metadata": {}, + "source": [ + "
    \n", + "Note: Some atoms may be missing even if the shot was successful. We recommend comparing pre_sequence of each shot with the requested atom filling in the AHS program specification. \n", + "
    " + ] + }, + { + "cell_type": "markdown", + "id": "c0d7eade", + "metadata": {}, + "source": [ + "To confirm that at the end of the AHS program, the average Rydberg density for the atoms in the triangles are around 1/3 for each atom, we can first collect the measurement result and aggregate over all triangles" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "4ed4a31c", + "metadata": {}, + "outputs": [], + "source": [ + "from ahs_utils import get_counts\n", + "\n", + "counts = get_counts(result)\n", + "average_density = [0, 0, 0]\n", + "average_num_triangles = [0, 0, 0, 0]\n", + "for key, val in counts.items():\n", + " for i in range(0, 3*k_max*m_max, 3):\n", + " short_seq = key[i:i+3]\n", + " for j in range(3):\n", + " if short_seq[j]==\"r\":\n", + " average_density[j] += val \n", + " \n", + " \n", + " average_num_triangles[short_seq.count('r')] += val\n", + " \n", + " \n", + "average_density = np.array(average_density) / (k_max * m_max * n_shots)\n", + "average_num_triangles = np.array(average_num_triangles) / n_shots" + ] + }, + { + "cell_type": "markdown", + "id": "15d35f76", + "metadata": {}, + "source": [ + "Note that although we only perform 100 shots for the given AHS program, since we have made the full usage of the area in the Aquila device, effectively, we have made 3,500 shots for the experiment of interest! We can plot the result as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "8fa10c84", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n", + "ax1.bar(range(len(average_density)), average_density)\n", + "ax1.set_xticks(range(3))\n", + "ax1.set_xticklabels(range(3))\n", + "ax1.set_xlabel(\"Indices of atoms\")\n", + "ax1.set_ylabel(\"Average Rydberg density\")\n", + "\n", + "ax2.bar(range(len(average_num_triangles)), average_num_triangles)\n", + "ax2.set_xlabel(\"Number of Rydberg atoms\")\n", + "ax2.set_ylabel(\"Average number of triangles\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e73773e1", + "metadata": {}, + "source": [ + "In the left panel, we show the average Rydberg density for each atom in the triangles. We see that indeed the average Rydberg density for the atoms in the triangles are around 1/3 as expected. In the right panel, we show the number of triangles with certain number of Rydberg atoms (0, 1, 2 or 3) averaged over the shots. It can be seen that almost no triangle has more than 1 Rydberg atoms since the atoms in the same triangle blockade each other. \n", + "\n", + "In summary, in this notebook we have demonstrated how to connect to QuEra's Aquila device, and define a valid AHS program for the device. " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "9180c117", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-east-1::device/qpu/quera/Aquila': {'shots': 100, 'tasks': {'COMPLETED': 1}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 1.30 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(tracker.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a9a8a075", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb new file mode 100644 index 000000000..84c5b9fcb --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb @@ -0,0 +1,606 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f82bf0f", + "metadata": {}, + "source": [ + "# Ordered phases in Rydberg systems\n", + "\n", + "In this example notebook, we show how one can prepare ordered phases in Rydberg systems, focusing on the 1D $Z_2$ phase and the 2D checkerboard phase. We will use an adiabatic time-evolution to prepare these many-body ground states.\n", + "\n", + "## Adiabatic evolution\n", + "\n", + "The adiabatic theorem of quantum mechanics states that \n", + "\n", + ">A physical system remains in its *instantaneous* eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. (Born & Fock, 1928)\n", + "\n", + "In other words, a slow-enough change in the parameters of the Hamiltonian will not induce transitions between its ground state and excited states: If the system starts in the ground state of the Hamiltonian at the beginning, it will smoothly transition into the ground state of the Hamiltonian at the end.\n", + "\n", + "The adiabatic theorem plays a key role in preparing the desired many-body ground states in the Rydberg system, the Hamiltonian of which can be expressed as\n", + "\n", + "\\begin{align}\n", + "H(t) = \\sum_{k=1}^N \\frac{\\Omega(t)}{2}\\left(|g_k\\rangle\\langle r_k| + |r_k\\rangle\\langle g_k|\\right) - \\Delta_\\text{global}(t){n}_k + \\sum_{j=1}^{N-1}\\sum_{k=j+1}^N V_{jk}{n}_j{n}_k,\n", + "\\end{align}\n", + "\n", + "where, for simplicity, we set the phase and the shifting field (See notebook 00 for detailed description of this Hamiltonian) to be zero throughout this notebook. We schedule the driving amplitude $\\Omega(t)$ to start from zero ($\\Omega(t=0)=0$). Hence, with negative detuning ($\\Delta_\\text{global}(t=0)<0$), the initial state where all atoms are in the ground state ($\\langle n_k\\rangle =0$) is the lowest energy eigenstate of the Hamiltonian, the many-body ground state.\n", + "\n", + "To arrive at a target Hamiltonian where the excited states of the atoms are favored, we ramp up the detuning $\\Delta_\\text{global}$ from large negative to large positive. During the ramp, we apply a large driving amplitude $\\Omega$ to open an energy gap between the first excited state and the ground state. According to the adiabatic theorem, if the ramping is slow enough, the system remains in the many-body ground state throughout the evolution. At the end of the AHS program, the Rabi frequency will be turned off and since $\\Delta_\\text{global}>0$, all the atoms tend to stay in the Rydberg state to lower the energy of the system. However, due to the strong Rydberg interaction, only one atom can be excited to the Rydberg state within its blockade radius.\n", + "\n", + "For a 1D chain of atoms, if we adjust the separation between the atoms such that only neighboring atoms are within the blockade radius, then we will arrive at a state where every second atom is excited, this is called the \"$Z_2$ phase\". For a 2D square array of atoms, a similar \"checkerboard phase\" emerges. The common feature of these phases is that the atoms are excited to the Rydberg states in an alternative pattern, complying with the blockade constraint, as shown in the figure below. In the figure, the shaded circles show *half* of the blockade radius such that sites with overlapped circles blockade each other. We show configurations, with black and white sites represent Rydberg and ground state atoms respectively, that comply with the blockade constraint. \n", + "\n", + "![Blockade_examples.png](Blockade_examples.png)\n", + "\n", + "We will realize these phases in this notebook. To begin, we import the necessary packages." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "9124196d", + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "tracker = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "id": "156c4218", + "metadata": {}, + "source": [ + "In this notebook, we will use `matplotlib` package and `ahs_utils.py` module in the current working directory for visualization purposes and other functionalities." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "08909afa", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from braket.ahs.atom_arrangement import AtomArrangement\n", + "\n", + "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n", + "\n", + "from ahs_utils import show_register, show_global_drive, show_final_avg_density, get_drive \n", + "\n", + "from braket.devices import LocalSimulator" + ] + }, + { + "cell_type": "markdown", + "id": "5b5eee4d", + "metadata": {}, + "source": [ + "## 1D $Z_2$ phase \n", + "\n", + "Here we consider a 1D chain of 9 atoms with neighboring atoms separated by $6.1\\mu m$. The setup of the system can be generated as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6702f2b8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "register = AtomArrangement()\n", + "separation = 6.1e-6 # in meters \n", + "num_atoms = 9\n", + "\n", + "for k in range(num_atoms):\n", + " register.add([k * separation, 0])\n", + " \n", + "show_register(register)" + ] + }, + { + "cell_type": "markdown", + "id": "33174b8a", + "metadata": {}, + "source": [ + "In order to prepare the $Z_2$ ordered state for the atomic chain, we shall design an AHS program that drives the system adiabatically. As described above, we start from $\\Omega(t=0)=0$ with $\\Delta(t=0)<0$, followed by turning on $\\Omega(t)$ and ramping up $\\Delta(t)$. We will turn off the driving amplitude at the end of the program. This program can be specified as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "12184869", + "metadata": {}, + "outputs": [], + "source": [ + "time_points = [0, 2.5e-7, 2.75e-6, 3e-6]\n", + "amplitude_min = 0\n", + "amplitude_max = 1.57e7 # rad / s\n", + "\n", + "detuning_min = -5.5e7 # rad / s\n", + "detuning_max = 5.5e7 # rad / s\n", + "\n", + "amplitude_values = [amplitude_min, amplitude_max, amplitude_max, amplitude_min] # piecewise linear\n", + "detuning_values = [detuning_min, detuning_min, detuning_max, detuning_max] # piecewise linear\n", + "phase_values = [0, 0, 0, 0] # piecewise constant\n", + "\n", + "\n", + "drive = get_drive(time_points, amplitude_values, detuning_values, phase_values)" + ] + }, + { + "cell_type": "markdown", + "id": "ee92d637", + "metadata": {}, + "source": [ + "We can plot the waveforms of these driving fields to make sure that they are correctly specified." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e8d369e3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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aOhSeLsXA8UHPm1KvDdeOu0Vkv4jsb25uprW1lebmZqLRKG1tbdTX19PV1UV1dTWJRIJIJAL8+i+lSCRCIpGgurqarq4u6uvraWtrY8+ePQyU19DQQCwWo6amhng8TmVl5WvKGPhZVVVFT08PtbW1dHR00NjYSEtLCy++0siJc928ftkMamtr6enpeXX5tKFlVFZWEo/HqampIRaL0dDQkDGnaDQ6Lqfy8vKLOrW0tNDY2EhHR0dWOY20n4Y6vfDCCznnNJ799Mtf/jLnnMazn5588smccxrvftq3b19WOO0oLSKhsLfudEb30zPPPJMxp5EQL2dsEZEngHeoau8EPrsSeERVLx3mvZ8Cn1XVvannTwEfV9URj0Ns3bpV9+/fP96meM5/PnuUv/1JNXs+fh3L5tmMZIZhGJmkrz9B2aef5O2blvLZneE8ry4i5aq6dbj3vD703QA8KyL/R0T+dOCRgXKbSB5GH6AEOJGBcsfMwF9amWBvbSsr50/Luk46kxlkI+Zv/q6TLRkU5udx9Zr57Kk9ndHpRP3y97qjPgE8kqpn5qBHujwMfCB19fc24NyQOcU9Z+PGzKwv0htP8NyRM+zIktnIBpOpDLIV8zd/18mmDHaUFtHU1sWxM50ZK9Mvf0876tR56d94jPY5Efk+8BxwiYg0icidInKPiNyT2uRR4AhQB3wD+APPJC5CXV0mTrVDpLGNzt7+rLota4BMZZCtmL/5u042ZbDj1elEM3ebll/+nsz1LSKfUtVPTXQbVb1jpM9q8tjFRyfcwAxQUlKSkXL21raSnydsWzM/I+X5SaYyyFbM3/xdJ5syWDF/GsvmTWV3bSvvv3plRsr0y9+rRTnuGmWqUAFuBz7lUf2e09rayowZ6U/yvqf2NJuXzWFWlkwbOphMZZCtmL/5u+wP2ZWBiLB97QIeqTxBX3+Cwvz0Dyj75e/Voe9v8Npz0kMfM1LbZC2Z2DltF3o5GD2XleenITMZZDPmb/6uk20ZXFtaxPmeOJXH2zNSnl/+noyox3IeOtvp60v/xvlf1Z9Blaya33swmcggmzF/83edbMvgDWuKyBPYXdvK1pXpr1Lol7/nc33nKolE+iux7Kk9zcwpBWwqmZ2BFvlPJjLIZszf/F0n2zKYPa2Qy0vmZGzeb7/8raOeINOmpXfPs6qyp7aVa9YUUZCBcyVBkG4G2Y75m7/rZGMG15YWUXG8nXNd6Y+G/fLPzh4iBJw9O9JU5KNztPUC0faurD3sDelnkO2Yv/m7TjZmsGPdAhIKz9Wnv0iHX/6edtQisk5EnhpYrlJELheRv/KyTr9YunRpWp/fk1rJ5dosvZAM0s8g2zF/83edbMzgimVzmDG54NX/g9PBL3+vR9TfAO4D+gBU9SDJ27KynqNHj6b1+T21p1kxfxrL52ffoaMB0s0g2zF/83edbMygMD+PbavnZ6Sj9svf6456mqq+MOS1uMd1+sL69esn/Nm+/gTP1Z9h+9rsPewN6WWQC5i/+btOtmZw7boiGs92cuzMhbTK8cvf6466VUTWAAogIu8GfJ2T2ysqKiom/NkDje1c6O3P2vunB0gng1zA/CuCbkKguO4P2ZvBwCAp3VG1X/5ed9QfBb4GrBeRKPDHwEc8rtMXysrKJvzZvbWnyRO4OgunDR1MOhnkAuZv/q6TrRmsKppO8Zypac/77Ze/14tyHFHVtwALgPWqul1VG7ys0y8GFv+eCLtrW7li2RxmT82+aUMHk04GuYD5m7/rZGsGIsK164r4Vd0Z4v0TvxfaL3/J5NqcrxY6yprTqvr5jFc6BrZu3ar79+8PoupXOdfZx+a/+xkfu76UP3nrukDbYhiG4So/PdjMR78X4YGPvIEtK+YG3RxEpFxVtw73nlcj6oE5vbeSPNRdnHrcA2zwqE5fiUQiE/rcr+pbSShZuazlUCaaQa5g/ubvOtmcwTVr5yOS3rKXfvl7MqJ+tXCRnwG3qer51POZwI9U9UbPKh2BTI6oE4kEeXnj/zvnvl1VPFJ5gshfvzUjq7cEyUQzyBXM3/xd9ofsz+CWLz9LQZ7wwEfeMKHPZ9I/iBH1AMuB3kHPe4GVHtfpCzU1NeP+THLa0NNcvWZ+1nfSMLEMcgnzN3/XyfYMdqxNTifa0T2x6UT98ve6t/gv4AUR+ZSI/A3wPPAdj+v0hVWrVo37M8fOdNLU1pUTh71hYhnkEuZv/q6T7RnsKC2iP6E8V39mQp/3y9/rq74/A3wYaAPagQ+r6j94WadfnDhxYtyfGTgXku33Tw8wkQxyCfM3f9fJ9gw2L5/L9En5Ez5P7Ze/J+tRDyAiy4FW4MHBr6lqo5f1+sG8eeNfy3R3bSvL5k1lRRZPGzqYiWSQS5i/+btOtmcwqSA5nejeCU584pe/14e+fwo8kno8BRwBHvO4Tl/o7Owc1/Z9/Qn21Z9h+9oFiIhHrfKX8WaQa5i/+btOLmSwo7SIhjOdNJ4Zv4tf/l4f+r5MVS9PPUqBK4G9XtbpF+O90q/yeDvne+JcmyPnp2H8GeQa5m/+rpMLGexYlzwVuadu/Ie//fL3NWVVjQCv97NOrygsHN+sYrtrW8kTeMOa3Omox5tBrmH+5u86uZDB6qLpLJ09ZUKHv/3y93o96j8d9PgzEfkekN7kqiEhFouNa/u9tae5vGQOs6dl/xd7gPFmkGuYv/m7Ti5kICLsKF3As3Wt455O1C9/r0fUMwc9JpM8Z32Lx3X6QlHR2EfG57r6qDjenlOHvWF8GeQi5m/+rpMrGexYV0RHd5yD0XPj+pxf/l531NWq+repx2dU9bvAOzyu0xeamprGvO1zA9OGrsuN27IGGE8GuYj5m7/r5EoG16wpQoRxH/72y9/rjvq+Mb6Wdaxdu3bM2+6pbWXG5AKuWDbHuwYFwHgyyEXM3/xdJ1cymDt9EpcVzx73/dR++XvSUYvITSLyJaBYRL446PEtIO5FnX5z6NChMW+7p7aVbatzY9rQwYwng1zE/M3fdXIpgx2lRUQa2zk/julE/fL3quc4AewHuoHyQY+HgRs8qtNXNm3aNKbtjp25QOPZTq5dlxvncgYz1gxyFfM3f9fJpQy2r11Af0LZd+TsmD/jl78nHbWqVqrqt4E1qvrtQY9dqtrmRZ1+M9YFw/ekznlsX5t7HXW2LhqfKczf/F0nlzIoWzGHaeOcTtQvf68Off8w9esBETk49DHGMm4UkVdEpE5EPjHM+28SkXMiUpF6/HVGJUZhy5YtY9puT+1piudMZVXRdI9b5D9jzSBXMX/zd51cymByQT7bVs9/dXA1Fvzy9+rQ9x+lfr6d5FXeQx8jIiL5wJeBm4ANwB0ismGYTfeo6hWpx6cz0vIxMpa/pOL9CX5Vd4Zr1xXlzLShg8mlv6Yngvmbv+vkWgbb1xZxtPUCx8+ObWrQrB5Rq2pz6uex4R5jKOJKoE5Vj6hqL/ADQnb/9Vj+kqpsOsf5njjb1+bWbVkD5NJf0xPB/M3fdXItg4FrifbWjW1UndUjahE5LyIdgx7nB/8cQxHFwPFBz5tSrw3lahGpFJHHRGTjRdpyt4jsF5H9zc3NtLa20tzcTDQapa2tjfr6erq6uqiuriaRSBCJRIBf/6UUiURIJBJUV1fT1dVFfX09bW1tPPfccwyU19DQQCwWo6amhng8TmVlJQA//OVBRGD6heS9dlVVVfT09FBbW0tHRweNjY20tLTQ0tJCY2MjHR0d1NbW0tPTQ1VV1WvaMfCzsrKSeDxOTU0NsViMhoaGjDlFo9FRnQa3p6qqKuecxrOfKioqcs5pPPvp2WefzTmn8eynp556KuecxrufIpFITjnlX2hl0czJ/LT8yJic9uzZkzGnkRBVHXGDIBCR9wA3qOpdqefvB65U1Y8N2mYWkFDVmIjcDHwhtfDHRdm6davu378/I23s6elh8uTJI25z21d+RTyh/Pij12SkzrAxlgxyGfM3f5f9ITcz+PMfVfKz6lNE/s9byc8b+ZRlJv1FpFxVtw73nuc39opImYj8oYh8TEQ2j/FjTcCyQc9LSN7y9Sqq2qGqsdTvjwKFIuLbpdWNjSMvqd3RnZw2dEcOXu09wGgZ5Drmb/6uk4sZ7Fi3gHNdfVSNYTpRv/y9XpTjr4FvA/OBIuBbIvJXY/joi0CpiKwSkUnA7STvwR5c9mJJXaElIleSdDmTyfaPxKJFi0Z8/7n6M/QnlB05Nr/3YEbLINcxf/N3nVzMYPva5HSiew6PfpuWX/5ej6jvAF6vqn+jqn8DbAPeN9qHVDUO3As8AbwM/FBVD4nIPSJyT2qzdwMviUgl8EXgdvXxOH57e/uI7++pPc30SflsXj7XnwYFwGgZ5Drm3x50EwLFdX/IzQzmTZ/ExqWz2DOGC8r88i/wuPwGYArJGcoguYJW/Vg+mDqc/eiQ17466Pd/A/4tI62cAFOmTBnx/b2paUMnFeTWtKGDGS2DXMf8zd91cjWDHaUL+MbuI8R64syYfPFu0i9/r3uRHuCQiHxLRP4TeAmIDcz97XHdgXH8bCcNZzpz+rC3YRhGrrKjtIh4QtlX79vZ1BHxekT9YOoxwDMe1+cb3d3dF31vYGabXFvWcigjZeAC5m/+rpOrGWxZMZephfnsrWvlLRsufh7aL39PO+rUfN85yZw5cy763p7a0yydPYXVOTht6GBGysAFzH9O0E0IFNf9IXczmFyQz1Wr57F7lHm//fL3+qrvt4vIARE5O84JT0LPqVOnhn29P6E8W9fKjtIFOTlt6GAuloErmL/5u04uZ7CjdAFHTl8g2t510W388vf6HPW/Ah8E5qvqLFWdqaqzPK7TF5YvXz7s6web2unojrMjB5e1HMrFMnAF8zd/18nlDAauMdo7wqjaL3+vO+rjwEt+3jblF4cPHx729T21rYjANWtyv6O+WAauYP7m7zq5nEHpwhksmjWZ3SOspuWXv9cXk30ceFREfknyCnAAVPXzHtfrOZdddtmwr++pPc1lxbOZO32Szy3yn4tl4Armb/6uk8sZiAg7Shfw85dP0Z/QYacT9cvf6xH1Z4BOkvdSzxz0yHqGW97sfHcfBxrbnbktK9eWuBsv5m/+rpPrGewoLaK9s49DJ4afTtQvf69H1PNU9W0e1xEIwy1vtu/IWeIJzdllLYeSa0vcjRfzN3/XyfUMrkmt1bCntpXLS+b8xvtZvczlIH4uIjnZUQ/3l9Se2tNMm5RP2Yo5/jcoAHL9r+nRMH/zd51cz6BoxmQ2Lp3F7ovM++2Xv6fLXIrIeWA6yfPTfYAAGtSV35lc5nI4rv+/z7Bi/jT+88NXelaHYRiG4R+ffexl7t97lIq/fhvTR5hONF0CW+YydTtWnqpOzbXbswYWFB/g+NlOjrReYEepG4e94TczcA3zN3/XcSGDa0sX0NevPH/0N6cT9cvf63PUiMhcoJTkBWUAqOpur+v1mo0bN77m+d7USivXOnD/9ABDM3AN8zd/13Ehgy0r5jKlMI/dh1u5fv1rpxP1y9/rmcnuAnaTXK7yb1M/P+VlnX5RV1f3mud7a1tZPGsKaxbMCKhF/jM0A9cwf/N3HRcymFKYz5Wr5r86GBuMX/5eX0z2R8DrgWOqeh2wGRh9Ne4soKSk5NXf+xPK3rpWdpQW5fy0oYMZnIGLmL/5u44rGVxbWkRdS4zmc6+dTtQvf6876m5V7QYQkcmqWgNc4nGdvtDa+uu/rqqi5zjX1Zfzq2UNZXAGLmL+5u86rmQwcO3RniGzlPnl73VH3SQic4CHgCdF5MfACY/r9IUZM359iHtgLthr1swPqjmBMDgDFzF/83cdVzJYt2gGC2dO/o2O2i9/r5e5vDX166dE5GlgNvC4l3X6RV9f36u/765t5dLiWcyfMTnAFvnP4AxcxPzN33VcyUBE2F5axDOvnCaRUPJS04n65e/1iPpVVPWXqvqwqvb6VaeXJBIJAGI9cSLH2py6LWuAgQxcxfzN33VcyuDa0gWcvdBLdfOvV2r2y9+3jjrXmDZtGgDPHzlDPKHsWOvObVkDDGTgKuZv/q7jUgYD04nuHrTspV/+1lFPkLNnzwLJiwumFOaxZeXcgFvkPwMZuIr5m7/ruJTBgpmTed2SWew5/Ovz1H75W0c9QZYuXQok/7ratno+kwvyA26R/wxk4Crmb/6u41oG15YWUX6sjc7eOOCfv3XUE+To0aNE27s4cvoC2x087A3JDFzG/M3fdVzLYHtpEb39CZ4/mhxJ++VvHfUEWb9+/au3ZV3r2P3TA6xfvz7oJgSK+Zu/67iWwetXzmNyQd6rh7/98reOeoJUVFSwu7aVRbMmU7rQjXsJh1JRURF0EwLF/CuCbkKguO4P7mWQnE50HnvrkoM0v/yto54gm67YzLN1rWxfu8CpaUMHU1ZWFnQTAsX8zd91XMxgR2kRh0/FOHmu2zd/66gnyP889TztnX1OrZY1lFxfNH40zN/8XcfFDH49nehp3/yto54grQXJDvoaRy8kA9iyZUvQTQgU8zd/13Exg/WLZ1I0YzJ761p98w9tRy0iN4rIKyJSJyKfGOZ9EZEvpt4/KCK+HoN5LHKUDUtmUeTYtKGDiUQiQTchUMzf/F3HxQxEhB2lReytbWW/yyNqEckHvgzcBGwA7hCRDUM2uwkoTT3uBr7iV/uerWulurWX0kVuXkQ2wBVXXBF0EwLF/K8IugmB4ro/uJvBjtIizlzo5eHjkyg/1uZ5faHsqIErgTpVPZKaG/wHwC1DtrkF+I4m2QfMEZElXjes/FgbH/7PF0goPFZ10pedFFZqamqCbkKgmL/5u46rGcyaUgjAf+1r5H3f3Od5PxDWjroYOD7oeVPqtfFug4jcLSL7RWR/c3Mzra2tNDc3E41GaWtro76+nq6uLqqrq0kkEq8eyhm4SCASiZBIJKiurqarq4tH99fS268AxBMJfvFSIw0NDcRiMWpqaojH41RWVr6mjIGfVVVV9PT0UFtbS0dHB42NjbS0tNDS0kJjYyMdHR3U1tbS09NDVVXVsGVUVlYSj8epqakhFovR0NCQtlN9fT1tbW1Eo1EGMhqL06pVq3LOaTz7qbi4OOecxrOfCgsLc85pPPspFovlnNN499PChQtzzmks+2l3ZS0ACvTFEzwRqU/baSREVUfcIAhE5D3ADap6V+r5+4ErVfVjg7b5KfBZVd2bev4U8HFVvehJg61bt+r+/fvTalv5sTbe94199MYTTCrM47t3bWPLCvfm+Qaor69nzZo1QTcjMMzf/F32B3czKD/Wxnu/sY++/gSTCjLTD4hIuapuHe49T9ejToMmYNmg5yXAiQlsk3G2rJjLd39/G08fauK6jSXOdtIA8+bNC7oJgWL+5u86rmawZcVcvudjPxDWQ98vAqUiskpEJgG3Aw8P2eZh4AOpq7+3AedUtdmPxm1ZMZc7Ns1zupMG6OzsDLoJgWL+5u86LmfgZz8QyhG1qsZF5F7gCSAfuF9VD4nIPan3vwo8CtwM1AGdwIf9bGNeXlj/xvEP1zMwf/N3Hdcz8Ms/lB01gKo+SrIzHvzaVwf9rsBH/W7XAIWFhUFVHRpcz8D8zd91XM/AL/9QXkzmFSJyGjiWoeKKgNZRt8ptXM/A/M3fZX+wDDLpv0JVh12K0amOOpOIyP6LXaHnCq5nYP7m77I/WAZ++bt9gsEwDMMwQo511IZhGIYRYqyjnjhfD7oBIcD1DMzfbVz3B8vAF387R20YhmEYIcZG1IZhGIYRYqyjNgzDMIwQYx21YRiGYYQY66gNwzAMI8RYR20YhmEYIcY6asMwDMMIMdZRG4ZhGEaIsY7aMAzDMEKMddSGYRiGEWKc66hF5H4RaRGRl8aw7b+ISEXqcVhE2n1oomEYhmG8inNTiIrItUAM+I6qXjqOz30M2Kyqv+dZ4wzDMAxjCM6NqFV1N3B28GsiskZEHheRchHZIyLrh/noHcD3fWmkYRiGYaQoCLoBIeHrwD2qWisiVwH/Dlw/8KaIrABWAb8IqH2GYRiGozjfUYvIDOANwI9EZODlyUM2ux34H1Xt97NthmEYhuF8R03y8H+7ql4xwja3Ax/1pzmGYRiG8WucO0c9FFXtAI6KyHsAJMmmgfdF5BJgLvBcQE00DMMwHMa5jlpEvk+y071ERJpE5E7gfcCdIlIJHAJuGfSRO4AfqGuXxxuGYRihwLnbswzDMAwjm3BuRG0YhmEY2YR11IZhGIYRYpy66ruoqEhXrlyZkbJ6e3uZNGlSRsrKVlzPwPzN32V/sAwy6V9eXt6qqguGe8+pjnrlypXs378/I2XFYjFmzJiRkbKyFdczMH/zd9kfLINM+ovIsYu9Z4e+J0hra2vQTQgc1zMwf/N3Hdcz8MvfOuoJ4vJfkQO4noH5m7/ruJ6BX/5OHfrOJH19fUE3IXBcz8D8zd91gszgsapmnq0/w6XFs1i/eJbv9dec7KDiyCnesy2fLSvmelqXddQTJJFIBN2EwHE9A/M3f9fxO4O2C7385OAJvvPcMepaYr7WfTEeeqmV7961zdPO2jrqCTJt2rSgmxA4rmdg/ubvOn5k0BtP8IuaFnZFmnj6lRb6+pUFMycjgAJ5ArduLubtly/1vC0DPHLwBLsiURToiyfYd+SMddRh5OzZs8yd6+3hjrDjegbmb/4u+4N3GagqFcfb2RWJ8pODJ2jv7GPBzMl86A0ruXVzCV19/bzvm/voiycoLMjjvVet8Pzw82BmTS3kp1XN9Kbq37Z6vqf1hXYKURFpAM4D/UBcVbcOeV+ALwA3A53Ah1Q1MlKZW7du1UzdntXV1cXUqVMzUla24noG5m/+LvtD5jOItnfx0IEoD0SaOHL6ApML8rhh42J2lhWzfW0RBfm/vv65/Fgb+46cYdvq+b520oPr3/vKSbZfsjgj9YtI+dB+boCwj6ivU9WLXf9+E1CaelwFfCX10xeOHj3Khg0b/KoulLiegfmbv8v+kJkMYj1xHqtqZlckynNHzgBw1ap53HPtGm68bDGzphQO+7ktK+YG0kEPrn/qhWY2+NCGsI+ot16soxaRrwHPqOr3U89fAd6kqs0XKzOTI+pEIkFentt3t7megfmbv8v+MPEM+hPKs3Wt7Io08fihk3T3JVg5fxo7y0q4dXMxy+Zlx/n/TH4HRhpRh/lbpsDPRKRcRO4e5v1i4Pig502p116DiNwtIvtFZH9zczOtra00NzcTjUZpa2ujvr6erq4uqqurSSQSRCLJo+fl5eUARCIREokE1dXVdHV1UV9fT1tbG7/61a8YKK+hoYFYLEZNTQ3xeJzKysrXlDHws6qqip6eHmpra+no6KCxsZGWlhZaWlpobGyko6OD2tpaenp6qKqqGraMyspK4vE4NTU1xGIxGhoaMuYUjUbH5VRRUZFzTuPZT+Xl5TnnNJ79tHfv3pxzGs9+euqpp3LOabz76cUXXxyXU3ldM/f94Hm2feZJPnD/C/z85ZO849KFfOHty3j8Y1dz3cJuls2bljX/nnbv3p2x/TQSYR5RL1XVEyKyEHgS+Jiq7h70/k+Bz6rq3tTzp4CPq2r5xcrM5IjaMAzDGJ3WWA8PV5xg14EmXop2UJAnvOmShdxWVsz1r1vI5IL8oJsYCrJyRK2qJ1I/W4AHgSuHbNIELBv0vAQ44U/rfv1Xkcu4noH5m7/rXCyD7r5+fnqwmTu/9SJX/cNTfPqRavJE+NQ7NvD8X76Zb35wKzddtiTrO2m/vgOhHFGLyHQgT1XPp35/Evi0qj4+aJvfAu4ledX3VcAXVXVoZ/4abERtGIbhDapK+bE2HohEeeTgCc53x1k8awq3lhWzc3MxpYtmBt3EUJONV30vAh5M3oFFAfA9VX1cRO4BUNWvAo+S7KTrSN6e9WE/GxiJRCgrK/OzytDhegbmb/4u+0Myg6IV69l1oIkHD0Q5dqaTqYX53HTpYnaWlXD1mvnk50nQzfQMv74DoRxRe4Vd9Z1ZXM/A/M3fVf+O7j5+erCZB8qb2H+sDRF4w5r57Nxcwo2XLmb65LCOATOLX1d9u5GmB9TU1Dh/D6XrGZi/+bvkH+9PsKe2lQciTfys+hS98QTLZhfy8Rsv4V1XFLN0jnuTv/j1HbCOeoKsWrUq6CYEjusZmL/55zqqSnVzB7siUX5cEaU11svcaYW898rl7CwrZu28SU7Pee7Xd8A66gly4sQJ1qxZE3QzAsX1DMzf/HPV/1RHNz+uiLIrEqXm5HkK84U3r1/EbVtKeOO6BUwqSB7ura+vz9kMxoJf3wHrqCfIvHnzgm5C4Liegfmbfy7R1dvPz6pP8kAkyt7a0yQUNi+fw9+961LecfkS5kyb9BufybUMxotf/tZRT5DOzk7nV85xPQPzN/9s908klBcazvJAeROPvXSSWE+c4jlT+eh1a7l1czGrF8wY8fO5kEE6+OVvHfUEcfVqz8G4noH5m3+2cuR0jAcPJA9tR9u7mDG5gJsvS95SdeXKeeSN8ZaqbM4gE/jlbx31BCksHH5FF5dwPQPzN/9sor2zl58cbGZXpIkDje3kCWwvXcDHb7yEt21YzNRJ458lLNsyyDR++VtHPUFisRhFRUVBNyNQXM/A/M0/7P698QTPvNLCrkiUX9S00Nuf4JJFM/nLm9dzyxXFLJo1Ja3ysyEDL/HL3zrqCeLyl3MA1zMwf/MPI6rKwaZz7Io08XDlCdo6+yiaMYn3X72CnWXFbFgyi9Ssj2kT1gz8wi//CXXUIjKWOdP6VLVqIuVnA01NTaxfvz7oZgSK6xmYv/mHyf9EexcPpW6pqmuJMakgj7dtWMRtZSXsKC2iID/z51PDloHf+OU/oSlEReQ88CIw0p9lq1R15QTb5QmZnEI0Ho9TUOD2AQnXMzB/8w/a/0JPnMdfOsmuA038qv4MqvD6lXO5rayEmy5bwuyp3p5DDUMGQZJJfy+mEH1RVa8fpdJfTLDsrODQoUNs2rQp6GYEiusZmL/5B+Hfn1Ceqz/Drkjylqquvn6Wz5vGH725lFs3F7Ni/nTf2mLfAX/8bVEOwzCMLKD21HkeiER56ECUkx3dzJxSwNsvX8ptZcVsWTE3Y+edjWAYaUSd1kkLEbkmtV40IvK7IvJ5EVmRTpnZgi0abxmYv/l7zZlYD//57FHe8aW9vPVfdvONPUfYuHQWX35vGS9+8i18dudlbF05L7BO2r4D/vinNaIWkYPAJuBy4L+A/wB2quobM9O8zGIjasMwwk5PvJ9fvNzCA5Eoz7zSQjyhXFo8i52bS3jnFUspmjE56CYaHuDZiBqIa7KnvwX4gqp+AZiZZplZget/SYJlYP7mnylUlfJjbXzywSqu/MxTfOS7EQ42tXPn9lU88cfX8sjHdvB721eFrpO270B2jKh/CTwOfBi4FjgNVKjqZZlpXmaxEbVhGGHi+NnO1FSeTTSc6WRKYR43bkxO5XnN2iLyxziVp5H9eDmi/h2gB7hTVU8CxcA/p1lmVlBVlbO3iI8Z1zMwf/OfCB3dffz3i4389teeY8c/Pc3nnzzMktlT+ed3X87+v3or/3r7Zq5dtyArOmn7DvjjP9H7qJ8gOZJ+TFVrMt4okWXAd4DFQAL4euqw+uBt3gT8GDiaemmXqn56pHIzOaLu6elh8uRwHYbyG9czMH/zH6t/vD/BnrpWdkWi/OzQSXriCVYXTee2LSXccsVSSuZO87i13mDfgcz5e3Ef9QeBG4FPicg64HmSHfdTqhqbYJmDiQP/W1UjIjITKBeRJ1W1esh2e1T17Rmob9w0NjZSWloaRNWhwfUMzN/8R/N/ubmDXZEmHqo4wenzPcyZVsjvvH4ZO8tK2FQyO+tvqbLvgD/+E+qoU4e5vwV8S0TygKuAm4CPi0gX8DNV/aeJNkpVm4Hm1O/nReRlkofVh3bUgbFo0aKgmxA4rmdg/uY/HC3nu3m44gQPRKK83NxBYb5w3SUL2VlWwvXrFzKpIHeWhrTvgD/+aX9jVDWhqs+p6l+r6jXA7UA0/aYlEZGVwGaSo/ahXC0ilSLymIhsvMjn7xaR/SKyv7m5mdbWVpqbm4lGo7S1tVFfX09XVxfV1dUkEgkikQjw66v5IpEIiUSC6upqurq6qK+vp62tjaNHjzJQXkNDA7FYjJqaGuLxOJWVla8pY+BnVVUVPT091NbW0tHRQWNjIy0tLbS0tNDY2EhHRwe1tbX09PS8eu5jaBmVlZXE43FqamqIxWI0NDRkzCkajY7Lqb29PeecxrOfTp8+nXNO49lPdXV1Oec0nv1UUVHxqlNnTx9f+ekLvP+b+9j2D0/x9z99GUnE+d9vWsZj/2szf3ltEdtXzuBI3eFQO413P508eTL0+8nL794rr7ySMaeRmOg56i8BF/2gqv7huAsdvp4ZwC+Bz6jqriHvzQISqhoTkZtJ3h424jGITJ6jbmlpYeHChRkpK1txPQPzd9v/5KlTHLtQwK5IlEermjnfE2fp7CncWlbMrZtLWLtwRtBN9BzXvwOZ9PfiHPVAb3cNsAH479Tz9wAZubFMRAqBB4DvDu2kAVS1Y9Dvj4rIv4tIkaq2ZqJ+wzCM4WhovcCuA1H+Z38jJ871MH1SPjddtoSdZcVsWzWfvCy4WtvILiZ6jvrbACLyIeA6Ve1LPf8q8LN0GyXJKyz+A3hZVT9/kW0WA6dUVUXkSpKH8c+kW/dY6e7u9quq0OJ6Bubvjv+5zj4eqTrBrkiU8mNtiMDWkhl8/MbX8baNi5g2yc0VpFz6DgyHX/7pfruWkpyJ7Gzq+YzUa+lyDfB+oEpEKlKv/SWwHEBVvwq8G/iIiMSBLuB29XGFkTlz5vhVVWhxPQPznxN0Ezylrz/BL185za4DTfy8uoXe/gSlC2fwiZvW864ripkmvcyaNSvoZgZKrn8HRsMv/3Q76s8BB0Tk6dTzNwKfSrNMVHUvI691jar+G/Bv6dY1UU6dOuX8P1LXMzD/3PNXVV6KdvBApImfVJ7gzIVe5k+fxPu2Lee2shI2Lp316i1VtbXHc85/vOTid2A8+OWf9jKXqUPQV6WePp+6dSuU2IQnmcX1DMw/d/xPnut+dSrP2pYYk/LzeOuGRewsK+badQsozP/NG2RyyX+iuJ6BXxOeZOKGvh6S9zy3AetE5NoMlBl6Dh8+HHQTAsf1DMw/u/07e+M8eKCJ9//H81z9uaf4x8drmD21kH+49TJe/ORb+PL7ynjz6xYN20lD9vtnAtcz8Ms/3UU57gL+CCgBKoBtwHOqen1GWpdhbFEOw3CbRELZd+QMD0SiPPZSM529/SybN5Wdm0u4dXMxK4umB91Ew1G8HFH/EfB64JiqXkdyYpLTaZaZFbi+vBtYBuafPf51LTH+6fEatv/jL3jvN5/nZ4dO8s5NS/nRPVez+8+v40/eum7cnXQ2+XuF6xlkyzKXL6rq61NXZl+lqj0iUqGqV2SqgZnERtSG4Q5nL/Tyk8oT7Io0Udl0jvw84drSInaWlfDWDYuYUpgfdBMN41W8HFE3icgc4CHgSRH5MXAizTKzAtf/kgTLwPzD598T7+fxl07y+9/Zz5Wf+Tl/8/Ah+vqVv/qt1/Hcfdfznx++kndsWpqRTjqM/n7jegZZMaJ+TUEibwRmA4+ram9GCs0wNqI2jNxDVak43s6uSJSfHDxBe2cfC2ZO5tbNxdy6uZjXLXH39iEje/BiClFSq2YdVNVLAVT1lxMtKxuprKxk06ZNQTcjUFzPwPyD9W9q6+ShA1F2RaIcab3A5II8bti4mJ1lxWxfW0TBRa7WzhRB+4cB1zPwyz/dc9TfBe5T1cbMNck7MjmijsfjFBS4OW3gAK5nYP7++5/v7uOxl06yK9LEviPJCRGvWjWP28pKuOmyxcycUuhbW1zf/2AZZNLfkxF1iiXAIRF5Abgw8KKqvjPNckNPXV0d69evD7oZgeJ6Bubvj39/Qtlb18quSBNPHDpJd1+CVUXT+d9vXce7NhezbN40z9swHK7vf7AM/PJPt6P+24y0IgspKSkJugmB43oG5u+t/ysnz/NApImHDkRpOd/D7KmFvHtLCTvLSti8bM6rU3kGhev7HywDv/zT6qhdOy89mNbWVmbMyP31ZkfC9QzMP/P+p8/38HDqlqpDJzooyBPedMlC3r2lmOvWL2RyQXhuqXJ9/4Nl4Jf/hDpqEXlEVd+e7jbZjMtfzgFcz8D8M+Pf3dfPz18+xa5IlF8ePk1/Qrm8ZDafescG3rFpKfNnhHMuadf3P1gGfvlPdES9XUQeHuF9ATZMsOysoK+vL+gmBI7rGZj/xP1Vlf3H2tgVaeKRg82c746zZPYU7r52NTs3F1O6aGYGW+oNru9/sAz88p9oR33LGLYJ5b3UmSKRSATdhMBxPQPzH7//sTMX2BWJ8uCBKI1nO5k2KZ8bL13MbWUlbFs9n/y8YM87jwfX9z9YBn75T6ijdvnc9ADTpgVzpWmYcD0D8x+b/7muPh6tauaB8ib2H2tDBK5ZU8Qfv6WUGzYuZvrk7Ly9x/X9D5aBX/7Z+S8kBJw9e5a5c+cG3YxAcT0D87+4f19/gj21p3kgEuXJ6lP0xhOsXTiDv7hxPe/avJQls6f63NrM4/r+B8vAL//QdtQiciPwBSAf+Kaqfm7I+5J6/2agE/iQqkb8at/SpUv9qiq0uJ6B+b/WX1U5dKKDXZEoD1dGaY31Mm/6JN575XJ2lhVzWfHswG+pyiSu73+wDPzyD2VHLSL5wJeBtwJNwIsi8rCqVg/a7CagNPW4CvhK6qcvHD16lA0bcvp6uVFxPQPzT/qf6uh+dSrPV06dZ1J+Hm9+3UJ2lpXwxnULmFTg7VSeQeH6/gfLwC//dKcQrQKGFnAO2A/8vaqemWC5VwOfUtUbUs/vA1DVzw7a5mvAM6r6/dTzV4A3qWrzxcrN5BSiiUSCvLzc/A9orLiegcv+Xb39PP5SM7sORHm2rpWEQtnyOewsK+Htly9hzrRJQTfRc1ze/wO4nkEm/b2cQvQxoB/4Xur57amfHcC3gHdMsNxi4Pig50385mh5uG2KgYt21JmkoqKCsrIyP6oKLa5n4Jp/IqE8f/QsuyJNPFrVzIXefornTOXe69Zya1kJq4qmB91EX3Ft/w+H6xn45Z/unwLXqOp9qlqVenyS5Kj2H4GVaZQ73ImsoSP3sWyDiNwtIvtFZH9zczOtra00NzcTjUZpa2ujvr6erq4uqqurSSQSRCLJ09wD64xGIhESiQTV1dV0dXVRX19PW1sbixYtYqC8hoYGYrEYNTU1xONxKisrX1PGwM+qqip6enqora2lo6ODxsZGWlpaaGlpobGxkY6ODmpra+np6aGqqmrYMiorK4nH49TU1BCLxWhoaMiYUzQaHZdTWVlZzjmNZz9t3Lgx55yG208PP/M8//eJV7jq75/gjm/s46cHo7ztdQv4wjtX8uCdl3HHZbOY1NOeVU6Z2E8DRyNzyWm8+2ndunU55zSe/TRz5syMOY1Euoe+K4G7VfX51PMrgW+o6iYROaCqmydYbugPfZeXl7Nly5aMlJWtuJ5BLvu3XejlkYMneCASpeJ4O3kCO0oXsLOsmLdtWMzUSfk57T8WXPcHyyCT/iMd+k63o349cD8wg+QItwO4CzgE/Jaq/nCC5RYAh4E3A1HgReC9qnpo0Da/BdxL8qrvq4AvquqVI5WbyY7aMHKN3niCp19pYVekiV/UtNDXr6xfPJPbykq45YqlLJw1JegmGkbO4tk5alV9EbhMRGaT7PTbB709oU46VW5cRO4FniB5e9b9qnpIRO5Jvf9V4FGSnXQdyduzPjzR+iZCJBJx+twMWAa54K+qHGw6x65IEw9XnqCts4+iGZP54NUr2VlWwoalsy762VzwTwfX/cEy8Ms/3RH1ZOA2kuejX+30VfXTabfMA+yq78ziegbZ7B9t70rdUtVE/ekLTC7I420bF7OzrJgda4soyB/dK5v9M4Hr/mAZZMtV3z8meTtWOdCTZllZRU1NjdP3D4JlkG3+sZ44j790kl2RJp47cgZVuHLlPH5/x2puvnwJs6YUjqu8bPPPNK77g2Xgl3+6HXWJqt6YkZZkGatWrQq6CYHjegbZ4N+fUH5V38quSJTHXzpJV18/K+ZP44/fvI5bNxezfP7E5yrOBn8vcd0fLAO//NPtqH8lIpepalVGWpNFnDhxgjVr1gTdjEBxPYMw+x8+dZ4HIk08dCDKqY4eZk0p4NayYm4rK6Zs+dyMTOUZZn8/cN0fLAO//NPtqLcDHxKRoyQPfQugqnp52i0LOfPmzQu6CYHjegZh82+N9fCTyhPsikSpip4jP0+47pIF/M07Srh+/UKmFOZntL6w+fuN6/5gGfjln25HfVNGWpGFdHZ2Or1qDFgGYfDv7uvnFzXJW6qeeeU08YRyWfFs/uYdG3jHpqUUzZjsWd1h8A8S1/3BMvDLf0IdtYjMUtUO4HyG25M1uHyl4wCuZxCUv6oSaWzjgUiURypP0NEdZ9Gsydy5YxU7N5dwyeKZvrTD9r/b/mAZ+OU/0RH194C3k7zaW3ntdJ4KrE6zXaGnsHB8V8jmIq5n4Lf/8bOd7IpE2XWgiWNnOplamM+NlyZvqXrDmiLy8/xdQtL2v9v+YBn45T+hjlpV35766ewlf7FYjKKioqCbESiuZ+CHf0d3H48ebGZXJMoLDWcRgatXz+dj15dy46WLmTE5uJVqbf+77Q+WgV/+af8rF5FiYAWvnfBkd7rlhh2Xv5wDuJ6BV/7x/gR76lp5oLyJJ6tP0RNPsHrBdP78hkt41+ZiiudM9aTe8WL7321/sAz88k+roxaRfwR+B6gmudwlJA9953xH3dTUxPr164NuRqC4nkGm/atPdLAr0sRDFSdojfUwZ1ohv/P6ZewsK2FTyeyM3FKVSWz/u+0PloFf/ulOIfoKcLmqZsWsZJmcQjQej1NQENxhxzDgegaZ8G/p6ObHFSd4INJEzcnzFOYL169fyM6yEq67ZCGTCsJ7sY7tf7f9wTLIpP9IU4im+7/AEcDJqwkOHTo0+kY5jusZTNS/q7efH1dE+eD9L7Dts0/xmUdfZkphPn93y0Ze+Mu38LX3b+WGjYtD3UmD7X/X/cEy8Ms/3RH1A8Am4CkGzfWtqn+YftMyjy1zaQRFIqG80HCWXZEmHq06SawnTvGcqdy6uZhby4pZs2BG0E00DCNAvFyU4+HUwzlcXzAdLIOx+B9tvcCDkSZ2HYjS1NbF9En53HzZEnaWlXDVqnnk+XxLVSax/e+2P1gGfvmnNaLONmxEbfhBe2cvjxxsZlekiUhjO3kC16wt4rayEt62cRHTJrl7Ts8wjOHx7By1iBwVkSNDH+mUmS2Ul5cH3YTAcT2Dwf59/QmerD7FR/6/cq78zFP81UMvEeuJc99N6/nVJ97Mf915Fe/aXJxTnbTtf7f9wTLwyz/dc9TzBz2dArwHmKeqf51uw7zARtRGJlFVqqLn2BWJ8nDlCc5e6GX+9EncckUxO8uK2bh0VuhuqTIMI5x4do5aVc8MeelfRWQvEMqOOpNUVVVx2WWXBd2MQHE1g+ZzXTx4IMr3f1XP8Y44kwryeOuGRdxWVsyO0gUU5of7au1M4er+H8B1f7AM/PJPd8KTskFP84CtQForAojIPwPvAHqBeuDDqto+zHYNJBcF6QfiF/tLxCvWrVvnZ3WhxKUMLvTEeeLQSXZFojxb34oqlC2fzR+8ZTk3X7aE2VPdu0vRpf0/HK77g2Xgl3+6J8z+36Df48BR4LfTLPNJ4D5VjadmPrsP+IuLbHudqramWd+EaGxspLS0NIiqQ0OuZ9CfUPYdOcMDkSYef+kknb39LJs3lT+8vpSdZcX0nj1BaenyoJsZGLm+/0fDdX+wDPzyT7ejvlNVX3PxmIiktVCHqv5s0NN9wLvTKc8rFi1aFHQTAidXM6hrOc8DkSgPHYjSfK6bmZMLuOWKpewsK2HrirmvnnfuKMxN/7GSq/t/rLjuD5aBX/7pnkz7nzG+NlF+D3jsIu8p8DMRKReRuy9WgIjcLSL7RWR/c3Mzra2tNDc3E41GaWtro76+nq6uLqqrq0kkEkQiEeDXV/NFIhESiQTV1dV0dXVRX19PW1sbR48eZaC8hoYGYrEYNTU1xONxKisrX1PGwM+qqip6enqora2lo6ODxsZGWlpaaGlpobGxkY6ODmpra+np6aGqqmrYMiorK4nH49TU1BCLxWhoaMiYUzQaHZdTe3t7zjidvdDL3/33bt75b3t5y+d38/XdR1g+K59/ftd6dn3wEv5k+2JWTItz/PjxV51Onz4daievv3t1dXU55zSe/VRRUZFzTuPdTydPnsw5p/Hsp1deeSVjTiMxoau+RWQ9sBH4J+DPB701C/hzVd04yud/Diwe5q1PquqPU9t8kuQ57506TCNFZKmqnhCRhSQPl39stFW7MnnVd0tLCwsXLsxIWdlKtmfQE+/n6ZoWHohEebqmhXhC2bh0FjvLSnjnpqUsmDl5xM9nu3+6mL/b/mAZZNLfi6u+LwHeDswheeHXAOeB3x/tw6r6lpHeF5EPpsp/83CddKqME6mfLSLyIHAlDqzaZaSHqnLgeDu7Ik38pLKZc119LJg5md/bvoqdZcWsXzwr6CYahmG8hgl11KlR749F5GpVfS6TDRKRG0lePPZGVe28yDbTgTxVPZ/6/W3ApzPZjtHo7u72s7pQkk0ZHD/byUMHouw6EOVo6wWmFOZxw8bF7Cwr4Zo18ymYwC1V2eTvBebvtj9YBn75p3sx2RkReQpYpKqXisjlwDtV9e/TKPPfgMnAk6mLdvap6j0ishT4pqreDCwCHky9XwB8T1UfT8tknMyZM8fP6kJJ2DM4393HY1UneSDSxPNHzwKwbfU8PvKmNdx06WJmTknvlqqw+3uN+c8JugmB43oGfvmn21F/g+Q56q8BqOpBEfkeMOGOWlXXXuT1E8DNqd+PkFy1KzBOnTrFrFluHyYNYwbx/gR761rZFYnyxKGT9MQTrCqazp+9bR3v2lxMydxpGasrjP5+Yv5u+4Nl4Jd/uh31NFV9Ycg0ifE0y8wKli939/7ZAcKUQc3JDnalbqlqOd/D7KmF/PbWZewsK+aKZXM8mcozTP5BYP5u+4Nl4Jd/uh11q4isIXmrFCLybqA57VZlAYcPH3Z66jwIPoPT53v4cUWUXZEo1c0dFOQJ161fyG1lxVy3fiGTC/I9rT9o/6Axf7f9wTLwyz/dRTlWA18H3gC0kZyZ7HdVtSEjrcswtihH9tPd18+T1afYFWlid20r/QllU8lsdpaV8I5NS5k3fVLQTTQMwxg3ni1zqapHUrdaLQDWq+r2sHbSmcb15d3AvwxUlReOnuUTDxzk9X//cz72/QPUnDzP/7p2NT//02v58b3b+eAbVvreSbv+HTB/t/3BMgj1Mpci8qcjva+qn59wizzERtTZxbEzF3ggEuXBA00cP9vFtEn53HTpEm4rK2bb6vnk5dkSkoZh5AZejKhnph5bgY8AxanHPcCGCZaZVbj+lyR4k8G5zj6+93wj7/7Kr3jjPz/Dl35Ry8r50/mX39nE/r96C//vtzfxhrVFoeikXf8OmL/b/mAZhHpE/eqHRX4G3Kaq51PPZwI/UtUbM9S+jGIj6nDS159g9+HT7IpEefLlU/TGE6xdOIPbykp41+alLJk9NegmGoZheIpn56iB5STXjR6gF1iZZplZwcBk7S6TTgaqykvRc/ztTw6x7R+e4s5v7+e5I2d475XL+cm923nyT67lI29aE+pO2vXvgPm77Q+WgV/+6Y6oP0ly/ekHSd6idSvw36r62cw0L7NkckQdj8cpKEj37rbsZiIZnDzXzUMVUXZFmjh8Ksak/DzesmEhOzeX8MZLFlA4gak8g8L174D5u+0PlkEm/b1YlAMAVf2MiDwG7Ei99GFVPZBOmdlCXV0d69evD7oZgTLWDDp74/zs0CkeiDSxt64VVdiyYi6fufVS3n7ZUmZPS28qz6Bw/Ttg/m77g2Xgl3/afwqoagSIZKAtWUVJSUnQTQickTJIJJR9R8+wKxLlsapmLvT2UzJ3Kh+7bi23lpWwqmi6jy31Bte/A+bvtj9YBn75u3vMIk1aW1uZMWNG0M0IlOEyqGuJ8eCBJh6MRDlxrpsZkwt4++VL2VlWzOtXzgvF1dqZwvXvgPm77Q+WgV/+1lFPEJe/nAMMZNB2oZefHDzBA5EolcfbyRO4dt0CPnHz63jr6xYxdZK3U3kGhevfAfN32x8sA7/8raOeIH19fUE3IVB64wmefPk0Tx9t4OlXWujrV163ZBZ/9Vuv452blrJw1pSgm+g5rn8HzN9tf7AM/PK3jnqCJBKJoJvgO6pKZdM5dkWaeLjyBO2dfRTNmMyH3rCSWzeXsGGpW8vdufgdGIz5u+0PloFf/tZRT5Bp0zK3rnHYibZ38dCBKA9Emjhy+gKTC/J428bFvK10NjdtXklBFt1SlUlc+g4Mh/m77Q+WgV/+1lFPkLNnzzJ37tygm+EZsZ44j1U1sysS5bkjZwC4ctU8/te1q7npsiXMmlJIfX29s5005P53YDTM321/sAz88reOeoIsXbo06CZknP6E8mxdK7siTTx+6CTdfQlWzp/Gn751HbduLmbZvNf+9ZiLGYwH8zd/13E9A7/8QzccEpFPiUhURCpSj5svst2NIvKKiNSJyCf8bufRo0f9rtIzXjl5ns8++jJv+NxTfOD+F/hFTQu3lZXwwEfewNN/9ib+8M2lv9FJQ25lMBHM3/xdx/UM/PJPawpRLxCRTwExVf2/I2yTDxwG3go0AS8Cd6hq9UhlZ3IK0UQiQV5e6P7OGTOtsR4erjjBrgNNvBTtoCBPeNMlC7itrITr1i9kSuHot1RlewbpYv7m77I/WAaZ9PdyUY6guBKoU9UjqtoL/AC4xc8GVFRU+FldRuju6+enB5u581svctU/PMWnH6lGEP7mHRvY95dv5psffD03XbZkTJ00ZGcGmcT8K4JuQqC47g+WgV/+Ye2o7xWRgyJyv4gMd6a+GDg+6HlT6rXfQETuFpH9IrK/ubmZ1tZWmpubiUajtLW1UV9fT1dXF9XV1SQSCSKR5GyoA+uMRiIREokE1dXVdHV1UV9fT1tbG4sWLWKgvIaGBmKxGDU1NcTj8VdXVBkoY+BnVVUVPT091NbW0tHRQWNjIy0tLbS0tNDY2EhHRwe1tbX09PRQVVU1bBmVlZXE43FqamqIxWI0NDSM6NTf3893f7aP+3ZVUfbpJ/jo9yIcONbKXdtX8ZV3FvPDu7Zw7eIE+X2dRKPRcTmVlZUF4jSe/TRep/Hsp40bN+ac03j207x583LOaTz7aeBoZC45jXc/rVu3LuecxrOfZs6cmTGnkQjk0LeI/BxYPMxbnwT2Aa0kV+P6O2CJqv7ekM+/B7hBVe9KPX8/cKWqfmykejN56Lu8vJwtW7ZkpCwvaDzTya4DTTx4IMqxM51MLcznpksXs7OshKvXzCc/A1N5hj0DrzF/83fZHyyDTPqPdOg7dOeoByMiK4FHVPXSIa9fDXxKVW9IPb8PYLTlNTPZUYeRju4+Hj2YvKXqhYaziMAb1sxn5+YSbrx0MdMn20X+hmEYYSSrzlGLyJJBT28FXhpmsxeBUhFZJSKTgNuBh/1o3wADh1WCJt6f4OmaFu79XoStf/9zPrGrijMXevjzGy7h2b+4nu/etY3btpR40kmHJYOgMH/zdx3XM/DLP3QjahH5L+AKkoe+G4D/parNIrIU+Kaq3pza7mbgX4F84H5V/cxoZWdqRP1sXSt7a0+zdeU8Li+Zk3Z54+VgUzu/fOU0Zzt72XfkLK2xHuZOK+Sdm5ays6yEy0tmI+L9KlV2xaf5m7+7/mAZ+HXVd+g6ai/JREddfqyN3/nac8QT4cjtqlXzuHP7Kt50yUImFfj7D6a6upoNGzb4WmeYMH/zd9kfLINM+o/UUdtJy3Gy78gZEqk/bgR484ZFvHHdAt/q/+Xh0zxVfQoF8lPLSb5t43DX5XnPqlWrAqk3LJi/+buO6xn45W8d9TjZtno+kwry6I0nmFSQx0feuIYtK/yb63bDklnsrT1NXzxBYUEe21bP963uoZw4cYI1a9YEVn/QmL/5u+wPloFf/tZRj5MtK+by3bu28fShJq7bWOJrJz24/n1HzrBt9Xzf6x/MvHnzAqs7DJi/+buO6xn45W8d9QTYsmIuiws6KS4OppPcsmJuoB30AJ2dnU6vnGP+5u+yP1gGfvm7e7lemrh8peMArmdg/ubvOq5n4Je/2ymnQWFhYdBNCBzXMzB/83cd1zPwy9+p27NE5DRwLEPFFZGc6tRlXM/A/M3fZX+wDDLpv0JVh72FyKmOOpOIyP6L3fPmCq5nYP7m77I/WAZ++duhb8MwDMMIMdZRG4ZhGEaIsY564nw96AaEANczMH+3cd0fLANf/O0ctWEYhmGEGBtRG4ZhGEaIsY7aMAzDMEKMddSGYRiGEWKsozYMwzCMEGMdtWEYhmGEGOuoDcMwDCPEWEdtGIZhGCHGOmrDMAzDCDHWURuGYRhGiLGO2jAMwzBCjHXUhmEYhhFirKM2DMMwjBBjHbVhGIZhhBjrqA3DMAwjxFhHbRiGYRghxjpqwzAMwwgx1lEbhmEYRoixjtowDMMwQox11IZhGIYRYgqCboCfFBUV6cqVKzNSVm9vL5MmTcpIWdmK6xmYv/m77A+WQSb9y8vLW1V1wXDvOdVRr1y5kv3792ekrFgsxowZMzJSVrbiegbmb/4u+4NlkEl/ETl2sffs0PcEaW1tDboJgeN6BuZv/q7jegZ++VtHPUFc/ityANczMH/zdx3XM/DL3zrqCdLX1xd0EwLH9QzM3/xdx/UM/PK3jnqCJBKJoJsQOK5nYP7m7zquZ+CXv3XUE2TatGlBNyFwXM/A/M3fdVzPwC9/66gnyNmzZ4NuQuC4noH5m7/ruJ6BX/7WUU+QpUuXBt2EwHE9A/M3f9dxPQO//K2jniBHjx4NugmB43oG5m/+ruN6Bn75i6r6UlEY2Lp1q2ZqwpNEIkFentt/57iegfmbv8v+YBlk0l9EylV163DvuZtwmlRUVATdhMBxPQPzrwi6CYHiuj9YBn7524jaMAzDMALGRtQeUF5eHnQTAsf1DMzf/F3H9Qz88g90RC0iNwJfAPKBb6rq54a8L6n3bwY6gQ+pamTQ+/nAfiCqqm8frT4bURuGYRhhJJQj6lQn+2XgJmADcIeIbBiy2U1AaepxN/CVIe//EfCyx00dlkgkMvpGOY7rGZi/+buO6xn45R/koe8rgTpVPaKqvcAPgFuGbHML8B1Nsg+YIyJLAESkBPgt4Jt+NnqAK664IohqQ4XrGZj/FUE3IVBc9wfLwC//IDvqYuD4oOdNqdfGus2/Ah8HAplstqamJohqQ4XrGZi/+buO6xn45R9kRy3DvDb0hPmw24jI24EWVR31TL6I3C0i+0Vkf3NzM62trTQ3NxONRmlra6O+vp6uri6qq6tJJBKvHsoYuEggEomQSCSorq6mq6uL+vp62tramDp1KgPlNTQ0EIvFqKmpIR6PU1lZ+ZoyBn5WVVXR09NDbW0tHR0dNDY20tLSQktLC42NjXR0dFBbW0tPTw9VVVXDllFZWUk8HqempoZYLEZDQ0PGnKLR6LicVq1alXNO49lPxcXFOec0nv1UWFiYc07j2U+xWCznnMa7nxYuXJhzTuPZT0DGnEYisIvJRORq4FOqekPq+X0AqvrZQdt8DXhGVb+fev4K8CbgD4H3A3FgCjAL2KWqvztSnZm8mKy+vp41a9ZkpKxsxfUMzN/8XfYHyyCT/qG8mAx4ESgVkVUiMgm4HXh4yDYPAx+QJNuAc6rarKr3qWqJqq5Mfe4Xo3XSmWbevHl+VhdKXM/A/M3fdVzPwC//wDpqVY0D9wJPkLxy+4eqekhE7hGRe1KbPQocAeqAbwB/EEhjh6GzszPoJgSO6xmYv/m7jusZ+OVf4EstF0FVHyXZGQ9+7auDflfgo6OU8QzwjAfNGxGX57cdwPUMzN/8Xcf1DPzydzvlNCgsLAy6CYHjegbmb/6u43oGfvlbRz1BRrtKzwVcz8D8zd91XM/AL3/rqCdIUVFR0E0IHNczMH/zdx3XM/DL3zrqCdLU1BR0EwLH9QzM3/xdx/UM/PK3ZS4nSDwep6Ag0GvxAsf1DMzf/F32B8sgk/5hvY86qzl06FDQTQgc1zMwf/N3Hdcz8MvfRtSGYRiGETA2ovYA1xdMB8vA/M3fdVzPwC9/G1EbhmEYRsDYiNoDXP9LEiwD8zd/13E9AxtRe4CNqA3DMIwwYiNqDxhYY9RlXM/A/M3fdVzPwC9/G1FPkJ6eHiZPnpyRsrIV1zMwf/N32R8sg0z624jaAxobG4NuQuC4noH5m7/ruJ6BX/7WUU+QRYsWBd2EwHE9A/M3f9dxPQO//APtqEXkRhF5RUTqROQTw7wvIvLF1PsHRaQs9foyEXlaRF4WkUMi8kd+t729vd3vKkOH6xmYf3vQTQgU1/3BMvDL/6KTlIpIxyifFaBZVddNpGIRyQe+DLwVaAJeFJGHVbV60GY3AaWpx1XAV1I/48D/VtWIiMwEykXkySGf9ZQpU6b4VVVocT0D8zd/13E9A7/8RxpR16vqrBEeM4ELadR9JVCnqkdUtRf4AXDLkG1uAb6jSfYBc0Rkiao2q2oEQFXPAy8DxWm0xTAMwzBCyUgd9W1j+PxYtrkYxcDxQc+b+M3OdtRtRGQlsBl4frhKRORuEdkvIvubm5tpbW2lubmZaDRKW1sb9fX1dHV1UV1dTSKRIBKJAL++kT0SiZBIJKiurqarq4v6+nra2tpobm5moLyGhgZisRg1NTXE43EqKytfU8bAz6qqKnp6eqitraWjo4PGxkZaWlpoaWmhsbGRjo4Oamtr6enpefWy/6FlVFZWEo/HqampIRaL0dDQkDGnaDQ6Lqfu7u6ccxrPfjp//nzOOY1nPzU1NeWc03j2U01NTc45jXc/tbe355zTePbTsWPHMuY0EoHdniUi7wFuUNW7Us/fD1ypqh8btM1Pgc+q6t7U86eAj6tqeer5DOCXwGdUdddodWby9qyOjg5mzZqVkbKyFdczMH/zd9kfLINM+k/o9iwROS8iHRd7ZKBdTcCyQc9LgBNj3UZECoEHgO+OpZPONKdOnfK7ytDhegbmb/6u43oGfvlf9GKy1DloROTTwEngv0heQPY+YGYG6n4RKBWRVUAUuB1475BtHgbuFZEfkLyI7JyqNouIAP8BvKyqn89AW8bN8uXLg6g2VLiegfmbv+u4noFf/mO5PesGVf13VT2vqh2q+hXSOzcNgKrGgXuBJ0heDPZDVT0kIveIyD2pzR4FjgB1wDeAP0i9fg3wfuB6EalIPW5Ot03j4fDhw35WF0pcz8D8zd91XM/AL/9Rz1GLyK9I3kb1A0CBO4CPquobvG9eZrFFOQzDMIwwku4Uou8Ffhs4lXq8h988RO0cri/vBpaB+Zu/67iegS1z6QE2ojYMwzDCSFojahGZIiIfFZF/F5H7Bx6Zb2Z24fpfkmAZmL/5u47rGYRmRC0iPwJqSB7u/jTJq75fVlXf59dOFxtRG4ZhGGEk3XPUa1X1/wAXVPXbwG8Bl2WygdnIwIw1LuN6BuZv/q7jegZ++Y9lRP2Cql4pIrtJ3h51EnhBVVf70cBMkskRdTwep6DgorehO4HrGZi/+bvsD5ZBJv3THVF/XUTmAn9FcgKSauAfM9KyLKauri7oJgSO6xmYv/m7jusZ+OU/4p8CIpIHdKhqG7AbyLpRtFeUlJQE3YTAcT0D8zd/13E9A7/8RxxRq2qC5OxhxhBaW1uDbkLguJ6B+Zu/67iegV/+Yzn0/aSI/JmILBOReQMPz1sWcmbMmBF0EwLH9QzM3/xdx/UM/PIfy1nw30v9/Oig1xTHD4P39fUF3YTAcT0D8zd/13E9A7/8R+2oVXWVHw3JNhKJRNBNCBzXMzB/83cd1zPwy3+k9ajLRvvwWLbJVaZNmxZ0EwLH9QzM3/xdx/UM/PIf6Rz1f4rI3MHnpYc+SK4J7SRnz54NugmB43oG5m/+ruN6Bn75j3ToezZQDsgI25zObHOyh6VLlwbdhMBxPQPzN3/XcT0Dv/wvOqJW1ZWqulpVV43wuDKdykXkRhF5RUTqROQTw7wvIvLF1PsHBx9qH+2zXnP06FG/qwwdrmdg/ubvOq5n4Jf/WG7P8gQRyQe+DNwEbADuEJENQza7CShNPe4GvjKOz3pG+bE2fnGykPJjbX5V+Rv1f/npusDqH2D9+vWB1h805m/+rhNkBkH/P+hnPxDkJK1XAnWqegRARH4A3EJyitIBbgG+o8kJyfeJyBwRWQKsHMNnPaH8WBu//bXn6E8oeXKY9YtnMnNKodfVvsr57j5qTp4noZAn+F7/YGKxmNP3UZq/+bvsD8FlEPT/g4Prn1JYx3fv2saWFXM9qy+wETVQDBwf9Lwp9dpYthnLZwEQkbtFZL+I7G9ubqa1tZXm5mai0ShtbW3U19fT1dVFdXU1iUSCSCQC/Hqd0UgkQiKRoLq6mq6uLh7dX0t/IrmQSUKh/UIP3d3d9Pf309nZiapy4UIMgFjs/Gt+XrhwAdUEXV1d9Pf309PTQ19fH319ffT09NDf309XVxeqCS5cuDBsGWc6OklVT0LhbKybvr4+ent76e3tIR6P093dRSKRoLOzM/XZoe1JPu/s7CSRSNDd3UU8Hqe3t4fe3l76+vrG5DRjxoyMOF24EENV6ezspL+/n+7u4JzGs5+mT5+Wc07j2U8FBQU55zSe/ZScTiK3nMa7n6ZOnRqI09lY92v+H2zv7PX1uzf4/+G+eIInIvW0tLTQ0tJCY2MjHR0d1NbW0tPTQ1VVFfDrPmXgZ2VlJfF4nJqamkHfqeEZdUQtIkJyDerVqvppEVkOLFbVF0b77GhFD/Pa0KW8LrbNWD6bfFH168DXIbl6VlFR0Wvenzs3+VfQhg3JI+dlZcnT4Fu2bHnN84H3b95ayncrztDbl2BSYR5fet9WT/+SGkr5sTbe98199MUTFBbk8eXffb2v9b+mLeXlbNlydSB1h4Gk/zVBNyMwkv5bgm5GYLjuDwMZbPe/3iH/D37pvVsC+X+4ty9Z/w1la1i48LX1z5o1C4DLLkuuCj3wXRn4uWnTJmBspw/GsszlV4AEcL2qvi61ktbPVPX14/AartyrgU+p6g2p5/cBqOpnB23zNeAZVf1+6vkrwJtIHvoe8bPDkallLsuPtbHvyBm2rZ4fSCcZdP2GYRhBE/T/g5muP91lLq9S1Y8C3QCplbQmpd0qeBEoFZFVIjIJuJ3kMpqDeRj4QOrq723AOVVtHuNnPWPLirlcPbsjsE5yy4q5fPS6tYF30gOnCVzF/M3fdYLMIOj/B/3sB8ZyMVlf6iprBRCRBSRH2GmhqnERuRd4AsgH7lfVQyJyT+r9rwKPAjcDdUAn8OGRPptum8bDFVdc4Wd1ocT1DMz/iqCbECiu+4Nl4Jf/WEbUXwQeBBaKyGeAvcA/ZKJyVX1UVdep6hpV/Uzqta+mOmk0yUdT71+mqvtH+qyf1NTU+F1l6HA9A/M3f9dxPQO//Ec9Rw0gIuuBN5O8iOspVX3Z64Z5QabOUQN0dXUxderUjJSVrbiegfmbv8v+YBlk0j+tc9QisgY4qqpfBl4C3ioiczLSsizmxIkTQTchcFzPwPzN33Vcz8Av/7Ec+n4A6BeRtcA3gVXA9zxtVRYwb968oJsQOK5nYP7m7zquZ+CX/1g66oSqxoGdwBdU9U+AJd42K/wM3FTvMq5nYP7m7zquZ+CX/1g66j4RuQP4APBI6rVg5qwMEXl5QU7qFg5cz8D8zd91XM/AL/+x1PJh4GrgM6p6VERWAf+ft80KP4WFzv+t4nwG5m/+ruN6Bn75j9pRq2q1qv7hwOxgqnpUVT/nfdPCzWhzs7qA6xmYv/m7jusZ+OU/lrm+S4HPklxOcsrA66q62sN2hZ6hc4a7iOsZmL/5u47rGfjlP5ZD3/9Jch3oOHAd8B3gv7xsVDbQ1NQUdBMCx/UMzN/8Xcf1DPzyH8uiHOWqukVEqlT1stRre1R1hy8tzCCZnPAkHo9TUBDkct7B43oG5m/+LvuDZZBJ/3QX5egWkTygVkTuFZFbgYUZaVkWc+iQr1OLhxLXMzB/83cd1zPwy38sI+rXAy8Dc4C/A2YD/6Sq+zxvXYbJ5IjaMAzDMDJFWiNqVX1RVWOq2qSqH1bVndnYSWea8vLyoJsQOK5nYP7m7zquZ+CX/1hG1OuAPwdWMOgqcVW93tumZR4bURuGYRhhJN1z1D8CIsBfkeywBx7pNGieiDwpIrWpn8OuvC0iN4rIKyJSJyKfGPT6P4tIjYgcFJEHg1gkxPW/JMEyMH/zdx3XMwjTiLpcVbdktFKRfwLOqurnUh3wXFX9iyHb5AOHgbcCTcCLwB2qWi0ibwN+oapxEflHgKGfHw4bURuGYRhhZEIj6tSodx7wExH5AxFZMvBa6vV0uAX4dur3bwPvGmabK4E6VT2iqr3AD1KfQ1V/llooBGAfUJJme8ZNVVWV31WGDtczMH/zdx3XM/DLf6RD3+XAfuCDJA91/yr12sDr6bBIVZsBUj+Hu92rGDg+6HlT6rWh/B7w2MUqEpG7RWS/iOxvbm6mtbWV5uZmotEobW1t1NfX09XVRXV1NYlEgkgkAvz6kEYkEiGRSFBdXU1XVxf19fW0tbUxc+ZMBspraGggFotRU1NDPB6nsrLyNWUM/KyqqqKnp4fa2lo6OjpobGykpaWFlpYWGhsb6ejooLa2lp6enle/AEPLqKysJB6PU1NTQywWo6GhIWNO0Wh0XE7r1q3LOafx7KeVK1fmnNN49tPUqVNzzmk8+6m7uzvnnMa7n4qLi3POaTz7qaCgIGNOIzHqoe+JIiI/BxYP89YngW+r6pxB27ap6mvOU4vIe4AbVPWu1PP3A1eq6scGbfNJYCuwU8cgkslD37W1tZSWlmakrGzF9QzM3/xd9gfLIJP+Ix36Hstc31OAPwC2AwrsAb6qqt0jfU5V3zJCmadEZImqNovIEqBlmM2agGWDnpcAJwaV8UHg7cCbx9JJZ5pFixb5XWXocD0D8zd/13E9A7/8x3LV93eAjcCXgH8juThHunN9P0zykDqpnz8eZpsXgVIRWSUik4DbU59DRG4E/gJ4p6oGsnJ5e3t7ENWGCtczMP/2oJsQKK77g2Xgl/9YJim9RFU3DXr+tIhUplnv54AfisidQCPwHgARWQp8U1VvTl3RfS/wBJAP3K+qA/O1/RswGXhSRAD2qeo9abZpXEyZMmX0jXIc1zMwf/N3Hdcz8Mt/LB31ARHZNjAbmYhcBTybTqWqegZ48zCvnwBuHvT8UeDRYbZbm079hmEYhpEtjKWjvgr4gIg0pp4vB14WkSpAVfVyz1oXYgau+HQZ1zMwf/N3Hdcz8Mt/LB31jZ63IguZM2dO0E0IHNczMP85QTchUFz3B8vAL/+xLMpxbKSHH40MI6dOnQq6CYHjegbmb/6u43oGfvmP5apvYxiWL18edBMCx/UMzN/8Xcf1DPzyt456ghw+fDjoJgSO6xmYv/m7jusZ+OXv2cxkYcQW5TAMwzDCSLrLXBrD4PrybmAZmL/5u47rGYRmmctcwkbUhmEYRhixEbUHuP6XJFgG5m/+ruN6Bjai9gAbURuGYRhhxEbUHjCwTqnLuJ6B+Zu/67iegV/+NqKeIPF4nIKCsUzslru4noH5m7/L/mAZZNLfRtQeUFdXF3QTAsf1DMzf/F3H9Qz88reOeoKUlJQE3YTAcT0D8zd/13E9A7/8raOeIK2trUE3IXBcz8D8zd91XM/AL/9AOmoRmSciT4pIbern3Itsd6OIvCIidSLyiWHe/zMRUREp8r7Vr2XGjBl+Vxk6XM/A/M3fdVzPwC//oEbUnwCeUtVS4KnU89cgIvnAl4GbgA3AHSKyYdD7y4C3Ao1DP+sHfX19QVQbKlzPwPzN33Vcz8Av/6A66luAb6d+/zbwrmG2uRKoU9UjqtoL/CD1uQH+Bfg4EMhl64lEIohqQ4XrGZi/+buO6xn45R9UR71IVZsBUj8XDrNNMXB80POm1GuIyDuBqKqOehObiNwtIvtFZH9zczOtra00NzcTjUZpa2ujvr6erq4uqqurSSQSRCIR4NczzkQiERKJBNXV1XR1dVFfX09bWxuxWIyB8hoaGojFYtTU1BCPx1+9t26gjIGfVVVV9PT0UFtbS0dHB42NjbS0tNDS0kJjYyMdHR3U1tbS09NDVVXVsGVUVlYSj8epqakhFovR0NCQMadoNDoup2nTpuWc03j2U0FBQc45jWc/nTt3LuecxrOfGhsbc85pvPtJRHLOaTz76cyZMxlzGgnP7qMWkZ8Di4d565PAt1V1zqBt21T1NeepReQ9wA2qelfq+ftJjrL/AngaeJuqnhORBmCrqo56Vj+T91HX19ezZs2ajJSVrbiegfmbv8v+YBlk0n+k+6g9u1NdVd8yQoNOicgSVW0WkSVAyzCbNQHLBj0vAU4Aa4BVQKWIDLweEZErVfVkxgRGYenSpX5VFVpcz8D8zd91XM/AL/+gDn0/DHww9fsHgR8Ps82LQKmIrBKRScDtwMOqWqWqC1V1paquJNmhl/nZSQMcPXrUz+pCiesZmL/5u47rGfjlH8gUoiIyH/ghsJzkVdvvUdWzIrIU+Kaq3pza7mbgX4F84H5V/cwwZTUQwKHvRCJBXp7bt6G7noH5m7/L/mAZZNI/dFOIquoZVX2zqpamfp5NvX5ioJNOPX9UVdep6prhOunUNivH0klnmoqKCr+rDB2uZ2D+FUE3IVBc9wfLwC9/W5TDMAzDMAImdCPqXMD1BdPBMjB/83cd1zPwy99G1IZhGIYRMDai9oCBm+ldxvUMzN/8Xcf1DPzytxH1BHH9akewDMzf/F32B8sgp6/6zgVqamqCbkLguJ6B+Zu/67iegV/+1lFPkFWrVgXdhMBxPQPzN3/XcT0Dv/yto54gJ06cCLoJgeN6BuZv/q7jegZ++VtHPUHmzZsXdBMCx/UMzN/8Xcf1DPzyt456gnR2dgbdhMBxPQPzN3/XcT0Dv/yto54gLl/pOIDrGZi/+buO6xn45e92ymlQWFgYdBMCx/UMzN/8Xcf1DPzyd+o+ahE5DRzLUHFFgO+LgYQM1zMwf/N32R8sg0z6r1DVBcO94VRHnUlEZP/Fbk53BdczMH/zd9kfLAO//O3Qt2EYhmGEGOuoDcMwDCPEWEc9cb4edANCgOsZmL/buO4PloEv/naO2jAMwzBCjI2oDcMwDCPEWEdtGIZhGCHGOupREJEbReQVEakTkU8M876IyBdT7x8UkbIg2ukVY/B/k4icE5GK1OOvg2inV4jI/SLSIiIvXeT9XN//o/nn+v5fJiJPi8jLInJIRP5omG1y9jswRv9c/w5MEZEXRKQylcHfDrONt98BVbXHRR5APlAPrAYmAZXAhiHb3Aw8BgiwDXg+6Hb77P8m4JGg2+phBtcCZcBLF3k/Z/f/GP1zff8vAcpSv88EDjv2f8BY/HP9OyDAjNTvhcDzwDY/vwM2oh6ZK4E6VT2iqr3AD4BbhmxzC/AdTbIPmCMiS/xuqEeMxT+nUdXdwNkRNsnl/T8W/5xGVZtVNZL6/TzwMlA8ZLOc/Q6M0T+nSe3XWOppYeox9CpsT78D1lGPTDFwfNDzJn7zSzqWbbKVsbpdnTos9JiIbPSnaaEhl/f/WHFi/4vISmAzyRHVYJz4DozgDzn+HRCRfBGpAFqAJ1XV1+9AQaYKylFkmNeG/iU1lm2ylbG4RUjOURsTkZuBh4BSrxsWInJ5/48FJ/a/iMwAHgD+WFU7hr49zEdy6jswin/OfwdUtR+4QkTmAA+KyKWqOvi6DU+/AzaiHpkmYNmg5yXAiQlsk62M6qaqHQOHhVT1UaBQRIr8a2Lg5PL+HxUX9r+IFJLspL6rqruG2SSnvwOj+bvwHRhAVduBZ4Abh7zl6XfAOuqReREoFZFVIjIJuB14eMg2DwMfSF31tw04p6rNfjfUI0b1F5HFIiKp368k+Z0643tLgyOX9/+o5Pr+T7n9B/Cyqn7+Ipvl7HdgLP4OfAcWpEbSiMhU4C1AzZDNPP0O2KHvEVDVuIjcCzxB8gro+1X1kIjck3r/q8CjJK/4qwM6gQ8H1d5MM0b/dwMfEZE40AXcrqnLIHMBEfk+yatai0SkCfgbkheT5Pz+hzH55/T+B64B3g9Upc5RAvwlsByc+A6MxT/XvwNLgG+LSD7JP0J+qKqP+NkP2BSihmEYhhFi7NC3YRiGYYQY66gNwzAMI8RYR20YhmEYIcY6asMwDMMIMdZRG4ZhGMZFkFEWpplAectF5GephU6qUzO+jYh11IZhGIZxcb7Fb05wkg7fAf5ZVV9Hcj2FltE+YB21YTiEiMwRkT8Y9HypiPyPB/V8SkSiIvLpEbZZk1oWMXaxbQwjaIZbmCb13X1cRMpFZI+IrB9LWSKyAShQ1SdTZcdUtXO0z1lHbRhuMQd4taNW1ROq+m6P6voXVb3o2sSqWq+qV3hUt2F4ydeBj6nqFuDPgH8f4+fWAe0isktEDojIP6cmUhkRm5nMMNzic8Ca1CxTTwJfJrmW8KUi8iHgXSRnobsU+H8k1yF/P9AD3KyqZ0VkTepzC0jOwvT7qjp0SsXXICJvBL6QeqrAtallEw0jq0gtUPIG4EepmVMBJqfe2wkMdxQpqqo3kOxzd5BchawR+G/gQySnab0o1lEbhlt8Arh0YCQ7zIUsl5L8T2QKyekQ/0JVN4vIvwAfAP6V5GjiHlWtFZGrSI4mrh+l3j8DPqqqz6b+o+vOjI5h+E4e0D7c0aDUoiXDLdwyQBNwQFWPAIjIQ8A2Rumo7dC3YRiDeVpVz6vqaeAc8JPU61XAyiGjiQrgayTnQh6NZ4HPi8gfAnNUNZ75phuG96SW+TwqIu+B5MIlIrJpjB9/EZgrIgtSz68Hqkf7kHXUhmEMpmfQ74lBzxMkj8C9OpoY9HjdaIWq6ueAu4CpwL6xXnxjGEGTWpjmOeASEWkSkTuB9wF3ikglcAi4ZSxlpda1/jPgKRGpIrmO9TdG+5wd+jYMtzgPzJzoh1W1Q0SOish7VPVHqeUNL1fVypE+JyJrVLWK5CpMVwPr+c2lAg0jdKjqHRd5a0K3bKWu+L58PJ+xEbVhOISqngGeFZGXROSfJ1jMREYTf5yqs5LkUoiPTbBuw3AOW+bSMIyMIyKfAmKq+n/HsG1MVWd43yrDyE5sRG0YhhfEgLvHMuEJcMq3VhlGFmIjasMwDMMIMTaiNgzDMIwQYx21YRiGYYQY66gNwzAMI8RYR20YhmEYIeb/B9Yk8l13kD3CAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "show_global_drive(drive);" + ] + }, + { + "cell_type": "markdown", + "id": "ecd5fce7", + "metadata": {}, + "source": [ + "Finally, we construct out AHS program from the atomic registers, and the Hamiltonian defined above. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ef5318d9", + "metadata": {}, + "outputs": [], + "source": [ + "ahs_program = AnalogHamiltonianSimulation(\n", + " register=register, \n", + " hamiltonian=drive\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "37e89b67", + "metadata": {}, + "source": [ + "Before running the program on Quera's Aquila device (See notebook 01), we can first run it on the local simulator to make sure the outcome is the expected $Z_2$ state. Below we have explicitly specified the values of `steps` and `shots`, which are the number of time steps in the simulation and the number of sampling for the final stats, respectively. One could increase the accuracy of the result by increasing the values of these arguments, at the expense of longer runtime. " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "18447781", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "device = LocalSimulator(\"braket_ahs\")\n", + "result = device.run(ahs_program, shots=1000, steps=100).result()\n", + "show_final_avg_density(result)" + ] + }, + { + "cell_type": "markdown", + "id": "daf77070", + "metadata": {}, + "source": [ + "We see that the average Rydberg density approximately forms the $Z_2$ pattern. The discrepancy can be attributed to finite size of the system and nonadiabaticity throughout the evolution. We expect that as one increase the system size and the duration of the AHS program, the final Rydberg density will approach the ideal $Z_2$ pattern.\n", + "\n", + "The $Z_2$ phase can be characterized by the density correlation $g_{ij}$ of the $i$-th and the $j$-th atom, which is defined as\n", + "\n", + "\\begin{align}\n", + "g_{ij} = \\langle n_i n_j\\rangle - \\langle n_i\\rangle\\langle n_j\\rangle,\n", + "\\end{align}\n", + "\n", + "where $\\langle\\cdot\\rangle$ is the average over the shots." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4ba0163e", + "metadata": {}, + "outputs": [], + "source": [ + "def get_density_correlation_Z2(result):\n", + " post_sequences = np.array([list(measurement.post_sequence) for measurement in result.measurements])\n", + " return np.cov(post_sequences.T)\n", + "\n", + "gij = get_density_correlation_Z2(result)" + ] + }, + { + "cell_type": "markdown", + "id": "c405519e", + "metadata": {}, + "source": [ + "The Rydberg density correlation function can be visualized as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "dd0c5d4a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(gij, cmap='bwr', vmin=-0.25, vmax=+0.25)\n", + "plt.xticks(range(num_atoms), [f'{i}' for i in range(num_atoms)])\n", + "plt.xlabel(\"atom index\")\n", + "plt.yticks(range(num_atoms), [f'{j}' for j in range(num_atoms)])\n", + "plt.ylabel(\"atom index\")\n", + "plt.title('Rydberg density correlation')\n", + "plt.gca().set_aspect('equal')\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "276bb5b6", + "metadata": {}, + "source": [ + "For more explanation and interpretation of the Rydberg density correlation functions, see \"Probing many-body dynamics on a 51-atom quantum simulator\" by [Bernien et al. (2017)](https://arxiv.org/abs/1707.04344). " + ] + }, + { + "cell_type": "markdown", + "id": "fc7d3074", + "metadata": {}, + "source": [ + "## 2D checkerboard phase \n", + "\n", + "In two dimension, Rydberg system can exhibit the checkerboard phase, which is analogous to the $Z_2$ phase in 1D. For simplicity, here we create a $3\\times 3$ square lattice." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "22477060", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "register_2D = AtomArrangement()\n", + "separation = 6.7e-6 # in meters \n", + "\n", + "for k in range(3):\n", + " for l in range(3):\n", + " register_2D.add((k * separation, l * separation))\n", + "\n", + "show_register(register_2D)" + ] + }, + { + "cell_type": "markdown", + "id": "eb0fcacf", + "metadata": {}, + "source": [ + "We will use the same driving field as the one for generating the $Z_2$ phase. We then assemble the 2D array with the driving field, and run the AHS program on the local simulator. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "df3a2aae", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ahs_program_2D = AnalogHamiltonianSimulation(\n", + " register=register_2D, \n", + " hamiltonian=drive\n", + ")\n", + "\n", + "result_2D = device.run(ahs_program_2D, shots=1000, steps=200).result()\n", + "show_final_avg_density(result_2D)" + ] + }, + { + "cell_type": "markdown", + "id": "08e49477", + "metadata": {}, + "source": [ + "We see that the overall pattern mimics the checkerboard pattern, but the central site suffers strong discrepancy. This is due to the finite size of the system and the finite duration of the AHS program, which cause non-adiabatic errors.\n", + "\n", + "For more explanation and interpretation of the 2-d results, see \"Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator\" by [Ebadi et al. (2020)](http://arxiv.org/abs/2012.12281). " + ] + }, + { + "cell_type": "markdown", + "id": "68ffc633", + "metadata": {}, + "source": [ + "## Realizing $Z_2$ and checkerboard phase on a QPU\n", + "\n", + "In previous sections, we have demonstrated two AHS programs for realizing many-body ground states. The results from the local simulator show that the results of the programs meet our expectations. Here we will run the same AHS program on the Aquila device. " + ] + }, + { + "cell_type": "markdown", + "id": "525d3c27", + "metadata": {}, + "source": [ + "
    \n", + "Note: Some atoms may be missing even if the shot was successful. We recommend comparing pre_sequence of each shot with the requested atom filling in the AHS program specification. \n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "31901542", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.aws import AwsDevice \n", + "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "07a73135", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "result_1D_aquila = device.run(ahs_program, shots=100).result()\n", + "show_final_avg_density(result_1D_aquila)" + ] + }, + { + "cell_type": "markdown", + "id": "69fc4e5d", + "metadata": {}, + "source": [ + "We can calculate the density correlation function for the result obtained from Aquila" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "e07e91f5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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kvLrz5s1vo+pmNmq6uDVXRZVT3ZcDJwCfAS4B/kPS7CrBI+LJiNiZYjyt3SQ9v8UxT82rO3Pm1u3U3cxGS4+f6lZpix4HvLF/rktJrwd+DuxYtZCIuE/SJcBi4IaNqKeZdYsxcDtLldq/tDzBb5oYfI/h3iRpa0nT0/JkYG/gdxtZTzPrJj3e4qtSs2dLukjSDQCSXgj8c4X3zQIulnQdxQWRCyPihxtfVTPrCmPgqm6VU93/Bj4C/BdARFwn6ZvA54Z6U0RcB+wy4hqaWffp4iu2VVSp/ZSI+I30tLl/12eqj5l1uzHQx1cl8a2V9GzSPXiS3gCszlorM+tuDUh87wWWADtKugu4DXhr1lqZWfdqQosvIm4F9pY0FRgXEQ/mr5aZdbWxmvgkfXCQ7QBExPGZ6mRm3WyMj8c3Lf1cALwYWJrWD6AYdcXMmmqstvgi4tMAkn4K7Np/iivpGOA7OSozTsHkCU/kCA3Ab6ftmS02wJdmfjFrfOjAvLdLJ2eN/9nnP5I1/idn5L9VtO+R/bPGnzvx7myxx2+o4e+rCX18wHzg8dL648B2WWpjZr2hAYnvG8BvJJ1HcUvL64DTs9bKzLrbWE98EfF5SRcA/eeJh0bENXmrZWZdqyGnugDXUty0PAFA0vyIuCNXpcysi43xq7oASHo/cDRwN/AkIIpT3hfmrZqZda0GtPgOBxZExL25K2NmPaAhp7p3AvfnroiZ9ZAGJL5bgUsk/Yhi5jTAT26YNVqPJ74qtb8DuBCYRPE0R/+rEknjJV0jyYOQmo0FNQ5EKmmxpJsl3SLpyBb7Jekraf91knat4yNUuZ3l0yMs43DgJmDzEcYxs25Q01XdNAvjV4F9gD7gKklLy1NdAPsCO6TX7sDX0s8RGWqQgi9HxBGSfkCL+XAj4rXDBZc0F/g74PNAy0EPzKwH1XOquxtwSxoBCknfAg4EyonvQOD0iAjgCknTJc2KiBGNCTpU2v5G+nncCOJ/GfgoQ5wal+fVnT/f8+qa9YJAwx9UmClpWWl9SUQsSctzKC6e9uvjr1tzrY6ZwwgHQx5qkILl6ecvNiawpP2BNRGxXNJeQ5SzhGKgUxa96EV/1bI0s+6zYUPlQ9dGxKJB9rXKngNzQJVj2pbz9us9gNdK2g/YFNhc0hkR4dGbzXpYRFuJbyh9wLzS+lxg1UYc07Zs16Qj4qiImBsR2wFvBn7upGfW+yJg/fpqr2FcBewgaXtJkyjyxNIBxywF/ild3X0JcP9I+/cgb4vPzMaoOlp8EbFe0vuAnwDjgVMiYoWk96T9JwLnA/sBtwAPA4eOvORqz+ouAj4BbJuOV1GnqPysbkRcAlyycVU0s25T06kuEXE+RXIrbzuxtBwUE57VqkqL70yKCcWvB2r6uGbWq2rs4xs1VRLfPREx8LzbzBqsCYnvaEknARfx9Gd1z81WKzPrWk1p8R0K7AhM5H9OdQNw4jNroP6rur2sSuJbGBEvyF4TM+sZvd7iq3If3xWSdspeEzPrGRs2VHt1qyotvj2Bt0m6jaKPr+3bWap6Yr1YvXZi3WGfsvDRK7PFBrh+v49ljQ9w9jNPyxo/+7y3X5udNf7hbxzxTf3DOmHqxVnjr3zWK7LFfjxG/vfVlD6+xdlrYWY9ZcwnvohYKWkh8LK06ZcR8du81TKzbjUWWnzD9vFJOpziJuZt0uuMNPOamTVUTc/qjpoqp7qHAbtHxDoASV8ELgf+PWfFzKw7jYUWX5XEJ4r5dPv1z61rZg3VhMT3deBKSeel9YOAU7LVyMy6WiNafBFxvKRLKG5rEXBoRFyTu2Jm1r3GfOKT9I2IOAS4usU2M2uYpjyy9rzySpoS7kVVgku6HXiQol9w/RBj75tZDxmzLT5JRwEfByZLeoD/uaDxOGlyoIpeERFrN76KZtZNxkIf36D38UXEFyJiGvCliNg8Iqal14yIOKqDdTSzLjPmn9WNiKMkbUkxk/mmpe2XVogfwE8lBfBfpfk0n1KeV3fOHM+ra9YLujmpVVHl4sY7gcMppnW7FngJxQ3Mr6wQf4+IWCVpG+BCSb8bmDDL8+ouXLjI8+qadbkxfapbcjjwYmBlRLwC2AW4p0rwiFiVfq4BzgN228h6mlmXqHF6yVFTJfE9GhGPAkjaJCJ+BywY7k2Spkqa1r8MvBq4YSSVNbPuMOb7+IA+SdOB71Gcrv6FajOZPwM4T1J/Od+MiAs2sp5m1kW6OalVUeXixuvS4jGSLga2AIZNYBFxK7BwZNUzs24zFvr4qrT4nhIRv8hVETPrHY1KfGZmjWvxmZlBd1+xrcKJz8za4hafmTWSE5+ZNYpbfDWbqPXMmnRvtvg3T989W2yAF2y+Omt8gB9v87as8T8544dZ4+ee9/aEC4a9t37ELnvjzVnj77n+j9liT4rHaonjxGdmjdKUgUjNzJ7GLT4za5Sx0MdXZZACM7On6cQgBZK2knShpD+kn1sOctwpktZIqjwIihOfmbWlv8XXgdFZjgQuiogdgIvSeiunAovbCezEZ2Zt61DiOxA4LS2fRjGn919Jgxv/uZ3A7uMzs7Z08KruMyJidVFmrE4judfCic/M2tZGa26mpGWl9SXluXck/Qx4Zov3fWLjaze8rIkvDWB6EvB8iomH3hERl+cs08zyavOq7tqh5tOOiL0H2yfpbkmzUmtvFrCmvZoOLncf3wnABRGxI8WgpDdlLs/MOqBDfXxLgf5Hld4GfH/EEZNsiU/S5sDLgZMBIuLxiLgvV3lm1jkdSnzHAvtI+gOwT1pH0mxJ5/cfJOksipkfF0jqk3TYcIFznuo+i2I2tq9LWggsBw6PiHXlg8rz6s6fOzdjdcysDp26uBER9wKvarF9FbBfaf3gdmPnPNWdAOwKfC0idgHW0eI+nIhYEhGLImLR1jNmZKyOmdWhg/fxZZMz8fUBfRFxZVo/hyIRmlmPc+IbRET8CbhTUv84Qa8CbsxVnpl1Tq8nvtz38b0fOFPSJOBW4NDM5ZlZZmNhkIKsiS8irgUGvYfHzHqTE5+ZNYoHIjWzRnKLz8waxX18ZtZITnxm1ihu8ZlZIznxmVmj+Kpu3caNgylTsoVfMHfd8AeNxKSZeeMD++6Wb8J1gL5H9s8a/4SpF2eNn3uyb4A9L/5s1vhXvvqT2WKvW79JLXHc4jOzRnEfn5k1khOfmTWOE5+ZNYovbphZ47iPz8wayYnPzBqn1xNfzlnWFki6tvR6QNIRucozs84YC3NuZGvxRcTNwM4AksYDdwHn5SrPzDqnm5NaFZ061X0V8MeIWNmh8swsE1/Vre7NwFkdKsvMMuv1Fl/O6SUBSBMNvRb4ziD73yVpmaRl96xdm7s6ZjZCY6GPL3viA/YFro6Iu1vtfNqE4jPzP+RvZiPX64mvE6e6B+PTXLMxwzcwD0PSFGAf4N05yzGzznLiG0JEPAzMyFmGmXWWr+qaWSO5xWdmjeI+PjNrJCc+M2sUt/jMrJF8ccPMGmUstPg68eSGmY0xnXhyQ9JWki6U9If0c8sWx8yTdLGkmyStkHR4ldhd1eILjeOxcZOzxZ8wKVtoAMY/mnneXuD+CXlvi5w7seWThbVZ+axXZI2/5/o/Zo0Peee9Bdj9N/+eLfbUdWtGHKODLb4jgYsi4lhJR6b1jw04Zj3woYi4WtI0YLmkCyPixqECu8VnZm3r0LO6BwKnpeXTgIMGHhARqyPi6rT8IHATMGe4wF3V4jOz3tBGUpspaVlpfUlELKn43mdExGooEpykbYY6WNJ2wC7AlcMFduIzs7a0+cja2ohYNNhOST8Dntli1yfaqZOkzYDvAkdExAPDHe/EZ2ZtqbOPLyL2HmyfpLslzUqtvVlAyw5KSRMpkt6ZEXFulXLdx2dmbetQH99S4G1p+W3A9wceIEnAycBNEXF81cBOfGbWtg4lvmOBfST9gWJ4u2MBJM2WdH46Zg/gEOCVpRkd9xsusE91zawtnbqdJSLupZiobOD2VcB+afkyQO3GduIzs7b1+pMbuUdg/hfgnUAA1wOHRsSjOcs0s7zGwkCk2fr4JM0BPgAsiojnA+Mpppk0sx7nyYaGjz9Z0hPAFGBV5vLMLDMPUjCEiLgLOA64A1gN3B8RPx143NPm1b3nnlzVMbMa9XqLL+ep7pYUz9ptD8wGpkp668Djnjav7tZb56qOmdXEE4oPbW/gtoi4JyKeAM4F/jZjeWbWIevXV3t1q5x9fHcAL0lz6z5CcT/OsqHfYmbdbiz08WVLfBFxpaRzgKspxsy6Bqg6KoOZdTEnviFExNHA0TnLMLPOcovPzBrJic/MGseJz8waZSw8subEZ2ZtcR+fmTWSE5+ZNU6vJz5FxGjX4SmS7gFWtvGWmcDaTNVx/LEfvxNldFv8bSNiRM+GSroglVvF2ohYPJLycuiqxNcuScuGmsHJ8R1/tMvo9fhjlefcMLPGceIzs8bp9cSX+9lfxx/b8TtRRq/HH5N6uo/PzGxj9HqLz8ysbU58ZtY4PZn4JC2WdLOkWyQdmSH+KZLWSLqh7tgp/jxJF0u6SdIKSYfXHH9TSb+R9NsU/9N1xi+VM17SNZJ+mCH27ZKul3StpNoHsJU0XdI5kn6X/h1eWmPsBane/a8HJB1RV/xUxr+kf9sbJJ0ladM64491PdfHJ2k88HtgH6APuAo4OCJurLGMlwMPAaenqTFrJWkWMCsirpY0DVgOHFTXZ5AkYGpEPCRpInAZcHhEXFFH/FI5HwQWAZtHxP41x76dYmrSLDf/SjoN+GVEnCRpEjAlIu7LUM544C5g94ho5+b8oWLOofg33SkiHpH0beD8iDi1jvhN0Istvt2AWyLi1oh4HPgWxaRGtYmIS4E/1xlzQPzVEXF1Wn4QuAmYU2P8iIiH0urE9Kr1fzhJc4G/A06qM24nSNoceDlwMkBEPJ4j6SWvAv5YV9Ir6Z+6dQKeurVtvZj45gB3ltb7qDFpdJqk7YBdgCtrjjte0rXAGuDCiKg1PvBl4KNArqc2A/ippOWS3lVz7GcB9wBfT6fqJ0maWnMZ/d4MnFVnwKpTt9rgejHxqcW23jpfTyRtBnwXOCIiHqgzdkQ8GRE7A3OB3STVdsouaX9gTUQsrytmC3tExK7AvsB7U/dDXSYAuwJfi4hdgHVAjr7iScBrge/UHLfS1K02uF5MfH3AvNL6XHqwmZ/63r4LnBkR5+YqJ53CXQLU+aD4HsBrUz/ct4BXSjqjxvhExKr0cw1wHkUXR136gL5SK/gcikRYt32BqyPi7prjeurWEerFxHcVsIOk7dP/qG8Glo5yndqSLj6cDNwUEcdniL+1pOlpeTLFH8rv6oofEUdFxNyI2I7i+/95RNTW4pA0NV30IZ2Cvhqo7Qp7RPwJuFPSgrTpVUBtF8dKDqbm09zkqalb0+/Sqyj6ia2inhuPLyLWS3of8BNgPHBKRKyoswxJZwF7ATMl9QFHR8TJNRaxB3AIcH3qhwP4eEScX1P8WcBp6YriOODbEVH7LScZPQM4r/ibZgLwzYi4oOYy3g+cmf7zvBU4tM7gaT7pfYB31xkXPHVrHXrudhYzs5HqxVNdM7MRceIzs8Zx4jOzxnHiM7PGceIzs8Zx4msISR/PFHeRpK+0+Z5jJH04R33MqnDia44siS8ilkXEB3LENsvFiW+MkfS99GD/iv6H+yUdSzGSx7WSzkzbPpjGcruhf6w4Sdul8elOStvPlLS3pF9J+oOkv3psTNJe/ePxpZbcKZIukXSrpA+UjvuEijEUfwYsKG1/tqQLUp1/KWlHSRMkXSVpr3TMFyR9PtuXZs0TEX6NoRewVfo5meIxrxlp/aHSMS8CrgemApsBKyhGiNmO4kmAF1D8p7gcOIViYIgDge+1KG8v4Idp+Rjg18AmFBNO30sxJFZ/eVOAzYFbgA+n91wE7JCWd6d4/A3geRSPYe1D8WTCpNH+bv0aO6+ee2TNhvUBSa9Ly/OAHSgSUNmewHkRsQ5A0rnAyyieeb4tIq5P21cAF0VESLqeIjEO50cR8RjwmKQ1FI+fvSyV93CKuzT93Izi4frvpMfToEiaRMQKSd8AfgC8NIqxF81q4cQ3hqRTw70pEsXDki4BWg1J3mpor36PlZY3lNY3UO33pfz+J0vvafVs5DjgviiGz2rlBcB9FMnTrDbu4xtbtgD+kpLejsBLSvueSENhAVwKHJRG95gKvA74ZcZ6XQq8TtLkNOrKAQBRjEF4m6Q3QjFqjaSFafn1wAyKkZK/0j/ajFkdnPjGlguACZKuAz4LlOfYWAJcJ+nMKIa9PxX4DcXIzydFxDW5KpXKOxu4lmIMwnKSfQtwmKTfUvQ1HihpJnAscFhE/B74D+CEXPWz5vHoLGbWOG7xmVnjOPGZWeM48ZlZ4zjxmVnjOPGZWeM48ZlZ4zjxmVnj/H9YXnYdKN8/jAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "gij_aquila = get_density_correlation_Z2(result_1D_aquila)\n", + "\n", + "plt.imshow(gij_aquila, cmap='bwr', vmin=-0.25, vmax=+0.25)\n", + "plt.xticks(range(num_atoms), [f'{i}' for i in range(num_atoms)])\n", + "plt.xlabel(\"atom index\")\n", + "plt.yticks(range(num_atoms), [f'{j}' for j in range(num_atoms)])\n", + "plt.ylabel(\"atom index\")\n", + "plt.title('Rydberg density correlation')\n", + "plt.gca().set_aspect('equal')\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "fcc2c8b3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "result_2D_aquila = device.run(ahs_program_2D, shots=100).result()\n", + "show_final_avg_density(result_2D_aquila)" + ] + }, + { + "cell_type": "markdown", + "id": "1c5e689d", + "metadata": {}, + "source": [ + "In summary, in this notebook we have demonstrated how to realize the 1D $Z_2$ phase and 2D checkerboard phase via adiabatic transition on the Rydberg systems. These are interesting many body phases in their own right, and serve as the starting points for the more involved use cases. " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "eba213ef", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-east-1::device/qpu/quera/Aquila': {'shots': 200, 'tasks': {'COMPLETED': 2}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 2.60 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(tracker.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a6a296d5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/03_Parallel_tasks_on_Aquila.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/03_Parallel_tasks_on_Aquila.ipynb new file mode 100644 index 000000000..0a8ab4415 --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/03_Parallel_tasks_on_Aquila.ipynb @@ -0,0 +1,569 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "43ae51e2", + "metadata": { + "tags": [] + }, + "source": [ + "# Parallel tasks on Aquila\n", + "\n", + "For tasks with few qubits in the register, we can use parallel execution that makes use of full area allowed by the QPU. In this tutorial we go through the previously explored checkerboard preparation but now we take advantage of the full area. \n", + "\n", + "We will break up the register into __batches__ which will run in parallel." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8af10669-31a2-4eef-993c-6fb2f29c698f", + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "tracker = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "id": "f31e9ade-6b2d-4727-bd4e-cc6a8bbb302e", + "metadata": {}, + "source": [ + "## Defining batches\n", + "\n", + "First, we will define a _single_ batch containing a 3x3 square grid of atoms" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e5598963", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.ahs.hamiltonian import Hamiltonian\n", + "from braket.ahs.atom_arrangement import AtomArrangement\n", + "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "4a9c026d", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "# distance between atoms\n", + "distance = 6.7e-6\n", + "\n", + "# number of atoms in a batch\n", + "Lx = 3\n", + "Ly = 3\n", + "\n", + "register = AtomArrangement()\n", + "\n", + "for ix in range(Lx):\n", + " for iy in range(Ly):\n", + " pos = (ix * distance, iy * distance)\n", + " register.add(pos)" + ] + }, + { + "cell_type": "markdown", + "id": "fa2efd6c", + "metadata": {}, + "source": [ + "## Bounding box\n", + "\n", + "Next, we define a bounding box by calculating its width and height of the batch. This will prove useful in setting up multiple batches in parallel." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "db0da94b", + "metadata": {}, + "outputs": [], + "source": [ + "x_min = min(*[site.coordinate[0] for site in register])\n", + "x_max = max(*[site.coordinate[0] for site in register])\n", + "y_min = min(*[site.coordinate[1] for site in register])\n", + "y_max = max(*[site.coordinate[1] for site in register])\n", + "\n", + "single_problem_width = x_max - x_min\n", + "single_problem_height = y_max - y_min" + ] + }, + { + "cell_type": "markdown", + "id": "08ff59e6", + "metadata": {}, + "source": [ + "### Calculating batch placement\n", + "\n", + "To prevent entanglement via the Rydberg interaction between batches, we need to place them far apart. Each batch needs an area occupied by its bounding box plus a padding that ensure proper separation.\n", + "\n", + "We pick the distance between the batches to be $3 \\times d$, where $d$ is the distance between neighboring atoms in a single batch. This means the ratio between intra- and inter-batch interaction strengths (using the van der Waals formula, $V = C_6/d^6$) is at most $\\frac{1}{3^6} \\approx 0.001372$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "36a82617", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from braket.ahs.atom_arrangement import AtomArrangement, SiteType\n", + "from braket.aws import AwsDevice\n", + "import json\n", + "\n", + "qpu = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")\n", + "\n", + "# get values from device capabilities\n", + "field_of_view_width = qpu.properties.paradigm.lattice.area.width\n", + "field_of_view_height = qpu.properties.paradigm.lattice.area.height\n", + "n_site_max = qpu.properties.paradigm.lattice.geometry.numberSitesMax\n", + "\n", + "# set distance between batches to be 3 x d\n", + "interproblem_distance = 3 * distance\n", + "\n", + "# setting up a grid of problems filling the total area\n", + "n_width = int(float(field_of_view_width) // (single_problem_width + interproblem_distance))\n", + "n_height = int(float(field_of_view_height) // (single_problem_height + interproblem_distance))" + ] + }, + { + "cell_type": "markdown", + "id": "8f83106e", + "metadata": {}, + "source": [ + "## Generating registers for all batches\n", + "\n", + "We now loop create the total set of registers that will run on the QPU. \n", + "\n", + "We will keep track of which set of registers (by atom number) belongs to which batch using a dictionary called `batch_mapping`.\n", + "\n", + "We stop generating batches once we have reached the maximum number of sites allowed by the QPU. In this case we check to make sure we can fit the necessary number of atoms into a batch in case the number of atoms per batch is not a factor of `n_site_max`. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ab083fd7", + "metadata": {}, + "outputs": [], + "source": [ + "batch_mapping = dict()\n", + "parallel_register = AtomArrangement()\n", + "\n", + "atom_number = 0 #counting number of atoms added\n", + "\n", + "for ix in range(n_width):\n", + " x_shift = ix * (single_problem_width + interproblem_distance)\n", + "\n", + " for iy in range(n_height): \n", + " y_shift = iy * (single_problem_height + interproblem_distance)\n", + "\n", + " # reached the maximum number of batches possible given n_site_max\n", + " if atom_number + len(register) > n_site_max: break \n", + "\n", + " atoms = []\n", + " for site in register:\n", + " new_coordinate = (x_shift + site.coordinate[0], y_shift + site.coordinate[1])\n", + " parallel_register.add(new_coordinate,site.site_type)\n", + "\n", + " atoms.append(atom_number)\n", + "\n", + " atom_number += 1\n", + "\n", + " batch_mapping[(ix,iy)] = atoms" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "9fab538e-e7fb-4d24-8458-d8de0a38446c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(0, 0): [0, 1, 2, 3, 4, 5, 6, 7, 8],\n", + " (0, 1): [9, 10, 11, 12, 13, 14, 15, 16, 17],\n", + " (1, 0): [18, 19, 20, 21, 22, 23, 24, 25, 26],\n", + " (1, 1): [27, 28, 29, 30, 31, 32, 33, 34, 35]}" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Key indicates the position of the batch itself on a unitless grid, \n", + "# with dictionary value being the atom number\n", + "batch_mapping" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b26b7e0a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# [Optional] We visually inspect the register\n", + "from ahs_utils import show_register\n", + "\n", + "show_register(register)\n", + "show_register(parallel_register)" + ] + }, + { + "cell_type": "markdown", + "id": "8e30df2e-45fc-4a41-8000-4ee88a3a1519", + "metadata": {}, + "source": [ + "## AHS program for creating the checkerboard phase" + ] + }, + { + "cell_type": "markdown", + "id": "46bae3ef-1c23-43df-b153-a527d64eea3d", + "metadata": {}, + "source": [ + "We use the same values and timings for the Amplitude, Phase, and Detuning from the [Ordered phases in Rydberg Systems](./02_Ordered_phases_in_Rydberg_systems.ipynb) example " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5a31ab21", + "metadata": {}, + "outputs": [], + "source": [ + "from ahs_utils import get_drive\n", + "\n", + "time_points = [0, 2.5e-7, 2.75e-6, 3e-6] # s\n", + "\n", + "amplitude_min = 0\n", + "amplitude_max = 1.5708e7 # rad / s\n", + "\n", + "detuning_min = -5.49778714e7 # rad / s\n", + "detuning_max = 5.49778714e7 # rad / s\n", + "\n", + "amplitude_values = [amplitude_min, amplitude_max, amplitude_max, amplitude_min]\n", + "detuning_values = [detuning_min, detuning_min, detuning_max, detuning_max]\n", + "phase_values = [0, 0, 0, 0]\n", + "\n", + "drive = get_drive(time_points, amplitude_values, detuning_values, phase_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "9993d59b-7a20-4098-b99c-dcf4e3d1b0ad", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from ahs_utils import show_global_drive\n", + "\n", + "# [Optional] We visually inspect the time series\n", + "\n", + "show_global_drive(drive);" + ] + }, + { + "cell_type": "markdown", + "id": "e8d1fc59-54e2-4518-a65b-ddd2fdcb1f0e", + "metadata": {}, + "source": [ + "We now construct the AHS program to be run. Note that we create two programs and execute them to allow us to compare the accuracy of our results, with `parallel_ahs_program` being run on Aquila and `ahs_program` just being simulated with the local simulator. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "20d44c2e-cdc5-44e3-9592-f934999cf914", + "metadata": {}, + "outputs": [], + "source": [ + "parallel_ahs_program = AnalogHamiltonianSimulation(\n", + " register=parallel_register, \n", + " hamiltonian=drive\n", + ")\n", + "\n", + "ahs_program = AnalogHamiltonianSimulation(\n", + " register=register, \n", + " hamiltonian=drive\n", + ")\n", + "\n", + "ahs_program = ahs_program.discretize(qpu)\n", + "parallel_ahs_program = parallel_ahs_program.discretize(qpu)" + ] + }, + { + "cell_type": "markdown", + "id": "d6c6e1ed-c726-4d46-b5f3-749f9eb07ec0", + "metadata": {}, + "source": [ + "## Run on simulator" + ] + }, + { + "cell_type": "markdown", + "id": "69aad79a-a494-463f-911f-2e7fc71d0ff7", + "metadata": {}, + "source": [ + "First, we run a non-parallelized register on the local simulator, and sample 400 shots. Below we also explicitly specified the values of `steps`, which are the number of time steps in the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "88cdddd1", + "metadata": {}, + "outputs": [], + "source": [ + "from braket.devices import LocalSimulator\n", + "sim = LocalSimulator(\"braket_ahs\")\n", + "\n", + "sim_result = sim.run(ahs_program, shots=400, steps=100).result()" + ] + }, + { + "cell_type": "markdown", + "id": "b8d716b5-acbb-48a4-909d-4d5470d246d9", + "metadata": {}, + "source": [ + "We compute the average Rydberg density on the 9 sites." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "025f3a2f-d0c0-493e-b6d6-7fd15b7ee348", + "metadata": {}, + "outputs": [], + "source": [ + "from ahs_utils import get_avg_density\n", + "\n", + "sim_density = get_avg_density(sim_result)" + ] + }, + { + "cell_type": "markdown", + "id": "b27fd6ec-c677-4c18-aee3-533f6faeb24d", + "metadata": {}, + "source": [ + "## Run on Aquila\n", + "\n", + "Next, we run a the parallelized register on the QPU. This time, we only need to run 100 shots to get to the same statistical certainty, because we are running four batches in parallel in each shot." + ] + }, + { + "cell_type": "markdown", + "id": "767ec35c-b9f2-4027-a2b6-ea10a3c40512", + "metadata": {}, + "source": [ + "
    \n", + "Note: Some atoms may be missing even if the shot was successful. We recommend comparing pre_sequence of each shot with the requested atom filling in the AHS program specification. \n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "fc86d8ac-9ea0-4005-b156-e271782e3377", + "metadata": {}, + "outputs": [], + "source": [ + "# This cell submits the task, waits for its completion, and gets the results.\n", + "# To check the status of the task, go to the Amazon Braket tasks page at\n", + "# https://us-east-1.console.aws.amazon.com/braket/home?region=us-east-1#/tasks\n", + "\n", + "qpu_result = qpu.run(parallel_ahs_program, shots=100).result()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "5a799030", + "metadata": {}, + "outputs": [], + "source": [ + "# collecting QPU Data\n", + "\n", + "all_sequences = []\n", + "for measurement in qpu_result.measurements:\n", + " # iterate over key and values\n", + " for (ix,iy),inds in batch_mapping.items():\n", + " batch_sequence = list(measurement.post_sequence[inds])\n", + " all_sequences.append(batch_sequence)\n", + "\n", + "all_rydberg = 1 - np.array(all_sequences)\n", + "qpu_density = all_rydberg.mean(axis=0)" + ] + }, + { + "cell_type": "markdown", + "id": "19f42800-41ee-4ca4-960c-2da6495d5777", + "metadata": {}, + "source": [ + "After running the separate programs, we can analyze the results.\n", + "\n", + "We average the data across all the batches that ran in parallel across multiple shots, represented visually as a single batch versus the simulator result which just ran a single batch." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "8f897f5b-2c9f-4bc7-9f71-b2ab227b1e9e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from ahs_utils import plot_avg_density_2D\n", + "\n", + "# Compare results side-by-side\n", + "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12,5))\n", + "\n", + "# plot density of all batches that ran in parallel with geometry and averaged values of single batch\n", + "\n", + "plot_avg_density_2D(qpu_density, parallel_register, batch_mapping=batch_mapping, custom_axes = ax1);\n", + "ax1.set_title(\"Averages of Densities across parallelized batches\");\n", + "\n", + "# plot density of simulator result\n", + "plot_avg_density_2D(sim_density, register, custom_axes = ax2);\n", + "ax2.set_title(\"Simulator Result\");\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9c1e79d8-c9ff-4d5d-8b4f-3aa0e0b7d7cb", + "metadata": {}, + "source": [ + "As we can see from the results, the simulated single batch result and the results from the batches running in parallel line up with what we expect for the checkerboard phase." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5974573a-2a03-46bc-aad9-9a39fefb906a", + "metadata": {}, + "outputs": [], + "source": [ + "print(\"Task Summary\")\n", + "print(tracker.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/04_Maximum_Independent_Sets_with_Analog_Hamiltonian_Simulation.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/04_Maximum_Independent_Sets_with_Analog_Hamiltonian_Simulation.ipynb new file mode 100644 index 000000000..3ccb95418 --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/04_Maximum_Independent_Sets_with_Analog_Hamiltonian_Simulation.ipynb @@ -0,0 +1,578 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Maximum Independent Sets with Analog Hamiltonian Simulation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction to the maximum independent set problem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook, we'll demonstrate how to set up a unit disk graph and solve for its maximum independent set using the Amazon Braket analog Hamiltonian simulation (AHS) local simulator. This code can then be generalized to run on the actual AHS device, QuEra's Aquila.\n", + "\n", + "Finding a maximum indepenent set (MIS) is a common problem in graph theory with many real-life applications. What is an \"independent set\", let alone a \"maximum\" one? Consider a graph with vertices $V$ and edges $E$. An independent set is any subset $V_{is}$ of $V$ such that no pair of vertices in $V_{is}$ are connected by an edge in $E$. The *maximum* independent set is the largest such subset. Let's make this a little more concrete with a visual example." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Raw graph](py_graph.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can select vertices to be part of the maximum independent set:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![MIS graph](mis_graph.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example, we see that the vertices in the MIS (the red ones) are not connected by any edge. We can also see there is no way to add another vertex to the set without it being connected to another vertex already present. We can also determine that no larger independent set can be found through brute-force enumeration of all possible independent sets (not shown)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finding maximum independent sets is a problem with many applications. Consider, for example, a business owner who wants to put branches of their chain store on as many street corners as possible so that potential customers never have to walk very far to find a location. However, the owner doesn't want to have multiple branches at the same intersection — this is inefficient. Maximizing the number of branches in a city, given its particular street grid, while avoiding opening branches which are too close together is an example of the MIS problem. There are many other applications, including to \"knapsack packing\" style problems, routing, and others." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit disk graphs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A unit disk graph is a graph in which, if and only if any two vertices are within a unit disk radius of each other, they are connected. This type of graph is very well suited for AHS devices because it can be simulated with no overhead — the number of atoms needed in the trap corresponds exactly to the total number of vertices in the graph. The phenomenon of Rydberg blockade enforces the condition that vertices connected by an edge cannot both be in the independent set." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [], + "source": [ + "# necessary imports\n", + "import networkx as nx\n", + "\n", + "from braket.ahs.hamiltonian import Hamiltonian\n", + "from braket.ahs.atom_arrangement import AtomArrangement\n", + "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n", + "\n", + "from braket.timings.time_series import TimeSeries\n", + "from braket.ahs.driving_field import DrivingField\n", + "from braket.ahs.shifting_field import ShiftingField\n", + "from braket.ahs.field import Field\n", + "from braket.devices import LocalSimulator\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import time\n", + "import numpy as np\n", + "\n", + "from scipy import optimize" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [], + "source": [ + "# constants\n", + "atoms_w = 3\n", + "atoms_l = 4\n", + "blockade_radius = 7.5\n", + "np.random.seed(92)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function generates both the `AtomArrangement`, which will be passed to the simualtor or AHS device, and the graph it corresponds to. We set up the atoms in a square grid, such that nearest- (horizontal or vertical neighbors) and next-nearest-neighbors (diagonal neighbors) are within the unit disk range. In the graph this means the next-nearest-neighbors are connected by an edge. We perform a random dropout on this square grid — removing some of the atoms — to generate a more interesting graph." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [], + "source": [ + "def generate_unit_disk(atoms_l: int, atoms_w: int, scale=4.0*1e-6, dropout=0.45):\n", + " atom_list = []\n", + " edge_dict = {}\n", + " atom_to_edge = {}\n", + " for ii in range(atoms_l):\n", + " for jj in range(atoms_w):\n", + " atom_list.append((ii*scale, jj*scale))\n", + " atom_to_edge[(ii*scale, jj*scale)] = ii*atoms_w + jj\n", + " edge_dict[ii*atoms_w + jj] = []\n", + " if jj < atoms_w - 1:\n", + " edge_dict[ii*atoms_w + jj].append(ii*atoms_w + jj + 1)\n", + " if ii < atoms_l - 1:\n", + " edge_dict[ii*atoms_w + jj].append((ii+1)*atoms_w + jj)\n", + " if ii < atoms_l - 1 and jj < atoms_w - 1:\n", + " # nearest neighbor\n", + " edge_dict[ii*atoms_w + jj].append((ii+1)*atoms_w + jj + 1)\n", + " if jj > 0 and ii < atoms_l - 1:\n", + " # nearest neighbor\n", + " edge_dict[ii*atoms_w + jj].append((ii+1)*atoms_w + jj - 1)\n", + "\n", + " graph = nx.from_dict_of_lists(edge_dict)\n", + " \n", + " # perform dropout\n", + " new_len = int(np.round(len(atom_list) * (1 - dropout)))\n", + " atom_arr = np.empty(len(atom_list), dtype=object)\n", + " atom_arr[:] = atom_list\n", + " remaining_atom_list = np.random.choice(atom_arr, new_len, replace=False)\n", + " \n", + " dropped_edge_dict = {}\n", + " atoms = AtomArrangement()\n", + " for atom in remaining_atom_list:\n", + " atoms.add(atom)\n", + " graph.remove_nodes_from([atom_to_edge[atom] for atom in set(atom_list) - set(list(remaining_atom_list))])\n", + "\n", + " return atoms, graph" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [], + "source": [ + "atoms, graph = generate_unit_disk(atoms_l, atoms_w)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot the graph:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "pos = {ii: (ii/atoms_w,ii%atoms_w) for ii in graph.nodes()}\n", + "nx.draw(graph, pos=pos, ax=ax, with_labels=True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can define our loss function. For this problem, we'll use the Quantum Adiabatic Algorithm to train variational parameters. These parameters encode the shape of the global detuning waveform `Delta`. We'll train 3 variational parameters. As these parameters change, so too does the shape of the global detuning waveform." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [], + "source": [ + "def loss_piecewise_linear(atoms: AtomArrangement, x: list):\n", + " assert len(x) == 3\n", + " Delta_start = -13 * 2 * np.pi * 1e6\n", + " Delta_0 = 11 * 2 * np.pi * 1e6\n", + " Delta_end = 11 * 2 * np.pi * 1e6\n", + "\n", + " Omega_max = 2.5e7 # 4 * 2 * np.pi * 1e6\n", + " T_max = 0.6 * 1e-6\n", + "\n", + " Deltas = TimeSeries()\n", + " Deltas.put(0.0, Delta_start)\n", + " Deltas.put(0.05 * 1e-6, Delta_start)\n", + " Deltas.put(0.2 * 1e-6, Delta_0 * x[0])\n", + " Deltas.put(0.3 * 1e-6, Delta_0 * x[1])\n", + " Deltas.put(0.4 * 1e-6, Delta_0 * x[2])\n", + " Deltas.put(0.55 * 1e-6, Delta_end)\n", + " Deltas.put(T_max, Delta_end)\n", + " \n", + " # keep amplitude (Rabi frequency) constant once we turn it on\n", + " Omegas = TimeSeries()\n", + " Omegas.put(0.0, 0.0)\n", + " Omegas.put(0.05 * 1e-6, 0.0)\n", + " Omegas.put(0.1 * 1e-6, Omega_max)\n", + " Omegas.put(0.5 * 1e-6, Omega_max)\n", + " Omegas.put(0.55 * 1e-6, 0.0)\n", + " Omegas.put(T_max, 0.0)\n", + "\n", + " # do not use the phase parameter\n", + " Phi = TimeSeries().put(0.0, 0.0).put(T_max, 0.0)\n", + "\n", + " # for this problem, our Hamiltonian has no shifting field\n", + " H = DrivingField(amplitude=Omegas, phase=Phi, detuning=Deltas)\n", + "\n", + " \n", + " program = AnalogHamiltonianSimulation(hamiltonian=H, register=atoms)\n", + " device = LocalSimulator(\"braket_ahs\")\n", + " \n", + " # if you want to use Aquila, uncomment these lines\n", + " # keep in mind that you may have to modify the fields\n", + " #device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")\n", + " #program = program.discretize(device)\n", + " \n", + " # run the AHS program and extract measurements\n", + " results = device.run(program, shots=1000, steps=100).result()\n", + " \n", + " \n", + " r_counts = []\n", + " \n", + " # states are one of:\n", + " # 'e' - empty\n", + " # 'r' - Rydberg\n", + " # 'g' - groundstate\n", + " states = ['e', 'r', 'g']\n", + " for shot in results.measurements:\n", + " pre = shot.pre_sequence\n", + " post = shot.post_sequence\n", + " state_idx = np.array(pre) * (1 + np.array(post))\n", + " state_labels = [states[s_idx] for s_idx in state_idx]\n", + " r_count = np.count_nonzero([sl == 'r' for sl in state_labels])/len(atoms)\n", + " r_counts.append(r_count)\n", + "\n", + " # the mean density of Rydberg states - this will be our cost\n", + " # higher is better, as it corresponds to a larger independent set\n", + " density_sum = np.mean(r_counts)\n", + " \n", + " return -density_sum, results, Deltas" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial density: -0.3674285714285714\n", + "Final density: -0.37371428571428567\n", + "Final values: [0.10333333 0.76 0.82666667]\n", + "Time to run AHS with local simulator: 19.06173086166382\n" + ] + } + ], + "source": [ + "start = time.time()\n", + "# initial waveform parameters\n", + "x0 = [0.1, 0.8, 0.8]\n", + "initial_rydberg_density, initial_registers, initial_Deltas = loss_piecewise_linear(atoms, x0)\n", + "print(f\"Initial density: {initial_rydberg_density}\")\n", + "# perform optimization\n", + "optresult = optimize.minimize(lambda x: loss_piecewise_linear(atoms, x)[0], x0, method='Nelder-Mead', options={'maxiter': 10})\n", + "final_rydberg_density, final_registers, final_Deltas = loss_piecewise_linear(atoms, optresult.x)\n", + "print(f\"Final density: {final_rydberg_density}\")\n", + "print(f\"Final values: {optresult.x}\")\n", + "stop = time.time()\n", + "print(f\"Time to run AHS with local simulator: {stop-start}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's visualize the solutions generated by the AHS program, to verify that they are independent sets and to see how large they are." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": false, + "vscode": { + "languageId": "python" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Independent set of 0-th most likely outcome\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Independent set of 1-th most likely outcome\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Independent set of 2-th most likely outcome\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Independent set of 3-th most likely outcome\n" + ] + }, + { + "data": { + "image/png": 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vLSqViuvXr9O+fXulQykwOZEm6czz58+ZMmUKQUFBLFy4kJ49expcss30v//9j7fffptatWopHUq2PvzwQ44fP07fvn3ZtWtXgYdlrl69yrBhw7hx4wbbtm3D09NTS5FqX0BAAAMHDjS64jZZkT1dSSf27duHq6srd+/eRaVS0atXL4NNuGA820pnzpxJRkYG06dPz/c1MjIy+OWXX2jYsCHvvPMOERERBp1wjbq4TVaUHt+QTMuLM9/GUlz6xo0bws7Ozmi2ld6+fVtUqFAhX+Ob586dE82aNRNNmjQxmgdjrl+/XrRo0ULpMLRG9nQlrXl15rtTp05Kh5Qrxrat1NnZmZCQEAYNGkRCQkKuXpOens6cOXN455138PHx4ciRI9StW1e3gWqJsdyF5JrSWV8yfpkz3zVq1BAHDx5UOpw8ycjIEDVr1jTKx+XMmzdPNGzYUCQlJeV4XnR0tGjQoIFo27atuHTpkp6i047M4ja6fAKFvsmerpRv4pWZ79jYWFq0aKF0WHly9OhRrKysaNSokdKh5NnYsWOpUqUKY8aMyfJ4cnIyX3/9Ne3atWPkyJHs3r2bqlWr6jfIAlqxYgU9evSgWLFiSoeiNcY/FSgpInPm+/r16wY/850TY95WamFhQUBAAJ6enqxatYqPP/74n2PHjx/H19eXOnXqEBMTQ7ly5RSMNH8yMjIICAggKChI6VC0S+mutmRc1Gq1WLx4sXBwcBAzZ85UvEBNQWRuK71z547SoRRIbGyscHBwELGxseLp06di9OjRoly5cmLdunUGuQkltw4ePCjq1atn1N9DVmRPV8q1P//8Ez8/P9LS0jh06JDRTMRkJzQ0lNatW+Pk5KR0KAXi6urKvHnzeP/997G0tKRVq1bExcVhb2+vdGgFYsx3ITmRY7rSG7048929e3eOHj1q9AkX/v1QG7uHDx9y4MABHj16RKVKlVi+fLnRJ9zHjx8TFhZG//79lQ5F62TSlXIUExNDo0aN2Lt3L+Hh4Xz++ecGU6CmIOLj47l27RodOnRQOpQC2bhxIy4uLpQoUYJLly6RmJjIggULlA6rwEJCQmjbtq3xF7fJitLjG5JhSkpKEpMnTxYODg7C39/f5MbVxo0bJyZNmqR0GPl269Yt0b17d/H222+LI0eO/PP3ly5dEk5OTuLo0aMKRldwXl5eYvv27UqHoROypyu95vjx49SvX5/4+HhiYmIYPHiwSY2rGfO2UiEEK1aswM3NjVq1ahEdHc277777z/GqVasSEBBA7969tVoYR5/i4uK4efOmSRS3yYqcSJP+8ezZMyZPnsy6dev48ccf6d69u0kl20z/+9//qF27NjVr1lQ6lDxJSEjg008/5e7du+zatYv69etneV6nTp0YMGAAffr0Yffu3UY3HJRZ3MbY4s4t2dOVANi9ezeurq48evSIuLg4fHx8TDLhgvFtK83IyGDRokV4enrSsmVLTp8+nW3CzTRjxgwsLCyYOnWqnqLUjtTUVNasWWOUdyG5pvT4hqSsBw8eiIEDB4pKlSqJHTt2KB2OzmVuKzWW4jZnz54VTZs2FU2bNhVnz57N02vv3LkjKlasKMLCwnQUnfatW7dOtGzZUukwdEr2dM3Yxo0bqVevHsWLF0elUhncY2p0wViK26SlpfHdd9/x7rvv0rt3bw4fPkzt2rXzdA0nJydCQ0Px9fXl0qVLOopUu4ztLiRflM76kv5lznzXqlVLHD58WOlw9CYjI0PUqFFDnDx5UulQcnTmzBnh4eEhOnToIBISEgp8vfnz54sGDRq8sTCO0q5du2ZyxW2yInu6ZkS8MPNds2ZNYmJiaNasmdJh6c2RI0coUqQI3t7eSoeSpeTkZCZNmkSHDh0YM2YMO3bsoHLlygW+7ueff0716tUZPXq0FqLUnRUrVtCzZ0+TKm6TFbl6wUy8OPO9c+dOGjRooHRIemfI20qPHj2Kr68vbm5uxMbGUrZsWa1d28LCgmXLluHl5cWKFSsYMGCA1q6tLZnFbUJCQpQORfeU7mpLuqVWq8WPP/4o7O3txXfffSdSU1OVDkkRjx49Era2tuLu3btKh/KSJ0+eiBEjRojy5cuLDRs26LStuLg44eDgIGJiYnTaTn7s379fuLq6mtwmnKzInq4J++OPP/Dz80MIwdGjR/M8EWNKQkNDadOmjUFtK925cyeffvopbdq0QaVSUbp0aZ225+Liwvz58+nevTsRERHY2trqtL28yJxAM8S7EK1TOutL2peamiq+/fZbYW9vLxYtWiTUarXSISnO29s7X88U04X79++LTz75RFSpUkXs3r1b7+0PGzZMdOvWzWB6lQ8fPhS2trbi3r17SoeiF3IizcRERUXh7e3NoUOHiIiIYOTIkVhamvfbrFKpuH79uuLbSoUQrF+/HldXV+zs7IiLi6Ndu3Z6j2PBggVcvXqVH374Qe9tZyUkJIR27drh4OCgdCj6oXTWl7QjKSlJ/Oc//xGOjo4iMDDQYHoxhmDs2LHiq6++UjSGmzdvio8++kjUrl1bHDt2TNFYhBAiISFBODk5GcSSQU9PT7PYmJPJvLtAJuLo0aO4u7tz4cIFYmNjGTBggHmMjeWC0sVthBAEBATg7u5OvXr1iIqK4p133lEklhdVrlyZwMBA+vTpw+3btxWLIzY2ltu3byvS41eKnEgzYk+fPmXSpEls3LiRn376iW7duikdksHZunUrdevWpUaNGnpv+/LlywwdOpSHDx+yZ88e3N3d9R5DTjp27MjgwYPp3bs3e/fuxcpK/+nA1IvbZEX2dI3Uzp07cXFxITExkfj4eJlws6HEtlK1Ws3ChQvx8vKiXbt2nDx50uASbqZp06ZRpEgRvv76a723nZKSYvrFbbKi9PiGlDeZM9+VK1cWu3btUjocg5ZZ3Eaf20rj4+NFkyZNRLNmzcS5c+f01m5B3L17V7z11ltiy5Ytem137dq1olWrVnpt0xDInq6REK/MfKtUKsVn4w3dihUr6NGjh162laalpTFr1ixatGjBxx9/zMGDB6lVq5bO29UGR0dHQkND8fPz4+LFi3pr1yyK22RF6awvvdmLM9/G/hgWfVGr1aJ69eri1KlTOm8rIiJCuLm5iY4dO4orV67ovD1dWbhwofDw8BCJiYk6b+vq1auiTJkyemnL0MiergETL8x8161bl6ioKJo2bap0WEbh8OHD2NjY4OXlpbM2kpKSmDhxIu+//z5ffvkl27Zto1KlSjprT9dGjRpFrVq1GDVqlM7bCgwMpFevXtjY2Oi8LUMjVy8YqMyZ7wcPHrB79248PDyUDsmo6Hpb6aFDh/Dz86Nhw4bExcXh5OSkk3b0KbMwjre3N8uXL9fZBFdGRgbLly9n7dq1Orm+wVO6qy29LD09XSxYsEDY29uL2bNni7S0NKVDMjq6LG7z+PFjMWzYMFGhQgWxefNmrV/fEKhUKuHg4CCioqJ0cv19+/YJNzc3s93AI3u6BuT333/Hz88PKysrjh8/bjQTMYYmJCSEtm3bar24zfbt2xk2bBgdOnRApVJhZ2en1esbinr16rFw4UJ8fHyIiIjQ+vdpVsVtsqJ01pc0BWpmzpwp7O3txeLFi2WBmgLy8vIS27dv19r17t27J/r16yeqVasm9u7dq7XrGroRI0aILl26aLVHmlnc5v79+1q7prGRE2kKi4iIwNPTk2PHjnHmzBmGDx9u9gVqCiIuLo6bN29qZTmdEILQ0FBcXV1xcnIiNjaWNm3aaCFK4zBv3jxu3brF3LlztXbN4OBg2rdvj729vdauaXSUzvrmKjExUXz55ZfCyclJrFq1ymzHt7RtzJgxYvLkyQW+zvXr10Xnzp1F3bp1xYkTJ7QQmXG6cuWKcHZ2FgcPHtTK9Ro2bCh27typlWsZK9mlUsChQ4dwc3PjypUrxMXF0b9/f/Md39Ki1NTUAm8rFUKwdOlSPDw8qF+/PmfOnKFx48ZajNK4VKpUiRUrVtC3b19u3bpVoGvFxMRw9+5d2rZtq6XojJOcSNOjJ0+eMHHiRMLCwli8eDFdu3ZVOiSTEhYWRr169ahevXq+Xn/x4kWGDBnC06dP2b9/P66urlqO0Dh16NCBIUOG0Lt3b/bt25fvwjjmWNwmK7Knqyfbt2/HxcWFtLQ04uPjZcLVgfxuK1Wr1fzwww80atSITp06ceLECZlwXzFlyhSKFi3KV199la/Xp6SkEBQUxMCBA7UbmDFSenzD1GXOfFetWtWsZr717dq1a/kqbhMXFye8vb1FixYtxPnz53UUnWm4d++eqFSpkti0aVOeXxsaGipat26t/aCMkOzp6oh4ZeY7Li7OrGa+9S1zW2lui9ukpqYyY8YMWrVqha+vL/v371ek5q4xcXBwYO3atQwdOpQLFy7k6bX+/v74+vrqKDIjo3TWN0Vy5lu/1Gq1qFatmjh9+nSuzj916pRwcXERH3zwgbh27ZqOozM9ixYtEu7u7rkuVnPlyhWzLW6TFdnTzUpGBjx+DImJIESuXyZemPn28PAw+5lvXUlPh4cPITVV8+dDhw5RvHhxPD09c3xdYmIiX3zxBZ07d+arr74iLCyMihUr6iFi0zJixAjq1KnDiBEjsjyekqJ5f9RqzZ8DAwPp3bu3WRa3yZLSWd9gpKYKERoqRIMGQlhaClG4sBBWVkIUKSJE795ChIfn+PILFy6IVq1aCU9PTxETE6OnoM3Hw4dCzJ8vRMWKQlhYaN4WS0sh7OyEqFt3q5g6dVmOr9+/f7+oXr266Nu3r05qMpibp0+fijp16ohlyzT/7pcuCTFmjBClSmnelyJFNO9T5coZokyZqeLgwTMKR2w4ZNIVQojfftN8ekuWFELTt335y9JSiGLFhKhbV4jY2Jdemp6eLubNmyfs7e3F3LlzZYEaLUtNFWLECCGKFtW8BVm9PZAsrK0zRMeOQvz118uvf/TokRg6dKioWLGiCAsLU+abMFG///67KFOmtvD2fiyKFtUk2qzeHwuL58LGJkOMGydEerrSUStPJt2JE3P6NL/+Vby4EIcOCSHkzLeuJSUJ0bx57t+eIkWEqFRJiOvXNa8PCwsTFStWFJ9++ql49OiRst+MCbp8WQg7u0QBKbl6f4oVE6J9e80vUnNm3kl3/vy8Jdy/vzKKFxeLhw8XDg4OYsmSJbJAjQ6o1UJ88IEQNjZ5e3usrISoUiVN+PgMFjVq1BAHDhxQ+lsxSX/9pfkFZ2mZt/fHxkYzWmfOu94thMjDTJEpuXMHqlSB5OSX/vonIBCIA/r8/f+vygAu2NpSTKWSEzE6snUr9OkDz59nd8Z5wBXwAVa/ciyZRo2OsX9/E708H80cff45LFny72Tmv0q88uckYDiw6J+/KV4ctmwBc11Bab6rF377DbKod1Ae+BrIaV+TJVAzNZWKT5/qKDhpzpycEi7ACCC7R/EU5dy5NhQuLBOuLiQlQUBAVgkX4NkLX3cAG6DHS2c8fw7/93+6jtJwmWfSVavhxx81Pz2v6AZ0Bd5UeM4iLQ0WLtRBcNLFixAZmdMZIYAdkH1XSa3W9KYk7cv9U3bWA05As9eOHDwIN25oLyZjYp5J98wZzWLCgkhPh3XrtBOP9JItWzRLpbP2BJgKzMvxGk+fwqpVWg5MAmDlSnj2LDdnrgA+AV6/o7S01AwhmSPzTLr37mne9YKSwws6cft2dreuAFMAX+CtN17nzh0tBiX9I3f/rleBQ8CALI8mJ8P9+1oMyoiYZ2nH7LtReZKelkZhWQdXB+YCX2Tx99HAXiAqV1c5dSocCwtv7YUl/U0F1HvDOSuBd4GqWR4V4t8da+bGPJNumTJ52t6bHatSpRCPH2shIOlFc+bA119rRnBedhBIACr9/edngBr4HTjz2nXee8+LHTvMc3GOLjVrBkePvumslcB/sj1qba35GJoj8xxeaNAg295uOpCM5qOs/vv/X/vsg2Z4ol07XUVo1tq1gyJFsjoyFLiIpscbDQwDOgG7XjuzRAno1k1nIZq1jz6CnFfiHQdu8OqqhRdZWJjvx8c8k27RojB4MBQu/NqhWWgWucxGs/rT5u+/e42NDXyR1S2wVFANGmiWUL+uGFD2ha8SQFHg9UetZ2RA3766i9GcDRr0phG6FWjWAZXM9gwXF6hdW8uBGQnzTLoAo0dDFo8NmQ6IV76mZ/X6cuWgUSPdxWfmPvggHguLHBfqonlnXt0YAVZW8PHHmkX4kvaVLq25i8h+LvpXIPulIyVKwMSJuojMOJhv0q1eXfMrOz87lmxs4Ndfs9xcIRXMo0eP8PPzIyioC5Urq7O6GXmjUqVgyhTtxyb969tvoWT2HdlsFSkC9epBly7aj8lYmG/SBVi0SLMXMS+J18ZGs/+xdWvdxWWmNm/ejIuLC9bW1sTHnyE8vBQVK2Y3vpsVNcWLq9m/HypU0GWkUpUqsHu3JvHmtu9hbQ1Vq8LOnZq7EXNlvrUXMqnVMG4c/PYbaWlpFM5uHUuJEpr7qaAg6NRJvzGauDt37jBq1Ciio6NZtmwZzZs3/+fYo0fQtSuEh2v2s+T09hQr9gwrqw+Ijd2Avf2b9hRK2hAfDx07wsOHgmfPBFn146ysNNMnzZrB+vX56yGbEvPu6YJmXHfhQlLPnmWhtTXqUqU0n2BbW819atGimlH/X36Bu3dlwtUiIQSrVq3Czc2NatWqERMT81LCBbCz02wZPXFCM05rY6P50Ga+PdbW0KGDZhfb7dsl6NWrAR9//DEZWlqLLeWsXj1ISIBPPtmKk9PvWFtr3hdbW837ZGOjGcWLiIBdu2TCBdnT/cf69etZvHgxB3bvhkuXNM8bKVIEHB3hrTfvfpLy5urVqwwbNoybN2/i7+9Pw4YNc/W6Z8/gyhV48kQzUVahArzYqU1LS6NVq1a89957fP311zqKXnpVgwYNmDNnDh4e7bh5U/OkK1tbqFxZTmi+RsGykgalY8eOYuXKlUqHYfLUarVYvHixcHBwELNmzRKpOqhoff36dVG2bFmxZ88erV9bet2ZM2dEpUqVZF3pXJI9XeD69eu4ublx/fp1WX9Vh86dO8eQIUNIT0/H39+fOnXq6Kyt/fv3069fP8LDw2XNYx0bNWoU9vb2TJ8+XelQjIIc00XztNJevXrJhKsj6enpzJ49m6ZNm+Lj48ORI0d0mnABWrduzejRo+nZsyep2VfPkQooOTmZ4OBgBg0apHQoRsPsk25GRgbLly9n8OCcypZL+RUdHU2jRo3Yv38/ERERjB49mkJZbErRhYkTJ2Jvb8+ECRP00p452rx5M/Xr16dy5cpKh2I0zD7pHjp0iOLFi+Pp6al0KCYlOTmZyZMn0759e0aNGsWuXbuokvXeXp2xtLRk5cqVhIWFsTb3lbelPPD398fX11fpMIyKGS9R1ggICGDw4MFYyN1lWnP8+HF8fX2pU6cOMTExlCtXTrFYSpcuzfr16+nQoQNubm7UNtcN/zqQkJBAVFQUXbt2VToUo2LWE2mPHj2iSpUqXLhwAQcHB6XDMXrPnj3jq6++Yv369SxatIju3bsrHdI/li5dyoIFCzh16hQlSrz68EQpP6ZPn85ff/3FokWL3nyy9A+zHl4ICQmhXbt2MuFqwe7du3F1deXJkyeoVCqDSrgAfn5+eHl58emnn2LG/QytkXMh+WfWSVeORxXcgwcPGDRoEEOHDmXJkiUEBgZSxgCrU1tYWPDzzz+jUqn45ZdflA7H6O3btw97e3vq16+vdChGx2yTbmxsLLdv36aduVZS1oINGzbg4uJCiRIliIuLo0OHDkqHlKNixYqxfv16pk2bxunTp5UOx6gFBATIDks+me2Y7pgxYyhZsiQzZ85UOhSjc/v2bUaOHIlKpWLZsmW8++67SoeUJxs3bmTcuHFERkbKwjj58ODBA6pVq8bly5cpXbq00uEYHbPs6aakpLBmzRq5oDuPhBAEBgbi5uZGrVq1iI6ONrqEC9CtWzd8fHzo37+/LIyTD0FBQbz//vsy4eaTWSbdsLAwXF1dqVatmtKhGI2EhATee+89Fi5cyK5du/juu+8oWrSo0mHl2/fff8/z58+ZNSvLhzFJOfD395cTaAVglklXjkflXkZGBosWLcLT05NWrVpx+vRpk5g8KVy4MKGhofz666/s3r1b6XCMRlRUFA8fPqS1LOKfb2Y3pnvt2jU8PDy4fv06NjY2Sodj0M6ePYufnx+WlpYsW7aMt99+W+mQtO7gwYP07t2b8PBw3pIlPN9o5MiRODo6Mm3aNKVDMVpm19PNLG4jE2720tLS+O6772jWrBl9+/bl0KFDJplwAVq2bMnYsWPp0aOHLIzzBklJSQQHBzNw4EClQzFqZpV05YLuNztz5gze3t4cPnyYyMhIRowYgWX2j301CRMmTMDZ2ZkvvvhC6VAM2ubNm2nYsKEsblNApv1pesXBgwcpWbJkrp9SYE6SkpKYNGkSHTt2ZOzYsezYscNsPlwWFhasWLGCbdu2ERISonQ4BktuJtIOsyp4I4vbZO3o0aP4+vri5uZGbGwszs7OSoekd3Z2dqxfv5727dvj7u6u83q/xiYhIYHo6GhZ3EYLzGYiLbO4zcWLF+WC+L89ffqUSZMmsWnTJn766Sc++ugjpUNSnL+/P/PmzeP06dOyMM4Lpk2bxsOHD/nxxx+VDsXomc3wQnBwMO3bt5cJ9287duzAxcWFpKQkVCqVTLh/8/X1pXHjxgwZMkQWxvmbWq1m+fLlcmhBS8wm6crxKI2//vqLTz75hOHDh+Pv74+/v7/cWfSKxYsXc/bsWRYvXqx0KAZh3759ODo64u7urnQoJsEskm5MTAx3796lbdu2SoeiGCEE69atw8XFhTJlyhAXF2fW/x45sbGxYf369XzzzTecPHlS6XAUJzcTaZdZjOl+/vnn2Nra8s033ygdiiJu3brF8OHDOXfuHP7+/jRp0kTpkIzCli1bGD16NJGRkWZbc/mvv/6ievXqsriNFpl8TzclJYWgoCCzXNAthCAgIAB3d3dcXFyIioqSCTcPunTpQu/evenXrx9qtVrpcBQRFBREp06dZMLVIpNPulu2bMHNzc3sittcunSJ9u3b8/PPP7Nnzx5mzpyJtbW10mEZnW+//ZaUlBSzLAEqhJDFbXTA5JOuuY1HqdVqFixYgLe3N+3bt+fkyZNyAqQArKysCAkJYenSpezcuVPpcPQqKiqKx48f06pVK6VDMSkmvTni6tWrhIeHs2nTJqVD0Yvff/8dX19fihQpwvHjx6lVq5bSIZmEsmXLEhwcTM+ePTl9+jSVKlVSOiS98Pf3Z9CgQSa/DVzfTPpfMzAwkN69e5t8cZvU1FRmzpxJixYtGDBgAAcOHJAJV8uaN2/O+PHj6dGjBykpKUqHo3NJSUmEhISY5VyIrpls0jWX4jYRERF4eXlx4sQJzpw5w7Bhw2TPREe++OILypcvz/jx45UORec2bdqEl5eX2fTq9clkP50HDhzA1taWBg0aKB2KTiQmJjJhwgQ6derEhAkT2LZtm6wHq2MWFhYsX76cnTt3EhQUpHQ4OiUn0HTHZJOuKRe3OXToEO7u7ly7do24uDj69etnkt+nIbKzs2PDhg18/vnnxMfHKx2OTly+fJnY2Fi6dOmidCgmySQ3Rzx8+JCqVauaXHGbJ0+eMHHiRLZu3crPP/9M586dlQ7JbAUGBjJ79mzCw8MpWbKk0uFo1dSpU3n8+DELFy5UOhSTZJI93eDgYDp06GBSCXfbtm24uLigVqtRqVQy4Sps4MCBNGvWDD8/P5MqjKNWqwkMDJRDCzpkkknXlIrb3L9/n/79+zN69GgCAwP57bffsLOzUzosCVi0aBHnz59n0aJFSoeiNXv37sXJyUmu7dYhk0u60dHR3Lt3jzZt2igdSoEIIQgJCcHFxQVnZ2diY2PlE1gNTNGiRVm/fj2zZs3ixIkTSoejFea2mUgJJjemO3r0aEqXLs2MGTOUDiXfbty4wfDhw7l48SL+/v40atRI6ZCkHGzdupURI0YQGRmJo6Oj0uHkW2Zxm4SEBHk3pUMm1dNNTk426uI2QgiWLl2Kh4cH9evX58yZMzLhGoEPP/yQfv360bdvX6MujLNmzRo++OADmXB1zKSS7pYtW/Dw8KBq1apKh5JnFy9epE2bNixdupT9+/czffp0ihQponRYUi7NnDkTtVpttHdYmcVt5NCC7plU0jXGHxq1Ws0PP/xAo0aN6NSpEydOnMDV1VXpsKQ8srKyIjg4mICAAHbs2KF0OHkWGRnJ06dPadGihdKhmDyTKXhz5coVIiMj2bJli9Kh5JpKpcLX15dixYpx8uRJatSooXRIUgE4OzsTHByMj48Pp0+fNqpH2GduJpJbyHXPZP6FAwMD6dOnj1EUt0lNTWXGjBm0atUKX19f9u3bJxOuiWjWrBkTJkzAx8fHaArjJCUlERoayoABA5QOxSyYRNI1puI2p0+fpmHDhkRERBAVFcXQoUNl78LEjBs3jkqVKjF27FilQ8mVjRs34u3tLWt36IlJfNr3799P6dKlDbq4TWJiIuPHj6dz585MnjyZsLAwKlasqHRYkg5kFsbZu3cvq1evVjqcN5LFbfTLJJJu5niUoTpw4ACurq7cvn0blUpF7969ZYEaE1eqVCk2bNjA2LFjUalUSoeTrUuXLhEXFye3leuR0W+OyCxuc+nSJcqUKaN0OC95/PgxX375JTt27OCXX37hgw8+UDokSc9WrlzJt99+S3h4OKVKlVI6nNdMmTKFp0+fsmDBAqVDMRtG39MNCgrivffeM7iEu3XrVlxcXLC0tESlUsmEa6Y++eQTWrZsia+vr8EVxsksbmNsyyyNndEnXUNbm3vv3j369OnD2LFjWbVqFUuWLMHW1lbpsCQFLVy4kEuXLhlcqcQ9e/ZQrlw5uS5cz4w66UZFRfHXX38ZRHEbIQRr1qzB1dWVt956i9jYWFq2bKl0WJIByCyM8/3333Ps2DGlw/mHoc+FmCqjHtMdNWoU9vb2TJ8+XdE4rl27xmeffcbVq1cJCAjA09NT0Xgkw7Rt2zaGDRtGZGQkTk5OisZy//59atSowZUrV+SdmJ4ZbU83OTmZ4OBgBg0apFgMGRkZLFmyhAYNGtCoUSMiIiJkwpWy1alTJz755BODKIyzZs0aPvzwQ5lwFWC0SXfz5s3Ur19fsa2W58+fp3Xr1gQGBnLw4EGmTJkiC9RIb/TNN98ghGDatGmKxSCL2yjLaJOuUj806enpzJ07lyZNmtC1a1eOHTtGvXr19B6HZJwKFSpEcHAwK1asYNu2bYrEEBERwfPnz2nevLki7Zs7oyx4k5CQQFRUFF27dtVru7Gxsfj6+mJra8vp06epVq2aXtuXTIOTkxOhoaF89NFHnDp1iipVqui1fVncRllG+a+eWdymaNGiemkvJSWFqVOn0rZtW4YNG8aePXtkwpUK5J133mHSpEn4+PiQnJyst3YTExNlcRuFGV3S1XdxmxMnTlC/fn1iY2OJjo7G19dXbuGVtOLzzz+nWrVqjBkzRm9tbty4kcaNG8u6HwoyuqS7b98+7O3tqV+/vk7bef78OWPGjKFbt27MmDGDTZs2Ub58eZ22KZkXCwsLli1bxoEDB1i5cqVe2pTFbZRndElXHwu69+7di6urKw8ePEClUtGjRw/Zu5V0IrMwzvjx44mLi9NpWxcvXiQ+Pl4Wt1GYUW2OePDgAdWqVdNZcZtHjx4xfvx49u7dy5IlS+jYsaPW25CkrKxevZpvvvmG8PBwna2d/frrr0lMTOSHH37QyfWl3DGqnm5QUBAdO3bUScLdvHkz9erVo2jRosTFxcmEK+lV//79adOmDYMHD9ZJYZzM4jZyaEF5RpV0dbE2986dO/Ts2ZMJEyYQHBzM4sWLDbIEn2T6FixYwNWrV5k/f77Wr717924qVKiAi4uL1q8t5Y3RJN2oqCgePnxI69attXI9IQQrV67Ezc2N6tWrExMTIxeLS4qytrZm3bp1zJkzh6NHj2r12rK4jeEwmjHdkSNH4ujoqJXtk1evXuXTTz/l1q1b+Pv707BhQy1EKEnasWPHDoYMGUJkZCTOzs4Fvt69e/eoWbOmLG5jIIyip5ucnExISAgDBw4s0HUyMjJYvHgxDRo0oFmzZoSHh8uEKxmcjh07MnjwYPr06UN6enqBr7dmzRo6d+4sE66BMIqku2nTJho0aFCg4jbnzp2jRYsWrFmzhiNHjvDVV19RuHBhLUYpSdozbdo0rKysmDp1aoGuI4vbGB6jSLoF+aFJS0tj9uzZNG3alJ49e3LkyBHq1Kmj5QglSbsKFSrEmjVrWL16NVu3bs33dcLDw0lKSpLzFQbE4AveJCQkEB0dTZcuXfL82qioKHx9fXFwcCAiIkLvhUUkqSAcHR0JDQ2la9eunDhxIl/1PjIn0OTmHsNh8D3d5cuX07dv3zwVt0lOTmby5Ml06NCB0aNHs2vXLplwJaPUpEkTJk+eTI8ePfJcGCcxMZG1a9fK4jYGxqCTrlqtznNxm2PHjuHh4cEff/xBbGwsAwcOlL/lJaM2atQoatSowejRo/P0ug0bNtCkSRMqVKigo8ik/DDopLtv3z4cHR3x8PB447nPnj1j9OjR9OjRg2+//ZYNGzZQtmxZ3QcpSTqWWRjnyJEjBAYG5vp1cgLNMBnMmO6dO3D7NqSkgJ0dVKmS+wXdu3fvZujQobRs2RKVSqWTbcKSpKSSJUuyfv16WrZsSf369XF3d//nWGoqJCTAo0dgbQ3OzvDs2QXOnj3LBx98oFjMUtYUTbrp6bB1K8yZA9HRmh8YCwvQPLMvg9TUd/jqq/7Zvv7BgweMHz+eAwcO8Ouvv9KhQwd9hS5JelevXj0WLlyIj48PERERPHliy+LFsGSJ5jOT+SCIlBQoU8Yab+85WFjI5/YZGsV2pJ04AV26QHIyPH2a9TmWlmkUKVKYHj1g2TJ48bmPGzZsYNSoUfj4+PDdd99RokQJ/QQuSQr77LPRbN/+IXfutAUsSEnJ+rzixdUULVqITZugWTO9hijlQJGku2sXdOsGiYm5O79YMWjQAPbuhQcPbjFy5Eji4+Px9/enadOmug1WkgxIWhq0a6fmyJFUMjJscvWaYsUgNBTkSINh0PtEWkwMdO+e+4QLmnMjIwVNmybg5uZO7dq1iY6OlglXMjsDBkB4eKFcJ1zQfH569YKICB0GJuWa3nu6zZvDkSNZHXkA+AK7AQfge6DvS2dYWiayYsV1+vevpeswJcngREXBu+/m1GEJAWYAV4GyQCDw77hCo0Zw8qSOg5TeSK893UuXIDw8u6MjgCLAHWAN8BkQ/8o5NmzZIhOuZJ7mzSPb8VvYA0wElgNPgcPAyzvYYmPh3DldRijlhl57umPGwM8/a8alXvYcKA2ogMyk+jFQAZj90pnW1nD9Ojg46DZWSTIkjx5BuXKaieesvYPmTjH7dblWVuDnB7/8ov34pNzTa083LCyrhAvwJ1CIfxMugDuv93Q1STfr4QlJMl3Hjr28eudlaiACuAfUACoCI4Gkl87KXKIpKUuvSffx4+yOPANerfVpi+Y26WXp6fDwoXbjkiRD9+ABZGRkd/QOkAasB44A0UAUMOu1M7Nbninpj16TrmW2rZUAnrzyd0+Akq+daWGR03UkyTRZWmp+9rOWuZJhFFAOzUT0OGD7a2fKMiTK02v6Kl06uyO1gHTg/At/FwPUe+3MQoXkeK5kfhwcckqYpdEMKbw5o9rZaS8mKX/0mnT794esKzQWB7oBU9FMqh0DtqCZTHtZWhq0bKm7GCXJEDVvnrk9PjuDgEXAXeAhsAB4eTeEtTX066ejAKVc02vSHToUsl8r8TOagX8noA/wC6/2dK2s4OOPQe74lcyNjQ0MGgTZP2FqCuCF5q6xDlAfmPzaWZ99pqsIpdzS++aIzp1h+/Y3/dbOmo0NREaCfNqOZI4uXABX15yWjWXP0hLatIHdu7Ufl5Q3ep+SWrQISpXK++uKF9f8lpYJVzJXNWrA2LGaWgp5VbKkphqZpDxFCt5ER2vGZZ8+zWkZzL+KF9cUyAkMlCsXJPMmBAwZAsHBuatfYmGhSbj79oGnp+7jk95MkRTm4QFnzmj+a2OjGavNSokSmoQ7eTKsWCETriRZWMDSpTBjhubzkd38RqFCmh6xm5um0I1MuIZDsXq6meLiYP58zW/u9HTND0tqKtSqBRMnaqoj5ed2SpJMXVISrFsHs2fDH39odqyp1ZrPUK9eMG4cvPCACclAKJ50MwmhuV1KSdGM+WbX+5Uk6XXp6fDkiWZZWLFichOEITOYpCtJkmQO5CipJEmSHsmkK0mSpEcy6UqSJOmRTLqSJEl6JJOuJEmSHsmkK0mSpEcy6UqSJOmRTLqSJEl6JJOuJEmSHsmkK0mSpEcy6UqSJOmRTLqSJEl6JJOuJEmSHsmkK0mSpEcy6UqSJOnR/wP7PF/84kYWNwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Independent set of 4-th most likely outcome\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from collections import Counter\n", + "\n", + "states = ['e', 'r', 'g']\n", + "state_labels = []\n", + "for shot in final_registers.measurements:\n", + " pre = shot.pre_sequence\n", + " post = shot.post_sequence\n", + " state_idx = np.array(pre) * (1 + np.array(post))\n", + " state_labels.append(\"\".join([states[s_idx] for s_idx in state_idx]))\n", + "\n", + "occurence_count = Counter(state_labels)\n", + "\n", + "most_frequent_regs = occurence_count.most_common(5)\n", + "for ii in range(len(most_frequent_regs)):\n", + " fig, ax = plt.subplots()\n", + " vert_colors = ['red' if (most_frequent_regs[ii][0][i] == 'r') else 'blue' for i in range(len(most_frequent_regs[ii][0]))]\n", + " print(f'Independent set of {ii}-th most likely outcome')\n", + " nx.draw(graph, pos = {ii: (ii/atoms_w,ii%atoms_w) for ii in graph.nodes()}, ax=ax, with_labels=True, node_color=vert_colors)\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Indeed, the most likely solution is the maximum independent set. Other solutions are either missing vertices or invalid." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also visualize the intial and final waveforms:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(initial_Deltas.times(), initial_Deltas.values())\n", + "ax.plot(final_Deltas.times(), final_Deltas.values())\n", + "ax.set_xlabel(\"Time (s)\")\n", + "ax.set_ylabel(\"Delta/2*pi (MHz)\")\n", + "ax.legend([\"initial\", \"optimized\"], loc=\"lower right\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "vscode": { + "languageId": "python" + } + }, + "source": [ + "## Conclusion\n", + "\n", + "In this example, we generated a unit disk graph and found its maximum independent set. Because we are using the Amazon Braket local AHS simulator, we are restricted to relatively small graphs of fewer than 15 vertices. QuEra's Aquila device, by contrast, can handle far larger graphs of up to 256 vertices. See the [Braket Developer Guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-get-started-hello-ahs.html) to learn more about working with Aquila and analog Hamiltonian simulation in general." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/05_Running_Analog_Hamiltonian_Simulation_with_local_simulator.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/05_Running_Analog_Hamiltonian_Simulation_with_local_simulator.ipynb new file mode 100644 index 000000000..d59bfa2c4 --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/analog_hamiltonian_simulation/05_Running_Analog_Hamiltonian_Simulation_with_local_simulator.ipynb @@ -0,0 +1,451 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "20e6ca17", + "metadata": {}, + "source": [ + "# Running analog Hamiltonian simulation with local simulator\n", + "\n", + "We recommend to test and debug an analog Hamiltonian simulation (AHS) program on the local simulator before submitting it to a QPU. In this notebook, we introduce several features of the local simulator that will be useful to streamline this testing process.\n", + "\n", + "To begin, we import the necessary packages." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d1173d71", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import time\n", + "\n", + "from braket.ahs.atom_arrangement import AtomArrangement\n", + "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n", + "from braket.devices import LocalSimulator\n", + "\n", + "from ahs_utils import show_register, show_global_drive, plot_avg_density_2D, get_drive, get_avg_density" + ] + }, + { + "cell_type": "markdown", + "id": "e5e39b46", + "metadata": {}, + "source": [ + "## 2D checkerboard phase \n", + "We consider a $3\\times3$ square gird with 9 atoms. As shown in [this notebook](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb), we can realize the 2D checkerboard phase via adiabatically tuning the Rabi frequency and detuning. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "06439adb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "register = AtomArrangement()\n", + "separation = 6.7e-6 # in meters \n", + "\n", + "for k in range(3):\n", + " for l in range(3):\n", + " register.add((k * separation, l * separation))\n", + "\n", + "\n", + "time_points = [0, 2.5e-7, 2.75e-6, 3e-6]\n", + "amplitude_min = 0 # rad / s\n", + "amplitude_max = 1.57e7 # rad / s\n", + "\n", + "detuning_min = -5.5e7 # rad / s\n", + "detuning_max = 5.5e7 # rad / s\n", + "\n", + "amplitude_values = [amplitude_min, amplitude_max, amplitude_max, amplitude_min] # piecewise linear\n", + "detuning_values = [detuning_min, detuning_min, detuning_max, detuning_max] # piecewise linear\n", + "phase_values = [0, 0, 0, 0] # piecewise constant\n", + "\n", + "\n", + "drive = get_drive(time_points, amplitude_values, detuning_values, phase_values) \n", + " \n", + " \n", + "show_register(register)\n", + "show_global_drive(drive)" + ] + }, + { + "cell_type": "markdown", + "id": "b90c4ceb", + "metadata": {}, + "source": [ + "The AHS program can be constructed by assembling the atomic register with the driving field." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f1878620", + "metadata": {}, + "outputs": [], + "source": [ + "ahs_program = AnalogHamiltonianSimulation(\n", + " register=register, \n", + " hamiltonian=drive\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "a9ca31a1", + "metadata": {}, + "source": [ + "We can then run the program on the local simulator." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a70c804e", + "metadata": {}, + "outputs": [], + "source": [ + "device = LocalSimulator(\"braket_ahs\")" + ] + }, + { + "cell_type": "markdown", + "id": "d760b11b", + "metadata": {}, + "source": [ + "Below we explicitly specify `shots=1000` and `steps=100` respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "7a3ebaec", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The elapsed time = 7.236017227172852 seconds\n" + ] + } + ], + "source": [ + "start_time = time.time()\n", + "result_full = device.run(ahs_program, shots=1000, steps=100).result()\n", + "print(f\"The elapsed time = {time.time()-start_time} seconds\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "dac877bf", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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uwMfHBwDg4+ODmzdv2vLpCSFEPwftiuFDkBdeTS3KTwhp2VJSUpCSkgKgPl80Fwc4ZCudD5sm+QcffBDXrl2Dj48Prl27Bm9vb73lTC3KTwhp2e5t+N3bIGwOZ23J23Q9+bi4OKxfvx4AsH79eowZM8aWT08IIQbRhVczTZgwAf3798fFixchl8uxdu1avP7668jKykK3bt2QlZWF119/3VpPTwgh/PEcPumAOd563TWpqal6H2/YDYUQQoSCA2e1jbTtTZAXXgkhxNYcsZXOByV5QgiB8y5rQEmeEEIctL+dD+fshCKEEDPUr10jzNE1Z8+ebdb5lOQJIQTCHV0ze/ZsPPTQQ/j3v/+N8vJys8+nJE8IIRDu2jUHDhzApk2bUFhYiOjoaEycOBFZWVm8z6c+eUIIEfh68t26dcP777+P6OhozJs3DydPngRjDB988AHi4+ONnksteUJIiyfk9eTPnDmD+fPnIzg4GNnZ2fj+++9x4cIFZGdnY/78+SbPp5Y8IYRAuEsWvPjii5g1axY++OADuLm5aR/39fXF+++/b/J8askTQgiE25KPj4/Hc889p5PgV61aBQB47rnnTJ5PSZ4QQjjhXnjdsGFDo8e+/PJL3udTdw0hpMVrGCcvJKmpqdi8eTPy8/MRFxenffzu3bvw9PTkXQ8leUIIgfCS/IABA+Dj44PS0lK88sor2sfbtGmD8PBw3vVQkieEEAhvWYPOnTujc+fOOHToULPqoSRPCCEQXkt+4MCBOHDgANq0aaMTG2MMHMehoqKCVz2U5AkhRIALlB04cABAfR98c9DoGkJIi1e/aYgwR9fk5eVBoVAAAPbu3YtPPvnErDVsKMkTQggAEcfxutna2LFjIRaL8fvvvyMxMRH5+fmYOHEi7/MpyRNCCCw7GSozMxM9evRAUFAQli1bprfM3r17ERERgZCQEAwePNhgXSKRCBKJBNu2bcPLL7+MlStX4tq1a7xfF/XJE0JaPM6CC5Sp1WrMnTsXWVlZkMvliImJQVxcHHr16qUtU15ejhdeeAGZmZnw9/fHzZs3DdYnlUqRmpqK9evX4/vvvwcAKJVK3vFQS54QQgCIOH43U44ePYqgoCAEBgZCJpMhISEB6enpOmU2b96M+Ph4+Pv7AwC8vb0N1rdu3TocOnQIixYtQkBAAPLz8zF58mT+r4t3SQtauXIlQkJCEBoaigkTJqC2ttYeYRBCiJalLrwWFxejU6dO2vtyuRzFxcU6ZS5duoSysjIMGTIEUVFRepcuaNCrVy988sknmDBhAgAgICAAr7/+Ov/XxbukhRQXF+OTTz5BTk4Ozp49C7VajbS0NFuHQQghWhzqR9jw+a+kpATR0dHaW0pKik5djLHG9d/XFaRSqXD8+HHs2LEDP/zwA9577z1cunRJb2wHDx5EbGwsunfvjsDAQAQEBCAwMJD3a7NLn7xKpUJNTQ2kUimqq6vh6+trjzAIIUSL7+hILy8v5OTkGDwul8tRWFiovV9UVNQox8nlcnTo0AHu7u5wd3fHoEGDcPr0aXTv3r1RfYmJiVi5ciWioqIgFov5BXkPm7fk/fz8sGDBAvj7+8PHxwceHh4YNmyYThlTn5SEkJYtJSVFmx9KSkqaXyHPTbz5XJyNiYlBbm4u8vPzUVdXh7S0NJ0FxgBgzJgx+Pnnn6FSqVBdXY0jR44gODhYb30eHh544okn4O3tDU9PT+2NL5u35MvKypCeno78/Hy0a9cOzzzzDDZu3KhzIcHUJyUhpGVLSkpCUlISACA6OtoidVpqCLxEIsGaNWswfPhwqNVqzJgxAyEhIUhOTgZQvzF3cHAwRowYgfDwcIhEIsycOROhoaF663v00UexcOFCxMfHw8XFRft4ZGQkv3ia/5LM89NPPyEgIABeXl4A6hfE/+WXX8y6WkwIIZbEARad6DRy5EiMHDlS57HZs2fr3F+4cCEWLlxosq4jR44AgE7Dl+M4ZGdn84rF5kne398fhw8fRnV1Ndzc3LB7926LfRITQkhT2WPJAj727NnTrPMNJvnbt2+bPFkkEqFdu3ZmPWHfvn0xbtw4REZGQiKRoE+fPtqvXYQQYg/22tqPjxs3buDNN9/E1atXsWvXLpw/fx6HDh1CYmIir/MNJnlfX1/4+vrqHQ7UQK1W48qVK2YHvXjxYixevNjs8wghxFrssS4NH9OmTcP06dOxZMkSAED37t3x7LPPNj/JBwcH4+TJk0ZP7tOnjxmhEkKIcAkzxQOlpaUYP348li5dCqD+wq45QykNJnk+u5E0d8cSQggRCqFtGtLA3d0dt27d0sZ3+PBheHh48D7fYJJ3dXXV/rusrAyFhYVQqVTaxyIjI3XKEEKIo6ofXWPvKPT7+OOPERcXh7y8PDz88MMoKSnBli1beJ9vcnTN22+/jS+//BJdu3bVfpKYM3yHEEIEj7PPhiB8REZGYt++fbh48SIYY+jRowekUinv800m+W+++QZ5eXmQyWTNCtTSGGNQM0CjARj+XHuCAyQi4X7tIua7XVGDrXvOIf9qOSqqFPBq1wphQQ9i1MM9IJOaP8WbCJOGMag1AGP17+d7V3201ftZiHnj1q1b2Lx5M3777TcA9ddKfX190b59e951mEzyoaGhKC8vN7oUpi1pGINKDag0+o8r1YCYY5CKhTvulZh26tI1fJz6CzIO/AYxJ0K14q/1s1u3kkEs4jBrTDTmxD8E3w5t7BgpaaqGhppKDWjuG8Sn/vP/HACJiEEitm4SFmJ3zYULFzB06FAMHz4cffr0AWMMx44dwwcffIDs7Gz07NmTVz0mk/wbb7yBPn36IDQ0VGdKbUZGRtOjbyK1hkGh4lGOAWoVIBUxSCUC+80Rk/6VdgjvfrEHCqUaGg3DX2/5epXVdQCA1d8cxn+35eDbZQkY2LuzHSIlTcVY/Xv5/uTeqBwApaa+UeciZVYd5ii0lvzbb7+NVatWYfz48TqPb926FYsWLcLWrVt51WMyyU+dOhWvvfYawsLCIBLZb48Rvgn+XkoNwFQMMkr0DuOfGw9g2Vc/o4bHL1uhVEOhVGPMws34/qNJGBDmb4MISXPxTfA65wCoVQJuUma1ZCy0LPHrr7/qvcA6duxYvPnmm7zrMZnkO3TogHnz5pkXnYU1/FE0hUoDiDUMYqF9FyONZB39HUs3/IwaBf+tzQCgWqHE06+l4tdNL8L7AXcrRUcsRamne4avWiXgaoVEz3EQXI5wdzf8t2zs2P1MJvmoqCi88cYbiIuLa9IKaJagVBs+FvfkCJw+dQIvvDgPr73xlsHzxbTRoeAtXrvXaILXVJei7vinkIVPg8hDt3umTqXG5xnH8ebUQdYOkzQDY8zg9bQLF85j/ry5AACFQoHfcy+h8Fqp7vmo/4AQWyEfC6275ubNm/j4448bPc4YM2t5ZZNJvmHW6+HDh7WP2XIIpbE/CgD4z38/R3b2T7haXGSwjIbVX7AV6rRlAvxWUIJz+YY3MwYA1ZV9EHl00XusVqHCp1uO4LXJAyGmT3TBUhlpsAUH90JmVv1iXFu3fIN9e/TnGGs12oSWHmbNmoW7d+/qPTZz5kze9ZhM8vpWQMvPz+f9BM2lNvG1zk8u51WPSg3I7LIPFuEjedsxqIx8mmsqisDJWoNxht/ddSo1fjz6O57o33h3HSIMxhps90rbvAnzX9G/DK+G1Tf+LNny5sAJrhH4zjvvWKQek2nv3Xff1bmvVquxYcMGmyV6I+ujmaWpfYDENk5cvAaV2nAGUF3ZD2mPp6C8/IPBMrUKFS4UlFKSFyjGGPi8DW/duoVLF39D/wEPGyxj8S4bAa9C2Vwmk/y9HfxKpRL79+9vNKTHmiyV5C1VD7GOimqFwWPqW5cgauMLTtrKaB0qtQZ3KmstHRqxsa3/+xpPjx1n8z5yofXJW4rJJP/KK6/o3H/11VcRExNjtYDuZ7Gfu3P+/pyGu6vhadqs6ho05QWoq/gKmqobUFaXQhb8DDjXdjrlxCIOrVsJa2Y2Md/XaZvx6X8+s+lzcgDELTXJ36+srAwdO3a0Rix6mfqxz50zC0cOHYJCocCJ48fx9ZZtessJbHQUuU8P/w44dek6NHq+ckn8BwP+gwEAdRe3QdIxslGCBwA3Fym6+Dxg7VBJE9W3lI1/pc6/fBkKhQI9DWxq3cAa72eh5gh9I2w8PDwQFRWFiIgIk+ebTPJhYWHarzGMMRQUFMDT01P7+JkzZ8yP2gxiEe6f8KiD7ye+hAZcCNrzT8cg4+ffUFVrfIy8rMfTBo8xMIx+uIelQyMWJBEZv/gaEBiIA4eOGa3DWuvZCDXJ5+TkICcnB6NHjwYA7NixAzExMUhOTsYzzzyDV1991ej5JpP89u3bLRNpE3EcB4nI+DBKk3VAuL9AUu+hXn7o6NkaecVlTTpfKhFh6sg+cHWhIVRCJhXzH2FjrA5L42y4EJq5bt26hRMnTqB169YA6nfWGzduHPbv34+oqKjmJ/nOne2/JoikmX8YUisvbkSaj+M4vDFlEOat3IlqE615fSRiEeaOfcgKkRFL4jgOYo6ZHBpt8HxYr8Em1IbglStXdFYBlkql+OOPP+Dm5qYzQdUQg0k+MjISJ06cMHoynzKWIOI4SMXM6MxXQ8Qimu3qKCYOD8eeE/nYtveCzqqTpri5SJD86mgE+vFffpXYj0xSvzxBU/K8i9R6DTahtgMnTpyIfv36YcyYMQCA77//HhMmTEBVVRV69epl8nyDSf7ChQsIDw83eCJjDHfu3GlCyEB5eTlmzpyJs2fPguM4fPHFF+jfv7/Rc6Ti+os25iR6sQiQUSveYXAch+RX4yDiOGzde95ki57jAFeZBKvmj8T4x8NsFCVpLo7j4CplZid6V4n1NtvmAEgEmCcYY5g2bRpGjhyJAwcOgDGG5ORkREdHAwA2bdpksg6DSb5hkXpjzNlM9l4vvfQSRowYgS1btqCurg7V1dW8zpOKOYg4ZnKBIw71XTRi2kDE4UgkIvz39TjE9g3Csg37kX+1DHVKNdT3/MJdZRIwxvBoVAAWTRuM6GA/O0ZMmqIh0SuN7A3RQCyqfz9be0aqEFMFx3F46qmncPz4cURFRTWpDoNJ3lp98RUVFdi/fz++/PJLAIBMJjNr1ymxiINY9NfmIRqmuzOUVESbhTg6juPwzNAQPDM0BKcuXcPnGSfwe9EtVNcq0a61K2J6+SExLoo2C3FwHMdBJgGkjEHz5+YhDH+9nyUi2zXUOE54yxo06NevH44dO9bk+Uk2H4pw+fJleHl5Yfr06Th9+jSioqKwatUqs5bOBOo/1WktGucX0d0HaxY8ae8wiBXVX4y1/7UzgeZ47NmzB8nJyejSpQvc3d216/bwHb5u8zSpUqlw4sQJrF69Gn379sVLL72EZcuW4b333tOWKSkp0fY5AUBSUhKSkpJsHSohRKBSUlKQkpICAGYtu2uMUDsAdu3a1azzTX52rlmzBmVlTRu7rI9cLodcLkffvn0BAOPGjWs0QsfLy0s7ASAnJ4cSPCFER1JSkjY/eHl5Nbs+Dg1dwaZvtta5c2cUFhYiOzsbnTt3RqtWraDR8B9TbjLJX79+HTExMRg/fjwyMzPBmrnSV8eOHdGpUydcvHgRALB7925ew4AIIcRquPqWPJ+brS1evBjLly/H0qVLAdQvFDl58mTe55tM8u+//z5yc3ORmJiIL7/8Et26dcObb76JvLy8Jge9evVqTJo0CeHh4Th16pRZ+xUSQog1cDz/s7Vt27YhIyNDe93S19fX4GYi+vDqk+c4Dh07dkTHjh0hkUhQVlaGcePGITY2FitWrDA76IiICOTk5Jh9HiGEWIOQlz6RyWTgOE47yqiqqsqs80225D/55BPt+ggPP/wwfv31V/znP//B8ePHsXXr1qZFTQghAiPU7prx48fj+eefR3l5OT777DM8/vjjmDVrFu/zTbbkS0tL8e233zYaNy8Siey+eBkhhFiKUCdOLliwAFlZWWjbti0uXbqEd999F7GxsbzPN3v7v3sFm1jzmRBCHAEngHH6xoSFhaGmpgYcxyEszLwlPAT8sgghxHZEf856NXXjIzMzEz169EBQUBCWLVtmsNyxY8cgFouxZcsWg2U+//xzPPTQQ/j222+xZcsW9OvXD1988QXv10VzRgkhLZ4lL7yq1WrMnTsXWVlZkMvliImJQVxcXKOh4mq1Gq+99hqGDx9utL5//vOfOHnyJDw9PQHUry8/YMAAzJgxg1c81JInhBA0bBxi+mbK0aNHERQUhMDAQMhkMiQkJCA9Pb1RudWrV2Ps2LHw9vY2Wp9cLkebNn+t09SmTRt06tSJ9+uiljwhhICDiOcYeFPLrhQXF+skYblcjiNHjujUUVxcjG3btiE7OxvHjunf7rBhb1c/Pz/07dsXY8aMAcdxSE9Px0MP8d8gh5I8IaTFa1jFlo+GZVcM0bcqwP0jd15++WUsX77c6HLtDROeunbtiq5du2ofb9g8hC9K8oQQwgESC3XKy+VyFBYWau8XFRXB19dXp0xOTg4SEhIA1A9T37lzJyQSCZ566iltmXfeecci8VCSJ4S0eOa05E2JiYlBbm4u8vPz4efnh7S0NGzevFmnTH5+vvbf06ZNw6hRo3QSPACMHj3a6Nj9jIwMXvFQkieEEFhu5ymJRII1a9Zg+PDhUKvVmDFjBkJCQpCcnAwAmD17Nq96FixYAAD49ttvcf36de2iZKmpqejSpQv/eMwLnxBCnJMlJ7yOHDkSI0eO1HnMUHJv2CXvfoMHDwYAvP3229i/f7/28dGjR2PQoEG8Y6EhlISQFo9DfTLkc7O1kpISXL58WXs/Pz/frI1SqCVPCCGc9TcKb6qVK1diyJAhCAwMBAAUFBRod8Xig5I8IaTFq5/xKswkP2LECOTm5uK3334DAPTs2RMuLi68z6fuGkIIwZ8jbHjcbC06Ohpr166Fv78/evfubVaCByjJE0IIAMsta2BpaWlpKC4uRkxMDBISEvDDDz+YtQ0rJXlCCAGn3X3J1M3WgoKCsGTJEly6dAkTJ07EjBkz4O/vj3feeQe3b982eT4leUJIiyfk0TUAcObMGbzyyitYuHAhxo4diy1btqBt27YYOnSoyXPpwishhEC4F16joqLQrl07JCYmYtmyZdo++b59++LgwYMmz6ckTwghnHC3//vf//6nHT4J1K9Dn5aWhkmTJuHbb781eb7dumvUajX69OmDUaNG2SsEQggBIMzumoqKCixduhQff/wxsrKywBjD6tWrERgYiG+++YZ3PXZrya9atQrBwcGoqKiwVwiEEKIltJb8c889hwceeAD9+/fHZ599hhUrVqCurg7p6emIiIjgXY9dknxRURF27NiBRYsWaRfGJ4QQexJWigcuX76MX3/9FQAwc+ZMdOjQAVeuXNHZJYoPu3TXvPzyy1ixYgVEIv1P37DzSsPNnCm8hBDnl5KSos0P5qzjYozQxslLpVLtv8ViMQICAsxO8IAdWvLbt2+Ht7c3oqKisHfvXr1lTO28Qghp2e7dcu/erfiaigMgFlh3zenTp9G2bVsA9btN1dTUoG3btmCMgeM43l3dNk/yBw8eREZGBnbu3Ina2lpUVFRg8uTJ2Lhxo61DIYSQP3HgBNZho1arLVKPzbtrli5diqKiIhQUFCAtLQ1Dhw6lBE8IsTuhdddYCo2TJ4S0ePVDKB0wg/Ng1yQ/ZMgQDBkyxJ4hEELIn5Oh7B2EdVBLnhBCINxlDZqLkjwhpMWr3zTE3lFYByV5QggBBDe6xlIoyRNCCKhPnhBCnBq15AkhxElRnzwhhDgzjqPRNYQQ4sycM8VTkieEkD+7a5wzzVOSJ4QQUEueEEKcm5NmeUryhBAC6q4hhBCn5pwpnpI8IYTUc9IsT0meENLicaAZr4QQ4ryceD15m2//RwghQsTxvPGRmZmJHj16ICgoCMuWLWt0fNOmTQgPD0d4eDgGDBiA06dPW+Q16EMteUIIAQfOQk15tVqNuXPnIisrC3K5HDExMYiLi0OvXr20ZQICArBv3z488MAD2LVrF5KSknDkyBGLPP/9qCVPCCGw3EbeR48eRVBQEAIDAyGTyZCQkID09HSdMgMGDMADDzwAAOjXrx+Kioqs8ZIAUJInhBDeXTV82vrFxcXo1KmT9r5cLkdxcbHB8mvXrsUTTzzR5NhNsXmSLywsxKOPPorg4GCEhIRg1apVtg6BEEIa45nlS0pKEB0drb2lpKToVMMYa1y1ga8Ae/bswdq1a7F8+XJLvhIdNu+Tl0gk+OijjxAZGYm7d+8iKioKsbGxOv1VhBBia3yHUHp5eSEnJ8fgcblcjsLCQu39oqIi+Pr6Nip35swZzJw5E7t27YKnp6f5AfNk85a8j48PIiMjAQBt2rRBcHCw0a8yhBBiC5bqk4+JiUFubi7y8/NRV1eHtLQ0xMXF6ZS5cuUK4uPj8dVXX6F79+5WekX17Dq6pqCgACdPnkTfvn3tGQYhpKWz4Dh5iUSCNWvWYPjw4VCr1ZgxYwZCQkKQnJwMAJg9ezbeffdd3Lp1Cy+88IL2HGPfDpqDY/o6kGygsrISgwcPxqJFixAfH69zrHPnzvDy8tLeT0pKQlJSkq1DJIQIVEpKirYvvKSkBH/88Uez6gvpHYlvdv7Mq+zUMYOtlpCtwS4teaVSibFjx2LSpEmNEjxgus+LENKy3dvwi46ObnZ9HJx3xqvNkzxjDImJiQgODsbf/vY3Wz89IYTo5aQ53vYXXg8ePIivvvoK2dnZiIiIQEREBHbu3GnrMAghRJcl1zUQEJu35AcOHKh3HCkhhNgTbRpCCCFOzDlTPCV5Qgip56RZnpI8IaTFo01DCCHEmTnxpiGU5AkhBE7bW0NJnhBCLLlpiNBQkieEEFB3DSGEOC0HnefECyV5QggBnDbLU5InhBDQEEpCCHFq1CdPCCHOigNElOQJIcSZOWeWpyRPCGnxaNMQQghxck6a4x03yRffvIO12w7jyNkruFNZi1ZuMnT374BZ8f3Ru7uvvcMjFqJhDEo1wAAwVt/aEnGAROS863+3NGq1Bj8cuoiNu07gemkF1GoNPD3c8eQjwUgY3gfubjKbxOGsf04Ol+SPnr2C9z/Pwv4TlwEGKJQq7bFfTuUjNfMkuvi2x2vTh+KZx3s77VRlZ8YYg5pBm9x1jwEaBqg0gIhjkIoAsbNeMXNy1bV1WJ12AGu+PojaOiUqq+t0ju8/eRmvrtqOiU9E4rVpQyH39rBqPM6aKxwqya/POIb5H6WjRqHUe1ytYaiuVeL85RuYs2QLfjp8Cf9+YywkErGNIyVNxRhDnRpQ89g8TMMAhRqQMgap2DnfoM6qpKwSI178DJeLbqG2TqW3TFVNfdL/MuMYtv50BjtWz0SfHn5Wi8lZ/4JsvsdrU6VmnjCa4O9XXavE1p/OYM4HW2m7QQdhToK/l1IDKM09idjN3SoFhj6fjNwrJQYT/L1Uag3K7tZg2Asp+K3gplVi4jj+N0fjEEk+r7AUc5d+yzvBN6hWKPFt9hmkZp60UmTEklQa8xN8A6Wmvv+eCN+cpVtReKMcSpXGrPOqauow6qW1UKvNO48vjud/jsYhkvyarw9ApVbrPaYq+RWKcxuhOLcJmqrrjY5X1yqx9Ivd1JoXOMYYDL3nKyoqMHTQwxjx+KMYNKAv9mTv1ltOpf9PhAjIzduV2P7zeSgMtOA1lddRd+Fr1J1PhfKPPTrHGGO4U1mDrCOXrBMcx/PmYOyS5DMzM9GjRw8EBQVh2bJlRstW19Zhw/bjej/1maoW6uvHIQueAGnXJ6Es0P/mv1pyBznniywSO7EODWt8kbVB69at8WP2PmT+tAfrN6bi74ve0FtOxUAf5gL3+XeHDXZ5MI0aqsK9kHZ/CrJeEyDt/GijMpXVdfh44z6rxOakOd72SV6tVmPu3LnYtWsXzp8/j9TUVJw/f95g+Yx95yAyEKWm8ipEbTqBE4khcm0HaJRgmsYthFqFCslbfrHQKyDWYOybu0gkgkRSP0agoqICoWFhBstS17ywpWw9jFqF/lY8qywGRDIoc79H3flUaCoK9ZY7eq4Q10orLBwZBxHH7+ZobJ7kjx49iqCgIAQGBkImkyEhIQHp6ekGy/9xtQzVtQb64lW1gMTlr/tiWf1j99EwhtwrJc0NnViRxkRyvlpcjMeHPIK4J4cjbszTBstRQ164GGO4WVZl+HhdJVj1TUiDRkMaNArKy5l6v5m5SCUovFFu0dgaZrw644VXmw+hLC4uRqdOnbT35XI5jhw5olOmpKQE0dHRAIDroq7QiLror0ziCqgVf91X19U/pkdltULv48Qx+Pr54ae9P+OPggKMiH0UTzw5Sm85SvLCpahTgeOM/I4kruDa+IGTuABwAaRugKoakLrrluOAb/63DS9M/QpAfb4ghtm8Ja/vk/n+SQheXl7IyclBTk4OXnpxNsQGxkCLWvtCc7cITKMGU1QAIik4kf7Prbat3ZofPLELheKvD+g2bduides2Bss6YkurpXCRSYz2aYta+4LVlIExDZhaASirAYme9y1jmPDsWG2O8PLyskh81JK3ELlcjsLCv/raioqK4OtreBmCXgEPws1FprclzklcIfbug7oLqQA4SDsP1VuHVCJCZE/rTaIgzSfiDPennz93Fq8t+BvEYjGUSiVWfLTSaD1EmDiOQ2efB3C5+Lb+4xJXSDpGou78ZkCjgcR/CDiucTu0TqlGgG97y8fnkJdVTbN5ko+JiUFubi7y8/Ph5+eHtLQ0bN682WD54f17QGZkxqrEOxwS73CjzykWizDnmQFNjplYn1QMqA3Mi+kTGYUfs/mNqKAkL2wvTRyEN9fs1M5mvZ/YKxRir1CD54s4DiMG9ER7j1aWDcxBW+l82Ly7RiKRYM2aNRg+fDiCg4Mxfvx4hISEGCkvxgvPDoCrrOmfR+HdfNHN3zJf6Yh11I9caF4dEpHzrj/iLCYM7wONqavsRri5SPHypEEWjKieM194tcs4+ZEjR+LSpUvIy8vDokWLTJaf+VQ/SKVNW3/GzUWKv8+KbdK5xLakzfxrbO75xPrauLsgaWw/tHKVmn2uVCJC985eeCikk+nCTUAzXu3oQc822PbRdLiZ+YfRylWKNxMfx2N9u1spMmJJYhEHSRP/Il3E1Ip3FO/PGYG+of5wc+H/fpaIRfBs5470ldOt9numlrydPRwRgIx/JaJNKxe4SI133YhFHNxcpPjH7OFYMGWIbQK8T0pKil2e1xChxQPoj0km5sxukbuILbPcsNB+RkKLB7BMTBKJGNs+mo7H+3bjtVZ8K1cpAvza45d1/wevB1pbPJ4GlpzxampWP2MM8+bNQ1BQEMLDw3HixAmLvAZ9HCbJA8DAiACc+noBXpr4CDxau6J1Kxed461cpXCVSfBMbAT2fPYC/i/hETtFKrw3qNDiAQzHJBVzcJUAplYPlnCAm8Ry68kL7WcktHgAy8XkIpMgbelkfLk4AQPCO8NVJoHsni5ZkYiDu5sMAX7tseKlUTi8fh58OrS1WjwALJbl+czq37VrF3Jzc5Gbm4uUlBTMmTPHcq/jPg61njwA+Hq1xeI5I/DWrFh8v/8czv5+DaXlVdi25Wu889J8jH0sHA+0tfCVd2JzIo6Di+SvhcvYn2vbcABEovoPAOqecWwikQijHumFUY/0Ql5hKdL3ncON23ehVKrh3b41BkcFoV+Yv01+zxwst9PYvbP6AWhn9ffq1UtbJj09HVOmTAHHcejXrx/Ky8tx7do1+Pj4WCSGewkyyRcUFGhnvPIlKilB8pIXkbzESkGZ6d5Zu0IgtHgA4cVE8Zhmy5i28ChTUlKCqirDSyXw5eXVAQP78XtdNTU1Oj+DpKQkJCUlae/zmdWvr0xxcXHLSfKlpaX2DoEQ0oJkZmZarC4+s/r5lLEUh+qTJ4QQoeMzq9/cmf/NQUmeEEIs6N5Z/XV1dUhLS0NcXJxOmbi4OGzYsAGMMRw+fBgeHh5W6aoBnCDJm7MBiS0UFhbi0UcfRXBwMEJCQrBq1Sp7hwSg/op/nz59MGqU/tUbbam8vBzjxo1Dz549ERwcjEOHDtk1npUrVyIkJAShoaGYMGECamsbL1dtbTNmzIC3tzdCQ/+a0n/79m3ExsaiW7duiI2NRVlZmV3jWbhwIXr27Inw8HA8/fTTKC8vt1k8hmJq8OGHH4LjOEF09Rqa1Z+cnIzk5GQA9RNCAwMDERQUhFmzZuHf//639QJiDkylUrHAwECWl5fHFAoFCw8PZ+fOnbNrTFevXmXHjx9njDFWUVHBunXrZveYGGPso48+YhMmTGBPPvmkvUNhU6ZMYZ999hljjDGFQsHKysrsFktRURHr0qULq66uZowx9swzz7B169bZPI59+/ax48ePs5CQEO1jCxcuZEuXLmWMMbZ06VL26quv2jWeH374gSmVSsYYY6+++qpN4zEUE2OMXblyhQ0bNoz5+/uzkpISm8bkCBy6JW/uBiS24OPjg8jISABAmzZtEBwcjOLiYrvGVFRUhB07dmDmzJl2jQOo39lp//79SExMBADIZDK0a9fOrjGpVCrU1NRApVKhurraan2jxgwaNAjt2+uurJieno6pU6cCAKZOnYrvvvvOrvEMGzZMu0NXv379UFRk2y019cUEAPPnz8eKFStoSK0BDp3kDQ1DEoqCggKcPHkSffv2tWscL7/8MlasWAGRoX0Ubejy5cvw8vLC9OnT0adPH8ycOdMiQ+Cays/PDwsWLIC/vz98fHzg4eGBYcOG2S2ee924cUPbT+vj44ObN2/aOaK/fPHFF3jiiSfsHQYyMjLg5+eH3r172zsUwbL/u74ZmA2HIZmrsrISY8eOxb/+9S+0bdt4pp6tbN++Hd7e3oiKirJbDPdSqVQ4ceIE5syZg5MnT8Ld3d2u11LKysqQnp6O/Px8XL16FVVVVdi4caPd4nEES5YsgUQiwaRJk+waR3V1NZYsWYJ3333XrnEInUMneVsOQzKHUqnE2LFjMWnSJMTHx9s1loMHDyIjIwNdunRBQkICsrOzMXnyZLvFI5fLIZfLtd9uxo0bZ9V1O0z56aefEBAQAC8vL0ilUsTHx+OXX4Sx6fuDDz6Ia9euAQCuXbsGb29vO0cErF+/Htu3b8emTZvs3qDKy8tDfn4+evfujS5duqCoqAiRkZG4fv26XeMSGodO8nyGKtkaYwyJiYkIDg7G3/72N7vGAgBLly5FUVERCgoKkJaWhqFDh9q1pdqxY0d06tQJFy9eBADs3r1bZ7q3rfn7++Pw4cOorq4GYwy7d+9GcHCw3eK5V1xcHNavXw+gPrmOGTPGrvFkZmZi+fLlyMjIQKtW9l86JCwsDDdv3kRBQQEKCgogl8tx4sQJdOzY0d6hCYudL/w2244dO1i3bt1YYGAge//99+0dDvv5558ZABYWFsZ69+7NevfuzXbs2GHvsBhjjO3Zs0cQo2tOnjzJoqKiWFhYGBszZgy7ffu2XeP5+9//znr06MFCQkLY5MmTWW1trc1jSEhIYB07dmQSiYT5+fmxzz//nJWWlrKhQ4eyoKAgNnToUHbr1i27xtO1a1cml8u1f9fPP/+8zeIxFNO9OnfuTKNr9OAYo/3tCSHEWTl0dw0hhBDjKMkTQogToyRPCCFOjJI8IYQ4MUryhBDixCjJE0EpKCiAm5sbIiIiLFJfTU0NIiIiIJPJBLFCISG2RkmeCE7Xrl1x6tQpi9Tl5uaGU6dOCWImNCH2QEme2MyxY8cQHh6O2tpaVFVVISQkBGfPnjV6TkFBgc764R9++CH+8Y9/AACGDBmC+fPnY9CgQQgODsaxY8cQHx+Pbt264a233rLmSyHEYQhyj1finGJiYhAXF4e33noLNTU1mDx5st4NIMwhk8mwf/9+rFq1CmPGjMHx48fRvn17dO3aFfPnz4enp6eFoifEMVGSJzb197//HTExMXB1dcUnn3zS7Poa1ioKCwtDSEiIdmnewMBAFBYWUpInLR511xCbun37NiorK3H37l3e2+zdu/KGUqnUOebi4gIAEIlE2n833FepVBaImBDHRkme2FRSUhLee+89TJo0Ca+99hqvc/744w+UlJRAo9Fg//79UKvVVo6SEOdBSZ7YzIYNGyCRSDBx4kS8/vrrOHbsGLKzs02e5+npiSlTpiAqKgqhoaHYsGED8vLybBAxIY6PVqEkglJQUIBRo0ZpR93cf7+punTpgpycHHTo0MESYRLiMKglTwRFLBbjzp07Fp8MpVQqBbHHLSG2Ri15QghxYtS0IYQQJ0ZJnhBCnBgleUIIcWKU5AkhxIlRkieEECdGSZ4QQpzY/wOlwX3iaKk7zAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# show_final_avg_density(result_full)\n", + "plot_avg_density_2D(get_avg_density(result_full), register)" + ] + }, + { + "cell_type": "markdown", + "id": "0f8623ff", + "metadata": {}, + "source": [ + "## Run AHS program in the blockade subspace\n", + "\n", + "The above simulation is performed using the *full* Hamiltonian with size $2^{9}\\times 2^{9}$. However, because of Rydberg blockade, if neighboring atoms are within each other's Rydberg blockade radius $R_b$, they are very unlikely to be excited to the Rydberg states simultaneously. Given that (see [this notebook](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb))\n", + "\\begin{align}\n", + "R_b = \\left[\\frac{C_6}{\\sqrt{\\Delta^2+\\Omega^2}}\\right]^{1/6},\n", + "\\end{align}\n", + "\n", + "we have 6.752 $\\mu m$ < $R_b$ < 6.796 $\\mu m$ throughout the program, which is always larger than $6.7~ \\mu m$, the distances between neighboring atoms. Hence we can approximate the full Hamiltonian of the system with a smaller *effective* Hamiltonian. We can take advantage of this fact to speed up the simulation by setting the parameter `blockade_radius` as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "c92cd79b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The elapsed time = 0.3601689338684082 seconds\n" + ] + } + ], + "source": [ + "start_time = time.time()\n", + "result_blockade = device.run(ahs_program, shots=1000, blockade_radius=6.796e-6, steps=100).result()\n", + "print(f\"The elapsed time = {time.time()-start_time} seconds\")" + ] + }, + { + "cell_type": "markdown", + "id": "b6ce420c", + "metadata": {}, + "source": [ + "Indeed, the runtime for the simulation with the effective Hamiltonian is one magnitude less than the one with the original Hamiltonian. We can visually confirm that the checkerboard phase is created successfully using the Rydberg blockade approximation. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4152af92", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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HDhyI9u3bN3gsKysLU6ZMAQBMmTIFP/zwg71enhBCrCIScbxursahffJXr15FQEAAACAgIADXrl1z5MsTQohxLtoVw4cgL7xaWpSfENKyZWRkICMjA4A+XzQXB7hkK50Phyb5e+65B5cvX0ZAQAAuX74Mf39/o+UsLcpPCGnZ6jf86jcIm8NdW/IOXU8+OTkZK1euBACsXLkSo0aNcuTLE0KISXTh1Urjx49Hv379cO7cOSgUCixbtgyvvvoqduzYgW7dumHHjh149dVX7fXyhBDCH8/hky6Y4+3XXbN27Vqjj9/ZDYUQQoSCA2e3jbSdTZAXXgkhxNFcsZXOByV5QgiB+y5rQEmeEEJctL+dD/fshCKEECvo164R5uiaU6dONet4SvKEEALhjq6ZMWMG7r33Xnz++eeoqKiw+nhK8oQQAuGuXbN3716sXr0aRUVFiI+Px4QJE7Bjxw7ex1OfPCGECHw9+W7duuH9999HfHw8nnvuORw7dgyMMXzwwQcYPXq02WOpJU8IafGEvJ78yZMnMXv2bISHhyMnJwc//vgjzpw5g5ycHMyePdvi8dSSJ4QQCHfJgmeffRZPP/00PvjgA3h6ehoeDwwMxPvvv2/xeGrJE0IIhNuSHz16NCZPntwgwS9ZsgQAMHnyZIvHU5InhBBOuBdeV61a1eixFStW8D6eumsIIS3enXHyQrJ27VqsWbMGBQUFSE5ONjxeWVkJX19f3vVQkieEEAgvyffv3x8BAQEoKyvDiy++aHjcx8cH0dHRvOuhJE8IIRDesgadO3dG586dsX///mbVQ0meEEIgvJb8gAEDsHfvXvj4+DSIjTEGjuNw69YtXvVQkieEEAEuULZ3714A+j745qDRNYSQFk+/aYgwR9fk5+dDqVQCAHbv3o1PP/3UqjVsKMkTQggAEcfxujnamDFjIBaL8eeffyI1NRUFBQWYMGEC7+MpyRNCCGw7GSo7Oxs9evRAWFgYFixYYLTM7t27ERMTg4iICDzwwAMm6xKJRJBIJNi4cSNeeOEFLF68GJcvX+Z9XtQnTwhp8TgbLlCm1Woxa9Ys7NixAwqFAgkJCUhOTkavXr0MZSoqKvDMM88gOzsbwcHBuHbtmsn6pFIp1q5di5UrV+LHH38EAKjVat7xUEueEEIAiDh+N0sOHTqEsLAwhIaGQiaTISUlBVlZWQ3KrFmzBqNHj0ZwcDAAwN/f32R9y5cvx/79+zF37lx06dIFBQUFmDRpEv/z4l3ShhYvXoyIiAhERkZi/PjxqKurc0YYhBBiYKsLryUlJejUqZPhvkKhQElJSYMy58+fR3l5OQYNGoS4uDijSxfc0atXL3z66acYP348AKBLly549dVX+Z8X75I2UlJSgk8//RS5ubk4deoUtFotMjMzHR0GIYQYcNCPsOHzr7S0FPHx8YZbRkZGg7oYY43rv6srSKPR4MiRI9iyZQu2b9+O9957D+fPnzca2759+5CUlITu3bsjNDQUXbp0QWhoKO9zc0qfvEajQW1tLaRSKWpqahAYGOiMMAghxIDv6Eg/Pz/k5uaafF6hUKCoqMhwv7i4uFGOUygU6NChA7y9veHt7Y2BAwfixIkT6N69e6P6UlNTsXjxYsTFxUEsFvMLsh6Ht+SDgoLw0ksvITg4GAEBAWjTpg2GDBnSoIylT0pCSMuWkZFhyA+lpaXNr5DnJt58Ls4mJCQgLy8PBQUFUKlUyMzMbLDAGACMGjUKv/76KzQaDWpqanDw4EGEh4cbra9NmzZ45JFH4O/vD19fX8ONL4e35MvLy5GVlYWCggK0bdsWjz/+OL755psGFxIsfVISQlq2tLQ0pKWlAQDi4+NtUqethsBLJBIsXboUQ4cOhVarxbRp0xAREYH09HQA+o25w8PDMWzYMERHR0MkEmH69OmIjIw0Wt+DDz6IOXPmYPTo0ZDL5YbHY2Nj+cXT/FOyzs8//4wuXbrAz88PgH5B/N9++82qq8WEEGJLHGDTiU7Dhw/H8OHDGzw2Y8aMBvfnzJmDOXPmWKzr4MGDANCg4ctxHHJycnjF4vAkHxwcjAMHDqCmpgaenp7YuXOnzT6JCSGkqZyxZAEfu3btatbxJpP8jRs3LB4sEonQtm1bq16wb9++GDt2LGJjYyGRSNCnTx/D1y5CCHEGZ23tx8fVq1fx+uuv46+//sK2bdtw+vRp7N+/H6mpqbyON5nkAwMDERgYaHQ40B1arRaXLl2yOuh33nkH77zzjtXHEUKIvThjXRo+pk6diqeeegrz5s0DAHTv3h1PPPFE85N8eHg4jh07ZvbgPn36WBEqIYQIlzBTPFBWVoZx48Zh/vz5APQXdq0ZSmkyyfPZjaS5O5YQQohQCG3TkDu8vb1x/fp1Q3wHDhxAmzZteB9vMsl7eHgY/l9eXo6ioiJoNBrDY7GxsQ3KEEKIq9KPrnF2FMZ98sknSE5ORn5+Pu677z6UlpZi3bp1vI+3OLrmzTffxIoVK9C1a1fDJ4k1w3cIIUTwOOdsCMJHbGwsfvnlF5w7dw6MMfTo0QNSqZT38RaT/HfffYf8/HzIZLJmBWprjDFodIBWx8Dw9zhXqVi4X7uI9W7cqsX6X86g4K8K3KpRwq+NF6K6+mNE/+6QSa2f4k2ESatj0GgB3e2BHhzHQSICxCLHvZ+FmDeuX7+ONWvW4OzZswD010oDAwPRvn173nVYTPKRkZGoqKgwuxSmI+kYg0rDoNIae5ahTgNIRAxyCQexQD+ZiWXH867gk28PYNPecxCLONQo/+4qbOUpg1i0FU8nx2Lmo/EI7ODjxEhJU91pqCnVDNpGg/gYlNAPa5SLGWQSfksKNJUQu2vOnDmDwYMHY+jQoejTpw8YYzh8+DA++OAD5OTkoGfPnrzqsZjkX3vtNfTp0weRkZENptRu2rSp6dE3kUbHUKMyPaTz73KARsUgFzPIpbRkvqv5z3cH8O6KPVCqtdDpGv++q2pVAIDP1h3C/8s6gg3zxmFAdLCjwyTNwJj+vazRWSoH1GkAlZbBW27fYY5Ca8m/+eabWLJkCcaNG9fg8fXr12Pu3LlYv349r3osJvkpU6bglVdeQVRUFEQi5yVMvgm+PqUWAHSU6F3Ih2v2YcE3v6G2XsvdFKVaC6Vai1GvZuLHRePRP7KTxWOI8zHGUK1i0FpI8PXpGFBVx9DKw36JXlgpHvj999+NXmAdM2YMXn/9dd71WEzyHTp0wHPPPWdddDamY9Yn+DuUWkAsYpCIhfYrJHfbcfgC5n+zj1eCr69GqcFjr32L31fNhH87bztFR2ylTm1dgr+DAahWMrSS277VzXEQXPeut7fpv2Vzz93NYpKPi4vDa6+9huTk5CatgGYLKo3pBP/YyGE4cfwYZs56DnNenWu0TJ2GoRUlecF7Z/kvZhO8rqYMqoNLIOuTClHbkAbPqTQ6fLn5GF6fPMDOUZLmYMzU9TTg7JnTePGFZwEAKqUSf/55HgXFDZcR1jFAqwMkdrjmLrTummvXruGTTz5p9DhjzKrllS0m+TuzXg8cOGB4zJFDKBljUJv4owCApf/7Ert3/Yy/7tpeqz79HwYT3Cc1+dvZi2X4o8D8H66mYBdEbbsYfa5OpcF/NxzGKxP6Qyym7jmhMtdg6xneC1u26/PKxvXfYc9u4wtzKTX2+WYusByPp59+GpWVlUafmz59Ou96LCZ5YyugFRQU8H6B5tLo9F/TTAlSKHjVo9IyeFKSF6z0H3KhMfMdXnerCJy8FZiZd6JKrcVPhy/gkcQwe4RIbEBppsFW37drV+P5fxtfhlej03fh2rJvngMnuLVr3n77bZvUYzHJv/vuuw3ua7VarFq1ymGJ3sjgiqbV04Q+QOI4R89fMZvkNYW7IQ0fA3XeVpNl6lQanLlYRkleoBhjMLPeocGN69eRd/4cEvvdZ7KMjtl4yKOAV6FsLotJvn4Hv1qtxp49exoN6bEnc6tgWlWPTWoh9nKrRmnyOW3ZWYh8gsBJvczWodHqcLOqztahEQfbsO47PPrYWPN95HZ4QwutT95WLCb5F198scH9l19+GQkJCXYL6G76HzylaHfn7WF6mjarugxdeQFUN1dAV3UF6poyyCKeAOfZrkE5sYhDKy9hzcwm1vv+2zX49HML+zrbOB9zAMQtNcnfrby8HB07drRHLEZZ+kr2r2fScOjAfiiVShw7kos1329sUj3EuXp08sXxvKuGae31SUIeBEIeBACoTq+DJDC+UYIHAE+5FCEd29o7VNJEHMeBAzPbZCssuAClUokePY1van2HPd7PQs0RxkbYtGnTBnFxcYiJibF4vMUkHxUVZfgawxhDYWEhfH19DY+fPHnS+qitILEwUOIzS5/4t8klAv0NEgDAPx+Nx6Z951FdpzZbTtZrrMnnGGMYeV93W4dGbEgmAcxNgwjpEord+w6ZrUMsss+EKKEm+dzcXOTm5mLkyJEAgC1btiAhIQHp6el4/PHH8fLLL5s93mKS37x5s20ibSKO4yAVmx9GaYmIE+4vkOjdGx6Ijr6tkF9S3qTjpRIRpjzSGx4yh29bTKwgk3BQmhlGyYc9Gmz67f+EmSSuX7+Oo0ePolWrVgD0O+uNHTsWe/bsQVxcXPOTfOfOnW0TaTPIxRzUjVcw4s3eixuR5uM4Dq9NGoDnlmSjxkJr3hiJWIRZox13rYg0jYjjIBHrV5xsCg6Wv903lVAbgpcuXWqwCrBUKsXFixfh6enZYIKqKSaTfGxsLI4ePWr2YD5lbEEk4uAh0a8waS2JCKCla1zDhKRI7DpagI17zjZYddIST7kE6S/9A6GBjfvpifB4STlU6ViThkd7y+3XYBNqO3DChAlITEzEqFGjAAA//vgjxo8fj+rqavTq1cvi8SaT/JkzZxAdHW3yQMYYbt682YSQgYqKCkyfPh2nTp0Cx3H46quv0K9fP7PHyCQiADqrEr1UBHhIqRXvKjiOQ/qcERCJOKz/5azFFj3HAR4yCZY8PwzjBkc4KErSXBzHwVuuX4fGmkTfSm6/5cM5ABIB5gnGGKZOnYrhw4dj7969YIwhPT0d8fHxAIDVq1dbrMNkkr+zSL051mwmW9/zzz+PYcOGYd26dVCpVKipqeF1nEwigljEoNSYX6JUxOn77SQO3HCA2IZELML/mzMCSQldseCbfSi4XA6VWgttvWzgIRODMeDBPiGYO+V+xPcMdGLEpClEHIdWcv0SBSqN+UHSMjEgl9p/RqoQUwXHcXj00Udx5MgRxMXFNakOk0neXn3xt27dwp49e7BixQoAgEwms2rXKbGIg5eMM2weor297AEHQCQCZGLaLMTVcRyHxx/shccf7IXjeVfw5eZj+LP4Bmrq1GjbygMJ4YFIHdGHNgtxcRzHwUPKQS7RN9pU2tszYpk+4UrFjtvpjeOEt6zBHYmJiTh8+HCT5yc5fCjChQsX4Ofnh6eeegonTpxAXFwclixZYtXSmYC+JeAhFeYvhdhOTLeOWDr7EWeHQeyIu71tp9TJK8UKNMdj165dSE9PR0hICLy9vcEYs2r4usOTvEajwdGjR/HZZ5+hb9++eP7557FgwQK89957hjKlpaWGPicASEtLQ1pamqNDJYQIVEZGBjIy9HNkrFl21xyhdgBs27atWcdbHHeydOlSlJc3beyyMQqFAgqFAn379gUAjB07ttEIHT8/P8MEgNzcXErwhJAG0tLSDPnBz8+v2fVx0HcF87k5WufOnVFUVIScnBx07twZXl5e0Fmx4qLFJH/lyhUkJCRg3LhxyM7ObvaCYR07dkSnTp1w7tw5AMDOnTt5DQMihBC74f6eNGnp5mjvvPMOFi5ciPnz5wPQLxQ5adIk3sdbTPLvv/8+8vLykJqaihUrVqBbt254/fXXkZ+f3+SgP/vsM0ycOBHR0dE4fvy4VfsVEkKIPXA8/znaxo0bsWnTJsN1y8DAQJObiRjDq0+e4zh07NgRHTt2hEQiQXl5OcaOHYukpCQsWrTI6qBjYmKQm5tr9XGEEGIPHITbJy+TyfSLu92+MlxdXW3V8RZb8p9++qlhfYT77rsPv//+O/73v//hyJEjWL9+fdOiJoQQgRFqd824cePwz3/+ExUVFfjiiy/w8MMP4+mnn+Z9vMWWfFlZGTZs2NBo3LxIJHL64mWEEGIrQp04+dJLL2HHjh1o3bo1zp8/j3fffRdJSUm8j7d6+7/6wsPNr/lMCCGugOP0SxgLVVRUFGpra8FxHKKioqw6VsCnRQghjiO6PevV0o2P7Oxs9OjRA2FhYViwYIHJcocPH4ZYLMa6detMlvnyyy9x7733YsOGDVi3bh0SExPx1Vdf8T4vWnybENLi2fLCq1arxaxZs7Bjxw4oFAokJCQgOTm50VBxrVaLV155BUOHDjVb34cffohjx47B19cXgH59+f79+2PatGm84qGWPCGE4M7GIZZvlhw6dAhhYWEIDQ2FTCZDSkoKsrKyGpX77LPPMGbMGPj7+5utT6FQwMfn73WafHx80KlTJ97nRS15QggBBxHPMfCWll0pKSlpkIQVCgUOHjzYoI6SkhJs3LgROTk5OHz4sNHXubO3a1BQEPr27YtRo0aB4zhkZWXh3nvv5X1mlOQJIS0eB/4LlN1ZdsUUY6sC3D1y54UXXsDChQvNLtd+Z8JT165d0bVrV8PjdzYP4YuSPCGEcIDERp3yCoUCRUVFhvvFxcUIDGy450Fubi5SUlIA6Iepb926FRKJBI8++qihzNtvv22TeCjJE0JaPGta8pYkJCQgLy8PBQUFCAoKQmZmJtasWdOgTEFBgeH/U6dOxYgRIxokeAAYOXKk2bH7mzZt4hUPJXlCCAFstmmIRCLB0qVLMXToUGi1WkybNg0RERFIT08HAMyYMYNXPS+99BIAYMOGDbhy5YphUbK1a9ciJCSEfzzWhU8IIe7JlhNehw8fjuHDhzd4zFRyv7NL3t0eeOABAMCbb76JPXv2GB4fOXIkBg4cyDsWGkJJCGnxOOiTIZ+bo5WWluLChQuG+wUFBVZtlEIteUII4WzXXWNrixcvxqBBgxAaGgoAKCwsNOyKxQcleUJIi6ef8SrMJD9s2DDk5eXh7NmzAICePXtCLpfzPp66awghBLdH2PC4OVp8fDyWLVuG4OBg9O7d26oED1CSJ4QQALZb1sDWMjMzUVJSgoSEBKSkpGD79u1WbcNKSZ4QQsAZdl+ydHO0sLAwzJs3D+fPn8eECRMwbdo0BAcH4+2338aNGzcsHk9JnhDS4gl5dA0AnDx5Ei+++CLmzJmDMWPGYN26dWjdujUGDx5s8Vi68EoIIRDuhde4uDi0bdsWqampWLBggaFPvm/fvti3b5/F4ynJE0IIJ9zt/77//nvD8ElAvw59ZmYmJk6ciA0bNlg83mndNVqtFn369MGIESOcFQIhhAAQZnfNrVu3MH/+fHzyySfYsWMHGGP47LPPEBoaiu+++453PU5ryS9ZsgTh4eG4deuWs0IghBADobXkJ0+ejHbt2qFfv3744osvsGjRIqhUKmRlZSEmJoZ3PU5J8sXFxdiyZQvmzp1rWBifEEKcSVgpHrhw4QJ+//13AMD06dPRoUMHXLp0qcEuUXw4pbvmhRdewKJFiyASGX/5Ozuv3LlZM4WXEOL+MjIyDPnBmnVczBHaOHmpVGr4v1gsRpcuXaxO8IATWvKbN2+Gv78/4uLisHv3bqNlLO28Qghp2epvuVd/K76m4gCIBdZdc+LECbRu3RqAfrep2tpatG7dGowxcBzHu6vb4Ul+37592LRpE7Zu3Yq6ujrcunULkyZNwjfffOPoUAgh5DYOnMA6bLRarU3qcXh3zfz581FcXIzCwkJkZmZi8ODBlOAJIU4ntO4aW6Fx8oSQFk8/hNIFMzgPTk3ygwYNwqBBg5wZAiGE3J4M5ewg7INa8oQQAuEua9BclOQJIS2eftMQZ0dhH5TkCSEEENzoGluhJE8IIaA+eUIIcWvUkieEEDdFffKEEOLOOI5G1xBCiDtzzxRPSZ4QQm5317hnmqckTwghoJY8IYS4NzfN8pTkCSEE1F1DCCFuzT1TPCV5QgjRc9MsT0meENLicaAZr4QQ4r7ceD15h2//RwghQsTxvPGRnZ2NHj16ICwsDAsWLGj0/OrVqxEdHY3o6Gj0798fJ06csMk5GEMteUIIAQfORk15rVaLWbNmYceOHVAoFEhISEBycjJ69eplKNOlSxf88ssvaNeuHbZt24a0tDQcPHjQJq9/N2rJE0IIbLeR96FDhxAWFobQ0FDIZDKkpKQgKyurQZn+/fujXbt2AIDExEQUFxfb45QAUJInhBDeXTV82volJSXo1KmT4b5CoUBJSYnJ8suWLcMjjzzS5NgtcXiSLyoqwoMPPojw8HBERERgyZIljg6BEEIa45nlS0tLER8fb7hlZGQ0qIYx1rhqE18Bdu3ahWXLlmHhwoW2PJMGHN4nL5FI8PHHHyM2NhaVlZWIi4tDUlJSg/4qQghxNL5DKP38/JCbm2vyeYVCgaKiIsP94uJiBAYGNip38uRJTJ8+Hdu2bYOvr6/1AfPk8JZ8QEAAYmNjAQA+Pj4IDw83+1WGEEIcwVZ98gkJCcjLy0NBQQFUKhUyMzORnJzcoMylS5cwevRofP311+jevbudzkjPqaNrCgsLcezYMfTt29eZYRBCWjobjpOXSCRYunQphg4dCq1Wi2nTpiEiIgLp6ekAgBkzZuDdd9/F9evX8cwzzxiOMfftoDk4ZqwDyQGqqqrwwAMPYO7cuRg9enSD5zp37gw/Pz/D/bS0NKSlpTk6REKIQGVkZBj6wktLS3Hx4sVm1RfROxbfbf2VV9kpox6wW0K2B6e05NVqNcaMGYOJEyc2SvCA5T4vQkjLVr/hFx8f3+z6OLjvjFeHJ3nGGFJTUxEeHo5///vfjn55Qggxyk1zvOMvvO7btw9ff/01cnJyEBMTg5iYGGzdutXRYRBCSEO2XNdAQBzekh8wYIDRcaSEEOJMtGkIIYS4MfdM8ZTkCSFEz02zPCV5QkiLR5uGEEKIO3PjTUMoyRNCCNy2t4aSPCGE2HLTEKGhJE8IIaDuGkIIcVsuOs+JF0ryhBACuG2WpyRPCCGgIZSEEOLWqE+eEELcFQeIKMkTQog7c88sT0meENLi0aYhhBDi5tw0x7tuki8pvYVlPxzCwT+KcLNKCS8PKboHd8DTj92L3t0CnB0esRGtjkGtZdDpAAb9G1EsAqQSzm3X/25ptFodth/IwzfZx3ClrBJarQ6+bbzwjwE9kTKkN7w9ZQ6Jw13/nFwuyR/6owjvf5WDPccKAcagVGsNz/128iLWbj+BkMB2eGXKA3j8oSi3narszhhj0OgApYbB2P4yWi2g0jKIOQa5lIPYXa+YubmaOhU++/Y3LP1uP+rUGlTVqBo8v+d4IV7+bBsmDI3BK1MegMK/jV3jcddc4VJJfuXmI5i9eAtqlWqjz2t1DDVKNU4XXMPMBT/g50N/4vOXR0EiETs4UtJUjDHUqfVJ3hItA2pUDHIJg0zi8J0sSTOUlldj2PNf4ULxDdSpNEbLVNfqk/6KzUewPucUtvxnKvr0CLRbTO6Z4p2wx2tTrd1+3GyCv1tNnRrrd57CzIVZtN2gi7Amwden1AAqaw8iTlNZo8TgZ75A3qUykwm+Po1Wh/LKWgz51zKcLbxml5g4jv/N1bhEks8vvo5ZizbxTvB31CjV2LDrFNZuP2GnyIgtqbXWJ/g7lBpAp6MPc1cwc8EPKLpaAbWVv+zqWjVGzF4JrdY+H+gcz3+uxiWS/NLv9kOj1Rp9TnP1BJQnV0B5cgV0VZcbPV9Tp8b8FbupNS9wjDGYatTdunULDw8agOFDBmPQgETs3rXTaDmVln7HQnetvAqb956FUmX8/ayrugzVH6uh+v1rqAsb/p4ZY7hZVYcdh/60T3Acz5uLcUqSz87ORo8ePRAWFoYFCxaYLVtTp8KqrUeNfuozTS20lw9DFjkZ0u6joL6w3Wgdf5XdQu6ZEpvETuxDx/SjZ4xp1aoVsn/eja0/5WD512vw9huvGy2n1oI+zAXuyx8Om+zyYDotNIU5kPYYC1nUZEhDHmpUpqpWhU9W/2qX2Nw0xzs+yWu1WsyaNQvbtm3D6dOnsXbtWpw+fdpk+U17zkBkYvSErvIviFp3AicSQ+TRDtCpwXSNm4N1Sg3S1x+w2TkQ21NpTCdnkUgEiUQ/RqDy1i1ERkWZLEtd88KWsfEQ6pTGv7KxymJALIP6/A9QnfoaupuXjJY7dLoYl8sqbRyZfkgun5urcXiSP3ToEMLCwhAaGgqZTIaUlBRkZWWZLH/xcjlq6kz0xWtqAYnH3/fFcv1jd9Exhryi680NndiRpe70v0pKMGTwQDw6chhGJD/a5HqI8zDGcK282vTzqkqw6quQdn8U0m6joM7fYvSbmVwqRtHVCpvGdmfGqzteeHX4EMqSkhJ06tTJcF+hUODgwYMNypSWliI+Ph4AcEXSHTpJV+OVSTwBjfLv+1ql/jEj7h6DS4TFUm4ODArCTzl7cPFiIf4xZDAeGT7CeD3szpQpIjRKlQYcB6NzHwAAEk9wrRXgJHJAIte/l9U1gMy7UdHv1m3EM1NWAdDnC2Kaw1vyxj6Z756E4Ofnh9zcXOTm5uL5WTNMTnYR+QRCd6sITKcFU94ERFJwIuOfW61byZsfPLEbc2lZqfz7g9zHpzVa+fiYLOuKX6dbCrlMYvb3LPIJAqu9AcZ0YBqlPsFLjTfaxj8xxpAj/Pz8bBIfteRtRKFQoKioyHC/uLgYgYGmJzj06uIPTw+p0ZY4J/GEOCAOqlNfAwCkXYYYrUMqESHWjpMoSPOJRYDO+IALnP7jFF57+UWIxWKo1Wos+PATk/XQ5Ffh4jgOnQPa4ULJDePPSzwgCYiH6vdVANNBEjIYHNe4HapSa9ElsJ3t43PTb4AOT/IJCQnIy8tDQUEBgoKCkJmZiTVr1pgsPzSxG2RmZqxK7omB5J4Ys68pFokwc0xiU0MmDiATc1CbGALZJzYO2T/v5lWP2CUGBbdcz6fch9c/z0Z1rfHrbGL/aIj9o00eL+I4DOvfHe1be9k2MBdtpfPh8LeERCLB0qVLMXToUISHh2PcuHGIiIgwU16MZx5PhIes6Z9H0d06oltwhyYfT+xPJOKa3QqXid13/RF3MX5ob+iaMQLKUy7BCykDbBfQbe584dUp7Z7hw4fj/PnzyM/Px9y5cy2Wnz7qXkilTVt/xlMuxVvTG4+3JcIjlzTvHSRt5vHE/ny85Eh7LAFeHlKrj5VKROje2Q/3RijsEBnNeHWqe9q3wsZFk+Ept+4Pw8tDitefGoSHEsLsExixKYmYg6yJa8l5ylxzDHNL9P6MIegb0Qmecv7fziViEXzbeCProyft9m2NWvJOdl/vztj0yZPw8ZJBbqFVLxZx8JRL8X9pD+OlSQMdFGFDGRkZTnldU4QWD2A8JrlUZHWi95RxkNjgiqvQfkZCiwewTUwSiRgbP5yMh+/txmuteC8PKboEtsNvy2bCr13D4ZS2/BnZcsarpVn9jDE899xzCAsLQ3R0NI4ePWqTczDGZZI8AAzoHYLja57H8yn3oU0rD7TyavgH4uUhhYdMgscfjsKu9Kfxr3H9nRSp8N6gQosHMB2TXCqCl4yDpdWDpWLAW26bBG8uHmcRWjyA7WKSyyTInJeCFW+PRf/oYHjIJJDVa7yJRBy8byf3Rf96BAeWP4OADo2Hztr0Z2SjLM9nVv+2bduQl5eHvLw8ZGRkYObMmbY7j7u41HryABDYoTXe+WcS3kgdjB9/PYNT+VdQVlGDjesy8fazszFmcCTatTY+tpa4DrGIg6eMA2MMaq1+1nL95yQiusjq6kQiEUYMCMeIAeHIL76OrD1ncPV6JdQaLfzbtcIDcaFIjOzkkN8zB9vNsag/qx+AYVZ/r169DGWysrLw5JP6rqfExERUVFTg8uXLCAiw/a52gkzyhYWFhhmvfIlKS5H+/nmkv2+noKxUf9auEAgtHkB4MVE8ljkypnU8ypSWlqK62vRSCXz5+XXAgER+51VbW9vgZ5CWloa0tDTDfT6z+o2VKSkpaTlJvqyszNkhEEJakOzsbJvVxWdWP58ytuJSffKEECJ0fGb1WzvzvzkoyRNCiA3Vn9WvUqmQmZmJ5OTkBmWSk5OxatUqMMZw4MABtGnTxi5dNYAbJHlrNiBxhKKiIjz44IMIDw9HREQElixZ4uyQAOiv+Pfp0wcjRhhfvdGRKioqMHbsWPTs2RPh4eHYv3+/U+NZvHgxIiIiEBkZifHjx6Ours7hMUybNg3+/v6IjIw0PHbjxg0kJSWhW7duSEpKQnl5uVPjmTNnDnr27Ino6Gg89thjqKiocFg8pmK646OPPgLHcYLo6jU1qz89PR3p6ekA9BNCQ0NDERYWhqeffhqff/65/QJiLkyj0bDQ0FCWn5/PlEoli46OZn/88YdTY/rrr7/YkSNHGGOM3bp1i3Xr1s3pMTHG2Mcff8zGjx/P/vGPfzg7FPbkk0+yL774gjHGmFKpZOXl5U6Lpbi4mIWEhLCamhrGGGOPP/44W758ucPj+OWXX9iRI0dYRESE4bE5c+aw+fPnM8YYmz9/Pnv55ZedGs/27duZWq1mjDH28ssvOzQeUzExxtilS5fYkCFDWHBwMCstLXVoTK7ApVvy1m5A4ggBAQGIjY0FAPj4+CA8PBwlJc7derC4uBhbtmzB9OnTnRoHoN+vdc+ePUhNTQUAyGQytG3b1qkxaTQa1NbWQqPRoKamxm59o+YMHDgQ7du3b/BYVlYWpkyZAgCYMmUKfvjhB6fGM2TIEMMOXYmJiSguLnZYPKZiAoDZs2dj0aJFNKTWBJdO8qaGIQlFYWEhjh07hr59+zo1jhdeeAGLFi2CSOT8X/eFCxfg5+eHp556Cn369MH06dNtMgSuqYKCgvDSSy8hODgYAQEBaNOmDYYMMb5ktaNdvXrV0E8bEBCAa9euOTmiv3311Vd45JFHnB0GNm3ahKCgIPTu3dvZoQiW89/1zcAcOAzJWlVVVRgzZgz+85//oHXr1k6LY/PmzfD390dcXJzTYqhPo9Hg6NGjmDlzJo4dOwZvb2+nXkspLy9HVlYWCgoK8Ndff6G6uhrffPON0+JxBfPmzYNEIsHEiROdGkdNTQ3mzZuHd99916lxCJ1LJ3lHDkOyhlqtxpgxYzBx4kSMHj3aqbHs27cPmzZtQkhICFJSUpCTk4NJkyY5LR6FQgGFQmH4djN27Fi7rtthyc8//4wuXbrAz88PUqkUo0ePxm+//ea0eOq75557cPnyZQDA5cuX4e/v7+SIgJUrV2Lz5s1YvXq10xtU+fn5KCgoQO/evRESEoLi4mLExsbiypUrTo1LaFw6yfMZquRojDGkpqYiPDwc//73v50aCwDMnz8fxcXFKCwsRGZmJgYPHuzUlmrHjh3RqVMnnDt3DgCwc+fOBtO9HS04OBgHDhxATU0NGGPYuXMnwsPDnRZPfcnJyVi5ciUAfXIdNWqUU+PJzs7GwoULsWnTJnh52XjTjiaIiorCtWvXUFhYiMLCQigUChw9ehQdO3Z0dmjC4uQLv822ZcsW1q1bNxYaGsref/99Z4fDfv31VwaARUVFsd69e7PevXuzLVu2ODssxhhju3btEsTommPHjrG4uDgWFRXFRo0axW7cuOHUeN566y3Wo0cPFhERwSZNmsTq6uocHkNKSgrr2LEjk0gkLCgoiH355ZesrKyMDR48mIWFhbHBgwez69evOzWerl27MoVCYfi7/uc//+mweEzFVF/nzp1pdI0RHGMm904nhBDi4ly6u4YQQoh5lOQJIcSNUZInhBA3RkmeEELcGCV5QghxY5TkiaAUFhbC09MTMTExNqmvtrYWMTExkMlkglihkBBHoyRPBKdr1644fvy4Tery9PTE8ePHBTETmhBnoCRPHObw4cOIjo5GXV0dqqurERERgVOnTpk9prCwsMH64R999BH+7//+DwAwaNAgzJ49GwMHDkR4eDgOHz6M0aNHo1u3bnjjjTfseSqEuAxB7vFK3FNCQgKSk5PxxhtvoLa2FpMmTTK6AYQ1ZDIZ9uzZgyVLlmDUqFE4cuQI2rdvj65du2L27Nnw9fW1UfSEuCZK8sSh3nrrLSQkJMDDwwOffvpps+u7s1ZRVFQUIiIiDEvzhoaGoqioiJI8afGou4Y41I0bN1BVVYXKykre2+zVX3lDrVY3eE4ulwMARCKR4f937ms0GhtETIhroyRPHCotLQ3vvfceJk6ciFdeeYXXMRcvXkRpaSl0Oh327NkDrVZr5ygJcR+U5InDrFq1ChKJBBMmTMCrr76Kw4cPIycnx+Jxvr6+ePLJJxEXF4fIyEisWrUK+fn5DoiYENdHq1ASQSksLMSIESMMo27uvt9UISEhyM3NRYcOHWwRJiEug1ryRFDEYjFu3rxp88lQarVaEHvcEuJo1JInhBA3Rk0bQghxY5TkCSHEjVGSJ4QQN0ZJnhBC3BgleUIIcWOU5AkhxI39f8s4oUI7bUO3AAAAAElFTkSuQmCC\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_avg_density_2D(get_avg_density(result_blockade), register)" + ] + }, + { + "cell_type": "markdown", + "id": "4f058f7d", + "metadata": {}, + "source": [ + "In order to quantify the difference in the final average Rydberg densities from the two simulations, we can calculate the root-mean-square difference (RMS) defined as \n", + "\\begin{align}\n", + "\\text{RMS} = \\sqrt{\\frac{1}{N}\\sum_{i=1}^N(\\bar{n}_i^\\text{full}-\\bar{n}_i^\\text{blockade})^2}.\n", + "\\end{align}\n", + "Here $\\bar{n}_i^\\text{full}$ and $\\bar{n}_i^\\text{blockade}$ are the final Rydberg density at the $i$-th site for the simulation with the full Hamiltonian and the effective Hamiltonian respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "cf902009", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The RMS_blockade for the final Rydberg densities = 0.016931233465600392\n" + ] + } + ], + "source": [ + "n_full = get_avg_density(result_full)\n", + "n_blockade = get_avg_density(result_blockade)\n", + "\n", + "RMS_blockade = np.sqrt(np.mean((np.array(n_full)-np.array(n_blockade))**2))\n", + "print(f\"The RMS_blockade for the final Rydberg densities = {RMS_blockade}\")" + ] + }, + { + "cell_type": "markdown", + "id": "b5663c2d", + "metadata": {}, + "source": [ + "Since the RMS is only around 1%, we are assured that the simulation with the effective Hamiltonian of smaller size gives quantitatively the same results as the one with the full Hamiltonian." + ] + }, + { + "cell_type": "markdown", + "id": "1a7270af", + "metadata": {}, + "source": [ + "## Tuning other parameters in the local simulator\n", + "\n", + "Another way to speed up the simulation, without using the blockade approximation, is to adjust other parameters of the local simulator, such as `steps`, the number of time points in the simulation. Previously, we have set `steps=100`, but it can be adjusted to be `40` as shown below. We expect that the less time point used in the simulation, the faster it will finish." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "49b3b95a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The elapsed time = 2.462913990020752 seconds\n" + ] + } + ], + "source": [ + "start_time = time.time()\n", + "result_reduced_nsteps = device.run(ahs_program, shots=1000, steps=40).result()\n", + "print(f\"The elapsed time = {time.time()-start_time} seconds\")" + ] + }, + { + "cell_type": "markdown", + "id": "61267635", + "metadata": {}, + "source": [ + "This indeed speed up the simulation as expected. We can confirm that the simulation produces result that is close to our expectation. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "32ad6d32", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_avg_density_2D(get_avg_density(result_reduced_nsteps), register)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "4861e840", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The RMS_reduced_nsteps for the final Rydberg densities = 0.07180219742846002\n" + ] + } + ], + "source": [ + "n_reduced_nsteps = get_avg_density(result_reduced_nsteps)\n", + "\n", + "RMS_reduced_nsteps = np.sqrt(np.mean((np.array(n_full)-np.array(n_reduced_nsteps))**2))\n", + "print(f\"The RMS_reduced_nsteps for the final Rydberg densities = {RMS_reduced_nsteps}\")" + ] + }, + { + "cell_type": "markdown", + "id": "ff29f595", + "metadata": {}, + "source": [ + "We note that if the Hamiltonian is almost constant throughout the AHS program, simulation with smaller `steps`, such as `80` or `50`, is likely sufficient to give qualitatively good result, as demonstrated here. On the other hand, if the Hamiltonian is varying drastically throughout the program, one may need to have higher `steps` around 200 or more.\n", + "\n", + "We see that although the runtime is reduced compared to the simulation with default parameters, it is still much longer than the simulation performed with the effective Hamiltonian that uses blockade approximation. The reason is that the local simulator will need to construct Hamiltonian used for the simulation, and this takes majority part of the runtime. \n", + "\n", + "We also note that when the dimension of the Hamiltonian is larger than $2^{10}\\times2^{10}$, the AHS local simulator use `scipy.integrate.ode` as the backend solver and support the following arguments: atol, rtol, solver_method, order, nsteps, first_step, max_step and min_step. For more information, please refer to the following documentation page. \n", + "\n", + "When the dimension of the Hamiltonian is less than or equal to $2^{10}\\times2^{10}$, we use a solver based on the implicit Runge-Kutta method written in `numpy`, which is more efficient than the `scipy.integrate.ode` solver in this case. The solver based on `numpy` does not support the arguments listed above." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e1b6a24", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, 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import DrivingField +from braket.ahs.shifting_field import ShiftingField +from braket.ahs.field import Field +from braket.ahs.pattern import Pattern +from collections import Counter + +from typing import Dict, List, Tuple +from braket.tasks.analog_hamiltonian_simulation_quantum_task_result import AnalogHamiltonianSimulationQuantumTaskResult +from braket.ahs.atom_arrangement import AtomArrangement + + +def show_register( + register: AtomArrangement, + blockade_radius: float=0.0, + what_to_draw: str="bond", + show_atom_index:bool=True +): + """Plot the given register + + Args: + register (AtomArrangement): A given register + blockade_radius (float): The blockade radius for the register. Default is 0 + what_to_draw (str): Either "bond" or "circle" to indicate the blockade region. + Default is "bond" + show_atom_index (bool): Whether showing the indices of the atoms. Default is True + + """ + filled_sites = [site.coordinate for site in register if site.site_type == SiteType.FILLED] + empty_sites = [site.coordinate for site in register if site.site_type == SiteType.VACANT] + + fig = plt.figure(figsize=(7, 7)) + if filled_sites: + plt.plot(np.array(filled_sites)[:, 0], np.array(filled_sites)[:, 1], 'r.', ms=15, label='filled') + if empty_sites: + plt.plot(np.array(empty_sites)[:, 0], np.array(empty_sites)[:, 1], 'k.', ms=5, label='empty') + plt.legend(bbox_to_anchor=(1.1, 1.05)) + + if show_atom_index: + for idx, site in enumerate(register): + plt.text(*site.coordinate, f" {idx}", fontsize=12) + + if blockade_radius > 0 and what_to_draw=="bond": + for i in range(len(filled_sites)): + for j in range(i+1, len(filled_sites)): + dist = np.linalg.norm(np.array(filled_sites[i]) - np.array(filled_sites[j])) + if dist <= blockade_radius: + plt.plot([filled_sites[i][0], filled_sites[j][0]], [filled_sites[i][1], filled_sites[j][1]], 'b') + + if blockade_radius > 0 and what_to_draw=="circle": + for site in filled_sites: + plt.gca().add_patch( plt.Circle((site[0],site[1]), blockade_radius/2, color="b", alpha=0.3) ) + plt.gca().set_aspect(1) + plt.show() + + +def rabi_pulse( + rabi_pulse_area: float, + omega_max: float, + omega_slew_rate_max: float +) -> Tuple[List[float], List[float]]: + """Get a time series for Rabi frequency with specified Rabi phase, maximum amplitude + and maximum slew rate + + Args: + rabi_pulse_area (float): Total area under the Rabi frequency time series + omega_max (float): The maximum amplitude + omega_slew_rate_max (float): The maximum slew rate + + Returns: + Tuple[List[float], List[float]]: A tuple containing the time points and values + of the time series for the time dependent Rabi frequency + + Notes: By Rabi phase, it means the integral of the amplitude of a time-dependent + Rabi frequency, \int_0^T\Omega(t)dt, where T is the duration. + """ + + phase_threshold = omega_max**2 / omega_slew_rate_max + if rabi_pulse_area <= phase_threshold: + t_ramp = np.sqrt(rabi_pulse_area / omega_slew_rate_max) + t_plateau = 0 + else: + t_ramp = omega_max / omega_slew_rate_max + t_plateau = (rabi_pulse_area / omega_max) - t_ramp + t_pules = 2 * t_ramp + t_plateau + time_points = [0, t_ramp, t_ramp + t_plateau, t_pules] + amplitude_values = [0, t_ramp * omega_slew_rate_max, t_ramp * omega_slew_rate_max, 0] + + return time_points, amplitude_values + + +def get_counts(result: AnalogHamiltonianSimulationQuantumTaskResult) -> Dict[str, int]: + """Aggregate state counts from AHS shot results + + Args: + result (AnalogHamiltonianSimulationQuantumTaskResult): The result + from which the aggregated state counts are obtained + + Returns: + Dict[str, int]: number of times each state configuration is measured + + Notes: We use the following convention to denote the state of an atom (site): + e: empty site + r: Rydberg state atom + g: ground state atom + """ + + state_counts = Counter() + states = ['e', 'r', 'g'] + for shot in result.measurements: + pre = shot.pre_sequence + post = shot.post_sequence + state_idx = np.array(pre) * (1 + np.array(post)) + state = "".join(map(lambda s_idx: states[s_idx], state_idx)) + state_counts.update((state,)) + + return dict(state_counts) + + +def get_drive( + times: List[float], + amplitude_values: List[float], + detuning_values: List[float], + phase_values: List[float] +) -> DrivingField: + """Get the driving field from a set of time points and values of the fields + + Args: + times (List[float]): The time points of the driving field + amplitude_values (List[float]): The values of the amplitude + detuning_values (List[float]): The values of the detuning + phase_values (List[float]): The values of the phase + + Returns: + DrivingField: The driving field obtained + """ + + assert len(times) == len(amplitude_values) + assert len(times) == len(detuning_values) + assert len(times) == len(phase_values) + + amplitude = TimeSeries() + detuning = TimeSeries() + phase = TimeSeries() + + for t, amplitude_value, detuning_value, phase_value in zip(times, amplitude_values, detuning_values, phase_values): + amplitude.put(t, amplitude_value) + detuning.put(t, detuning_value) + phase.put(t, phase_value) + + drive = DrivingField( + amplitude=amplitude, + detuning=detuning, + phase=phase + ) + + return drive + + +def get_shift(times: List[float], values: List[float], pattern: List[float]) -> ShiftingField: + """Get the shifting field from a set of time points, values and pattern + + Args: + times (List[float]): The time points of the shifting field + values (List[float]): The values of the shifting field + pattern (List[float]): The pattern of the shifting field + + Returns: + ShiftingField: The shifting field obtained + """ + assert len(times) == len(values) + + magnitude = TimeSeries() + for t, v in zip(times, values): + magnitude.put(t, v) + shift = ShiftingField(Field(magnitude, Pattern(pattern))) + + return shift + + +def show_global_drive(drive, axes=None, **plot_ops): + """Plot the driving field + Args: + drive (DrivingField): The driving field to be plot + axes: matplotlib axis to draw on + **plot_ops: options passed to matplitlib.pyplot.plot + """ + + data = { + 'amplitude [rad/s]': drive.amplitude.time_series, + 'detuning [rad/s]': drive.detuning.time_series, + 'phase [rad]': drive.phase.time_series, + } + + + if axes is None: + fig, axes = plt.subplots(3, 1, figsize=(7, 7), sharex=True) + + for ax, data_name in zip(axes, data.keys()): + if data_name == 'phase [rad]': + ax.step(data[data_name].times(), data[data_name].values(), '.-', where='post',**plot_ops) + else: + ax.plot(data[data_name].times(), data[data_name].values(), '.-',**plot_ops) + ax.set_ylabel(data_name) + ax.grid(ls=':') + axes[-1].set_xlabel('time [s]') + plt.tight_layout() + plt.show() + + +def show_local_shift(shift:ShiftingField): + """Plot the shifting field + Args: + shift (ShiftingField): The shifting field to be plot + """ + data = shift.magnitude.time_series + pattern = shift.magnitude.pattern.series + + plt.plot(data.times(), data.values(), '.-', label="pattern: " + str(pattern)) + plt.xlabel('time [s]') + plt.ylabel('shift [rad/s]') + plt.legend() + plt.tight_layout() + plt.show() + + +def show_drive_and_shift(drive: DrivingField, shift: ShiftingField): + """Plot the driving and shifting fields + + Args: + drive (DrivingField): The driving field to be plot + shift (ShiftingField): The shifting field to be plot + """ + drive_data = { + 'amplitude [rad/s]': drive.amplitude.time_series, + 'detuning [rad/s]': drive.detuning.time_series, + 'phase [rad]': drive.phase.time_series, + } + + fig, axes = plt.subplots(4, 1, figsize=(7, 7), sharex=True) + for ax, data_name in zip(axes, drive_data.keys()): + if data_name == 'phase [rad]': + ax.step(drive_data[data_name].times(), drive_data[data_name].values(), '.-', where='post') + else: + ax.plot(drive_data[data_name].times(), drive_data[data_name].values(), '.-') + ax.set_ylabel(data_name) + ax.grid(ls=':') + + shift_data = shift.magnitude.time_series + pattern = shift.magnitude.pattern.series + axes[-1].plot(shift_data.times(), shift_data.values(), '.-', label="pattern: " + str(pattern)) + axes[-1].set_ylabel('shift [rad/s]') + axes[-1].set_xlabel('time [s]') + axes[-1].legend() + axes[-1].grid() + plt.tight_layout() + plt.show() + + +def get_avg_density(result: AnalogHamiltonianSimulationQuantumTaskResult) -> np.ndarray: + """Get the average Rydberg densities from the result + + Args: + result (AnalogHamiltonianSimulationQuantumTaskResult): The result + from which the aggregated state counts are obtained + + Returns: + ndarray: The average densities from the result + """ + + measurements = result.measurements + postSeqs = [measurement.post_sequence for measurement in measurements] + postSeqs = 1 - np.array(postSeqs) # change the notation such 1 for rydberg state, and 0 for ground state + + avg_density = np.sum(postSeqs, axis=0)/len(postSeqs) + + return avg_density + + +def show_final_avg_density(result: AnalogHamiltonianSimulationQuantumTaskResult): + """Showing a bar plot for the average Rydberg densities from the result + + Args: + result (AnalogHamiltonianSimulationQuantumTaskResult): The result + from which the aggregated state counts are obtained + """ + avg_density = get_avg_density(result) + + plt.bar(range(len(avg_density)), avg_density) + plt.xlabel("Indices of atoms") + plt.ylabel("Average Rydberg density") + plt.show() + + +def constant_time_series(other_time_series: TimeSeries, constant: float=0.0) -> TimeSeries: + """Obtain a constant time series with the same time points as the given time series + + Args: + other_time_series (TimeSeries): The given time series + + Returns: + TimeSeries: A constant time series with the same time points as the given time series + """ + ts = TimeSeries() + for t in other_time_series.times(): + ts.put(t, constant) + return ts + + +def concatenate_time_series(time_series_1: TimeSeries, time_series_2: TimeSeries) -> TimeSeries: + """Concatenate two time series to a single time series + + Args: + time_series_1 (TimeSeries): The first time series to be concatenated + time_series_2 (TimeSeries): The second time series to be concatenated + + Returns: + TimeSeries: The concatenated time series + + """ + assert time_series_1.values()[-1] == time_series_2.values()[0] + + duration_1 = time_series_1.times()[-1] - time_series_1.times()[0] + + new_time_series = TimeSeries() + new_times = time_series_1.times() + [t + duration_1 - time_series_2.times()[0] for t in time_series_2.times()[1:]] + new_values = time_series_1.values() + time_series_2.values()[1:] + for t, v in zip(new_times, new_values): + new_time_series.put(t, v) + + return new_time_series + + +def concatenate_drives(drive_1: DrivingField, drive_2: DrivingField) -> DrivingField: + """Concatenate two driving fields to a single driving field + + Args: + drive_1 (DrivingField): The first driving field to be concatenated + drive_2 (DrivingField): The second driving field to be concatenated + + Returns: + DrivingField: The concatenated driving field + """ + return DrivingField( + amplitude=concatenate_time_series(drive_1.amplitude.time_series, drive_2.amplitude.time_series), + detuning=concatenate_time_series(drive_1.detuning.time_series, drive_2.detuning.time_series), + phase=concatenate_time_series(drive_1.phase.time_series, drive_2.phase.time_series) + ) + + +def concatenate_shifts(shift_1: ShiftingField, shift_2: ShiftingField) -> ShiftingField: + """Concatenate two driving fields to a single driving field + + Args: + shift_1 (ShiftingField): The first shifting field to be concatenated + shift_2 (ShiftingField): The second shifting field to be concatenated + + Returns: + ShiftingField: The concatenated shifting field + """ + assert shift_1.magnitude.pattern.series == shift_2.magnitude.pattern.series + + new_magnitude = concatenate_time_series(shift_1.magnitude.time_series, shift_2.magnitude.time_series) + return ShiftingField(Field(new_magnitude, shift_1.magnitude.pattern)) + + +def concatenate_drive_list(drive_list: List[DrivingField]) -> DrivingField: + """Concatenate a list of driving fields to a single driving field + + Args: + drive_list (List[DrivingField]): The list of driving fields to be concatenated + + Returns: + DrivingField: The concatenated driving field + """ + drive = drive_list[0] + for dr in drive_list[1:]: + drive = concatenate_drives(drive, dr) + return drive + + +def concatenate_shift_list(shift_list: List[ShiftingField]) -> ShiftingField: + """Concatenate a list of shifting fields to a single driving field + + Args: + shift_list (List[ShiftingField]): The list of shifting fields to be concatenated + + Returns: + ShiftingField: The concatenated shifting field + """ + shift = shift_list[0] + for sf in shift_list[1:]: + shift = concatenate_shifts(shift, sf) + return shift + + +def plot_avg_density_2D(densities, register, with_labels = True, batch_index = None, batch_mapping = None, custom_axes = None): + + # get atom coordinates + atom_coords = list(zip(register.coordinate_list(0), register.coordinate_list(1))) + # convert all to micrometers + atom_coords = [(atom_coord[0] * 10**6, atom_coord[1] * 10**6) for atom_coord in atom_coords] + + plot_avg_of_avgs = False + plot_single_batch = False + + if batch_index is not None: + if batch_mapping is not None: + plot_single_batch = True + # provided both batch and batch_mapping, show averages of single batch + batch_subindices = batch_mapping[batch_index] + batch_labels = {i:label for i,label in enumerate(batch_subindices)} + # get proper positions + pos = {i:tuple(coord) for i,coord in enumerate(list(np.array(atom_coords)[batch_subindices]))} + # narrow down densities + densities = np.array(densities)[batch_subindices] + + else: + raise Exception("batch_mapping required to index into") + else: + if batch_mapping is not None: + plot_avg_of_avgs = True + # just need the coordinates for first batch_mapping + subcoordinates = np.array(atom_coords)[batch_mapping[(0,0)]] + pos = {i:coord for i,coord in enumerate(subcoordinates)} + else: + # If both not provided do standard FOV + # handle 1D case + pos = {i:coord for i,coord in enumerate(atom_coords)} + + # get colors + vmin = 0 + vmax = 1 + cmap = plt.cm.Blues + + # construct graph + g = nx.Graph() + g.add_nodes_from(list(range(len(densities)))) + + # construct plot + if custom_axes is None: + fig, ax = plt.subplots() + else: + ax = custom_axes + + nx.draw(g, + pos, + node_color=densities, + cmap=cmap, + node_shape="o", + vmin=vmin, + vmax=vmax, + font_size=9, + with_labels=with_labels, + labels= batch_labels if plot_single_batch else None, + ax = custom_axes if custom_axes is not None else ax) + + ## Set axes + ax.set_axis_on() + ax.tick_params(left=True, + bottom=True, + top=True, + right=True, + labelleft=True, + labelbottom=True, + # labeltop=True, + # labelright=True, + direction="in") + ## Set 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "# access and visualize the device topology\n", + "print(aspen_m.properties.paradigm.connectivity.connectivityGraph)\n", + "nx.draw_kamada_kawai(aspen_m.topology_graph, with_labels=True, font_color=\"white\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can submit a task of the above program with verbatim box." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DECLARE ro BIT[2]\n", + "PRAGMA INITIAL_REWIRING \"NAIVE\"\n", + "RESET\n", + "RX(pi) 0\n", + "RX(pi) 0\n", + "CZ 0 1\n", + "MEASURE 1 ro[1]\n", + "MEASURE 0 ro[0]\n", + "\n" + ] + } + ], + "source": [ + "verbatim_task = aspen_m.run(OpenQASMProgram(source=program_with_verbatim_box), shots = 10)\n", + "verbatim_result = verbatim_task.result()\n", + "meta = verbatim_result.additional_metadata.rigettiMetadata\n", + "print(meta.compiledProgram)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As shown above, the two consecutive `rx` $\\pi$-rotation gates did not get optimized and we confirm that our program was indeed executed verbatim." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Requesting Result Types with OpenQASM\n", + "\n", + "Braket provides [a rich library of result types](https://docs.aws.amazon.com/braket/latest/developerguide/braket-result-types.html) for circuit executions. With OpenQASM, requesting different result types for our tasks is easier than ever using the `result` pragma. Next, we give an example of requesting result types for our Bell state program submitted to SV1. Before doing that, let's see what result types are supported on SV1:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "name='Sample' observables=['x', 'y', 'z', 'h', 'i', 'hermitian'] minShots=1 maxShots=100000\n", + "name='Expectation' observables=['x', 'y', 'z', 'h', 'i', 'hermitian'] minShots=0 maxShots=100000\n", + "name='Variance' observables=['x', 'y', 'z', 'h', 'i', 'hermitian'] minShots=0 maxShots=100000\n", + "name='Probability' observables=None minShots=1 maxShots=100000\n", + "name='Amplitude' observables=None minShots=0 maxShots=0\n", + "name='AdjointGradient' observables=['x', 'y', 'z', 'h', 'i'] minShots=0 maxShots=0\n" + ] + } + ], + "source": [ + "# print the result types supported by SV1\n", + "for iter in sv1.properties.action['braket.ir.openqasm.program'].supportedResultTypes:\n", + " print(iter)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With knowing the supported result types on SV1, we choose to request the `Expectation` of $X \\otimes Z$ observable on `q[0]` and `q[1]` and the `Amplitude` result type for a `shots=0` task of our bell program:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "bell_with_result_type = \"\"\"\n", + "OPENQASM 3;\n", + "\n", + "qubit[2] q;\n", + "\n", + "#pragma braket result expectation x(q[0]) @ z(q[1])\n", + "#pragma braket result amplitude \"00\", \"11\"\n", + "h q[0];\n", + "cnot q[0], q[1];\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The location of the `result` pragma is very flexible as long as it's after the qubit register definition (if you use physical qubits, you can put `result` pragmas anywhere after the program header).\n", + "\n", + "We can submit the above program and receive the results for our requested result types." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.0, {'00': (0.7071067811865475+0j), '11': (0.7071067811865475+0j)}]\n" + ] + } + ], + "source": [ + "bell_result_types_task = sv1.run(OpenQASMProgram(source=bell_with_result_type), shots = 0)\n", + "bell_result = bell_result_types_task.result()\n", + "values = bell_result.values\n", + "print(values)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At last, we want to remind our Braket OpenQASM users that there are two requirements when requesting result types:\n", + "1. For `shots=0` tasks, requesting non-simultaneously measurable result types is allowed, but for `shots>0` tasks, it is not allowed. For example, we can write the following OpenQASM program in a `shots=0` task but not in a `shots>0` task, since the two result types are not simultaneously measurable:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "program_with_non_simultaneously_measurable_result_types = \"\"\"\n", + "OPENQASM 3;\n", + "\n", + "qubit[2] q;\n", + "\n", + "h q[0];\n", + "cnot q[0], q[1];\n", + "\n", + "#pragma braket result expectation x(q[0]) @ z(q[1])\n", + "#pragma braket result expectation hermitian([[0, -1im], [1im, 0]]) q[0]\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. Do not use measurement instructions and request result types in the same OpenQASM program, otherwise a validation error will be raised. Since measurement instructions are basically equivalent to `#pragma braket result sample z(qubit)`, we encourage users to adapt a consistent style of requesting result types in the same program." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Conclusion\n", + "\n", + "In this notebook, you learned how to submit OpenQASM tasks and use OpenQASM features on Braket. Hope you enjoyed it! You can find more information about OpenQASM3.0 in its [live specification](https://openqasm.com/), and you can learn more about OpenQASM support on Braket in the [Amazon Braket documentation](https://docs.aws.amazon.com/braket/latest/developerguide/)." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 120, 'tasks': {'CREATED': 1, 'COMPLETED': 3}, 'execution_duration': datetime.timedelta(microseconds=14000), 'billed_execution_duration': datetime.timedelta(seconds=9)}, 'arn:aws:braket:::device/quantum-simulator/amazon/dm1': {'shots': 30, 'tasks': {'COMPLETED': 3}, 'execution_duration': datetime.timedelta(microseconds=264000), 'billed_execution_duration': datetime.timedelta(seconds=9)}, 'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 20, 'tasks': {'COMPLETED': 2}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.63 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.15" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/modules/1_Continue_Exploring/A_qtm_hw/compilation/Simulating_Advanced_OpenQASM_Programs_with_the_Local_Simulator.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/compilation/Simulating_Advanced_OpenQASM_Programs_with_the_Local_Simulator.ipynb new file mode 100644 index 000000000..3b09b3c35 --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/compilation/Simulating_Advanced_OpenQASM_Programs_with_the_Local_Simulator.ipynb @@ -0,0 +1,705 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulating Advanced OpenQASM Programs with the Local Simulator\n", + "\n", + "The `LocalSimulator` now supports simulating OpenQASM programs and the scope\n", + "of supported language features is larger than previously offered on Braket!\n", + "\n", + "This notebook serves as a references of all OpenQASM features supported by Braket\n", + "with the `LocalSimulator`. For detailed documentation about the language, see the [OpenQASM 3.0 specification](https://openqasm.com/language/index.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creating the Device\n", + "\n", + "We create the device using the LocalSimulator class." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from braket.devices import LocalSimulator\n", + "\n", + "device = LocalSimulator()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# to make the output a little neater\n", + "\n", + "import numpy as np\n", + "np.set_printoptions(precision=3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run a Bell circuit\n", + "\n", + "Let's do a Hello World example where we run a Bell circuit!" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'11': 56, '00': 44})\n" + ] + } + ], + "source": [ + "from braket.ir.openqasm import Program\n", + "\n", + "qasm_string = \"\"\"\n", + "qubit[2] q;\n", + "\n", + "h q[0];\n", + "cnot q[0], q[1];\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run a Bell circuit with a result type\n", + "\n", + "Let's run the same circuit, but with no shots, instead getting the\n", + "state vector.\n", + "\n", + "For more info on supported result types, see the [developer guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-openqasm-supported-features.html#braket-openqasm-supported-features-pragmas)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "State vector result: [0.707+0.j 0. +0.j 0. +0.j 0.707+0.j]\n" + ] + } + ], + "source": [ + "from braket.ir.openqasm import Program\n", + "\n", + "qasm_string = \"\"\"\n", + "qubit[2] q;\n", + "\n", + "h q[0];\n", + "cnot q[0], q[1];\n", + "\n", + "#pragma braket result state_vector\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program).result()\n", + "print(f\"State vector result: {result.result_types[0].value}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gate Modifiers\n", + "\n", + "You can use the following gate modifiers on any gate: `inv`, `ctrl`, `negctrl`, `pow`.\n", + "\n", + "For more documentation on gate modifiers, see the [OpenQASM specification](https://openqasm.com/language/gates.html#quantum-gate-modifiers)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'00': 54, '11': 46})\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit[2] q;\n", + "\n", + "h q[0];\n", + "ctrl @ x q[0], q[1];\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "State vector result: [1.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit q;\n", + "\n", + "pow(1/2) @ x q; // sqrt x\n", + "inv @ v q; // inv of (sqrt x)\n", + "\n", + "#pragma braket result state_vector\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=0).result()\n", + "print(f\"State vector result: {result.result_types[0].value}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## OpenQASM Built-in Gates\n", + "\n", + "You can use the built-in OpenQASM quantum directives, the parameterized unitary, `U`,\n", + "and the global phase instruction `gphase`.\n", + "\n", + "For more info on the built-in quantum operations, see the [OpenQASM specification](https://openqasm.com/language/gates.html#built-in-gates)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "State vector result: [6.123e-17+0.j 1.000e+00+0.j]\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit q;\n", + "\n", + "U(π, 0, π) q;\n", + "\n", + "#pragma braket result state_vector\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=0).result()\n", + "print(f\"State vector result: {result.result_types[0].value}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Classical Variables\n", + "\n", + "The `LocalSimulator` supports OpenQASM variables and constants of the\n", + "following types: `int`, `uint`, `float`, `bool`, `bit`.\n", + "\n", + "For more info on classical variables in OpenQASM, see the [OpenQASM specification](https://openqasm.com/language/types.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "State vector result: [1.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit q;\n", + "\n", + "int p1 = 2;\n", + "float p2 = .25;\n", + "\n", + "pow(p1) @ pow(p2) @ x q; // sqrt x\n", + "inv @ v q; // inv of (sqrt x)\n", + "\n", + "#pragma braket result state_vector\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=0).result()\n", + "print(f\"State vector result: {result.result_types[0].value}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Classical Operations\n", + "\n", + "You can use many standard operators on classical variables of different\n", + "types. There is also a list of built-in functions.\n", + "\n", + "For a full list of supported operations and functions, see the OpenQASM specification for [classical operations](https://openqasm.com/language/classical.html) and [built-in functions](https://openqasm.com/language/types.html#mathematical-functions-available-for-constant-initialization)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "State vector result: [0.915-0.279j 0.085+0.279j]\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit q;\n", + "\n", + "int p1 = floor(log(sin(20)));\n", + "float p2 = 4 * (π/3);\n", + "\n", + "pow(p1) @ pow(p2) @ x q;\n", + "\n", + "#pragma braket result state_vector\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=0).result()\n", + "print(f\"State vector result: {result.result_types[0].value}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Custom Gates\n", + "\n", + "You can define your own gates using built-in Braket and OpenQASM gates, as well as other\n", + "custom defined gates.\n", + "\n", + "For more information around defining custom gates, see the [OpenQASM specification](https://openqasm.com/language/gates.html#hierarchically-defined-unitary-gates)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'111': 100})\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit[3] q;\n", + "\n", + "gate majority a, b, c {\n", + " // set c to the majority of {a, b, c}\n", + " ctrl @ x c, b;\n", + " ctrl @ x c, a;\n", + " ctrl(2) @ x a, b, c;\n", + "}\n", + "\n", + "x q[0:1];\n", + "// this should flip q[2] to 1\n", + "majority q[0], q[1], q[2];\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Classical control\n", + "\n", + "The `LocalSimulator` supports the following classical control directives:\n", + "`if`, `for`, `while`, as well as simple subroutines (more on that later)\n", + "\n", + "For more info on classical control, see the [OpenQASM specification](https://openqasm.com/language/classical.html#looping-and-branching)." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'10': 100})\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit[2] q;\n", + "\n", + "bit[2] bitstring = \"10\";\n", + "\n", + "for int i in [0:1] {\n", + " if (bitstring[i]) {\n", + " x q[i];\n", + " }\n", + " else {\n", + " i q[i];\n", + " }\n", + "}\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Input\n", + "\n", + "The `LocalSimulator` supports parametric circuits using the `input` directive allowing users\n", + "to provide a dictionary to the `inputs` field in the OpenQASM Program object.\n", + "\n", + "For documentation on the input directive, see the [OpenQASM specification](https://openqasm.com/language/directives.html#input-output)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'0': 78, '1': 22})\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "input float theta;\n", + "qubit q;\n", + "rx(theta) q;\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string, inputs={\"theta\": 1.0})\n", + "\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## QASM Files\n", + "\n", + "Instead of providing an OpenQASM string, you can provide a filename." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2 + 11 = 13\n" + ] + } + ], + "source": [ + "a_in, b_in = 2, 11\n", + "inputs = {\"a_in\": a_in, \"b_in\": b_in}\n", + "\n", + "program = Program(source=\"adder.qasm\", inputs=inputs)\n", + "device = LocalSimulator()\n", + "\n", + "result = device.run(program).result()\n", + "probs = np.outer(\n", + " result.result_types[0].value,\n", + " result.result_types[1].value\n", + ").flatten()\n", + "answer = np.argmax(probs)\n", + "print(f\"{a_in} + {b_in} = {answer}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Subroutines\n", + "\n", + "The `LocalSimulator` supports creating subroutines to compartmentalize pieces of your code.\n", + "They can support both classical and quantum computation. Note that using variables that are in scope during\n", + "subroutine definition, but not passed as arguments is currently undefined behavior.\n", + "\n", + "For documentation around subroutines, see the [OpenQASM specification](https://openqasm.com/language/subroutines.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'1': 100})\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "const int[8] n = 4;\n", + "input bit[n] x;\n", + "\n", + "qubit q;\n", + "\n", + "def parity(bit[n] cin) -> bit {\n", + " bit c = false;\n", + " for int[8] i in [0: n - 1] {\n", + " c ^= cin[i];\n", + " }\n", + " return c;\n", + "}\n", + "\n", + "if(parity(x)) {\n", + " x q;\n", + "} else {\n", + " i q;\n", + "}\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string, inputs={\"x\": \"1011\"})\n", + "\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'0': 80, '1': 20})\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit q;\n", + "\n", + "def sum(const array[int[8], #dim = 1] arr) -> int {\n", + " int size = sizeof(arr);\n", + " int x = 0;\n", + " for int i in [0:size - 1] {\n", + " x += arr[i];\n", + " }\n", + " return x;\n", + "}\n", + "\n", + "array[int, 10] arr = {9, 3, 6, 2, 2, 4, 3, 1, 12, 7};\n", + "int s = sum(arr);\n", + "rx(s*π/4) q;\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string)\n", + "\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulating Noise\n", + "\n", + "You can simulate noise instructions on the density matrix simulator using\n", + "Braket noise pragmas.\n", + "\n", + "For more documentation around supported noise operations, see the [developer guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-openqasm-noise-simulation.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Measurement counts: Counter({'1': 92, '0': 8})\n" + ] + } + ], + "source": [ + "qasm_string = \"\"\"\n", + "qubit q;\n", + "\n", + "x q;\n", + "\n", + "#pragma braket noise bit_flip(.1) q\n", + "\"\"\"\n", + "qasm_program = Program(source=qasm_string, inputs={\"x\": \"1011\"})\n", + "\n", + "device = LocalSimulator(\"braket_dm\")\n", + "result = device.run(qasm_program, shots=100).result()\n", + "print(f\"Measurement counts: {result.measurement_counts}\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.15" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/compilation/Verbatim_Compilation.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/compilation/Verbatim_Compilation.ipynb new file mode 100644 index 000000000..07bca5b0a --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/compilation/Verbatim_Compilation.ipynb @@ -0,0 +1,983 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Verbatim compilation" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Usually, when you run a circuit on a QPU, behind the scenes, Amazon Braket will do a series of compilation steps to optimize your circuit and map the abstract circuit to the physical qubits on the QPU. However, in many situations, such as for error mitigation or benchmarking experiments, researchers require full control of the qubits and the gates that are being applied. In a [previous notebook](https://github.com/aws/amazon-braket-examples/blob/main/examples/braket_features/Allocating_Qubits_on_QPU_Devices.ipynb), we showed you how to manually allocate the qubits of your circuit, i.e., how you can exactly define which logical qubit maps to which physical qubit. In this notebook, you will learn how to use _verbatim compilation_ to run your circuits exactly as defined without any modification during the compilation process.\n", + "\n", + "### Table of contents:\n", + "\n", + "* [Recap: Running circuits on Amazon Braket](#Recap)\n", + "* [Using verbatim compilation to run circuits without further compilation](#Verbatim)\n", + "* [Programming verbatim circuits onto the Rigetti device](#Rigetti)\n", + "* [Programming verbatim circuits onto the Oxford Quantum Circuits device](#OQC)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Recap: Running circuits on Amazon Braket " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us begin with importing the usual dependencies. Verbatim compilation is supported by all Rigetti devices, and we will use the Aspen-M-3 device for this demonstration." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "import boto3\n", + "from braket.aws import AwsDevice\n", + "from braket.circuits import Circuit\n", + "from math import pi\n", + "import networkx as nx\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When you run a circuit on Amazon Braket, different compilation and optimization steps occur before the circuit is executed on the selected QPU. First, the gates of your circuit are decomposed into the _native gates_ of the QPU. Let's first remember what the native gates of the Aspen-M-3 device are:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The native gates for the Aspen-M device are:\n", + "rx\n", + "rz\n", + "cz\n", + "cphaseshift\n", + "xy\n" + ] + } + ], + "source": [ + "# set up the Rigetti Aspen-M-3 device\n", + "device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "\n", + "# list the native gate set\n", + "print(\"The native gates for the\", device.name, \"device are:\")\n", + "for gate in device.properties.paradigm.nativeGateSet:\n", + " print(gate)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we create a circuit with gates that are not part of that list, the gates will automatically be decomposed into a gate set that can be executed on the device." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note: This notebook uses the Rigetti Aspen-M-3 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|\n", + " \n", + "q0 : -H-C-\n", + " | \n", + "q1 : ---X-\n", + "\n", + "T : |0|1|\n", + "Counter({'11': 418, '00': 358, '10': 203, '01': 21})\n" + ] + } + ], + "source": [ + "bell = Circuit().h(0).cnot(0,1)\n", + "print(bell)\n", + "result = device.run(bell, shots=1000).result()\n", + "print(result.measurement_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's have a look at the circuit that was actually executed. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DECLARE ro BIT[2]\n", + "PRAGMA INITIAL_REWIRING \"PARTIAL\"\n", + "RESET\n", + "RZ(pi/2) 121\n", + "RX(pi/2) 121\n", + "RZ(pi/2) 121\n", + "RZ(-pi/2) 122\n", + "RX(pi/2) 122\n", + "RZ(pi/2) 122\n", + "CZ 122 121\n", + "RZ(pi) 121\n", + "RZ(-3*pi/2) 122\n", + "RX(pi/2) 122\n", + "RZ(3*pi/2) 122\n", + "MEASURE 122 ro[1]\n", + "MEASURE 121 ro[0]\n", + "\n" + ] + } + ], + "source": [ + "meta = result.additional_metadata.rigettiMetadata\n", + "print(meta.compiledProgram)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, the original gates, `h` and `cnot`, were decomposed into the native `rz`, `rx`, `cz`, and `cphase` gates. You will also note that the abstract qubit indices 0 and 1 (which were chosen as an example) were remapped to qubits that actually exist on the device, in this case, 121 and 122, respectively. At the time when you run this notebook, you might see a different remapping, as the compiler takes into account the latest calibration of the device and tries to map to the qubits that yield the best results. \n", + "\n", + "The compiler further performs circuit optimizations to minimize the number of operations, e.g., by removing redundant gates. Let's have a look at a single-qubit circuit containing two subsequent `x` gates:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "identity = Circuit().x(0).x(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course, if you do the math, two consecutive `x` gates just cancel each other out, and we are left with an empty circuit after compilation." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DECLARE ro BIT[1]\n", + "PRAGMA INITIAL_REWIRING \"PARTIAL\"\n", + "RESET\n", + "MEASURE 46 ro[0]\n", + "\n", + "Counter({'0': 994, '1': 6})\n" + ] + } + ], + "source": [ + "result = device.run(identity, shots=1000).result()\n", + "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n", + "print(compiled_program)\n", + "print(result.measurement_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using verbatim compilation to run circuits without further compilation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In some cases, however, you may need to run circuits exactly as defined, without any further modifications by the compiler. For instance, if you want to benchmark device performance you may want to control exactly which gates are executed on the hardware. Similarly, [certain error mitigation protocols](https://arxiv.org/pdf/2005.10921.pdf) require insertion of additional, redundant operations that would normally be removed by the compiler but are essential for the protocol to work. To prevent circuits (or parts of circuits) from further compiler optimizations, you can use the `add_verbatim_box` function in the Amazon Braket SDK." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note: add_verbatim_box is currently only supported on Rigetti, OQC, and IonQ devices.\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When you define a (sub-)circuit in a verbatim box, you need to make sure that everything inside the verbatim box can be executed on the device _exactly_ as you defined it. This means that\n", + "1. The circuit can only use qubit indices that exist on the device\n", + "2. All gates of the circuit have to be part of the native gate set of the device\n", + "3. All multi-qubit gates have to be between qubits that are connected according to the connectivity graph of the device " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Getting started with a minimal example\n", + "Let's have a look at the simple example from before of an identify circuit. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "identity = Circuit().rx(0,pi).rx(0,pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, we have chosen the Rigetti-native `rx` gate, which is identical to `x` if we choose the angle to be $\\pi$. Next, we wrap this circuit in a verbatim box to prevent the compiler from collapsing the two gates. You can see the circuit diagram indicates the start and end of the verbatim box." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | 3 |\n", + " \n", + "q0 : -StartVerbatim-Rx(3.14)-Rx(3.14)-EndVerbatim-\n", + "\n", + "T : | 0 | 1 | 2 | 3 |\n" + ] + } + ], + "source": [ + "circ = Circuit().add_verbatim_box(identity)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we run the circuit, both gates will be executed on the device." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note: To run a circuit that contains a verbatim box the disable_qubit_rewiring flag must be set to True \n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DECLARE ro BIT[1]\n", + "PRAGMA INITIAL_REWIRING \"NAIVE\"\n", + "RESET\n", + "RX(pi) 0\n", + "RX(pi) 0\n", + "MEASURE 0 ro[0]\n", + "\n", + "Counter({'0': 809, '1': 191})\n" + ] + } + ], + "source": [ + "result = device.run(circ, shots=1000, disable_qubit_rewiring=True).result()\n", + "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n", + "print(compiled_program)\n", + "print(result.measurement_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Programming verbatim circuits onto the Rigetti device " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we have mentioned above, to build circuits with multi-qubit gates, you need to take into consideration the connectivity graph of the device. When a circuit contains a verbatim box, automatic qubit rewiring has to be disables, and you have manually allocate the qubits on the device that you want to use for your circuit.\n", + "You can access the connectivity graph on the [device detail page](https://console.aws.amazon.com/braket/home?region=us-west-1#/devices/arn:aws:braket:us-west-2::device/qpu/rigetti/Aspen-M-3) in the Amazon Braket Console, or by using the code below." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'0': ['1', '7'], '1': ['0', '16', '2'], '10': ['11', '113', '17'], '100': ['101', '107'], '101': ['100', '102', '116'], '102': ['101', '103', '115'], '103': ['102', '104'], '104': ['103', '105', '7'], '105': ['104', '106'], '106': ['105', '107'], '107': ['100', '106'], '11': ['10', '12', '26'], '110': ['111', '117'], '111': ['110', '112', '126'], '112': ['111', '113'], '113': ['10', '112', '114'], '114': ['113', '115', '17'], '115': ['102', '114', '116'], '116': ['101', '115', '117'], '117': ['110', '116'], '12': ['11', '13', '25'], '120': ['121', '127'], '121': ['120', '122', '136'], '122': ['121', '123', '135'], '123': ['122', '124', '20'], '124': ['123', '125', '27'], '125': ['124', '126'], '126': ['111', '125', '127'], '127': ['120', '126'], '13': ['12', '14'], '130': ['131', '137'], '131': ['130', '132', '146'], '132': ['131', '133', '145'], '133': ['132', '134', '30'], '134': ['133', '135', '37'], '135': ['122', '134', '136'], '136': ['121', '135', '137'], '137': ['130', '136'], '14': ['13', '15'], '140': ['141', '147'], '141': ['140', '142'], '142': ['141', '143'], '143': ['142', '144', '40'], '144': ['143', '145', '47'], '145': ['132', '144', '146'], '146': ['131', '145', '147'], '147': ['140', '146'], '15': ['14', '16', '2'], '16': ['1', '15', '17'], '17': ['10', '16', '114'], '2': ['1', '15', '3'], '20': ['123', '21', '27'], '21': ['20', '22', '36'], '22': ['21', '23', '35'], '23': ['22', '24'], '24': ['23', '25'], '25': ['12', '24', '26'], '26': ['11', '25', '27'], '27': ['20', '26', '124'], '3': ['2', '4'], '30': ['133', '31', '37'], '31': ['30', '32', '46'], '32': ['31', '33', '45'], '33': ['32', '34'], '34': ['33', '35'], '35': ['22', '34', '36'], '36': ['21', '35', '37'], '37': ['30', '36', '134'], '4': ['3', '5'], '40': ['143', '41', '47'], '41': ['40', '42'], '42': ['41', '43'], '43': ['42', '44'], '44': ['43', '45'], '45': ['32', '44', '46'], '46': ['31', '45', '47'], '47': ['40', '46', '144'], '5': ['4', '6'], '6': ['5', '7'], '7': ['0', '6', '104']}\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# set up the Rigetti Aspen-M-3 device\n", + "rigetti = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n", + "\n", + "# access and visualize the device topology\n", + "# note that device topology can change day-to-day based on edge fidelity data\n", + "print(rigetti.properties.paradigm.connectivity.connectivityGraph)\n", + "nx.draw_kamada_kawai(rigetti.topology_graph, with_labels=True, font_color=\"white\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the connectivity graph, you can see that qubits 11, 10, and 17 are connected in a line, and with the code in the next cell you can access their respective 2-qubit gate fidelities to make sure you have selected a high-quality qubit subset. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'fCPHASE': 0.9337939355722039, 'fCPHASE_std_err': 0.009613787561716118, 'fCZ': 0.9422746489035245, 'fCZ_std_err': 0.007187651208699537, 'fXY': 0.9887022319066467, 'fXY_std_err': 0.003682831114426735}\n", + "{'fCPHASE': 0.919371151695913, 'fCPHASE_std_err': 0.003625200733935161, 'fCZ': 0.9557165619080631, 'fCZ_std_err': 0.00549970432762644, 'fXY': 0.9739503289969474, 'fXY_std_err': 0.005178345557993867}\n" + ] + } + ], + "source": [ + "print(rigetti.properties.provider.specs[\"2Q\"][\"10-11\"])\n", + "print(rigetti.properties.provider.specs[\"2Q\"][\"10-17\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note: At the time when you run this notebook the fidelity numbers may be different as QPU devices are periodically recalibrated\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After selecting the qubits and validating their gate fidelities, you can now construct a circuit and run it. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | 3 | 4 | 5 |\n", + " \n", + "q10 : -StartVerbatim-XY(0.79)-XY(1.57)-Rx(3.14)-XY(0.79)-EndVerbatim-\n", + " | | | | | \n", + "q11 : -|-------------XY(0.79)-|-----------------XY(0.79)-|-----------\n", + " | | | \n", + "q17 : -*************----------XY(1.57)-------------------***********-\n", + "\n", + "T : | 0 | 1 | 2 | 3 | 4 | 5 |\n" + ] + } + ], + "source": [ + "circ = Circuit().xy(10,11,pi/4).xy(10,17,pi/2).rx(10,pi).xy(10,11,pi/4)\n", + "verbatim_circ = Circuit().add_verbatim_box(circ)\n", + "print(verbatim_circ)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DECLARE ro BIT[3]\n", + "PRAGMA INITIAL_REWIRING \"NAIVE\"\n", + "RESET\n", + "XY(pi/4) 10 11\n", + "XY(pi/2) 10 17\n", + "RX(pi) 10\n", + "XY(pi/4) 10 11\n", + "MEASURE 17 ro[2]\n", + "MEASURE 11 ro[1]\n", + "MEASURE 10 ro[0]\n", + "\n", + "Counter({'100': 659, '010': 119, '000': 112, '110': 93, '101': 11, '011': 3, '001': 2, '111': 1})\n" + ] + } + ], + "source": [ + "result = rigetti.run(verbatim_circ, shots=1000, disable_qubit_rewiring=True).result()\n", + "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n", + "print(compiled_program)\n", + "print(result.measurement_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the program is faithfully executed exactly as it was defined." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Defining verbatim subcircuits " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In some situations, you might only be interested in executing parts of your circuits verbatim, and have the compiler nativize and optimize the rest. The next example demonstrates how to do this. Let's get started by defining the subcircuit we want to execute verbatim." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "verbatim_subcirc = Circuit().rx(10,pi).rx(10,pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, define the part of the circuit you want to compiler to process, so you don't have to worry about nativizing gates. " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "subcirc1 = Circuit().cnot(10,11).cnot(10,17)\n", + "subcirc2 = Circuit().cnot(10,17).cnot(10,11)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, put everything together" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1| 2 | 3 | 4 | 5 |6|7|\n", + " \n", + "q10 : -C-C-StartVerbatim-Rx(3.14)-Rx(3.14)-EndVerbatim-C-C-\n", + " | | | | | | \n", + "q11 : -X-|-|-------------------------------|-----------|-X-\n", + " | | | | \n", + "q17 : ---X-*************-------------------***********-X---\n", + "\n", + "T : |0|1| 2 | 3 | 4 | 5 |6|7|\n" + ] + } + ], + "source": [ + "circ = subcirc1.add_verbatim_box(verbatim_subcirc).add_circuit(subcirc2)\n", + "print(circ)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DECLARE ro BIT[3]\n", + "PRAGMA INITIAL_REWIRING \"NAIVE\"\n", + "RESET\n", + "RZ(-pi/2) 10\n", + "RZ(-pi/2) 11\n", + "RX(pi/2) 11\n", + "CZ 11 10\n", + "RZ(-pi/2) 10\n", + "RZ(-pi/2) 17\n", + "RX(pi/2) 17\n", + "RZ(pi/2) 17\n", + "CZ 17 10\n", + "RZ(pi) 10\n", + "RZ(-pi) 11\n", + "RX(pi/2) 11\n", + "RZ(3*pi/2) 11\n", + "RZ(-3*pi/2) 17\n", + "RX(pi/2) 17\n", + "RZ(3*pi/2) 17\n", + "RX(pi) 10\n", + "RX(pi) 10\n", + "RZ(pi/2) 10\n", + "RZ(-3*pi/2) 17\n", + "RX(pi/2) 17\n", + "RZ(pi) 17\n", + "CZ 10 17\n", + "RZ(-pi/2) 10\n", + "RZ(-pi/2) 11\n", + "RX(pi/2) 11\n", + "RZ(pi/2) 11\n", + "CZ 11 10\n", + "RZ(pi) 10\n", + "RZ(-3*pi/2) 11\n", + "RX(pi/2) 11\n", + "RZ(3*pi/2) 11\n", + "RX(pi/2) 17\n", + "RZ(pi/2) 17\n", + "MEASURE 17 ro[2]\n", + "MEASURE 11 ro[1]\n", + "MEASURE 10 ro[0]\n", + "\n", + "Counter({'000': 869, '010': 84, '100': 20, '001': 19, '011': 3, '111': 2, '101': 2, '110': 1})\n" + ] + } + ], + "source": [ + "result = rigetti.run(circ, shots=1000, disable_qubit_rewiring=True).result()\n", + "compiled_program = result.additional_metadata.rigettiMetadata.compiledProgram\n", + "print(compiled_program)\n", + "print(result.measurement_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Inspecting the compiled program, you can see that the `cnot` gates were nativized, however, the two `rx` gates in the middle of the circuit remain unaltered, and were not removed by the compiler. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Programming verbatim circuits onto the Oxford Quantum Circuits device " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oxford Quantum Circuits (OQC) also supports verbatim compilation. As mentioned above, a verbatim circuit does not allow automatic qubit rewiring. All qubits have to be allocated using the indices that exist on the device. The gates of a verbatim circuit have to come from the native gate set, and multi-qubits gates can only be applied according to the connectivity graph of the device. First, let's look at OQC's native gate set." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The native gates for the Lucy device are:\n", + "ecr\n", + "i\n", + "rz\n", + "v\n", + "x\n" + ] + } + ], + "source": [ + "# set up the OQC Lucy device\n", + "oqc_device = AwsDevice(\"arn:aws:braket:eu-west-2::device/qpu/oqc/Lucy\")\n", + "\n", + "# list the native gate set\n", + "print(\"The native gates for the\", oqc_device.name, \"device are:\")\n", + "for gate in oqc_device.properties.paradigm.nativeGateSet:\n", + " print(gate)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's check out the device connectivity graph to see what qubits are on the device and how they are connected. Notice that connections in the OQC device are unidirectional. This mean that two-qubits gates can only be applied one direction with verbatim compilation. In the topology graph, each arrow represents the direction that a two-qubit gate can be applied in verbatim mode. The tail of the arrow is the first qubit and the head is the second qubit. For example, `ecr(4,3)` is a valid gate while `ecr(3,4)` is not." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'0': ['1', '7'], '1': ['2'], '2': ['3'], '4': ['3', '5'], '6': ['5'], '7': ['6']}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# access and visualize the device topology\n", + "print(oqc_device.properties.paradigm.connectivity.connectivityGraph)\n", + "nx.draw_kamada_kawai(oqc_device.topology_graph, with_labels=True, font_color=\"white\", arrows=True, arrowsize=30)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this information, we can create a circuit and run it with verbatim mode. OQC currently only supports verbatim mode for the whole circuit, i.e. the verbatim box has to contain all the gates in a circuit when submitting to the device." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | 3 | 4 |\n", + " \n", + "q0 : -StartVerbatim-Rz(0.785)-Rz(-0.785)-----EndVerbatim-\n", + " | | \n", + "q1 : -|-------------ECR----------------------|-----------\n", + " | | | \n", + "q2 : -|-------------ECR-------X----------ECR-|-----------\n", + " | | | \n", + "q3 : -*************----------------------ECR-***********-\n", + "\n", + "T : | 0 | 1 | 2 | 3 | 4 |\n" + ] + } + ], + "source": [ + "circ = Circuit().rz(0,pi/4).rz(0,-pi/4).ecr(1,2).x(2).ecr(2,3)\n", + "verbatim_circ = Circuit().add_verbatim_box(circ)\n", + "print(verbatim_circ)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "OPENQASM 2.0;\n", + "include \"qelib1.inc\";\n", + "qreg q[4];\n", + "creg b[4];\n", + "\n", + "rz(0.7853981633974483) q[0];\n", + "rz(-0.7853981633974483) q[0];\n", + "ecr q[1], q[2];\n", + "x q[2];\n", + "ecr q[2], q[3];\n", + "measure q -> b;\n", + "Counter({'0110': 419, '0010': 243, '0100': 210, '0000': 103, '0011': 5, '0101': 5, '0111': 4, '0001': 3, '1000': 2, '1010': 2, '1100': 2, '1110': 2})\n" + ] + } + ], + "source": [ + "result = oqc_device.run(verbatim_circ, shots=1000).result()\n", + "compiledProgram = result.additional_metadata.oqcMetadata.compiledProgram\n", + "print(compiledProgram)\n", + "print(result.measurement_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Programming verbatim circuits onto the IonQ device" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "IonQ also supports verbatim compilation. Because qubits in the IonQ device have all-to-all connection, there is no restriction in qubit connectivity; all qubit pairs are avaialbe for 2-qubit gates. Because there is no circuit optimization or gate decomposition in verbatim compilation, all gates in the circuit must be native gates. Let's look at IonQ's native gate set." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The native gates for the Aria 1 device are:\n", + "GPI\n", + "GPI2\n", + "MS\n" + ] + } + ], + "source": [ + "# set up the IonQ device\n", + "ionq_device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Aria-1\")\n", + "\n", + "# list the native gate set\n", + "print(\"The native gates for the\", ionq_device.name, \"device are:\")\n", + "for gate in ionq_device.properties.paradigm.nativeGateSet:\n", + " print(gate)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In `device.property`, you can see `fullyConnected=True`, showing that qubits are fully connected. This manifests as the device having a complete topology graph." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fullyConnected=True connectivityGraph={}\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# access and visualize the device topology\n", + "print(ionq_device.properties.paradigm.connectivity)\n", + "nx.draw_kamada_kawai(ionq_device.topology_graph, with_labels=True, font_color=\"white\", arrows=True, arrowsize=30)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this information, you can write a circuit to run verbatim on an IonQ device. IonQ currently only supports verbatim compilation for the entire circuit, so every instruction in the circuit will need to be enclosed in a verbatim box. In other words, you cannot have any gates outside of the verbatim box. As well, note that IonQ native gates cannot be used outside of a verbatim box. To learn more about IonQ native gates and the best practice of using them, see the [Amazon Braket Developer Guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html?tag=local002-20#braket-qpu-partner-ionq) and [IonQ's documentation page](https://ionq.com/docs/getting-started-with-native-gates). " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | 3 |\n", + " \n", + "q0 : -StartVerbatim-GPi(3.13)-MS(0.10, 0.20, 0.30)-EndVerbatim-\n", + " | | | \n", + "q1 : -*************-----------MS(0.10, 0.20, 0.30)-***********-\n", + "\n", + "T : | 0 | 1 | 2 | 3 |\n" + ] + } + ], + "source": [ + "circ = Circuit().gpi(0,pi).ms(0, 1, 0.1, 0.2, 0.3)\n", + "verbatim_circ = Circuit().add_verbatim_box(circ)\n", + "print(verbatim_circ)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'10': 9, '01': 1})\n" + ] + } + ], + "source": [ + "task = ionq_device.run(verbatim_circ, shots=10)\n", + "print(task.result().measurement_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion \n", + "This notebook introduced the basic functionality of verbatim compilation of Amazon Braket, that allows you to run circuits or subcircuits to be executed exactly as defined without any compiler modifications. You can find further information in the [Amazon Braket documentation](https://docs.aws.amazon.com/braket/). " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 5000, 'tasks': {'COMPLETED': 5}}, 'arn:aws:braket:us-east-1::device/qpu/ionq/Harmony': {'shots': 10, 'tasks': {'COMPLETED': 1}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 3.650 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "conda_braket", + "language": "python", + "name": "conda_braket" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.13" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/1_Bringup_experiments.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/1_Bringup_experiments.ipynb new file mode 100644 index 000000000..6e5f187be --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/1_Bringup_experiments.ipynb @@ -0,0 +1,603 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Bringup Experiments\n", + "In this tutorial notebook, we will review common pulse sequences that are used as first steps during the bring up of more complex pulse experiments:\n", + "- measure the resonance frequency of a qubit\n", + "- calibrate a $\\pi$/2 pulse via Rabi spectroscopy\n", + "- measure the $T^*_2$ coherence time with a Ramsey sequence\n", + "\n", + "You can use either Rigetti's Aspen M-3 or OQC's Lucy device to run this notebook." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's first import some packages to construct pulse sequences and analyze results." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "from braket.aws import AwsDevice\n", + "from braket.pulse import PulseSequence, GaussianWaveform, ConstantWaveform\n", + "from braket.parametric import FreeParameter\n", + "\n", + "## Imports for function fitting\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import scipy.optimize\n", + "from scipy.fft import fft, fftfreq" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You will be able to switch from one device to the other by setting the `device_name` to `aspen` or `lucy`" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "device_name = \"aspen\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will use the following configuration to control the different parameters for our experiments across the available devices" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "experiment_configuration = {\n", + " \"aspen\": {\n", + " \"device_arn\": \"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\",\n", + " \"qubit\": 4,\n", + " \"drive_frame\": \"q4_rf_frame\",\n", + " \"readout_frame\": \"q4_ro_rx_frame\",\n", + " \"spectroscopy_wf\": GaussianWaveform(100e-9, 25e-9, 0.1, True),\n", + " \"rabi_wf\": GaussianWaveform(FreeParameter(\"length\"), FreeParameter(\"length\") * 0.25, 0.2, True)\n", + " },\n", + " \"lucy\": {\n", + " \"device_arn\": \"arn:aws:braket:eu-west-2::device/qpu/oqc/Lucy\",\n", + " \"qubit\": 0,\n", + " \"drive_frame\": \"q0_drive\",\n", + " \"readout_frame\": \"r0_measure\",\n", + " \"spectroscopy_wf\": ConstantWaveform(25e-9, 0.03),\n", + " \"rabi_wf\": ConstantWaveform(FreeParameter(\"length\"), 0.07)\n", + " }\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we will first instantiate a device that will provide access to some properties such as frames" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "device = AwsDevice(experiment_configuration[device_name][\"device_arn\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With both devices, frames are predefined in the device capabilities and can be loaded with the Amazon Braket SDK. In this notebook, we will drive a single qubit, which only requires the frames:\n", + "- `q4_rf_frame` to drive the qubit and `q4_ro_rx_frame` to measure it. (Rigetti Aspen M-3)\n", + "- `q0_drive` to drive the qubit and `r0_measure` to measure it. (OQC Lucy) \n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "qubit = experiment_configuration[device_name][\"qubit\"]\n", + "drive_frame = device.frames[experiment_configuration[device_name][\"drive_frame\"]]\n", + "readout_frame = device.frames[experiment_configuration[device_name][\"readout_frame\"]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Qubit spectropscopy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Qubit spectroscopy is one of the first step to charaterize a qubit. While this information is already present in the frame properties, we will build a pulse sequence to estimate the transition frequency between the ground state and the first excited state.\n", + "\n", + "For simplicity, we will use Gaussian or Constant waveforms as envelopes of the different pulses. The Gaussian waveforms are parametrized by their amplitude $A$ and the length $d$ of their pulse window. They are positioned at the center of the window ($d$/2) and their width (1/e) will be set to be a quarter of the window length ($d$/4). The Constant waveforms have a complex amplitude $iq$ . \n", + "\n", + "For qubit spectroscopy, while a prior knowledge of the systems helps choosing these parameters to increase the signal-to-noise ratio, it is not necessary to tune them precisely. \n", + "\n", + "With Aspen, we will use a pulse length of 100ns, the Gaussian has a width of 25ns and its amplitude is 0.1. With Lucy, We will use a pulse length of 25ns and an amplitude is 0.03. The amplitude unit should be considered as arbitrary, the maximum amplitude can be retrieved from the device capabilities, please see the documentation for more details." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "waveform = experiment_configuration[device_name][\"spectroscopy_wf\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "The pulse sequence below contains three instructions:\n", + "-\tThe first sets the frequency of the microwave signal to a chosen frequency among the range of frequency to probe\n", + "-\tThe second plays the waveform.\n", + "-\tThe third instruction is a readout instruction. Measurements are realized via the predefined function capture_v0() that executes a projective measurement of the qubit and returns the projected eigenstate.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "frequency = FreeParameter(\"frequency\")\n", + "\n", + "pulse_sequence = ( \n", + " PulseSequence()\n", + " .set_frequency(drive_frame, frequency)\n", + " .play(drive_frame, waveform)\n", + " .capture_v0(readout_frame)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will sweep the frequency over a range that is centered around the expected transition frequency. For that, we use the FreeParameter object that we defined in the previous cell and create a new pulse sequence by binding the FreeParameter to each tested frequency.\n", + "\n", + "We then run our batch of pulse sequence with `device.run_batch`, which returns a batch of quantum tasks." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "span = 75e6\n", + "N_steps = 25\n", + "N_shots = 100\n", + "frequencies = np.linspace(drive_frame.frequency-span/2, drive_frame.frequency+span/2, N_steps)\n", + "\n", + "qubit_spectroscopy_sequences = [pulse_sequence(frequency=frequency) for frequency in frequencies]\n", + "batch = device.run_batch(qubit_spectroscopy_sequences, shots=N_shots)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After executing this batch of tasks, we are ready to analyze the results. We will use a simple Gaussian fit function to extract the transition frequency." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def resonance_fit(x, A, A0, w, x0):\n", + " return A0-A*np.exp(-(x-x0)**2/w**2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result format is the same as with circuits, which means that `result()` will return a task result object that includes a counter with the number of occurences for each eigenstate of the measurement basis. Since we have been using a batch, we can quickly construct the probability to measure the state $|0\\rangle$. \n", + "\n", + "The data are then plotted and fitted with the previously defined fit function." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Expected resonance frequency: 4728.33 GHz\n", + "Measured resonance frequency: 4726.44 GHz\n" + ] + }, + { + "data": { + "image/png": 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laqMPYJ+94JzxulWsswOxeDXNTdP81OdGxBt0GgZX/gTWzyd522yCeZoKgi56idroA9TxPfDFS879m38PYWrO8AX+2qfIW6nmRsRbjJwBrWJpWXyA6eEr1UYv1RkGZPwC7BWQ+APoM9bsiKQe/LFPkbdSciPiLUJaQ+pTAPw/lhLDCbXRS1W7VsKuj8AaBDc971Pz2Yg0JyU3It6k/zi47Apa2E/xr6TP1EYv5zgcsMqZ/HLlFOdUAiJSI/W5EfEmVivc8DS8dhOd9r/LuodnsPFkhNroBba9C3nbICQSrk43OxoRr6bkRsTbdB7u7E+xZxW2T58j5Y6XzY5IzGavdM5iDXDV/6oTscglqFlKxBtd/2vn9uslcGynubGI+b5eAif2QXh7GDbV7GhEvJ6SGxFv1HEQ9BoDGPD5S2ZHI2ZyOGDdPOf+8P+FkFamhiPiC0xPbubPn0+XLl0IDQ1l2LBhbNy4sdZzKysrefrpp0lMTCQ0NJQBAwaQkZHRjNGKNKOrf+rcfr0Eio6YG4uYZ+cyOL4LQiNhcJrZ0Yj4BFOTmyVLlpCens6sWbPIyspiwIABjBo1iqNHj9Z4/q9//Wtefvll/vjHP7J9+3amTJnC7bffzpYtW5o5cpFmkHAFdBoOjkpY/2ezoxEzGAasm+vcv2IyhEaYG4+IjzA1uZkzZw6TJ08mLS2NpKQkFi5cSFhYGIsWLarx/DfeeINf/vKX3HzzzXTr1o2pU6dy88038+KLL9b6GuXl5RQVFVV5iPiMqx91bje9DmWFZkYiZsheD4c3Q4tQGDbF7GhEfIZpyU1FRQWbN28mNTX1XDBWK6mpqWRmZtZ4TXl5OaGhVef9aNmyJevWrav1dWbPnk1kZKT7kZCQ4JkCiDSH7jdA+95QUQxfvW12NNLcNv7Fue1/N7Rqb24sIj7EtOQmPz8fu91ObGxsleOxsbHk5ubWeM2oUaOYM2cOu3btwuFwsHLlSpYuXUpOTk6trzNjxgwKCwvdj4MHD3q0HCJNymqFKx507n/5V2czhQSG4lzY8YFz/4rJ5sYi4mNM71BcH3/4wx/o0aMHvXv3Jjg4mGnTppGWlobVWnsxQkJCiIiIqPIQ8Sn9x0FwK+cq0PvXmh2NNJfNr4PjDHRKgfj+Zkcj4lNMS26io6Ox2Wzk5eVVOZ6Xl0dcXFyN17Rv35733nuP0tJSDhw4wHfffUerVq3o1q1bc4QsYo7QCGeCA87aG/F/9krY9Jpz31VzJyJ1ZlpyExwczODBg1m1apX7mMPhYNWqVaSkpFz02tDQUDp27MiZM2d49913ufXWW5s6XBFzuT7gdvwHivMufq74vt0fQ0muc9K+PreYHY2IzzG1WSo9PZ1XXnmFxYsXs2PHDqZOnUppaSlpac65HCZMmMCMGTPc52/YsIGlS5eyd+9e1q5dy+jRo3E4HPz85z83qwgizSM2CS67Agw7fPNPs6ORprblTee2/zhoEWxuLCI+yNS1pcaNG8exY8eYOXMmubm5JCcnk5GR4e5knJ2dXaU/TVlZGb/+9a/Zu3cvrVq14uabb+aNN96gTZs2JpVApBkl/xgOfQlb/wEp08CiBTT9Uskx+P7s5KTJ95obi4iPshhGYA2/KCoqIjIyksLCQnUuFt9y+iT8vifYy+GhT6FDstkReZVTFWdImrkCgO1PjyIs2EfXBc6cDyt+CR0GwUOrzY5GxGvU5/Pbp0ZLiQS0lm2g9xjn/tZ/mBqKNCHXz3agam1EGkrJjYgvcTVTfPMv54ga8S9Hd0DeNrAGQd//MTsaEZ+l5EbEl3QbAWHRcLoA9n1qdjTiaduWOrfdU6FlW3NjEfFhSm5EfImtBSSdHRr87b/NjUU8yzDg27PJTd87zI1FxMcpuRHxNZef/eDb8SGcqTA3FvGc3K/h+G7nIpm9bjI7GhGfpuRGxNd0Hg6tYp2rhO9dY3Y04inb3nVue46CkNbmxiLi45TciPgaqw2Szs7K7WrGEN9mGLD9fef+5WqSEmksJTcivujy253bncs1asofHN0OJ/Y7m6R63GB2NCI+T8mNiC9KGAZh7ZxNUwe+MDsaaazvljm33UZCcLi5sYj4ASU3Ir7IaoOeo537O5ebG4s03nf/cW5dkzSKSKMouRHxVb1udm53Lnf22RDfVHgIcr4Ci1WjpEQ8RMmNiK9KHOnso3EyG/K+NTsaaajvzta8JQyD8GhzYxHxE0puRHxVcLizjwaoacqXuX52rpo4EWk0JTcivszVjPH9CnPjkIapKIUDnzv3XX2oRKTRlNyI+DLXsOHDm+FUgbmxSP3tWwv2CojsBNE9zI5GxG8ouRHxZREdIOZywIA9n5gdjdTX7pXObY9UsFjMjUXEjyi5EfF13X/g3O7+2Nw4pH4MA3adTW66a+I+EU9SciPi67qnOre7V4HDYW4sUnfHd8PJA2ALhq7Xmh2NiF9RciPi6zqlQFA4lB6FvG/MjkbqylVr0ykFQlqZG4uIn1FyI+LrWgRDt+uc+64PTPF+e1c7t65mRRHxGCU3Iv4g8Xrndt+n5sYhdWOvPLcmWLcRpoYi4o+U3Ij4g65na26yN0BlmbmxyKUd3gwVJdAyCmL7mR2NiN9RciPiD6J7QKs4sJfDoY1mRyOXsvdsDVvXa8Cqt2ERT9NflYg/sFjOjbjZq6Ypr+dqPlSTlEiTUHIj4i9cyc2+z8yNQy6uohQOnq1dczUniohHtTA7ABHxENeIqcObobwYQlqbG48AYHcYbNxXwNHiMmJahzLUvgWboxIiEyCqm9nhifglJTci/qJNJ2jbBU7sd47E6TnK7IgCXsa2HJ76cDs5hec6eT8d/g4TwFnTpiUXRJqEmqVE/EmXa5zb/evMjUPI2JbD1DezqiQ2AEmV2wD4psXlZoQlEhCU3Ij4k85XObeuOVTEFHaHwVMfbse44Hgo5fS37AHgya/bYHdceIaIeIKSGxF/0nm4c5uz1dlxVUyxcV9BtRobgIHW3QRb7OQYUWwuimTjvgITohPxf6YnN/Pnz6dLly6EhoYybNgwNm68+Bwd8+bNo1evXrRs2ZKEhAR++tOfUlamSctEAGe/m4iO4DgDhzaZHU3AOlpc83vSFZadAGx09AYstZ4nIo1janKzZMkS0tPTmTVrFllZWQwYMIBRo0Zx9OjRGs//xz/+wS9+8QtmzZrFjh07ePXVV1myZAm//OUvmzlyES9lsTgXYgQ1TZkopnVojceHWncAruSm9vNEpHFMTW7mzJnD5MmTSUtLIykpiYULFxIWFsaiRYtqPP+LL77gqquu4sc//jFdunThxhtv5J577rlkbY9IQHE1TWUruTHL0K5RxEeGcv5YqCDOMNi6C3AmN/GRoQztGmVOgCJ+zrTkpqKigs2bN5OamnouGKuV1NRUMjMza7xm+PDhbN682Z3M7N27l+XLl3PzzTfX+jrl5eUUFRVVeYj4NVdyc/BLOFNhbiwByma1MGtsEoA7welr2UdLSwXHjdbsNjoya2wSNquGgos0BdOSm/z8fOx2O7GxsVWOx8bGkpubW+M1P/7xj3n66ae5+uqrCQoKIjExkREjRly0WWr27NlERka6HwkJCR4th4jXie4FLdvCmdOQ85XZ0QSs0X3jWTB+EHGRzqanwdbvAdhm68OC8YMZ3TfezPBE/JrpHYrrY82aNfz2t7/lz3/+M1lZWSxdupRly5bxzDPP1HrNjBkzKCwsdD8OHjzYjBGLmMBqhYQrnfsHN5gbS4Ab3TeedY9fz1uTr+T+Ts6+hNeMHKPERqSJmTZDcXR0NDabjby8vCrH8/LyiIuLq/GaJ554gvvuu48HH3wQgH79+lFaWspDDz3Er371K6w1rK4bEhJCSEiI5wsg4s0SroDv/6sVwr2AzWohpVsUFH8NgLXTMJMjEvF/ptXcBAcHM3jwYFatWuU+5nA4WLVqFSkpKTVec+rUqWoJjM1mA8AwNBmWiNtlQ53bg1+aG4c4ncyGkjywtoAOyWZHI+L3TF1bKj09nYkTJzJkyBCGDh3KvHnzKC0tJS0tDYAJEybQsWNHZs+eDcDYsWOZM2cOAwcOZNiwYezevZsnnniCsWPHupMcEQE6DgKLDYqPQOEhiLzM7IgC26GzSWb8AAhqaW4sIgHA1ORm3LhxHDt2jJkzZ5Kbm0tycjIZGRnuTsbZ2dlVamp+/etfY7FY+PWvf83hw4dp3749Y8eO5Te/+Y1ZRRDxTsHhEHs55H4NBzcquTGbq++Tq0ZNRJqUxQiw9pyioiIiIyMpLCwkIiLC7HBEms6y/4Mv/wpX/gRGzzY7miZ3quIMSTNXALD96VGEBZv6v1tVL1/rHLl252vQ9w6zoxHxSfX5/Pap0VIiUg/ufjfqVGyqilLIda4EToJqbkSag5IbEX+VcIVzm/MVVGoNI9Mc2QqGHVp3UPOgSDNRciPir9p2hfD24KjUZH5mOrzZub1ssLlxiAQQJTci/spigY5nP1CPZJkbSyBzJTcdldyINBclNyL+rMMg5/awkhvTuL73rp+FiDQ5JTci/kw1N+YqOQaF2YBFk/eJNCMlNyL+rMNA5/b4bjh90tRQApIrqYzuCaGR5sYiEkCU3Ij4s/B20Kazc//IFnNjCUTqbyNiCiU3Iv5OTVPmcSc36m8j0pyU3Ij4u47qVGwKwzj3PVdyI9KslNyI+DtXzY2Sm+Z18gCcLgBrEMT2NTsakYCi5EbE38UPAIvVuUJ4cZ7Z0QQO18SJsUnQIsTcWEQCjJIbEX8XHA7tejj3c782N5ZAcmSrcxufbGYUIgFJyY1IIIjr59xqGYbm4/pexw8wNw6RAKTkRiQQxPd3bnO/MTeOQGEYkLPVua+aG5Fmp+RGJBDEuZIbNUs1i6LDcOo4WGwQe7nZ0YgEHCU3IoHAldwU7IWyInNjCQSu/jYxfSAo1NRQRAKRkhuRQBDeDiOiIwBrP19D5p7j2B2GyUH5MXd/m2RTwxAJVC3MDkBEml7GthzCS+K5hsN8/MnHLLbbiI8MZdbYJEb3jTc7PP+jzsQiplLNjYify9iWw9Q3s8iqSADgcst+AHILy5j6ZhYZ23JMjM5PuZIbrQQuYgolNyJ+zO4weOrD7RjAdkcXAJKsBwBwNUo99eF2NVF5UskxKMkFLOpMLGISJTcifmzjvgJyCssA+NboAkBPy0GCOAM4E5ycwjI27iswKUI/lLfNuY3q5pxAUUSanZIbET92tLjMvX/IiKbQCCPYYqeH5VCt50kjuZIb1dqImEbJjYgfi2l9/jBkS7WmqZrPk0bJ+9a5dc0KLSLNTsmNiB8b2jWK+MhQLGe//tboDJzrVGwB4iNDGdo1ypT4/FKuam5EzKbkRsSP2awWZo1NApyJzLfn1dy4Ep5ZY5OwWS01Xi/1ZK+EY98592P7mhuLSABTciPi50b3jWfB+EHERYay/WzNTZLlAPERwSwYP0jz3HhS/vfgqISQCGjTyexoRAKWJvETCQCj+8ZzQ1IcX+65HPtbM2ntOM3ahxKxRSux8ShXf5vYy8Gi2jARs6jmRiRA2KwWruwRhy3O2RfElqdFND3Oteq6+tuImErJjUigcY3icX0Qi+e4a27U30bETEpuRAKNa4XwXNXceJx7jhslNyJm8orkZv78+XTp0oXQ0FCGDRvGxo0baz13xIgRWCyWao8xY8Y0Y8QiPsyd3GwzNw5/U3IMSvIAC8T0MTsakYBmenKzZMkS0tPTmTVrFllZWQwYMIBRo0Zx9OjRGs9funQpOTk57se2bduw2WzcddddzRy5iI9yffAWH4HTJ00Nxa+4l13oCiGtzI1FJMCZntzMmTOHyZMnk5aWRlJSEgsXLiQsLIxFixbVeH5UVBRxcXHux8qVKwkLC1NyI1JXoREQ6Vwh3D0nizSe+tuIeA1Tk5uKigo2b95Mamqq+5jVaiU1NZXMzMw63ePVV1/lRz/6EeHhNS9QV15eTlFRUZWHSMBz1d64PpCl8dTfRsRrmJrc5OfnY7fbiY2NrXI8NjaW3NzcS16/ceNGtm3bxoMPPljrObNnzyYyMtL9SEhIaHTcIj7Pldwc3WFuHP7EldzEKbkRMZvpzVKN8eqrr9KvXz+GDh1a6zkzZsygsLDQ/Th48GAzRijipWKcSzIoufEQeyUc2+ncV82NiOlMnaE4Ojoam81GXl5eleN5eXnExcVd9NrS0lLefvttnn766YueFxISQkhISKNjFfEr7pqb7WAYmk23sfJ3gb1Cyy6IeAlTa26Cg4MZPHgwq1atch9zOBysWrWKlJSUi177r3/9i/LycsaPH9/UYYr4n+ieYLHC6QIoqXlkotRD3nkrgStRFDGd6c1S6enpvPLKKyxevJgdO3YwdepUSktLSUtLA2DChAnMmDGj2nWvvvoqt912G+3atWvukEV8X1BLiOrm3D+63dxY/MH5yY2ImM70hTPHjRvHsWPHmDlzJrm5uSQnJ5ORkeHuZJydnY3VWjUH27lzJ+vWreOjjz4yI2QR/xDTB47vdva7SRxpdjS+7fwFM0XEdKYnNwDTpk1j2rRpNT63Zs2aasd69eqFYRhNHJWIn4tJgh0fqubGE46enS/I1VFbRExlerOUiJhEw8E9o6wIig4599v3MjcWEQGU3IgELlctw7HvwOEwNxZflv+9c9sqDlq2NTcWEQGU3IgErqhuYAuGihIo1PxPDeZawkK1NiJeQ8mNSKCyBTmHhIOaphrD9b3TSuAiXqNByU1eXh733XcfHTp0oEWLFthstioPEfER7pmK1am4wVwzE6vmRsRrNGi01KRJk8jOzuaJJ54gPj4eiyatEvFN6lTceO5mKdXciHiLBiU369atY+3atSQnJ3s4HBFpVlpjqnHKi8/1V1LNjYjXaFCzVEJCguaZEfEHrpqb/J3OxR+lfo65RkrFQliUubGIiFuDkpt58+bxi1/8gv3793s4HBFpVpEJENzKuehjwV6zo/E9Gikl4pUa1Cw1btw4Tp06RWJiImFhYQQFBVV5vqCgwCPBiUgTs1qhfW84vMnZqVgf0vVz7GxznvrbiHiVBiU38+bN83AYImKamD7O5CZvO1x+u9nR+BaNlBLxSg1KbiZOnOjpOETELOf3u5H6ca8ppZobEW/S4IUz7XY77733Hjt2OKtlL7/8cm655RbNcyPia1wT+bk6x0rdlJdAYbZzv31vc2MRkSoalNzs3r2bm2++mcOHD9Orl7M6dvbs2SQkJLBs2TISExM9GqSINCFXcnN8N9jPgK3B//MEFldNV3iMRkqJeJkGjZZ65JFHSExM5ODBg2RlZZGVlUV2djZdu3blkUce8XSMItKUIhMgKAwclXBiv9nR+I6jGikl4q0a9C/ap59+yvr164mKOvffSrt27Xjuuee46qqrPBaciDQDqxXadYfcr521EdHdzY7INxxTfxsRb9WgmpuQkBCKi4urHS8pKSE4OLjRQYlIM3PVPhxTp+I60xw3Il6rQcnND3/4Qx566CE2bNiAYRgYhsH69euZMmUKt9xyi6djFJGmFn32Azp/l7lx+BKtKSXitRqU3Lz00kskJiaSkpJCaGgooaGhXHXVVXTv3p0//OEPno5RRJpadA/nVsPB66a8BE5qpJSIt2pQn5s2bdrw/vvvs2vXLr77zvnfS58+fejeXW31Ij7J3Sz1PRgGWCzmxuPt8s8Omw9vD+HtzI1FRKpp1JjPHj160KNHD0/FIiJmiUoEiw0qiqE4ByI6mB2Rd3M3SanWRsQb1Tm5SU9P55lnniE8PJz09PSLnjtnzpxGByYizahFMER1dc51c2ynkptLcdXcqDOxiFeqc3KzZcsWKisr3fsi4meiezmTm/zvIXGk2dF4N1fH63aquRbxRnVOblavXl3jvoj4ifY9Yeeyc7USUrvju51bzQkk4pUaNFrq/vvvr3Gem9LSUu6///5GByUiJnCvMaURUxflsEPBXud+OyU3It6oQcnN4sWLOX36dLXjp0+f5m9/+1ujgxIRE7jnulHNzUWdPAD2CrCFOJeuEBGvU6/RUkVFRe5J+4qLiwkNDXU/Z7fbWb58OTExMR4PUkSagWuum5I8OH0SWrYxMxrvdXyPc9suEaw2c2MRkRrVK7lp06YNFosFi8VCz549qz1vsVh46qmnPBaciDSj0Aho3QGKjzhrbxKGmh2Rd3J3JlaTlIi3qldys3r1agzD4Prrr+fdd9+tsnBmcHAwnTt3pkMHDSEV8VntezqTm2M7ldzU5vjZ5CZaI6VEvFW9kpvrrrsOgH379pGQkIDV2qAuOyLiraJ7wd41WobhYlRzI+L1GpSddO7cGavVyqlTp/juu+/4+uuvqzzqY/78+XTp0oXQ0FCGDRvGxo0bL3r+yZMnefjhh4mPjyckJISePXuyfPnyhhRDRC7kXmNKC2jWyjUMXHPciHitBi2/cOzYMdLS0vjvf/9b4/N2u71O91myZAnp6eksXLiQYcOGMW/ePEaNGsXOnTtr7JhcUVHBDTfcQExMDO+88w4dO3bkwIEDtGnTpiHFEJELudeYUs1NjcpLnMtTgOa4EfFiDaq5efTRRzl58iQbNmygZcuWZGRksHjxYnr06MEHH3xQ5/vMmTOHyZMnk5aWRlJSEgsXLiQsLIxFixbVeP6iRYsoKCjgvffe46qrrqJLly5cd911DBgwoCHFEJELuYaDnzwAlWXmxuKNXLU2YdHQsq25sYhIrRqU3HzyySfMmTOHIUOGYLVa6dy5M+PHj+d3v/sds2fPrtM9Kioq2Lx5M6mpqeeCsVpJTU0lMzOzxms++OADUlJSePjhh4mNjaVv37789re/vWhNUXl5OUVFRVUeIlKLVjEQGgmG49wHuZzjnplYTVIi3qxByU1paam72aht27YcO3YMgH79+pGVlVWne+Tn52O324mNja1yPDY2ltzc3Bqv2bt3L++88457Tp0nnniCF198kWeffbbW15k9ezaRkZHuR0KCJt0SqZXFct5kfmqaqsbdmTjR3DhE5KIalNz06tWLnTudb3wDBgzg5Zdf5vDhwyxcuJD4+HiPBng+h8NBTEwMf/nLXxg8eDDjxo3jV7/6FQsXLqz1mhkzZlBYWOh+HDx4sMniE/ELrloJ12R1cs5xLZgp4gsa1KF4+vTp5OQ4O9XNmjWL0aNH8/e//53g4GBef/31Ot0jOjoam81GXl5eleN5eXnExcXVeE18fDxBQUHYbOdmBe3Tpw+5ublUVFQQHBxc7ZqQkBBCQkLqWDIRcQ9x1oip6tQsJeITGlRzM378eCZNmgTA4MGDOXDgAF9++SUHDx5k3LhxdbpHcHAwgwcPZtWqVe5jDoeDVatWkZKSUuM1V111Fbt378bhcLiPff/998THx9eY2IhIA7hrbpTcVGEY5y29oORGxJt5ZBa+sLAwBg0aRHR0dL2uS09P55VXXmHx4sXs2LGDqVOnUlpaSlpaGgATJkxgxowZ7vOnTp1KQUEB06dP5/vvv2fZsmX89re/5eGHH/ZEMUQEztXcHN/j/EAXp+IcqCgBiw3adjE7GhG5iDo3S6Wnp9f5pnPmzKnTeePGjePYsWPMnDmT3NxckpOTycjIcHcyzs7OrjILckJCAitWrOCnP/0p/fv3p2PHjkyfPp3HH3+8zrGJyCVEdQOLFcqLoOQotI699DWBwNVM17YztFBNsYg3q3Nys2XLljqdZ7FY6hXAtGnTmDZtWo3PrVmzptqxlJQU1q9fX6/XEJF6aBECbTrBif3OpiklN07qTCziM+qc3Kxevbop4xARb9Ku+9nkZjd0udrsaLyDq7+NOhOLeD2tfCki1bXTGlPVaMFMEZ/RoKHgI0eOvGjz0yeffNLggETEC0Sf16lYnFzNUqq5EfF6DUpukpOTq3xdWVnJ1q1b2bZtGxMnTvREXCJiJveIKdXcAHCmHE5mO/dVcyPi9RqU3MydO7fG408++SQlJSWNCkhEvICrWerEfrBXgi3I1HBMV7DXud5WcGtopQ7WIt7Oo31uxo8fX+uK3iLiQyI6QFAYOM7AiQNmR2M+98zE3Z3rb4mIV/NocpOZmUloaKgnbykiZrBYzi0Oqaap8zoTq7+NiC9oULPUHXfcUeVrwzDIyclh06ZNPPHEEx4JTERM1q4H5H7j/GDvdZPZ0ZhLa0qJ+JQGJTeRkZFVvrZarfTq1Yunn36aG2+80SOBiYjJ3GtM7TY3Dm/grrlJNDcOEamTBiU3r732mqfjEBFv4x4xpeRGsxOL+JYGJTcumzZtYseOHQAkJSUxePBgjwQlIl7AldwE+kR+pwrg9AnnvmpuRHxCg5KbQ4cOcc899/D555/Tpk0bAE6ePMnw4cN5++23ueyyyzwZo4iYwZXclB6FskIIjbz4+f7KldxFXAbB4ebGIiJ10qDRUg8++CCVlZXs2LGDgoICCgoK2LFjBw6HgwcffNDTMYqIGUIjzs3pEshNU+6ZiTV5n4ivaFDNzaeffsoXX3xBr1693Md69erFH//4R6655hqPBSciJmvXA0ryIH83dAzQZmetKSXicxpUc5OQkEBlZWW143a7nQ4dOjQ6KBHxEtHqVOwuuzoTi/iMBiU3L7zwAv/7v//Lpk2b3Mc2bdrE9OnT+f3vf++x4ETEZFpjqursxCLiExrULDVp0iROnTrFsGHDaNHCeYszZ87QokUL7r//fu6//373uQUFBZ6JVESan6u2Ij9Aa24cdue6UqCaGxEf0qDkZt68eR4OQ0S8kmsiv4I94HCA1aMrtni/kwfAXgG2EIhMMDsaEamjBiU3EydO9HQcIuKN2nQCawuoPAXFRyAywKZ5cNVYtUsMvMROxIc1eBI/u93Oe++9557E7/LLL+eWW27BZrN5LDgRMZktCNp2dfa5yd8VeMnNcY2UEvFFDUpudu/ezc0338zhw4fdw8Fnz55NQkICy5YtIzFRs3iK+I123Z0f8sd3Q+JIs6NpXlowU8QnNaie9ZFHHiExMZGDBw+SlZVFVlYW2dnZdO3alUceecTTMYqImQJ5OHi+1pQS8UUNnsRv/fr1REVFuY+1a9eO5557jquuuspjwYmIF3CPmArA4eCquRHxSQ2quQkJCaG4uLja8ZKSEoKDgxsdlIh4kUBdHby8GIpznPtaMFPEpzQoufnhD3/IQw89xIYNGzAMA8MwWL9+PVOmTOGWW27xdIwiYiZXrcXJbKgsMzeW5uRK5sKioWVbc2MRkXppUHLz0ksv0b17d4YPH05oaCihoaFcddVVdO/enT/84Q+ejlFEzBTeHkIiAQNO7DM7muZzfI9zqyYpEZ9Trz43DoeDF154gQ8++ICKigpuu+02Jk6ciMVioU+fPnTvruGSIn7HYnE2yxzJcva7ieljdkTNQwtmiviseiU3v/nNb3jyySdJTU2lZcuWLF++nMjISBYtWtRU8YmIN4ju4UxuAmmNKVdZVXMj4nPq1Sz1t7/9jT//+c+sWLGC9957jw8//JC///3vOByOpopPRLyBa8SUq6kmEGgYuIjPqldyk52dzc033+z+OjU1FYvFwpEjRzwemIh4EddooUAZDm4Y5xI5NUuJ+Jx6JTdnzpwhNDS0yrGgoCAqKys9GpSIeBlX00ygNEsV50BlKVhs0LaL2dGISD3Vq8+NYRhMmjSJkJAQ97GysjKmTJlCeHi4+9jSpUvrFcT8+fN54YUXyM3NZcCAAfzxj39k6NChNZ77+uuvk5aWVuVYSEgIZWUBNERVpLlFna25OX0CThVAWNTFz/d1rhqqtl2ghebuEvE19UpualoNfPz48Y0KYMmSJaSnp7Nw4UKGDRvGvHnzGDVqFDt37iQmJqbGayIiIti5c6f7a4vF0qgYROQSgsMg4jIoOuT84O80zOyImpY6E4v4tHolN6+99prHA5gzZw6TJ09218YsXLiQZcuWsWjRIn7xi1/UeI3FYiEuLs7jsYjIRUR3dyY3x3f7f3KTf3YCP/W3EfFJDZrEz1MqKirYvHkzqamp7mNWq5XU1FQyMzNrva6kpITOnTuTkJDArbfeyrffflvrueXl5RQVFVV5iEgDBNIyDMc1x42ILzM1ucnPz8dutxMbG1vleGxsLLm5uTVe06tXLxYtWsT777/Pm2++icPhYPjw4Rw6dKjG82fPnk1kZKT7kZCQ4PFyiASEdgHUqVgLZor4NFOTm4ZISUlhwoQJJCcnc91117F06VLat2/Pyy+/XOP5M2bMoLCw0P04ePBgM0cs4ifcNTd+PtfNmXLnOlqgOW5EfFS9+tx4WnR0NDabjby8vCrH8/Ly6tynJigoiIEDB7J7d81V5SEhIVVGd4lIA7nmujm+Bxx2sNrMjaepFOwFwwEhEdCq5kENIuLdTK25CQ4OZvDgwaxatcp9zOFwsGrVKlJSUup0D7vdzjfffEN8fHxThSkiAG06gS0Y7OVQWHMzsF84f00pjcQU8UmmN0ulp6fzyiuvsHjxYnbs2MHUqVMpLS11j56aMGECM2bMcJ//9NNP89FHH7F3716ysrIYP348Bw4c4MEHHzSrCCKBwWqDqG7OfX/ud6POxCI+z9RmKYBx48Zx7NgxZs6cSW5uLsnJyWRkZLg7GWdnZ2O1nsvBTpw4weTJk8nNzaVt27YMHjyYL774gqSkJLOKIBI42nWHY985m6a6p176fF/k6lOkzsQiPsv05AZg2rRpTJs2rcbn1qxZU+XruXPnMnfu3GaISkSqCYTh4PmquRHxdaY3S4mID3F94PvzApqanVjE5ym5EZG6cy+g6afDwUuPO9fPgnPraYmIz1FyIyJ156q5KTwIlafNjaUpuGptIi5zrqclIj5JyY2I1F1YOwhtAxjO+WD8jXtmYvW3EfFlSm5EpO4sFv/ud3O2TI52Pcjcc5z3tx4mc89x7A7D5MBEpD68YrSUiPiQ6B5weJN/jpg6W6a5Wxz8ce169+H4yFBmjU1idF9NFiriC1RzIyL1c/4yDH6m5PAOALaeal/leG5hGVPfzCJjW44ZYYlIPSm5EZH6cc9141/NUvYzlYQUHwBgn1G1hsbVKPXUh9vVRCXiA5TciEj9uFbK9rNmqa+2fUMQZygzgjhstKv2vAHkFJaxcV9B8wcnIvWi5EZE6se1vtTpE855YfxEee53AOwz4jAu8tZ4tLisuUISkQZSciMi9RMcBpEJzn0/qr2Jr3SudL7XuHin4ZjWoc0Rjog0gpIbEak/d6di/+l304kjAOwzOtT4vAXnqKmhXaOaMSoRaQglNyJSf37Y78Z6tiz7HHFYLnjO9fWssUnYrBc+KyLeRsmNiNSfP64OfrYsd44aSVxk1aanuMhQFowfpHluRHyEJvETkfpzz1LsJ8lNeTEUO+ewSRl6JeuuiWTjvgKOFpcR09rZFKUaGxHfoeRGROrPtfZSwV5w2MFqMzeexnLVQIW3h5ZtsAEpidWHg4uIb1CzlIjUX2QC2ELAXu5cIdzXuWqgXH2JRMSnKbkRkfqz2s7Nd+MP/W5co75co8BExKcpuRGRhnElAv7Q78aVoEWr5kbEHyi5EZGG8acRU/mumhslNyL+QMmNiDRMtJ/MdWMY51Y4V82NiF9QciMiDeMvNTdFR6CyFCw2aNvF7GhExAOU3IhIw7iacAoPQuVpc2NpDFdn4rZdwBZkaigi4hlKbkSkYcKiILSNc9/VrOOL1JlYxO8ouRGRhrFY/KPfjXuOm+7mxiEiHqPkRkTqze4wyNxznGyLcwVtR74Prw6e/71zq5obEb+h5EZE6iVjWw5XP/8J97yyniV7QwBY8elaMrblmBxZA7kSs+he5sYhIh6j5EZE6ixjWw5T38wip7AMgD2Gs+amw5mDTH0zy/cSnIpTUJjt3I/uaW4sIuIxSm5EpE7sDoOnPtyOcd6x3WeTm26WHMD5vN1h1Hi9V3KNlAprB+FaKFPEXyi5EZE62bivwF1j43LAiOOMYaW15TQxnCCnsIyN+wpMirAB3E1SqrUR8SdKbkSkTo4Wl1U7VkkLDhixAHS3Hq71PK91bKdzq87EIn7FK5Kb+fPn06VLF0JDQxk2bBgbN26s03Vvv/02FouF2267rWkDFBFiWofWeNzV7ybRcuSi53kl90gpdSYW8SemJzdLliwhPT2dWbNmkZWVxYABAxg1ahRHjx696HX79+/nscce45prrmmmSEUC29CuUcRHhmK54LgruelhOUJ8ZChDu0Y1f3ANpWYpEb9kenIzZ84cJk+eTFpaGklJSSxcuJCwsDAWLVpU6zV2u517772Xp556im7dul30/uXl5RQVFVV5iEj92awWZo1NAqiS4Ox2dASgm+UIs8YmYbNemP54KYddsxOL+ClTk5uKigo2b95Mamqq+5jVaiU1NZXMzMxar3v66aeJiYnhgQceuORrzJ49m8jISPcjISHBI7GLBKLRfeNZMH4QcZHnmp5cNTeDw48yum+8WaHV38kDYC+HFqHQppPZ0YiIB7Uw88Xz8/Ox2+3ExsZWOR4bG8t3331X4zXr1q3j1VdfZevWrXV6jRkzZpCenu7+uqioSAmOSCOM7hvPDUlxbNxXwNHiMuJDkmDJTELLjkFZIYRGmh1i3biapNp1B6vN3FhExKNMTW7qq7i4mPvuu49XXnmF6OjoOl0TEhJCSEhIE0cmElhsVgspiefNC9M6HopznAnDZUPMC6w+NFJKxG+ZmtxER0djs9nIy8urcjwvL4+4uLhq5+/Zs4f9+/czduxY9zGHwwFAixYt2LlzJ4mJiU0btIhUF93jbHLzve8kNxopJeK3TO1zExwczODBg1m1apX7mMPhYNWqVaSkpFQ7v3fv3nzzzTds3brV/bjlllsYOXIkW7duVXOTiFlcCYKrNsQXuEdKqeZGxN+Y3iyVnp7OxIkTGTJkCEOHDmXevHmUlpaSlpYGwIQJE+jYsSOzZ88mNDSUvn37Vrm+TZs2ANWOi0gzcg2ldtWGeDvDgHxXs5SGgYv4G9OTm3HjxnHs2DFmzpxJbm4uycnJZGRkuDsZZ2dnY7WaPmJdRC6mvY8lN6eOw+kTgMXZoVhE/IrpyQ3AtGnTmDZtWo3PrVmz5qLXvv76654PSETqx1X7UbAPzlRAi2Bz47kUVxLWJgGCw8yNRUQ8TlUiItJ4reMhuDUYdijYa3Y0l3ZMTVIi/kzJjYg0nsVyrmNuvg90KnZ3JtZIKRF/pORGRDyj/dlEwRf63biHgWuklIg/UnIjIp7hauI55gvJzdnapfaquRHxR0puRMQzfGU4eMUpOHnQua8+NyJ+ScmNiHiGu1lqF5ydOdwrFewBDGjZFsLaXfJ0EfE9Sm5ExDPadgFrC6gshaLDZkdTu/NHSlks5sYiIk1CyY2IeIYtCKLOru3mzU1Tx75zbtv3NjcOEWkySm5ExHNcMxW7EghvdHSHcxuTZG4cItJklNyIiOe4Eoaj282N42LyvnVuY5XciPgrJTci4jnu5GaHuXHUpqIUTux37qvmRsRvKbkREc9xJzffeeeIqWM7AQPC20N4tNnRiEgTUXIjIp4T1Q1sIc4RUyf3mx1Nde7+Nn3MjUNEmpSSGxHxHFuLc52KvbFpytUXSE1SIn5NyY2IeFbM5c5tnhd2KlZyIxIQlNyIiGe5mny8ccSUhoGLBAQlNyLiWbFna268Lbk5VQDFOc59LZgp4teU3IiIZ7lqbo7vhjPl5sZyPtfEgpGdIDTC3FhEpEkpuRERz4roCCGR4DjjXETTW7hqkjR5n4jfU3IjIp5lsZzX78aLRky5OjhrGLiI31NyIyKe56odOfqtuXGcT52JRQKGkhsR8TxvW4bBMM4bBq6aGxF/p+RGRDzPldx4y1w3xblQdhIsNojuaXY0ItLElNyIiOe5akcKs6GsyNxY4FytTbvu0CLE3FhEpMkpuRERzwuLgtbxzn3XEGwzqUlKJKAouRGRpuFNMxWrM7FIQFFyIyJNw5v63ajmRiSgKLkRkabhHjFlcnLjcMDRs01jqrkRCQhKbkSkabjmusn71jkU2ywn9sGZ09AiFKK6mheHiDQbJTci0jSiewEWOF0AJUfNiyP3a+c2JgmsNvPiEJFm4xXJzfz58+nSpQuhoaEMGzaMjRs31nru0qVLGTJkCG3atCE8PJzk5GTeeOONZoxWROokOMw59Bog9xvz4sg5m9zE9zcvBhFpVqYnN0uWLCE9PZ1Zs2aRlZXFgAEDGDVqFEeP1vyfXlRUFL/61a/IzMzk66+/Ji0tjbS0NFasWNHMkYvIJcUPcG5ztpoXg6vmJk7JjUigMD25mTNnDpMnTyYtLY2kpCQWLlxIWFgYixYtqvH8ESNGcPvtt9OnTx8SExOZPn06/fv3Z926dc0cuYhckqu2xJVgmMFdczPAvBhEpFmZmtxUVFSwefNmUlNT3cesViupqalkZmZe8nrDMFi1ahU7d+7k2muvrfGc8vJyioqKqjxEpJm4a26+Muf1i3Oh9ChYrBopJRJATE1u8vPzsdvtxMbGVjkeGxtLbm5urdcVFhbSqlUrgoODGTNmDH/84x+54YYbajx39uzZREZGuh8JCQkeLYOIXISrKejEfjh9svlf31VrE93T2QdIRAKC6c1SDdG6dWu2bt3Kl19+yW9+8xvS09NZs2ZNjefOmDGDwsJC9+PgwYPNG6xIIAuLgshOzn0zOhXnnq0xUn8bkYDSwswXj46OxmazkZeXV+V4Xl4ecXFxtV5ntVrp3t05CiM5OZkdO3Ywe/ZsRowYUe3ckJAQQkK0UJ6IaeL7OxfQzP0aul7TvK+tkVIiAcnUmpvg4GAGDx7MqlWr3MccDgerVq0iJSWlzvdxOByUl5c3RYgi0lhm9rtxj5Tq1/yvLSKmMbXmBiA9PZ2JEycyZMgQhg4dyrx58ygtLSUtLQ2ACRMm0LFjR2bPng04+9AMGTKExMREysvLWb58OW+88QYLFiwwsxgiUhtXk1BOM4+YOn3C2dfn/BhEJCCYntyMGzeOY8eOMXPmTHJzc0lOTiYjI8PdyTg7Oxur9VwFU2lpKT/5yU84dOgQLVu2pHfv3rz55puMGzfOrCKIyMW4am7yd0JFKQSHN8/rHtni3Lbt6uz7IyIBw2IYZi760vyKioqIjIyksLCQiIgIs8MRCQwv9obiHEj7L3Qe3iQvcariDEkznZN5bn96FGHr58Inz0LfO+HOV5vkNUWk+dTn89snR0uJiI/pONi5Pby5+V7zcFbV1xaRgKHkRkSanivBOLSpeV7PMM4lUh0HNc9riojXUHIjIk3PXXOT1TyvV5QDJXlgsakzsUgAUnIjIk2vw0DA4pzvpqTmRXE96shW5zY2STMTiwQgJTci0vRCI6B9L+d+E/W7sTvOjY04suPs2nTqbyMSkJTciEjzaMJ+Nxnbckid86n76wPbvgDgG7p7/LVExPspuRGR5tFEI6YytuUw9c0s8orOzVLe17oPgJ9/0YKMbTkefT0R8X5KbkSkeZyf3DjsHrml3WHw1IfbuXCyrtaWMoqMML43LuOpD7dXabISEf+n5EZEmkdsXwhuBeVFkPetR265cV8BOYVlNT632dEDO1ZyCsvYuK/AI68nIr5ByY2INA9bC0gY6tzPdnb4tTsMMvcc5/2th8ncc7zeNSxHi2tObAC+dPSq03ki4n9MX1tKRAJIp+Gw5xM48AUZ4bfw1Ifbq9S8xEeGMmtsEqP7xtfpdjGtQ2t9btN5yc3FzhMR/6OaGxFpPp1TACjb+zlT39xcrUkpt7CMqW9m1bkT8NCuUcRHhmK54HiFYeMrIxELzoRpaFctnCkSSJTciEjz6TgYwxpEaNkxOlnyqj3tapSqaydgm9XCrLFJ1Y5/a3ShgmAAZo1Nwma9MP0REX+m5EZEmk9QS4rbOZdDGGr9rsZTDKhXJ+DRfeNZMH4QsREh7mObHT2IiwxlwfhBdW7iEhH/oeRGRJpVbpuBAFxh2XnR8+rTCXh033g+Tr/O/fW1I8ew7vHrldiIBCglNyLSrOwJwwEYbvsWqs1Qc059OwHbig6793sOvUFNUSIBTMmNiDSrnkNHUUELLrPk09WSW+35BncC3ndu+QVCIxoXpIj4NCU3ItKsbKGtKG4/BIDrrF9Xec5V19KgTsB7P730OSISEJTciEizazdgNACpIVVnKm5wJ2CHHQ6s81R4IuLjNImfiDS/xB/Ax09ylW0Hb98/iLxTDmJaO5uiGtRXJucrOH3S42GKiG9SciMizS+2L4S3x1J6jCuDdkHytY27355PPBOXiPgFNUuJSPOzWiHxeuf+7lWNv9/3Kxp/DxHxG0puRMQc3W9wbr9bBkb9FsysoigHDm30TEwi4heU3IiIOXqOAlswHN8FR3c0/D7f/ce57TjYM3GJiM9TciMi5giNcHYsBtj+XsPvs+MD57bXzY0OSUT8g5IbETHP5bc5t9++17DrS4/D/s+d+0puROQsJTciYp5eNzmbpvJ3wtGaF9K8qJ3LwLBDXD+I6uz5+ETEJym5ERHzhEaeGzX1zb/qf/2WN53by2/3XEwi4vOU3IiIufqPc26z/gZnKup+Xe42OLgBrC0g+d6miU1EfJKSGxExV5+x0CoOSo+e6xxcF5tfc257j4HWcU0Tm4j4JCU3ImIuWxAMud+5v/GVul1TXgJfLXHuu64VETnLK5Kb+fPn06VLF0JDQxk2bBgbN9Y+Idcrr7zCNddcQ9u2bWnbti2pqakXPV9EfMDgSWANgoPr4cjWS5+/5Q2oKIaoROjSyKUbRMTvmJ7cLFmyhPT0dGbNmkVWVhYDBgxg1KhRHD16tMbz16xZwz333MPq1avJzMwkISGBG2+8kcOHDzdz5CLiMa1jzw0L/3jWxWcsPn0CPn3euT98mnMpBxGR85j+rjBnzhwmT55MWloaSUlJLFy4kLCwMBYtWlTj+X//+9/5yU9+QnJyMr179+avf/0rDoeDVatqXp+mvLycoqKiKg8R8UIjfwW2ENi75tyswzVZ+6IzwWnfGwZOaLbwRMR3mJrcVFRUsHnzZlJTU93HrFYrqampZGZm1ukep06dorKykqioqBqfnz17NpGRke5HQkKCR2IXEQ+L6grD/9e5v+KXUFFa/Zy8b2HDy879G54BW4vmi09EfIapyU1+fj52u53Y2Ngqx2NjY8nNza3TPR5//HE6dOhQJUE634wZMygsLHQ/Dh482Oi4RaSJXJMOER3hZDa89SOoOHXuuZPZ8Ob/gL0CuqdCjxvMi1NEvJpP/9vz3HPP8fbbb7NmzRpCQ0NrPCckJISQkJBmjkxEGiQ4HO5aDG/cBvs+gzfvgGFT4HQBrJsHxTnO5qg7XgGLxexoRcRLmZrcREdHY7PZyMvLq3I8Ly+PuLiLz1vx+9//nueee46PP/6Y/v37N2WYItKcEq6Ae99x1tJkZzofLpEJMH4phNXcDC0iAiY3SwUHBzN48OAqnYFdnYNTUlJqve53v/sdzzzzDBkZGQwZMqQ5QhWR5tQ5BR5aDSnTILonxFwON/4GpqyFyI41XhIW3IL9z41h/3NjCAv26UppEWkk098B0tPTmThxIkOGDGHo0KHMmzeP0tJS0tLSAJgwYQIdO3Zk9uzZADz//PPMnDmTf/zjH3Tp0sXdN6dVq1a0atXKtHKIiIe17wWjfuN8iIjUg+nJzbhx4zh27BgzZ84kNzeX5ORkMjIy3J2Ms7OzsZ43j8WCBQuoqKjgzjvvrHKfWbNm8eSTTzZn6CIiIuKFLIZxsdmy/E9RURGRkZEUFhYSERFhdjgiIiJSB/X5/DZ9Ej8RERERT1JyIyIiIn5FyY2IiIj4FSU3IiIi4leU3IiIiIhfUXIjIiIifkXJjYiIiPgVJTciIiLiV5TciIiIiF9RciMiIiJ+RcmNiIiI+BUlNyIiIuJXTF8VvLm51gktKioyORIRERGpK9fndl3W+w645Ka4uBiAhIQEkyMRERGR+iouLiYyMvKi51iMuqRAfsThcHDkyBFat26NxWJp8H2KiopISEjg4MGDl1x63R+ovP5N5fVvgVZeCLwyB0J5DcOguLiYDh06YLVevFdNwNXcWK1WLrvsMo/dLyIiwm9/kWqi8vo3lde/BVp5IfDK7O/lvVSNjYs6FIuIiIhfUXIjIiIifkXJTQOFhIQwa9YsQkJCzA6lWai8/k3l9W+BVl4IvDIHWnkvJeA6FIuIiIh/U82NiIiI+BUlNyIiIuJXlNyIiIiIX1FyIyIiIn5Fyc0FnnvuOSwWC48++uhFzzt58iQPP/ww8fHxhISE0LNnT5YvX+5+vri4mEcffZTOnTvTsmVLhg8fzpdfftnE0ddfXco7YsQILBZLtceYMWPc5xiGwcyZM4mPj6dly5akpqaya9euZihB/XiqvEuXLuXGG2+kXbt2WCwWtm7d2vTBN5AnylxZWcnjjz9Ov379CA8Pp0OHDkyYMIEjR440UynqzlM/4yeffJLevXsTHh5O27ZtSU1NZcOGDc1QgvrxVHnPN2XKFCwWC/PmzWuaoBvBU+WdNGlStedHjx7dDCWoH0/+fHfs2MEtt9xCZGQk4eHhXHHFFWRnZzdxCcwRcDMUX8yXX37Jyy+/TP/+/S96XkVFBTfccAMxMTG88847dOzYkQMHDtCmTRv3OQ8++CDbtm3jjTfeoEOHDrz55pukpqayfft2Onbs2MQlqZu6lnfp0qVUVFS4vz5+/DgDBgzgrrvuch/73e9+x0svvcTixYvp2rUrTzzxBKNGjWL79u2EhoY2WRnqw5PlLS0t5eqrr+buu+9m8uTJTRZzY3mqzKdOnSIrK4snnniCAQMGcOLECaZPn84tt9zCpk2bmrQM9eHJn3HPnj3505/+RLdu3Th9+jRz587lxhtvZPfu3bRv377JylAfniyvy7///W/Wr19Phw4dPB5vY3m6vKNHj+a1115zf+1tw6g9Wd49e/Zw9dVX88ADD/DUU08RERHBt99+6zXvzx5niGEYhlFcXGz06NHDWLlypXHdddcZ06dPr/XcBQsWGN26dTMqKipqfP7UqVOGzWYz/vOf/1Q5PmjQIONXv/qVJ8NusPqU90Jz5841WrdubZSUlBiGYRgOh8OIi4szXnjhBfc5J0+eNEJCQoy33nrL06E3iCfLe759+/YZgLFlyxbPBeshTVVml40bNxqAceDAAQ9E23hNXd7CwkIDMD7++GMPRNt4TVHeQ4cOGR07djS2bdtmdO7c2Zg7d65ng24ET5d34sSJxq233ur5QD3E0+UdN26cMX78+CaI1DupWeqshx9+mDFjxpCamnrJcz/44ANSUlJ4+OGHiY2NpW/fvvz2t7/FbrcDcObMGex2e7WMuGXLlqxbt65J4q+v+pT3Qq+++io/+tGPCA8PB2Dfvn3k5uZWuVdkZCTDhg0jMzPTYzE3hifL6yuausyFhYVYLJYqNZZmasryVlRU8Je//IXIyEgGDBjQ2FA9wtPldTgc3HffffzsZz/j8ssv92SoHtEUP981a9YQExNDr169mDp1KsePH/dUuI3myfI6HA6WLVtGz549GTVqFDExMQwbNoz33nvPw1F7DzVLAW+//TZZWVl17hOzd+9ePvnkE+69916WL1/O7t27+clPfkJlZSWzZs2idevWpKSk8Mwzz9CnTx9iY2N56623yMzMpHv37k1cmkurb3nPt3HjRrZt28arr77qPpabmwtAbGxslXNjY2Pdz5nJ0+X1BU1d5rKyMh5//HHuuecer1ikr6nK+5///Icf/ehHnDp1ivj4eFauXEl0dLQnQm6Upijv888/T4sWLXjkkUc8FabHNEV5R48ezR133EHXrl3Zs2cPv/zlL7npppvIzMzEZrN5KvQG8XR5jx49SklJCc899xzPPvsszz//PBkZGdxxxx2sXr2a6667zpPhe4WAT24OHjzI9OnTWblyZZ3bHh0OBzExMfzlL3/BZrMxePBgDh8+zAsvvMCsWbMAeOONN7j//vvp2LEjNpuNQYMGcc8997B58+amLM4lNaS853v11Vfp168fQ4cObYLoPC/QygtNX+bKykruvvtuDMNgwYIFjQ230ZqyvCNHjmTr1q3k5+fzyiuvcPfdd7NhwwZiYmI8EXqDNEV5N2/ezB/+8AeysrKwWCyeDLfRmurn+6Mf/ci9369fP/r3709iYiJr1qzhBz/4QaPjbqimKK/D4QDg1ltv5ac//SkAycnJfPHFFyxcuNAvk5uA73Pz73//2wAMm83mfgCGxWIxbDabcebMmWrXXHvttcYPfvCDKseWL19uAEZ5eXmV4yUlJcaRI0cMwzCMu+++27j55pubrjB10JDyupSUlBgRERHGvHnzqhzfs2dPjf1Orr32WuORRx5pimLUWVOU93ze2OemKctcUVFh3HbbbUb//v2N/Pz8pipCvTT1z/h83bt3N3772996KvQGaYryzp071339+fe0Wq1G586dm7hEF9ecP9/o6Ghj4cKFngq9QZqivOXl5UaLFi2MZ555psrxn//858bw4cObpBxmC/iamx/84Ad88803VY6lpaXRu3dvHn/88RqrJ6+66ir+8Y9/4HA4sFqd3Za+//574uPjCQ4OrnJueHg44eHhnDhxghUrVvC73/2u6QpTBw0pr8u//vUvysvLGT9+fJXjXbt2JS4ujlWrVpGcnAxAUVERGzZsYOrUqR4vQ300RXm9XVOV2VVjs2vXLlavXk27du08HntDNOfP2OFwUF5e3qh4G6spynvfffdV69sxatQo7rvvPtLS0jwXfAM018/30KFDHD9+nPj4+EbH3BhNUd7g4GCuuOIKdu7cWeX4999/T+fOnT0XvDcxO7vyRhf2TL/vvvuMX/ziF+6vs7OzjdatWxvTpk0zdu7cafznP/8xYmJijGeffdZ9TkZGhvHf//7X2Lt3r/HRRx8ZAwYMMIYNG1brCCszXaq8LldffbUxbty4Gu/x3HPPGW3atDHef/994+uvvzZuvfVWo2vXrsbp06ebKuwG80R5jx8/bmzZssVYtmyZARhvv/22sWXLFiMnJ6epwm6Uxpa5oqLCuOWWW4zLLrvM2Lp1q5GTk+N+XFhb6Q0aW96SkhJjxowZRmZmprF//35j06ZNRlpamhESEmJs27atKUNvEE/8Tl/I20ZLna+x5S0uLjYee+wxIzMz09i3b5/x8ccfG4MGDTJ69OhhlJWVNWXoDeKJn+/SpUuNoKAg4y9/+Yuxa9cu449//KNhs9mMtWvXNlXYpgr4mpu6yM7OdtfQACQkJLBixQp++tOf0r9/fzp27Mj06dN5/PHH3ecUFhYyY8YMDh06RFRUFP/zP//Db37zG4KCgswoQr1cWF6AnTt3sm7dOj766KMar/n5z39OaWkpDz30ECdPnuTqq68mIyPDJ+ZQaEh5P/jggyr/0bra72fNmsWTTz7ZZLF6Sn3LfPjwYT744AMAd+2cy+rVqxkxYkRTheoR9S2vzWbju+++Y/HixeTn59OuXTuuuOIK1q5d65UjiS7UkN9pX9aQn+/XX3/N4sWLOXnyJB06dODGG2/kmWee8bq5bmrSkJ/v7bffzsKFC5k9ezaPPPIIvXr14t133+Xqq69ujpCbncUwDMPsIEREREQ8RfPciIiIiF9RciMiIiJ+RcmNiIiI+BUlNyIiIuJXlNyIiIiIX1FyIyIiIn5FyY2IiIj4FSU3IiIi4hGfffYZY8eOpUOHDlgsFt5777163+Of//wnycnJhIWF0blzZ1544YV630PJjYhIA1RUVNC9e3e++OILj943IyOD5ORk90rOIr6ktLSUAQMGMH/+/AZd/9///pd7772XKVOmsG3bNv785z8zd+5c/vSnP9XrPkpuRIRJkyZhsViqPXbv3m12aF5r4cKFdO3aleHDh7uP1faf6qRJk7jtttvqdN/Ro0cTFBTE3//+dw9FKtJ8brrpJp599lluv/32Gp8vLy/nscceo2PHjoSHhzNs2DDWrFnjfv6NN97gtttuY8qUKXTr1o0xY8YwY8YMnn/+eeqzoIKSGxEBnB+qOTk5VR5du3atdl5FRYUJ0XkXwzD405/+xAMPPNAk9580aRIvvfRSk9xbxEzTpk0jMzOTt99+m6+//pq77rqL0aNHs2vXLsCZ/Fy4JmHLli05dOgQBw4cqPPrKLkREQBCQkKIi4ur8rDZbIwYMYJp06bx6KOPEh0dzahRowDYtm0bN910E61atSI2Npb77ruP/Px89/1KS0uZMGECrVq1Ij4+nhdffJERI0bw6KOPus+pqaajTZs2vP766+6vDx48yN13302bNm2Iiori1ltvZf/+/e7nXbUiv//974mPj6ddu3Y8/PDDVFZWus8pLy/n8ccfJyEhgZCQELp3786rr76KYRh0796d3//+91Vi2Lp160VrrjZv3syePXsYM2ZMPb/LsH///hpryc5ffHTs2LFs2rSJPXv21Pv+It4qOzub1157jX/9619cc801JCYm8thjj3H11Vfz2muvATBq1CiWLl3KqlWrcDgcfP/997z44osA5OTk1Pm1lNyIyCUtXryY4OBgPv/8cxYuXMjJkye5/vrrGThwIJs2bSIjI4O8vDzuvvtu9zU/+9nP+PTTT3n//ff56KOPWLNmDVlZWfV63crKSkaNGkXr1q1Zu3Ytn3/+Oa1atWL06NFVapBWr17Nnj17WL16NYsXL+b111+vkiBNmDCBt956i5deeokdO3bw8ssv06pVKywWC/fff7/7jdXltdde49prr6V79+41xrV27Vp69uxJ69at61UegISEhCq1Y1u2bKFdu3Zce+217nM6depEbGwsa9eurff9RbzVN998g91up2fPnrRq1cr9+PTTT92J/OTJk5k2bRo//OEPCQ4O5sorr+RHP/oRQLWV0C/KEJGAN3HiRMNmsxnh4eHux5133mkYhmFcd911xsCBA6uc/8wzzxg33nhjlWMHDx40AGPnzp1GcXGxERwcbPzzn/90P3/8+HGjZcuWxvTp093HAOPf//53lftERkYar732mmEYhvHGG28YvXr1MhwOh/v58vJyo2XLlsaKFSvcsXfu3Nk4c+aM+5y77rrLGDdunGEYhrFz504DMFauXFlj2Q8fPmzYbDZjw4YNhmEYRkVFhREdHW28/vrrtX6/pk+fblx//fXVjgNGaGhole9jeHi40aJFC+PWW2+tdv7p06eNYcOGGT/84Q8Nu91e5bmBAwcaTz75ZK0xiHi7C/++3377bcNmsxnfffedsWvXriqPnJycKteeOXPGOHTokFFeXm4sX77cAIyjR4/W+bVbeDYvExFfNXLkSBYsWOD+Ojw83L0/ePDgKud+9dVXrF69mlatWlW7z549ezh9+jQVFRUMGzbMfTwqKopevXrVK6avvvqK3bt3V6shKSsrq9Jkc/nll2Oz2dxfx8fH88033wDOJiabzcZ1111X42t06NCBMWPGsGjRIoYOHcqHH35IeXk5d911V61xnT59ulq/AJe5c+eSmppa5djjjz+O3W6vdu79999PcXExK1eurPZfacuWLTl16lStMYj4moEDB2K32zl69CjXXHPNRc+12Wx07NgRgLfeeouUlBTat29f59dSciMigDOZqa0Z5vxEB6CkpISxY8fy/PPPVzs3Pj6+zqOsLBZLtREQ5/eVKSkpYfDgwTWOHDr/jS4oKKjafV1DqVu2bHnJOB588EHuu+8+5s6dy2uvvca4ceMICwur9fzo6Gh38nShuLi4at/H1q1bc/LkySrHnn32WVasWMHGjRtrbN4qKCio15u5iDcoKSmp8ve/b98+tm7dSlRUFD179uTee+9lwoQJvPjiiwwcOJBjx46xatUq+vfvz5gxY8jPz+edd95hxIgRlJWVufvofPrpp/WKQ8mNiNTboEGDePfdd+nSpQstWlR/G0lMTCQoKIgNGzbQqVMnAE6cOMH3339fpQalffv2VToJ7tq1q0ptxaBBg1iyZAkxMTFEREQ0KNZ+/frhcDj49NNPq9WouNx8882Eh4ezYMECMjIy+Oyzzy56z4EDB7JgwQIMw8BisdQ7pnfffZenn36a//73vyQmJlZ73lUzNXDgwHrfW8RMmzZtYuTIke6v09PTAZg4cSKvv/46r732Gs8++yz/93//x+HDh4mOjubKK6/khz/8ofuaxYsX89hjj2EYBikpKaxZs4ahQ4fWKw51KBaRenv44YcpKCjgnnvu4csvv2TPnj2sWLGCtLQ07HY7rVq14oEHHuBnP/sZn3zyCdu2bWPSpEnVml6uv/56/vSnP7FlyxY2bdrElClTqtTC3HvvvURHR3Prrbeydu1a9u3bx5o1a3jkkUc4dOhQnWLt0qULEydO5P777+e9995z3+Of//yn+xybzcakSZOYMWMGPXr0ICUl5aL3HDlyJCUlJXz77bf1+K45bdu2jQkTJvD4449z+eWXk5ubS25uLgUFBe5z1q9fT0hIyCXjEPE2I0aMwDCMag9XB/+goCCeeuop9u3bR0VFBUeOHGHp0qX069cPcNaKZmZmUlJSQmlpKR9//HGV5u26UnIjIvXWoUMHPv/8c+x2OzfeeCP9+vXj0UcfpU2bNu4E5oUXXuCaa65h7NixpKamcvXVV1fru/Piiy+SkJDANddcw49//GMee+yxKs1BYWFhfPbZZ3Tq1Ik77riDPn368MADD1BWVlavmpwFCxZw55138pOf/ITevXszefJkSktLq5zzwAMPUFFRQVpa2iXv165dO26//fYGTbS3adMmTp06xbPPPkt8fLz7cccdd7jPeeutt7j33nsv2jQmIrWzGBc2eIuINJERI0aQnJzMvHnzzA6lmrVr1/KDH/yAgwcPEhsbe8nzv/76a2644Qb27NlTY8fqhsrPz6dXr15s2rSpxkkUReTSVHMjIgGtvLycQ4cO8eSTT3LXXXfVKbEB6N+/P88//zz79u3zaDz79+/nz3/+sxIbkUZQh2IRCWhvvfUWDzzwAMnJyfztb3+r17WTJk3yeDxDhgxhyJAhHr+vSCBRs5SIiIj4FTVLiYiIiF9RciMiIiJ+RcmNiIiI+BUlNyIiIuJXlNyIiIiIX1FyIyIiIn5FyY2IiIj4FSU3IiIi4lf+P0kBgWnC1Z5RAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "probability_of_zero = [result.measurement_counts['0']/N_shots for result in batch.results()]\n", + "\n", + "x, y = frequencies, probability_of_zero\n", + "\n", + "initial_guess=[1/2, 1, 10e6, drive_frame.frequency] # Amplitude, Offset, width, centerFrequency\n", + "optimal_params, _ = scipy.optimize.curve_fit(resonance_fit, x, y, p0=initial_guess)\n", + "x_fit = np.arange(x[0],x[-1], np.diff(x)[0]/10)\n", + "y_fit = resonance_fit(x_fit, *optimal_params)\n", + "\n", + "plt.figure()\n", + "plt.plot(x,y, 'o')\n", + "plt.plot(x_fit,y_fit)\n", + "plt.xlabel(\"Frequency (Hz)\")\n", + "plt.ylabel(\"Population\")\n", + "plt.vlines(drive_frame.frequency, min(y_fit), 1)\n", + "resonance_frequency = optimal_params[3]\n", + "print('Expected resonance frequency:', round(drive_frame.frequency*1e-6,2), 'GHz')\n", + "print('Measured resonance frequency:', round(resonance_frequency*1e-6,2), 'GHz')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calibrating $\\pi$/2 pulses via Rabi spectroscopy \n", + "\n", + "Applying an electromagnetic field to a qubit leads to Rabi flopping, a cyclic behavior that is used to calibrate specific pulse parameters. Here, we will determine the optimal pulse length to realize a $\\pi$/2 pulse, an elementary block used to build more complex pulse sequences, such as the Ramsey sequence. \n", + "\n", + "Below, we will reuse the previous pulse sequence. First, we will fix the driving frequency to the resonance frequency and replace the coarsely-chosen pulse length by a FreeParameter.\n", + "\n", + "We also choose to increase the amplitude of the waveform to increase the rate of the expected oscillations.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "waveform = experiment_configuration[device_name][\"rabi_wf\"]\n", + "\n", + "rabi_sequence = ( \n", + " PulseSequence()\n", + " .set_frequency(drive_frame, drive_frame.frequency)\n", + " .play(drive_frame, waveform)\n", + " .capture_v0(readout_frame)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As for qubit spectroscopy, we will sweep one parameter of our pulse sequence, here the length of the waveform.\n", + "\n", + "We construct another batch of task with lengths ranging from 12ns to 200ns with a step of 12ns so all the sequences verify the 4-sample constraint (waveforms must have a length multiple of 4ns). " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "start_length=12e-9\n", + "end_length=2e-7\n", + "lengths = np.arange(start_length, end_length, 12e-9)\n", + "N_shots = 100\n", + "\n", + "pulse_sequences = [rabi_sequence(length=length) for length in lengths]\n", + "\n", + "batch = device.run_batch(pulse_sequences, shots=N_shots)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To increase the chances of fitting success, we estimate some initial parameters values:\n", + "- initial signal mean is taken as the mean of the measurement data\n", + "- initial Rabi frequency is set as the position of the maximum value of the measurement data's FFT" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "def damped_oscillation_fit(x, A, A0, Tau, f, x0):\n", + " return A*np.exp(-x/Tau)*np.cos(2*np.pi*(x-x0)*f)+A0\n", + "\n", + "def estimate_fit_parameters(x, y):\n", + " signal_mean = np.mean(y)\n", + " idx_max=np.argmax(np.abs(fft(y-np.mean(y))))\n", + " oscillation_frequency_estimate = fftfreq(len(x), np.diff(x)[0])[idx_max]\n", + "\n", + " return signal_mean, oscillation_frequency_estimate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The projected state after the qubit measurement reflects the oscillatory dynamics of the qubit that oscillates between the state $|0\\rangle$ and the state $|1\\rangle$. \n", + "From the measurement data, one can extract the Rabi frequency as the flipping rate and compute the length of $\\pi/2$ pulse." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rabi frequency: 13.13 MHz\n", + "rx(pi/2) length: 17.62 ns\n", + "Redefined rx(pi/2) length: 16.0 ns\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "probability_of_zero = [result.measurement_counts['0']/N_shots for result in batch.results()]\n", + "x, y = lengths, probability_of_zero\n", + "\n", + "signal_mean, oscillation_frequency_estimate = estimate_fit_parameters(x,y)\n", + "\n", + "initial_guess=[1/2, signal_mean, 8e-6, oscillation_frequency_estimate, 0]\n", + "optimal_params, _ = scipy.optimize.curve_fit(damped_oscillation_fit, x, y, p0=initial_guess)\n", + "x_fit = np.arange(x[0],x[-1], np.diff(x)[0]/10)\n", + "y_fit = damped_oscillation_fit(x_fit, *optimal_params)\n", + "\n", + "plt.plot(x,y, 'o')\n", + "plt.plot(x_fit,y_fit)\n", + "plt.xlabel(\"Pulse duration (s)\")\n", + "plt.ylabel(\"Population\")\n", + "\n", + "\n", + "rabi_frequency = optimal_params[3]\n", + "phase_offset = optimal_params[4]\n", + "x90_duration=(np.pi/2)/(2*np.pi*rabi_frequency)+phase_offset\n", + "plt.plot(x90_duration, damped_oscillation_fit(x90_duration, *optimal_params), 'ks')\n", + "\n", + "print('Rabi frequency:', round(rabi_frequency*1e-6, 2), ' MHz')\n", + "print('rx(pi/2) length: ', round(x90_duration*1e9, 2), ' ns')\n", + "\n", + "# Pulse duration must be a multiple of 4ns\n", + "x90_duration=x90_duration//4e-9*4e-9\n", + "plt.plot(x90_duration, damped_oscillation_fit(x90_duration, *optimal_params), 'rs')\n", + "print('Redefined rx(pi/2) length: ', round(x90_duration*1e9, 0), ' ns')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "experiment_configuration[\"aspen\"][\"x90_wf\"] = GaussianWaveform(x90_duration, x90_duration/4, 0.2, True)\n", + "experiment_configuration[\"lucy\"][\"x90_wf\"] = ConstantWaveform(x90_duration, 0.07)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ramsey sequence - $T^*_2$ Measurement" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the following, we implement a Ramsey sequence that allows you to measure the coherence time of a qubit. The Ramsey sequence consists of two $\\pi$/2 pulses separated by a varying gap. Starting from the $|0\\rangle$ state, the first pulse creates an equal superposition of $|0\\rangle$ and $|1\\rangle$ which will decay back to a mixed state after a characteristic time called $T^*_2$. \n", + "\n", + "For better visualization, the carrier frequency is shifted away from the resonance frequency by some arbitraryily-chosen detuning which causes the frame of the driving to rotate with respect to the qubit frame. This results in oscillations at a rate equal to the detuning on top of the decoherence decay. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "detuning=250e3\n", + "x90 = experiment_configuration[device_name][\"x90_wf\"]\n", + "\n", + "delay = FreeParameter(\"delay\")\n", + "ramsey_spectroscopy = ( \n", + " PulseSequence()\n", + " .set_frequency(drive_frame, drive_frame.frequency - detuning)\n", + " .play(drive_frame, x90)\n", + " .delay(drive_frame, delay)\n", + " .play(drive_frame, x90)\n", + " .capture_v0(readout_frame)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once again, we will sweep a parameter of the sequence which is the time gap between the two $\\pi$/2-pulses. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "start_delay=12e-9\n", + "end_delay=40000e-9\n", + "delays = np.arange(start_delay, end_delay, 512e-9)\n", + "N_shots=100\n", + "\n", + "pulse_sequences = [ramsey_spectroscopy(delay=delay) for delay in delays]\n", + "\n", + "batch = device.run_batch(pulse_sequences, shots=N_shots)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting and fitting are not different from what we have seen with Rabi oscillations. We can now experimentally verify that the oscillations correspond to the frequency detuning of our pulses, and we can extract the coherence time $T^*_2$ of the qubit " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Detuning: 258.53 kHz\n", + "T2: 33.33 us\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "probability_of_zero = [result.measurement_counts['0']/N_shots for result in batch.results()]\n", + "x, y = delays, probability_of_zero\n", + "plt.plot(x,y, 'o-')\n", + "\n", + "signal_mean, oscillation_frequency_estimate = estimate_fit_parameters(x,y)\n", + "initial_guess=[0.5, signal_mean, 2e-5, oscillation_frequency_estimate, 0]\n", + "\n", + "optimal_params, _ = scipy.optimize.curve_fit(damped_oscillation_fit, x, y, p0=initial_guess)\n", + "x_fit = np.arange(x[0],x[-1], np.diff(x)[0]/10)\n", + "y_fit = damped_oscillation_fit(x_fit, *optimal_params)\n", + "plt.plot(x_fit,y_fit)\n", + "plt.xlabel(\"Delay (s)\")\n", + "plt.ylabel(\"Population\")\n", + "print('Detuning:', round(optimal_params[3]*1e-3, 2), ' kHz')\n", + "print('T2: ', round(np.abs(optimal_params[2])*1e6, 2), ' us')" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 12000, 'tasks': {'COMPLETED': 120}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 40.200 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.9.14", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + }, + "vscode": { + "interpreter": { + "hash": "e8fe7b1d737818ec041fd05b4c8bbd1804e351a931e38c7cd860a34c69554183" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} \ No newline at end of file diff --git a/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/2_Bell_pair_with_pulses_OQC.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/2_Bell_pair_with_pulses_OQC.ipynb new file mode 100644 index 000000000..d96983dcd --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/2_Bell_pair_with_pulses_OQC.ipynb @@ -0,0 +1,401 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Creating a Bell state with cross-resonance pulses on OQC's Lucy\n", + "\n", + "In this notebook we will investigate cross-resonance mechanisms to create a Bell state, i.e., the `Hello world!` example in quantum computing. \n", + "\n", + "The simplest circuit to generate a Bell pair is an Hadamard gate on a first qubit followed by a CNOT gate between this qubit and a second qubit. However, diving deeper in the pulse implementation of such gates, we would realize that they require specific mechanisms that are tightly connected to the hardware type and device architecture. Focusing on the capabilities of OQC's Lucy device, we will replace the canonical CNOT gate with a different entangling gate that is either the cross-resonance (CR) gate or its echoed version. We will then see how two qubits interact when we drive one qubit at the frequency of the other and calibrate this process to be able to create a Bell pair." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's first start with importing some packages as usual." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from braket.aws import AwsDevice\n", + "from braket.pulse import PulseSequence, ConstantWaveform\n", + "\n", + "from braket.circuits import Circuit, Observable\n", + "from braket.parametric import FreeParameter\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will use two qubits, #0 amd #1, that are physically connected to each other. We also instantiate an OQC device to extract frames and submit circuits." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "a=0\n", + "b=1\n", + "\n", + "device = AwsDevice(\"arn:aws:braket:eu-west-2::device/qpu/oqc/Lucy\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bell pair with the H, ECR and V gates" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we show how to transform the canonical Bell state circuit into another one where we replace the CNOT gate by an echoed cross-resonance (ECR) gatet and a V gate, also known as SX (square-root of X). These gates are native on the Lucy device.\n", + "\n", + "As shown in Phys. Rev. B. 81, 134507 (2010) and Phys. Rev. Applied 12, 064013, the ECR gate implements an unitary evolution of the system that can be decomposed in two steps with a time reversal half way through the process to suppress most undesired evolution.\n", + "$$ R_{ZX}(\\pi/4)-R_X(\\pi)-R_{ZX}(\\pi/4).$$\n", + "The $R_{ZX}$ is interpretable as the rotation of the second qubit, conditioned by the state of the first qubit. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0| 1 |2|\n", + " \n", + "q0 : -H-ECR---\n", + " | \n", + "q1 : ---ECR-V-\n", + "\n", + "T : |0| 1 |2|\n" + ] + } + ], + "source": [ + "bell_pair_with_gates = Circuit().h(a).ecr(a, b).v(b)\n", + "print(bell_pair_with_gates)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The circuit is then executed on the OQC device and we plot the measurement histogram which indicates that we created $$\\frac{|00\\rangle+e^{i\\phi}|11\\rangle}{\\sqrt{2}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Population')" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nb_shots = 100\n", + "task = device.run(bell_pair_with_gates, shots = nb_shots)\n", + "counts = task.result().measurement_counts\n", + "\n", + "\n", + "plt.bar(sorted(counts), [counts[k]/nb_shots for k in sorted(counts)])\n", + "plt.xlabel(\"State\")\n", + "plt.ylabel(\"Population\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bell pair with the pulse implementation of the cross-resonance sequence" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Instead of tackling the implementation of the complete echoed cross resonance pulse sequence, we use a simple cross-resonance (CR) gate. The CR gate is a single-pulse gate that implements the unitary transformation $$ \\exp(−i \\beta Z X / 2),$$ where Z and X are the 2x2 Pauli matrices. Practically, you can understand the gate by isolating its action for each eigenstate of the control qubit. If it is in $|0\\rangle$ (resp. $|1\\rangle$), the target qubit undergoes a rotation of angle $\\beta$ (resp. $-\\beta$). \n", + "\n", + "We seek to measure the interaction strength between the qubits when we drive one of them at the frequency of the other. For this, we use the frame `q0_q1_cross_resonance` that is bound to qubit 0 but tuned up to the frequency of qubit 1. As we will test this pulse sequence in a quantum circuit containing single-qubit gates on other qubits, we also declare the 1-qubit drive frames for 0 and 1. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "q0_q1_CR = device.frames[f'q{a}_q{b}_cross_resonance']\n", + "q0 = device.frames[f'q{a}_drive']\n", + "q1 = device.frames[f'q{b}_drive']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The sequence consists of a single square pulse of amplitude 0.18. This value has been determined by running the circuits below for different amplitudes and choosing the one that optimizes the difference of the expectation values $\\langle IZ \\rangle$ taken for the opposite initialization of the control qubit." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "length = FreeParameter(\"length\")\n", + "const_wf = ConstantWaveform(length, 0.18)\n", + "\n", + "cross_resonance_sequence = (\n", + " PulseSequence()\n", + " .barrier([q0, q1, q0_q1_CR])\n", + " .play(q0_q1_CR, const_wf)\n", + " .barrier([q0, q1, q0_q1_CR])\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We run two batches of circuits where we vary the length of the pulse from 12ns to 1.4 µs. Each batch has a different initialized state: $|0\\rangle$ for the first, $|1\\rangle$ for the second. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "lengths = np.arange(12e-9, 1.5e-6, 36e-9)\n", + "nb_shots = 1000\n", + "\n", + "# Initialization of the control qubit in 0\n", + "circuit = (\n", + " Circuit()\n", + " .pulse_gate([0, 1], pulse_sequence=cross_resonance_sequence)\n", + " .expectation(observable = Observable.I() @ Observable.Z(),target=[0,1])\n", + ")\n", + "CR_circuits = [circuit(length=l) for l in lengths]\n", + "batch_init_0 = device.run_batch(CR_circuits, shots=nb_shots, disable_qubit_rewiring=True)\n", + "\n", + "# Initialization of the control qubit in 1\n", + "circuit = (\n", + " Circuit()\n", + " .x(0)\n", + " .pulse_gate([0, 1], pulse_sequence=cross_resonance_sequence)\n", + " .expectation(observable = Observable.I() @ Observable.Z(),target=[0,1])\n", + ")\n", + "CR_circuits = [circuit(length=l) for l in lengths]\n", + "batch_init_1 = device.run_batch(CR_circuits, shots=nb_shots, disable_qubit_rewiring=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We analyze the data by plotting the expectation value $\\langle IZ \\rangle$ versus the pulse duration for each batch. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "IZ_exp_value_init_0 = np.array([result.values[0] for result in batch_init_0.results()])\n", + "IZ_exp_value_init_1 = np.array([result.values[0] for result in batch_init_1.results()])\n", + "\n", + "plt.plot(lengths, IZ_exp_value_init_0, label=\"Control in 0\")\n", + "plt.plot(lengths, IZ_exp_value_init_1, label=\"Control in 1\")\n", + "plt.xlabel(\"Pulse duration (s)\")\n", + "plt.ylabel(\"\")\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot displays a state-dependent oscillatory behavior indicating that we have implemented a unitary evolution based on the ZX interaction. We see also from the previous plot that, for pulse duration of 700ns, the two qubits interacts long enough for the state of the target qubit (i) to be flipped if the control qubit is its ground state or (ii) to cycle back to the original state if the control is in the excited state. Adding an X gate after this sequence would give the expected for the CNOT gate. \n", + "\n", + "Fixing the duration of the pulse to this particular value, we can now create a circuit including our custom pulse sequence and create a Bell state" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "RZX_sequence = cross_resonance_sequence(length=700e-9)\n", + "\n", + "bell_pair_with_pulses = (\n", + " Circuit()\n", + " .h(a)\n", + " .pulse_gate([a ,b], pulse_sequence=RZX_sequence)\n", + " .x(b)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now can execute this circuit, which returns similar results as with the circuit using an ECR gate. \n", + "\n", + "We can however notice that the fidelity is worse than in the first case, due to the fact that we did not include any correction for crosstalks such as cross-resonant cancelation, pulse synchronization and an echo scheme. To dive deeper and investigate methods to improve these results, see the following paper Phys. Rev. Applied 12, 064013. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Population')" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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uYNWqVXI4HCosLFRlZaVSUlJkt9t15MiRVvuXlZVp6tSpWr9+vcrLyxUfH6/x48fr4MGD3j4LFizQ4sWLVVJSooqKCvXr1092u12nTp266HoBAEDPF+Tx41ZOVFSUTp48qW+++UZ9+/bVJZdc4nP8+PHjbR4rMzNT1157rZYsWSJJamlpUXx8vB577DE999xzFzy/ublZUVFRWrJkiXJycuTxeBQXF6cnn3xSTz31lCSptrZWMTExWrFihaZMmXLBMevq6hQZGana2lr179+/zXNpq4Tnft/hY6Jt9s2bEOgSAHQj/D0OjM76W9yef7/9WgNUXFzsz2lnaWpq0pYtW5Sfn+9tCw4Ols1mU3l5eZvGOHnypE6fPq2BAwdKkvbu3SuXyyWbzebtExkZqczMTJWXl7cagBobG9XY2Ojdr6ur83dKAACgB/ArAOXm5nbILz969Kiam5sVExPj0x4TE6OvvvqqTWM8++yziouL8wYel8vlHeP7Y5459n1FRUV68cUX21s+AADoofwKQNK3Hz2tXbtWO3bskCRdddVVuuOOO7r0PUDz5s3Te++9p7KyMoWFhfk9Tn5+vhwOh3e/rq5O8fHxHVEiAADohvwKQLt379Ztt92mgwcPavjw4ZK+vYsSHx+v3//+9xo2bFibxomOjlZISIjcbrdPu9vtltVqPe+5Cxcu1Lx58/SHP/xBY8aM8bafOc/tdis2NtZnzHM9tm+xWGSxWNpUMwAA6Pn8egrs8ccf17Bhw7R//35VVlaqsrJSVVVVSkxM1OOPP97mcUJDQ5WWlian0+lta2lpkdPpVFZW1jnPW7BggebMmaPS0lKlp6f7HEtMTJTVavUZs66uThUVFecdEwAAmMOvO0AbNmzQxo0bvQuPJemyyy7TvHnz9MMf/rBdYzkcDuXm5io9PV0ZGRkqLi5WQ0OD8vLyJEk5OTkaPHiwioqKJEnz589XQUGB3nnnHSUkJHjX9URERCgiIkJBQUGaOXOm5s6dq+TkZCUmJmrWrFmKi4vTxIkT/ZkuAADoZfwKQBaLRSdOnDirvb6+XqGhoe0aa/LkyaqurlZBQYFcLpdSU1NVWlrqXcRcVVWl4ODvblS9/vrrampq0j333OMzTmFhoWbPni1JeuaZZ9TQ0KCHHnpINTU1uv7661VaWnpR64QAAEDv4dd7gHJyclRZWal/+Zd/UUZGhiSpoqJC06dPV1pamlasWNHRdXYp3gPUe/EeIAD/F3+PA6M7vAfIrzVAixcv1rBhw5SVlaWwsDCFhYXphz/8oZKSkvTqq6/6VTQAAEBX8esjsAEDBujDDz/Url27vO/rGTlypJKSkjq0OAAAgM7g93uAJCk5OVnJyckdVQsAAECXaHMAcjgcmjNnjvr16+fz0sDWLFq06KILAwAA6CxtDkBbt27V6dOnvT8DgClYKBs4PLiAztLmALR+/fpWfwYAAOhp/HoK7P7772/1PUANDQ26//77L7ooAACAzuRXAFq5cqW+/vrrs9q//vprvfnmmxddFAAAQGdq11NgdXV18ng88ng8OnHihM+blZubm7Vu3ToNGjSow4sEegLWiQQO60QAtFe7AtCAAQMUFBSkoKAg/eAHPzjreFBQkF588cUOKw4AAKAztCsArV+/Xh6PRzfddJPef/99ny9DDQ0N1ZVXXqm4uLgOLxIAAKAjtSsAjRs3TpK0d+9excfH+3xJKQAAQE/h15ugr7zySknSyZMnVVVVpaamJp/jY8aMufjKAAAAOolfAai6ulp5eXn6z//8z1aPNzc3X1RRAAAAncmvz7BmzpypmpoaVVRUKDw8XKWlpVq5cqWSk5P1u9/9rqNrBAAA6FB+3QH65JNP9OGHHyo9PV3BwcG68sordcstt6h///4qKirShAk8kgoAALovv+4ANTQ0eN/3ExUVperqaknS6NGjVVlZ2XHVAQAAdAK/AtDw4cO1c+dOSVJKSop+9atf6eDBgyopKVFsbGyHFggAANDR/PoI7IknntDhw4clSYWFhcrOztZvf/tbhYaGasWKFR1ZHwAAQIfzKwDdd9993p/T0tL017/+VV999ZWGDBmi6OjoDisOAACgM/gVgL6vb9++Gjt2bEcMBQAA0OnaHIAcDkebB120aJFfxQAAAHSFNgegrVu3tqlfUFCQ38UAAAB0hTYHoPXr13dmHQAAAF2GbzMFAADG8WsR9N/93d+d96OuTz75xO+CAAAAOptfASg1NdVn//Tp09q2bZu++OIL5ebmdkRdAAAAncavAPSLX/yi1fbZs2ervr7+ogoCAADobB26Bui+++7TsmXLOnJIAACADtehAai8vFxhYWEdOSQAAECH8+sjsLvvvttn3+Px6PDhw9q8ebNmzZrVIYUBAAB0Fr8CUGRkpM9+cHCwhg8frpdeeknjx4/vkMIAAAA6i18BaPny5R1dBwAAQJe5qC9D3bx5s3bs2CFJGjVqlNLS0jqkKAAAgM7kVwA6cOCApk6dqs8++0wDBgyQJNXU1Oi6667Te++9pyuuuKIjawQAAOhQfj0F9uCDD+r06dPasWOHjh8/ruPHj2vHjh1qaWnRgw8+2NE1AgAAdCi/7gBt2LBBn3/+uYYPH+5tGz58uF577TXdcMMNHVYcAABAZ/DrDlB8fLxOnz59Vntzc7Pi4uIuuigAAIDO5FcAevnll/XYY49p8+bN3rbNmzfriSee0MKFCzusOAAAgM7g10dg06ZN08mTJ5WZmak+fb4d4ptvvlGfPn10//336/777/f2PX78eMdUCgAA0EH8CkDFxcUdXAYAAEDX8SsA5ebmdnQdAAAAXcbvL0Ntbm7W+++/r7lz52ru3Ln64IMP1Nzc3O5xli5dqoSEBIWFhSkzM1ObNm06Z9+//OUvmjRpkhISEhQUFNTqnajZs2crKCjIZxsxYkS76wIAAL2XXwFo9+7dGjlypHJycrRmzRqtWbNG9913n6666irt2bOnzeOsWrVKDodDhYWFqqysVEpKiux2u44cOdJq/5MnT2ro0KGaN2+erFbrOce96qqrdPjwYe/26aeftnuOAACg9/IrAD3++OMaNmyY9u/fr8rKSlVWVqqqqkqJiYl6/PHH2zzOokWLNH36dOXl5WnUqFEqKSlR3759tWzZslb7X3vttXr55Zc1ZcoUWSyWc47bp08fWa1W7xYdHd3uOQIAgN7LrwC0YcMGLViwQAMHDvS2XXbZZZo3b542bNjQpjGampq0ZcsW2Wy274oJDpbNZlN5ebk/ZXnt2rVLcXFxGjp0qP7xH/9RVVVV5+3f2Niouro6nw0AAPRefgUgi8WiEydOnNVeX1+v0NDQNo1x9OhRNTc3KyYmxqc9JiZGLpfLn7IkSZmZmVqxYoVKS0v1+uuva+/evbrhhhtarfeMoqIiRUZGerf4+Hi/fz8AAOj+/ApAf//3f6+HHnpIFRUV8ng88ng82rhxox5++GHdcccdHV1ju9x666269957NWbMGNntdq1bt041NTX613/913Oek5+fr9raWu+2f//+LqwYAAB0Nb8eg1+8eLGmTZum6667zudFiHfccYdeffXVNo0RHR2tkJAQud1un3a3233eBc7tNWDAAP3gBz/Q7t27z9nHYrGcd00RAADoXdp1B6ilpUXz58/XhAkTdPDgQU2cOFGrV6/Wv/3bv2nnzp364IMPFBkZ2aaxQkNDlZaWJqfT6TO+0+lUVlZW+2ZxHvX19dqzZ49iY2M7bEwAANCztesO0M9//nPNnj1bNptN4eHhWrdunSIjI8/51NaFOBwO5ebmKj09XRkZGSouLlZDQ4Py8vIkSTk5ORo8eLCKiookfbtw+ssvv/T+fPDgQW3btk0RERFKSkqSJD311FO6/fbbdeWVV+rQoUMqLCxUSEiIpk6d6leNAACg92lXAHrzzTf1y1/+Uj/5yU8kSX/4wx80YcIE/eY3v1FwcPuXE02ePFnV1dUqKCiQy+VSamqqSktLvQujq6qqfMY9dOiQrrnmGu/+woULtXDhQo0bN05lZWWSpAMHDmjq1Kk6duyYLr/8cl1//fXauHGjLr/88nbXBwAAeqd2BaCqqirddttt3n2bzaagoCAdOnRIV1xxhV8FzJgxQzNmzGj12JlQc0ZCQoI8Hs95x3vvvff8qgMAAJijXbdtvvnmG4WFhfm0XXLJJTp9+nSHFgUAANCZ2nUHyOPxaNq0aT5PTJ06dUoPP/yw+vXr521bs2ZNx1UIAADQwdoVgFr7Fvj77ruvw4oBAADoCu0KQMuXL++sOgAAALqMX2+CBgAA6MkIQAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAAAIBxCEAAAMA4BCAAAGAcAhAAADAOAQgAABiHAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYJ+ABaOnSpUpISFBYWJgyMzO1adOmc/b9y1/+okmTJikhIUFBQUEqLi6+6DEBAIB5AhqAVq1aJYfDocLCQlVWViolJUV2u11Hjhxptf/Jkyc1dOhQzZs3T1artUPGBAAA5gloAFq0aJGmT5+uvLw8jRo1SiUlJerbt6+WLVvWav9rr71WL7/8sqZMmSKLxdIhYwIAAPMELAA1NTVpy5Ytstls3xUTHCybzaby8vIuHbOxsVF1dXU+GwAA6L0CFoCOHj2q5uZmxcTE+LTHxMTI5XJ16ZhFRUWKjIz0bvHx8X79fgAA0DMEfBF0d5Cfn6/a2lrvtn///kCXBAAAOlGfQP3i6OhohYSEyO12+7S73e5zLnDurDEtFss51xQBAIDeJ2B3gEJDQ5WWlian0+lta2lpkdPpVFZWVrcZEwAA9D4BuwMkSQ6HQ7m5uUpPT1dGRoaKi4vV0NCgvLw8SVJOTo4GDx6soqIiSd8ucv7yyy+9Px88eFDbtm1TRESEkpKS2jQmAABAQAPQ5MmTVV1drYKCArlcLqWmpqq0tNS7iLmqqkrBwd/dpDp06JCuueYa7/7ChQu1cOFCjRs3TmVlZW0aEwAAIKABSJJmzJihGTNmtHrsTKg5IyEhQR6P56LGBAAA4CkwAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAAAIBxCEAAAMA4BCAAAGAcAhAAADAOAQgAABiHAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAAAIBxCEAAAMA4BCAAAGAcAhAAADAOAQgAABiHAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYJxuEYCWLl2qhIQEhYWFKTMzU5s2bTpv/9WrV2vEiBEKCwvT6NGjtW7dOp/j06ZNU1BQkM+WnZ3dmVMAAAA9SMAD0KpVq+RwOFRYWKjKykqlpKTIbrfryJEjrfb//PPPNXXqVD3wwAPaunWrJk6cqIkTJ+qLL77w6Zedna3Dhw97t3fffbcrpgMAAHqAgAegRYsWafr06crLy9OoUaNUUlKivn37atmyZa32f/XVV5Wdna2nn35aI0eO1Jw5czR27FgtWbLEp5/FYpHVavVuUVFRXTEdAADQAwQ0ADU1NWnLli2y2WzetuDgYNlsNpWXl7d6Tnl5uU9/SbLb7Wf1Lysr06BBgzR8+HA98sgjOnbs2DnraGxsVF1dnc8GAAB6r4AGoKNHj6q5uVkxMTE+7TExMXK5XK2e43K5Ltg/Oztbb775ppxOp+bPn68NGzbo1ltvVXNzc6tjFhUVKTIy0rvFx8df5MwAAEB31ifQBXSGKVOmeH8ePXq0xowZo2HDhqmsrEw333zzWf3z8/PlcDi8+3V1dYQgAAB6sYDeAYqOjlZISIjcbrdPu9vtltVqbfUcq9Xarv6SNHToUEVHR2v37t2tHrdYLOrfv7/PBgAAeq+ABqDQ0FClpaXJ6XR621paWuR0OpWVldXqOVlZWT79Jenjjz8+Z39JOnDggI4dO6bY2NiOKRwAAPRoAX8KzOFw6I033tDKlSu1Y8cOPfLII2poaFBeXp4kKScnR/n5+d7+TzzxhEpLS/XKK6/oq6++0uzZs7V582bNmDFDklRfX6+nn35aGzdu1L59++R0OnXnnXcqKSlJdrs9IHMEAADdS8DXAE2ePFnV1dUqKCiQy+VSamqqSktLvQudq6qqFBz8XU677rrr9M477+iFF17Q888/r+TkZK1du1ZXX321JCkkJETbt2/XypUrVVNTo7i4OI0fP15z5syRxWIJyBwBAED3EvAAJEkzZszw3sH5vrKysrPa7r33Xt17772t9g8PD9dHH33UkeUBAIBeJuAfgQEAAHQ1AhAAADAOAQgAABiHAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAAAIBxCEAAAMA4BCAAAGAcAhAAADAOAQgAABiHAAQAAIxDAAIAAMYhAAEAAOMQgAAAgHEIQAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwTrcIQEuXLlVCQoLCwsKUmZmpTZs2nbf/6tWrNWLECIWFhWn06NFat26dz3GPx6OCggLFxsYqPDxcNptNu3bt6swpAACAHiTgAWjVqlVyOBwqLCxUZWWlUlJSZLfbdeTIkVb7f/7555o6daoeeOABbd26VRMnTtTEiRP1xRdfePssWLBAixcvVklJiSoqKtSvXz/Z7XadOnWqq6YFAAC6sYAHoEWLFmn69OnKy8vTqFGjVFJSor59+2rZsmWt9n/11VeVnZ2tp59+WiNHjtScOXM0duxYLVmyRNK3d3+Ki4v1wgsv6M4779SYMWP05ptv6tChQ1q7dm0XzgwAAHRXfQL5y5uamrRlyxbl5+d724KDg2Wz2VReXt7qOeXl5XI4HD5tdrvdG2727t0rl8slm83mPR4ZGanMzEyVl5drypQpZ43Z2NioxsZG735tba0kqa6uzu+5nU9L48lOGRcX1lnXVOK6BlJnXleJaxtIXNveqbOu65lxPR7PBfsGNAAdPXpUzc3NiomJ8WmPiYnRV1991eo5Lper1f4ul8t7/Ezbufp8X1FRkV588cWz2uPj49s2EfQYkcWBrgCdgevae3Fte6fOvq4nTpxQZGTkefsENAB1F/n5+T53lVpaWnT8+HFddtllCgoKCmBl3UtdXZ3i4+O1f/9+9e/fP9DloANxbXsnrmvvxbVtncfj0YkTJxQXF3fBvgENQNHR0QoJCZHb7fZpd7vdslqtrZ5jtVrP2//M/7rdbsXGxvr0SU1NbXVMi8Uii8Xi0zZgwID2TMUo/fv35/9wvRTXtnfiuvZeXNuzXejOzxkBXQQdGhqqtLQ0OZ1Ob1tLS4ucTqeysrJaPScrK8unvyR9/PHH3v6JiYmyWq0+ferq6lRRUXHOMQEAgFkC/hGYw+FQbm6u0tPTlZGRoeLiYjU0NCgvL0+SlJOTo8GDB6uoqEiS9MQTT2jcuHF65ZVXNGHCBL333nvavHmzfv3rX0uSgoKCNHPmTM2dO1fJyclKTEzUrFmzFBcXp4kTJwZqmgAAoBsJeACaPHmyqqurVVBQIJfLpdTUVJWWlnoXMVdVVSk4+LsbVdddd53eeecdvfDCC3r++eeVnJystWvX6uqrr/b2eeaZZ9TQ0KCHHnpINTU1uv7661VaWqqwsLAun19vYrFYVFhYeNbHhej5uLa9E9e19+LaXrwgT1ueFQMAAOhFAv4iRAAAgK5GAAIAAMYhAAEAAOMQgAAAgHEIQGjV0qVLlZCQoLCwMGVmZmrTpk3eY6dOndJPf/pTXXbZZYqIiNCkSZPOejkluq/zXdtf//rXuvHGG9W/f38FBQWppqYmcIWizf74xz/q9ttvV1xcnIKCgs764mePx6OCggLFxsYqPDxcNptNu3btCkyxaJcLXds1a9Zo/Pjx3m8u2LZtW0Dq7IkIQDjLqlWr5HA4VFhYqMrKSqWkpMhut+vIkSOSpH/6p3/Sv//7v2v16tXasGGDDh06pLvvvjvAVaMtLnRtT548qezsbD3//PMBrhTt0dDQoJSUFC1durTV4wsWLNDixYtVUlKiiooK9evXT3a7XadOneriStFeF7q2DQ0Nuv766zV//vwurqwX8ADfk5GR4fnpT3/q3W9ubvbExcV5ioqKPDU1NZ5LLrnEs3r1au/xHTt2eCR5ysvLA1Eu2uF81/b/Wr9+vUeS529/+1sXV4iLJcnzwQcfePdbWlo8VqvV8/LLL3vbampqPBaLxfPuu+8GoEL46/vX9v/au3evR5Jn69atXVpTT8YdIPhoamrSli1bZLPZvG3BwcGy2WwqLy/Xli1bdPr0aZ/jI0aM0JAhQ1ReXh6IktFGF7q26J327t0rl8vlc90jIyOVmZnJdYfRCEDwcfToUTU3N3vfxH1GTEyMXC6XXC6XQkNDz/qy2DPH0X1d6NqidzpzbbnugC8CEAAAMA4BCD6io6MVEhJy1lNdbrdbVqtVVqtVTU1NZz0ddOY4uq8LXVv0TmeuLdcd8EUAgo/Q0FClpaXJ6XR621paWuR0OpWVlaW0tDRdcsklPsd37typqqoqZWVlBaJktNGFri16p8TERFmtVp/rXldXp4qKCq47jBbwb4NH9+NwOJSbm6v09HRlZGSouLhYDQ0NysvLU2RkpB544AE5HA4NHDhQ/fv312OPPaasrCz9v//3/wJdOi7gfNdWkned1+7duyVJ//M//6NLL71UQ4YM0cCBAwNZOs6jvr7ee82kbxc+b9u2TQMHDtSQIUM0c+ZMzZ07V8nJyUpMTNSsWbMUFxeniRMnBq5otMmFru3x48dVVVWlQ4cOSfr2P0glee/Y4zwC/RgauqfXXnvNM2TIEE9oaKgnIyPDs3HjRu+xr7/+2vPoo496oqKiPH379vXcddddnsOHDwewWrTH+a5tYWGhR9JZ2/LlywNXMC7ozGsLvr/l5uZ6PJ5vH4WfNWuWJyYmxmOxWDw333yzZ+fOnYEtGm1yoWu7fPnyVo8XFhYGtO6eIMjj8Xi6NnIBAAAEFmuAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAYhwAEAACMQwACAADGIQABAADjEIAA9CjV1dV65JFHNGTIEFksFlmtVtntdn322WeSpKCgIK1du7bd4yYkJKi4uLhjiwXQbfFdYAB6lEmTJqmpqUkrV67U0KFD5Xa75XQ6dezYsUCXBqAH4aswAPQYNTU1ioqKUllZmcaNG3fW8YSEBP31r3/17l955ZXat2+f9uzZI4fDoY0bN6qhoUEjR45UUVGRbDabJOnGG2/Uhg0bfMY686fx008/VX5+vjZv3qzo6GjdddddKioqUr9+/TpxpgA6Gx+BAegxIiIiFBERobVr16qxsfGs43/6058kScuXL9fhw4e9+/X19brtttvkdDq1detWZWdn6/bbb1dVVZUkac2aNbriiiv00ksv6fDhwzp8+LAkac+ePcrOztakSZO0fft2rVq1Sp9++qlmzJjRRTMG0Fm4AwSgR3n//fc1ffp0ff311xo7dqzGjRunKVOmaMyYMZK+XQP0wQcfaOLEiecd5+qrr9bDDz/sDTMJCQmaOXOmZs6c6e3z4IMPKiQkRL/61a+8bZ9++qnGjRunhoYGhYWFdfj8AHQN7gAB6FEmTZqkQ4cO6Xe/+52ys7NVVlamsWPHasWKFec8p76+Xk899ZRGjhypAQMGKCIiQjt27PDeATqXP//5z1qxYoX3zlNERITsdrtaWlq0d+/eDp4ZgK7EImgAPU5YWJhuueUW3XLLLZo1a5YefPBBFRYWatq0aa32f+qpp/Txxx9r4cKFSkpKUnh4uO655x41NTWd9/fU19frJz/5iR5//PGzjg0ZMqQjpgIgQAhAAHq8UaNGeR99v+SSS9Tc3Oxz/LPPPtO0adN01113Sfo22Ozbt8+nT2ho6FnnjR07Vl9++aWSkpI6rXYAgcFHYAB6jGPHjummm27S22+/re3bt2vv3r1avXq1FixYoDvvvFPSt2t5nE6nXC6X/va3v0mSkpOTtWbNGm3btk1//vOf9Q//8A9qaWnxGTshIUF//OMfdfDgQR09elSS9Oyzz+rzzz/XjBkztG3bNu3atUsffvghi6CBXoAABKDHiIiIUGZmpn7xi1/oRz/6ka6++mrNmjVL06dP15IlSyRJr7zyij7++GPFx8frmmuukSQtWrRIUVFRuu6663T77bfLbrdr7NixPmO/9NJL2rdvn4YNG6bLL79ckjRmzBht2LBB//u//6sbbrhB11xzjQoKChQXF9e1EwfQ4XgKDAAAGIc7QAAAwDgEIAAAYBwCEAAAMA4BCAAAGIcABAAAjEMAAgAAxiEAAQAA4xCAAACAcQhAAADAOAQgAABgHAIQAAAwDgEIAAAY5/8DRUe2Kgz1DzAAAAAASUVORK5CYII=\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nb_shots = 500\n", + "task = device.run(bell_pair_with_pulses, shots = nb_shots)\n", + "counts = task.result().measurement_counts\n", + "\n", + "\n", + "plt.bar(sorted(counts), [counts[k]/nb_shots for k in sorted(counts)])\n", + "plt.xlabel(\"State\")\n", + "plt.ylabel(\"Population\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:eu-west-2::device/qpu/oqc/Lucy': {'shots': 84600, 'tasks': {'COMPLETED': 86}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 55.410 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.9.14", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/3_Bell_pair_with_pulses_Rigetti.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/3_Bell_pair_with_pulses_Rigetti.ipynb new file mode 100644 index 000000000..ff2ea2159 --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/3_Bell_pair_with_pulses_Rigetti.ipynb @@ -0,0 +1,541 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Creating a Bell state with pulses on Rigetti's Aspen M-3\n", + "\n", + "Let's create a Bell state program, the `Hello world!` example in quantum computing, with pulses on a Rigetti's device. \n", + "\n", + "The canonical circuit to generate a Bell pair is constitued of an Hadamard gate on a first qubit followed by a CNOT gate between this qubit and a second qubit. In this notebook, we will realize that creating entangled states requires specific mechanisms that are tightly connected to the hardware type and device architecture. Specifically here, we will focus on the native gate set of the Rigetti's device and choose to use specific waveforms and frames that enable native CZ gates." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's first import few packages." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from braket.aws import AwsDevice\n", + "from braket.pulse import PulseSequence, ArbitraryWaveform\n", + "\n", + "from braket.circuits import Circuit\n", + "import braket.circuits.circuit as circuit\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will use two qubits, #10 amd #113, that are physically connected to each other. We also instantiate a Rigetti device to extract frames and submit circuits." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "a=10\n", + "b=113\n", + "\n", + "device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bell pair with the H and Ctrl-Z gates" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we show how to transform our common Bell state circuit into one that contains a CZ gate instead of a CNOT gate.\n", + "\n", + "As, CNOT and CZ only differ by a basis transform, we will add Hadamard gates before and after the CZ gate. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|\n", + " \n", + "q10 : -H-C---\n", + " | \n", + "q113 : -H-Z-H-\n", + "\n", + "T : |0|1|2|\n" + ] + } + ], + "source": [ + "bell_pair_with_gates = Circuit().h(a).h(b).cz(a, b).h(b)\n", + "print(bell_pair_with_gates)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The circuit is then executed on the Aspen-M-3 device and we plot the measurement histogram which hints that we created $$\\frac{|00\\rangle+|11\\rangle}{\\sqrt{2}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We use `disable_qubit_rewiring = True` to be sure that the Bell pair will be created on the specified qubit and not on remapped qubits so we have a fair comparison with the rest of the notebook." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Population')" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nb_shots = 100\n", + "task = device.run(bell_pair_with_gates, shots = nb_shots, disable_qubit_rewiring=True)\n", + "counts = task.result().measurement_counts\n", + "plt.bar(sorted(counts), [counts[k]/nb_shots for k in sorted(counts)])\n", + "plt.xlabel(\"State\")\n", + "plt.ylabel(\"Population\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bell pair with the pulse implementation of CZ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since Hadamard gates are not native gates on Aspen, we cannot add them to circuits containing pulse sequences. We need to first decompose them into a sequence of native gates. We will use the RX and RZ gates here.\n", + "\n", + "We will annotate this decomposition with `circuit.subroutine` to register this as a custom gate in the circuit allowing easy reuse." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | 3 |\n", + " \n", + "q10 : -Rz(3.14)-Rx(1.57)-Rz(1.57)-Rx(-1.57)-\n", + "\n", + "T : | 0 | 1 | 2 | 3 |\n" + ] + } + ], + "source": [ + "@circuit.subroutine(register=True)\n", + "def rigetti_native_h(q0):\n", + " return (\n", + " Circuit()\n", + " .rz(q0, np.pi)\n", + " .rx(q0, np.pi/2)\n", + " .rz(q0, np.pi/2)\n", + " .rx(q0, -np.pi/2)\n", + " )\n", + " \n", + "print(Circuit().rigetti_native_h(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the CZ gate, we will use an arbitrary waveform with parameters (amplitude, rise/fall time, duration) that have been predetermined beforehand. This waveform will be applied on the `q10_q113_cz_frame frame`." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "a_b_cz_wfm = ArbitraryWaveform([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00017888439538396808, 0.00046751103636033026, 0.0011372942989106456, 0.002577059611929697, 0.005443941944632366, 0.010731922770068104, 0.01976701723583167, 0.03406712171899736, 0.05503285980691202, 0.08350670755829034, 0.11932853352131022, 0.16107456696238298, 0.20614055551722368, 0.2512065440720643, 0.292952577513137, 0.328774403476157, 0.3572482512275353, 0.3782139893154499, 0.3925140937986156, 0.40154918826437913, 0.4068371690898149, 0.4097040514225177, 0.41114381673553674, 0.411813599998087, 0.4121022266390633, 0.4122174383870584, 0.41226003881132406, 0.4122746298554775, 0.4122792591252675, 0.4122806196003006, 0.41228098995582513, 0.41228108334474756, 0.4122811051578895, 0.4122811098772742, 0.4122811108230642, 0.4122811109986316, 0.41228111102881937, 0.41228111103362725, 0.4122811110343365, 0.41228111103443343, 0.4122811110344457, 0.4122811110344471, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.41228111103444737, 0.4122811110344471, 0.4122811110344457, 0.41228111103443343, 0.4122811110343365, 0.41228111103362725, 0.41228111102881937, 0.4122811109986316, 0.4122811108230642, 0.4122811098772742, 0.4122811051578895, 0.41228108334474756, 0.41228098995582513, 0.4122806196003006, 0.4122792591252675, 0.4122746298554775, 0.41226003881132406, 0.4122174383870584, 0.4121022266390633, 0.411813599998087, 0.41114381673553674, 0.4097040514225176, 0.4068371690898149, 0.40154918826437913, 0.3925140937986155, 0.37821398931544986, 0.3572482512275351, 0.32877440347615655, 0.2929525775131368, 0.2512065440720641, 0.20614055551722307, 0.16107456696238268, 0.11932853352131002, 0.08350670755829034, 0.05503285980691184, 0.03406712171899729, 0.01976701723583167, 0.010731922770068058, 0.005443941944632366, 0.002577059611929697, 0.0011372942989106229, 0.00046751103636033026, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To draw this waveform as it will be played on the device, we need to know the frame and the corresponding time separation between each sample. This information is stored in the device capabilities. \n", + "\n", + "First we retrieve the frame that we will use to create a CZ gate between qubit 10 and 113. The minimum time increment can then be extracted through the corresponding port.\n", + "\n", + "The pulse length will be the product of the number of samples and the minimum time increment. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CZ pulse duration: 124.0 ns\n" + ] + } + ], + "source": [ + "a_b_cz_frame = device.frames[f'q{a}_q{b}_cz_frame']\n", + "dt=a_b_cz_frame.port.dt\n", + "\n", + "a_b_cz_wfm_duration = len(a_b_cz_wfm.amplitudes)*dt\n", + "print('CZ pulse duration:', round(a_b_cz_wfm_duration * 1e9,0), 'ns')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With all these data, we call also plot the waveform and see that it is rounded square pulse. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Qy8vLaz1WVlbWpLEr77//Pl5//XWcPHkSFRUV0va6/mYa+/cwXz/qa/u6EqaWdGM328MPP4w+ffpg0qRJ+Oyzz+QLyo4xuXExffv2rdXHfSPz4NabGY3GRo89btw4DBgwAJs2bcLWrVvx2muvYfHixdi4cSNGjhwpVWVee+21Wv3hZrZc8O3maodZXa/vRlFRUUhPT4fBYLD45t2Q1NRUvPDCC+jfv7/FOBJbqOsiP2vWLLz77rt46qmnEB8fD39/fygUCjz44IN1Vr/qa4u6tt/YPiaTCVqtFh999FGdzw8JCWnqy2iQLc4THh6O9u3bY8+ePYiMjIQQAvHx8QgJCcGTTz6JCxcuYO/evejfv7+UIDf1PXn16lUAVR8q9SVCPXv2tPj9Vt9/TVXfYNSm/K02doyWEBYWBgB1ToPOzMxEeHh4g89ft24dJk2ahPvuuw9/+ctfoNVqoVKpkJKSIo0lvFFz/3u0JA8PD4wZMwaLFi1CaWlpkwcxuxImN2QhMDCwzrL5zVWR+oSFhWH69OmYPn06cnJy0KdPHyxcuBAjR45Ex44dAVRVRm6lstGuXTscPXoUJpPJonpz8uRJ6XFbGD16NFJTU/H55583aXr8tWvXpC6+jz/+GG5uzf9n9dlnnyEpKQmvv/66tK2srMzmsyc6duyI7du34+67777lC6jJZMJvv/0mVWsASFNkzTPwrDlPQx/IAwYMwJ49e9C+fXvExMTA19cXvXr1gr+/P7Zs2YK0tDQsWLDA4vUBjb8nQ0JC4OvrC6PRaNOqXF3n8fT0lCpKNzJ3t5mZKw83/5s39Ld65swZi6rGr7/+CpPJ1OBMyOZKgLp37w43NzccOnQI48aNk7YbDAakp6dbbKvLZ599hg4dOmDjxo0WMc6fP/+W4jFfP5rS9vagtLQUQggUFRUxuakDx9yQhY4dO+LkyZPIzc2Vtv3000+NTtU2Go21ukO0Wi3Cw8OlsnNsbCw6duyIpUuX1rkC6Y3nrMu9996LrKwsrF+/XtpWWVmJlStXwsfHB4MGDWr09TXF448/jrCwMPz5z3+uc52KnJwcvPLKK9LvkydPRkZGBt5++22bJViNUalUtb5xrly50qpv7U0xbtw4GI1GvPzyy7Ueq6ysbHIy9cYbb0j/LYTAG2+8AXd3dwwdOtTq83h7e9d73gEDBuD8+fNYv3691E2lVCrRv39/LFu2DBUVFRYzpZr6nlSpVLj//vvx+eef49ixY/Xud7tUKhUSExPxxRdfICMjQ9p+4sQJfPvttxb7+vn5ITg4GHv27LHY/q9//ave469atcri95UrVwKoWv+qPuZ1lWydOPv7+yMhIQHr1q2z6Ab+8MMPcf369QbXxwFqKjE3/h3s37+/wUUDGxIWFoaYmBi8//77Fteybdu24fjx47d0TFuoq0u2oKAAn3/+OSIiImw2ts/ZsHJDFiZPnoxly5YhMTERU6ZMQU5ODtasWYNu3bpBr9fX+7yioiK0adMGY8eORa9eveDj44Pt27fj4MGDUnVBqVTirbfewsiRI9GtWzckJyejdevWuHz5Mnbu3Ak/Pz989dVX9Z7jsccew7///W9MmjQJhw8fRmRkJD777DN8//33WL58+S0NAq5LYGAgNm3ahHvvvRcxMTEWKxSnpaXhk08+QXx8PABgzZo1+OKLL9CzZ0+UlJRg3bp1dR5z2LBhNpnKa/b73/8eH374Ifz9/REdHY3U1FRs377dJlP6bzRo0CBMmzYNKSkpSE9Px/Dhw+Hu7o4zZ85gw4YN+Oc//9nolHmNRoMtW7YgKSkJ/fr1wzfffIP//e9/eP7556XuJmvOExsbi9WrV+OVV15Bp06doNVqpfWazInLqVOn8Oqrr0oxDBw4EN988420vomZNe/JRYsWYefOnejXrx+mTp2K6Oho5OfnIy0tDdu3b0d+fr5N2nzBggXYsmULBgwYgOnTp0sJfLdu3XD06FGLfR999FEsWrQIjz76KOLi4rBnz54GF447d+4cxowZgxEjRiA1NRXr1q3D//3f/0ljkOoSExMDlUqFxYsXo7CwEGq1GkOGDGnwQ9Wc/P/yyy8AqhKWffv2AYDFGlELFy5E//79MWjQIDz22GO4dOkSXn/9dQwfPrzRxel+//vfY+PGjfjjH/+IUaNG4dy5c1izZg2io6Nv+fYNKSkpGDVqFO655x5MnjwZ+fn5Uts35ZgXLlyQViw/dOgQgJq2aNeuHR555BFp36+++go//fQTgKpJAUePHpX2HTNmjNTNOXLkSLRp0wb9+vWDVqtFRkYG3n33XVy5csXiix7dpOUnaJEczFOCDx482Oi+69atEx06dBAeHh4iJiZGfPvtt41OBS8vLxd/+ctfRK9evYSvr6/w9vYWvXr1Ev/6179qHf/IkSPiT3/6kwgKChJqtVq0a9dOjBs3TuzYsaPR2LKzs0VycrIIDg4WHh4eokePHrWmwpqnfr722mu1no+bpsg25MqVK+Lpp58Wd9xxh9BoNMLLy0vExsaKhQsXisLCQiFEzVTnxn4am0aLBqaC1/Vvdu3aNakdfHx8RGJiojh58mStabz1HcM8Ndg8FdssKSlJeHt71zrf2rVrRWxsrPD09BS+vr6iR48e4q9//au4cuVKg6/LfLyzZ8+K4cOHCy8vL6HT6cT8+fOF0Wi8pfNkZWWJUaNGCV9fXwGg1rRwrVYrAFhMxd+3b58AIAYMGFBnnE19T2ZnZ4sZM2aIiIgI4e7uLkJDQ8XQoUPF2rVrpX3MU8E3bNhg8dyGpm7fbPfu3SI2NlZ4eHiIDh06iDVr1kj/ZjcqKSkRU6ZMEf7+/sLX11eMGzdO5OTk1DsV/Pjx42Ls2LHC19dXBAYGipkzZ9aaTnzze0gIId58803RoUMHaTp6U97P9f3cbO/evaJ///5Co9GIkJAQMWPGDGlZh4aYTCbx6quvinbt2gm1Wi169+4tvv7661rXKmuvB59//rno2rWrUKvVIjo6WmzcuLHO619dzP/2df3c/D5t6Npx43vkjTfeEPfcc48IDg4Wbm5uIiQkRIwePbrOKfRUQyGEA46mIiJyMS+++CIWLFjgkANgiVoax9wQERGRU2FyQ0RERE6FyQ0RERE5FY65ISIiIqfCyg0RERE5FSY3RERE5FRcbhE/k8mEK1euwNfXV9b7qhAREVHTierbTYSHhzd6w2eXS26uXLlS607IRERE5BguXryINm3aNLiPyyU35iX6L168CD8/P5mjISIioqbQ6/WIiIho0q12XC65MXdF+fn5MbkhIiJyME0ZUsIBxURERORUmNwQERGRU2FyQ0RERE6FyQ0RERE5FSY3RERE5FSY3BAREZFTYXJDREREToXJDRERETkVJjdERETkVJjcEBERkVNhckNEREROhckNERERORWXu3Em0a0wmgQqjCaUV5pgMgkYhYBJCJhMgICAEFX7iQaOIURDjxI5tsZuZqgAoFAACiigVABKpQJKhQIqhQLubgp4qJRQKRVNuikiUWOY3JDLy7hagpNZevyWV4xzucXIyC9BYWkFCksroC+rQInBCKOJiQlRc1MoAE93Ffw93eGncYefpxtaB3iifbAP2od4o1OID6JCfaFUMgGihjG5IZcjhMAvV/T49pcsbDmWhTM512/pOEoFoFQopG+jqL7e8rJLZElU/4+5ymkSAnV9XxACKDEYUWIwIrOwDABwENcs9tH6qpHYLRQjuoeiX/tWcFNxdAXVphAuVivX6/Xw9/dHYWEh/Pz85A6HWtixy4V4ftPPOHqpUNrmplQgKswXHYJ90D7YG5HBXgj08qj69ujpDh+1GzxUSni4KeGuUsJNWZ3QsHxOdFvMXbwVRhMMlSYYjCaUlBuhL6uAvrQSBaUGXMwvxbm86ziXV4wTmUW4Xl4pPT/MX4MXx3RDYrdQGV8FtRRrPr9ZuSGXUGowYvn203hr3zkYTQIadyUG36HFiO6h+F2UFv6e7nKHSORylEoFlFDAXaWEl0f1Rt/69y+vNOKHs1fx7bEsbD2ejczCMkz78DBGdAvFgj90g85P0yJxk/1j5Yac3rHLhZj+URoy8ksAAKN6hmH+6GhofXkhJHJUZRVGrNhxBmv3/IZKk4Cvxg0pf+qB3/cMlzs0aias3BBVu1xQiknvHkTe9XKE+Wvw8h+6IyFaJ3dYRHSbNO4q/HVEFEb3Csdznx/FT5cK8dSn6Qj08sDdnYLlDo9kxpFY5LSKyiow5b2qxCYq1BffPj2QiQ2Rk+ka5oeN0+/GmF7hqDQJPL7uMH7NKZI7LJKZXSQ3q1atQmRkJDQaDfr164cDBw406XmffvopFAoF7rvvvuYNkBxOpdGEWZ8cwcmsIoT4qvHOpDvhp+G4GiJnpFIqsGRsT8S2C0RRWSUmv3cI+cUGucMiGcme3Kxfvx5z5szB/PnzkZaWhl69eiExMRE5OTkNPu/8+fN45plnMGDAgBaKlBzJK/87gV2ncqFxV+LtpDiEB3jKHRIRNSONuwprH4lFRCtPZOSX4LEPDqGswih3WCQT2ZObZcuWYerUqUhOTkZ0dDTWrFkDLy8vvPPOO/U+x2g04qGHHsKCBQvQoUOHFoyWHMHu07l474fzAIDl42PQs02ArPEQUcsI8lHj3Ul3wlfjhkMXrmHN7rNyh0QykTW5MRgMOHz4MBISEqRtSqUSCQkJSE1Nrfd5L730ErRaLaZMmdLoOcrLy6HX6y1+yHkJIbB8+2kAQPLdkRjRPUzmiIioJXXS+mLhH3sAAN7edw6FpRUyR0RykDW5ycvLg9FohE5nOchTp9MhKyurzufs27cPb7/9Nt58880mnSMlJQX+/v7ST0RExG3HTfZrz5k8HMkogNpNiScGd5Q7HCKSwe97hOEOnQ+Kyirx3vfn5Q6HZCB7t5Q1ioqK8Mgjj+DNN99EcHDTpvrNnTsXhYWF0s/FixebOUqSixAC/6yu2jx8VzuuY0PkopRKBWYN6QwAeHvfb9CXsXrjamRd5yY4OBgqlQrZ2dkW27OzsxEaWns57bNnz+L8+fMYPXq0tM1kMgEA3NzccOrUKXTsaPltXa1WQ61WN0P0ZG/2nslDWnXVZtogjsUicmX39gjDih1ncCbnOt77/jxmD+0sd0jUgmSt3Hh4eCA2NhY7duyQtplMJuzYsQPx8fG19o+KisLPP/+M9PR06WfMmDH43e9+h/T0dHY5uTAhBP654wwA4KF+rNoQuTqVUoFZ1QnNW3tZvXE1sq9QPGfOHCQlJSEuLg59+/bF8uXLUVxcjOTkZADAxIkT0bp1a6SkpECj0aB79+4Wzw8ICACAWtvJtez7NQ+HL1yD2k2Jx1m1ISIAo3qE4Z/bT+NsbjHe//68lOyQ85N9zM348eOxdOlSzJs3DzExMUhPT8eWLVukQcYZGRnIzMyUOUqydyu/+xUA8H/92kLLm+cREaqqN+buqLf2nUOJobKRZ5Cz4I0zyeFlFpYiPuU7KBTAD88NQZg/F+wjoipGk8Cg13bi0rVSrH6oD0b24PIQjsqaz2/ZKzdEt2vb8aoB6bFtA5nYEJEFlVKBEd2qJqhsPZ7dyN7kLJjckMP79peqNZESu9WeYUdElNi96tqw40Q2KowmmaOhlsDkhhxaYUkFfvwtHwAwjHf8JqI69GkbiCBvD+jLKrG/+npBzo3JDTm0HSezYTQJdNH5IjLYW+5wiMgOqZQK6cvP1uN1r35PzoXJDTm0mi4pVm2IqH7Dq68RW3/JhsnkUvNoXBKTG3JYpQYjdp/OBQAM53gbImpA/47B8PZQIUtfhp8vF8odDjUzJjfksPaeyUVZhQmtAzzRLZzT+omofhp3FQZ30QKoqfiS82JyQw7LPK1zWLQOCoVC5miIyN5JXVOcEu70mNyQQ6o0mrDjRNUFilPAiagpfhelhbtKgV9zruNs7nW5w6FmxOSGHNLB89dwraQCgV7uuDMyUO5wiMgB+GncEd8xGEDVwGJyXkxuyCF9d7LqwjQkSgc3Fd/GRNQ05pmV5sovOSd+KpBDOnzhGgDg7k5BMkdCRI6kf3Xl5ujlQhgquVqxs2JyQw7HUGnCsSt6AEBMRIC8wRCRQ4kM8kKAlzsMlSacyNTLHQ41EyY35HBOZRXBUGmCv6c72nNVYiKygkKhQK82AQCAny4VyBoLNR8mN+Rw0i9WdUn1igjgFHAispq54pueUSBrHNR8mNyQwzlysQAAu6SI6NbEtA0AAKRXX0vI+TC5IYdjviD1ZnJDRLcgprpb6re8YhSWVMgbDDULJjfkUApLKvBbbjGAqm4pIiJrBXp7oF2QFwAgneNunBKTG3Io5gGA7YK80MrbQ95giMhhcdyNc2NyQw4lneNtiMgGpOSmeoICORcmN+RQmNwQkS3UJDcFEELIGwzZHJMbchhCCCY3RGQT0eF+8FApca2kAhn5JXKHQzbG5IYcxsX8UuQXG+ChUiI63E/ucIjIgandVOhafR3hlHDnw+SGHMaR6r7xruF+ULupZI6GiBydeTmJIxxU7HSY3JDD4Po2RGRLN467IefC5IYcBsfbEJEtma8lx6/oUV5plDcYsikmN+QQDJUm/MI7gRORDbUL8kKglzsMRhNOZBbJHQ7ZEJMbcgjmO4EHeLlLK4sSEd0OhUIhrXT+E7umnAqTG3IIp7OrvlV1DfXjncCJyGa6hlXNmDqTw8qNM2FyQw7hbO51AEBHrbfMkRCRM+kY4gMAOJtTLHMkZEtMbsgh/JpTldx0qr4QERHZQidt1TXl1+ovUOQcmNyQQ6ip3DC5ISLb6RBSVQ3OLSpHYWmFzNGQrTC5IbtXYTThwtWq5dE7MbkhIhvy07hD56cGUPMlihwfkxuyexeulqDSJODloUKon0bucIjIydSMu2Fy4yyY3JDdk7qkQnw4U4qIbM5cET6by0HFzoLJDdk9aTAxu6SIqBmYKze/snLjNJjckN2rqdxwGjgR2Z75i9NvHHPjNJjckN07y8oNETUjc+XmQn4JDJUmmaMhW2ByQ3ZNCCH1g3fkGjdE1Ax0fmr4qN1gNAlcuMpxN86AyQ3ZtWx9Oa6XV0KlVKBdELuliMj2FAqF1O3NcTfOgckN2TXzeJt2rbzg4ca3KxE1D2k6OMfdOAV+WpBdM19oOrBLioiaUUdOB3cqTG7IrnEaOBG1BE4Hdy5MbsiucRo4EbWEmoX8rkMIIXM0dLuY3JBdY+WGiFpCuyAvuCkVKDEYkVlYJnc4dJuY3JDdKiqrQLa+HADH3BBR83JXKdEuyAsABxU7AyY3ZLfMA/tCfNXw93SXORoicnYcd+M8mNyQ3ZJWJmbVhohawI3jbsixMbkhuyUNJtZyMDERNT9prZscTgd3dExuyG79ysoNEbUgc+XmV1ZuHB6TG7JbNZUbJjdE1Pw6VC85kVtUjsLSCpmjodvB5IbskskkcDG/FAAQyXtKEVEL8NW4I9hHDQC4mF8iczR0O5jckF3KvV4Og9EElVKBMH+N3OEQkYuIaOUJALh0jcmNI2NyQ3bJfGEJ89fATcW3KRG1jDaBVWvdXLpWKnMkdDv4qUF2ydwl1SbQU+ZIiMiVmK85TG4cG5Mbskvmyo35WxQRUUswJzccc+PYmNyQXTJ/a2LlhohaErulnAOTG7JLNckNKzdE1HJquqVKeHdwB8bkhuySuVsqgpUbImpBrQOqrjnFBiMKSrjWjaNickN2x2QSuFxQXblpxcoNEbUcjbsKWt+qtW7YNeW4mNyQ3ckuKkOFUcBNqYCu+iJDRNRSbuyaIsfE5IbsjvnbUlgA17ghopbHQcWOj58cZHekaeAB7JIiopYnTQdn5cZhMbkhu3OJC/gRkYxYuXF8TG7I7pgvKBEcTExEMuD9pRwfkxuyO5cKzKsTs3JDRC3vxsoN17pxTExuyO7U3FeKlRsiannhARoAQInBiGtc68YhMbkhu2I0CVwp4JgbIpKP2k0FnZ95rRt2TTkiJjdkV7L1Zag0Va9x46eROxwiclEcVOzYmNyQXTFfSMIDPKFSKmSOhohcFRfyc2x2kdysWrUKkZGR0Gg06NevHw4cOFDvvhs3bkRcXBwCAgLg7e2NmJgYfPjhhy0YLTUnaY0bdkkRkYyktW7yWblxRLInN+vXr8ecOXMwf/58pKWloVevXkhMTEROTk6d+7dq1Qp/+9vfkJqaiqNHjyI5ORnJycn49ttvWzhyag7SNHAOJiYiGUVI3VKs3Dgi2ZObZcuWYerUqUhOTkZ0dDTWrFkDLy8vvPPOO3XuP3jwYPzxj39E165d0bFjRzz55JPo2bMn9u3b18KRU3O4mM/KDRHJj2NuHJusyY3BYMDhw4eRkJAgbVMqlUhISEBqamqjzxdCYMeOHTh16hQGDhxY5z7l5eXQ6/UWP2S/zBeSNq2Y3BCRfGrG3HCtG0cka3KTl5cHo9EInU5nsV2n0yErK6ve5xUWFsLHxwceHh4YNWoUVq5ciWHDhtW5b0pKCvz9/aWfiIgIm74Gsq2aBfzYLUVE8gkL0EChAEorjMgvNsgdDllJ9m6pW+Hr64v09HQcPHgQCxcuxJw5c7Br16469507dy4KCwuln4sXL7ZssNRklUYTMgvKALBbiojkpXZTQedbtRwFu6Ycj5ucJw8ODoZKpUJ2drbF9uzsbISGhtb7PKVSiU6dOgEAYmJicOLECaSkpGDw4MG19lWr1VCr1TaNm5pHdlE5Kk0C7ioFtL5c44aI5NUm0BNZ+jJculaKXhEBcodDVpC1cuPh4YHY2Fjs2LFD2mYymbBjxw7Ex8c3+Tgmkwnl5eXNESK1IPNg4tZc44aI7ID55r0XOWPK4chauQGAOXPmICkpCXFxcejbty+WL1+O4uJiJCcnAwAmTpyI1q1bIyUlBUDVGJq4uDh07NgR5eXl2Lx5Mz788EOsXr1azpdBNiANJuZ4GyKyA1zIz3HJntyMHz8eubm5mDdvHrKyshATE4MtW7ZIg4wzMjKgVNYUmIqLizF9+nRcunQJnp6eiIqKwrp16zB+/Hi5XgLZCBfwIyJ7cuOMKXIssic3ADBz5kzMnDmzzsduHij8yiuv4JVXXmmBqKilmW+YGR7A5IaI5Nc6oKqKfJnJjcNxyNlS5JwyC6tmSoX5czAxEckvtPpalKUvkzkSshaTG7Ib2dUXkFAmN0RkB8zXoqKyShSXV8ocDVmDyQ3ZDVZuiMie+Kjd4KuuGr3B6o1jYXJDdqG4vBJFZVXfjHR+TG6IyD7oqr9sZRcyuXEkTG7ILpi/Ffmo3eCrcZc5GiKiKuZKciaTG4fC5Ibsgvlbkc6Pq0kTkf0wV5LZLeVYmNyQXagZb8Np4ERkP8yVmyxWbhwKkxuyC1mcKUVEdiiU3VIOickN2QXzt6JQDiYmIjtiviZls1vKoTC5Ibtg/lbEyg0R2RNWbhwTkxuyC9ICfqzcEJEdMV+T8q6Xw1BpkjkaaiomN2QXWLkhInvUytsDHqqqj8qcIlZvHAWTG5KdodKEq8XlALg6MRHZF4VCUXOPKXZNOQwmNyS7nKIyCAF4qJRo5e0hdzhERBZCudaNw3GzZueCggJs2rQJe/fuxYULF1BSUoKQkBD07t0biYmJ6N+/f3PFSU7MPN5G56+GQqGQORoiIkus3DieJlVurly5gkcffRRhYWF45ZVXUFpaipiYGAwdOhRt2rTBzp07MWzYMERHR2P9+vXNHTM5mUxOAyciO8YZU46nSZWb3r17IykpCYcPH0Z0dHSd+5SWluKLL77A8uXLcfHiRTzzzDM2DZScl7TGDVcnJiI7xG4px9Ok5Ob48eMICgpqcB9PT09MmDABEyZMwNWrV20SHLmGmgX8eF8pIrI/7JZyPE3qlmossbnd/cm1ZepZuSEi+8XkxvHYbLZUZmYmMjIybHU4ciHZ0k0zOeaGiOyP+dqUrS+DySRkjoaawmbJzZAhQ9C+fXtbHY5ciHmQno4DionIDoX4qKFUAJUmgavFBrnDoSawaip4Qz744AOUlJTY6nDkIkwmIa36ycoNEdkjN5USIb5qZOvLkVVYhhBfjg+0dzZLbu68805bHYpcyNViAyqMAgoFeMEgIrsV6qdBtr4cmYWl6NHGX+5wqBFcoZhkZR6gF+KjhruKb0cisk+hN4y7IftndeVGqVQ2uIqs0Wi8rYDItZjXjWCXFBHZs7Dq2ZxcyM8xWJ3cbNq0yeL3iooKHDlyBO+//z4WLFhgs8DINWQVlgLgYGIism86LuTnUKxObv7whz/U2jZ27Fh069YN69evx5QpU2wSGLkGVm6IyBGEca0bh2KzQQ533XUXduzYYavDkYuQpoEzuSEiOyZVbpjcOASbJDelpaVYsWIFWrdubYvDkQvJZuWGiByAVLnRl0EILuRn76zulgoMDLQYUCyEQFFREby8vLBu3TqbBkfOjwv4EZEjMM+WKjEYoS+rhL+nu8wRUUOsTm6WL19u8btSqURISAj69euHwMBAW8VFLkAIIZV4w3hfKSKyYxp3FQK83FFQUoFsfRmTGztndXKTlJTUHHGQCyoqr0SJoWrpgFBWbojIzoX6aVBQUoHMwjLcofOVOxxqAFdNI9mYqzb+nu7w9FDJHA0RUcNq7g5eKnMk1BgmNyQb82BiVm2IyBGESjOmymWOhBrD5IZkk62vukBo/XhPKSKyf9rq5MZ8s1+yX0xuSDbmC4TWl5UbIrJ/2uqb++YUsXJj75jckGxyqis3OlZuiMgBmJesyOEtGOyezZKb559/HpMnT7bV4cgFmMfccI0bInIE5i9i5i51sl9WTwWvz+XLl3Hx4kVbHY5cgLm0ay71EhHZM3MXeu71cphMAkqlopFnkFxslty8//77tjoUuQhz5UbLyg0ROYBgHw8oFIDRJHC12IAQfjGzWxxzQ7IQQrByQ0QOxU2lRJC3eVAxx93Ys1uq3BQXF2P37t3IyMiAwWCweGz27Nk2CYycW2FpBQyVJgCcCk5EjkPnp0be9XLk6MvRLVzuaKg+Vic3R44cwb333ouSkhIUFxejVatWyMvLg5eXF7RaLZMbahJz1SbAyx1qN65OTESOQeurxi9g5cbeWd0t9fTTT2P06NG4du0aPD098eOPP+LChQuIjY3F0qVLmyNGckLSTCmucUNEDsQ8u5Mzpuyb1clNeno6/vznP0OpVEKlUqG8vBwRERFYsmQJnn/++eaIkZxQDlcnJiIHVLOQHys39szq5Mbd3R1KZdXTtFotMjIyAAD+/v6cCk5Nls3ViYnIAWlZuXEIVo+56d27Nw4ePIjOnTtj0KBBmDdvHvLy8vDhhx+ie/fuzREjOSFWbojIEUmVG65SbNesrty8+uqrCAsLAwAsXLgQgYGBeOKJJ5Cbm4u1a9faPEByTuaSro7TwInIgUi3YOD9peya1ZWbuLg46b+1Wi22bNli04DINdTcEZzdUkTkOMzV5twirlJsz7iIH8lCqtywW4qIHEiwjxoKBVBpEsgvMTT+BJJFk5KbESNG4Mcff2x0v6KiIixevBirVq267cDIeQkhaio3HFBMRA7E/YZVirM57sZuNalb6oEHHsD9998Pf39/jB49GnFxcQgPD4dGo8G1a9dw/Phx7Nu3D5s3b8aoUaPw2muvNXfc5MD0pZXS6sS8NwsRORqtb/UqxUXl6CZ3MFSnJiU3U6ZMwcMPP4wNGzZg/fr1WLt2LQoLCwEACoUC0dHRSExMxMGDB9G1a9dmDZgcn3kaeICXOzTuXJ2YiByLzk+N45mcMWXPmjygWK1W4+GHH8bDDz8MACgsLERpaSmCgoLg7u7ebAGS85HuBs6qDRE5IHN3Ote6sV+3dONMoGrRPn9/f1vGQi7CvMaNjjOliMgBmSdCcJVi+8XZUtTizN1SHG9DRI4ohKsU2z0mN9TiWLkhIkemk+4vxeTGXjG5oRaXU8QxN0TkuMyLj3JAsf1ickMtjpUbInJkuptWKSb7c0vJTUFBAd566y3MnTsX+fn5AIC0tDRcvnzZpsGRc8pm5YaIHBhXKbZ/Vs+WOnr0KBISEuDv74/z589j6tSpaNWqFTZu3IiMjAx88MEHzREnOQkhBCs3ROTQqlYp9kDedQNy9OUI9uEXNXtjdeVmzpw5mDRpEs6cOQONpubD6d5778WePXtsGhw5H31pJcq5OjERObgQ81o3nA5ul6xObg4ePIhp06bV2t66dWtkZWXZJChyXuYLgb8nVycmIsclrXXDQcV2yerkRq1WQ6/X19p++vRphISE2CQocl41XVKs2hCR49L5mmdMcTq4PbI6uRkzZgxeeuklVFRUAKi6t1RGRgaeffZZ3H///TYPkJxLza0XON6GiByXtvoLGrul7JPVyc3rr7+O69evQ6vVorS0FIMGDUKnTp3g6+uLhQsXNkeM5ETMi15pWbkhIgdWs9YNKzf2yOrZUv7+/ti2bRv27duHo0eP4vr16+jTpw8SEhKaIz5yMqzcEJEzMC9lkc1Viu3SLd8485577sE999xjy1jIBeQWccwNETk+81IWuRxQbJealNysWLGiyQecPXv2LQdDzo+VGyJyBtob7i9lMgkolQqZI6IbNSm5+cc//mHxe25uLkpKShAQEACgasViLy8vaLVaJjfUIPPgO1ZuiMiRmdfpMq9SzIX87EuTBhSfO3dO+lm4cCFiYmJw4sQJ5OfnIz8/HydOnECfPn3w8ssvN3e85MBuXJ2YlRsicmTmVYoBDiq2R1bPlnrhhRewcuVKdOnSRdrWpUsX/OMf/8Df//73Wwpi1apViIyMhEajQb9+/XDgwIF6933zzTcxYMAABAYGIjAwEAkJCQ3uT/bjxtWJOVuKiBydecYUp4PbH6uTm8zMTFRWVtbabjQakZ2dbXUA69evx5w5czB//nykpaWhV69eSExMRE5OTp3779q1CxMmTMDOnTuRmpqKiIgIDB8+nDftdAA51RcAP40bVycmIodnHneTy8qN3bE6uRk6dCimTZuGtLQ0advhw4fxxBNP3NJ08GXLlmHq1KlITk5GdHQ01qxZAy8vL7zzzjt17v/RRx9h+vTpiImJQVRUFN566y2YTCbs2LHD6nNTy8rmDTOJyImYxw5mc8aU3bE6uXnnnXcQGhqKuLg4qNVqqNVq9O3bFzqdDm+99ZZVxzIYDDh8+LBFUqRUKpGQkIDU1NQmHaOkpAQVFRVo1apVnY+Xl5dDr9db/JA8cqTBxExuiMjxma9lOVzrxu5Yvc5NSEgINm/ejNOnT+PkyZMAgKioKNxxxx1WnzwvLw9GoxE6nc5iu06nk47dmGeffRbh4eH1Vo1SUlKwYMECq2Mj28uWBhNzvA0ROT5pIT9WbuzOLS/id8cdd9xSQmNLixYtwqeffopdu3ZBo6m7GjB37lzMmTNH+l2v1yMiIqKlQqQbmCs3WlZuiMgJaFm5sVtWJzeTJ09u8PH6xsrUJTg4GCqVqtZA5OzsbISGhjb43KVLl2LRokXYvn07evbsWe9+5q4zkl8OKzdE5ESkhfxYubE7Vo+5uXbtmsVPTk4OvvvuO2zcuBEFBQVWHcvDwwOxsbEWg4HNg4Pj4+Prfd6SJUvw8ssvY8uWLYiLi7P2JZBMOOaGiJyJdAuG61WrFJP9sLpys2nTplrbTCYTnnjiCXTs2NHqAObMmYOkpCTExcWhb9++WL58OYqLi5GcnAwAmDhxIlq3bo2UlBQAwOLFizFv3jx8/PHHiIyMRFZWFgDAx8cHPj4+Vp+fWo405oZr3BCREzCvSlxhFLhWYkAQVym2G1ZXbuo8iFKJOXPm1LpNQ1OMHz8eS5cuxbx58xATE4P09HRs2bJFGmSckZGBzMxMaf/Vq1fDYDBg7NixCAsLk36WLl1qi5dCzUQIIQ2603F1YiJyAh5uNasUZ3OtG7tyywOKb3b27Nk6F/dripkzZ2LmzJl1PrZr1y6L38+fP39L5yB56cu4OjEROR+tnwZXiw3IKSpDNPzkDoeqWZ3c3DjzCKj6Rp6ZmYn//e9/SEpKsllg5FzMA+64OjEROROtrxonMnl/KXtjdXJz5MgRi9+VSiVCQkLw+uuvNzqTilyXeaokBxMTkTMxr1Kcw/tL2RWrk5udO3c2Rxzk5MzjbdglRUTORFs9hpBjbuyL1QOKhwwZUueUb71ejyFDhtgiJnJCUuWGg4mJyImwcmOfrE5udu3aBYPBUGt7WVkZ9u7da5OgyPmYKzchrNwQkRMJYeXGLjW5W+ro0aPSfx8/flxaXwYAjEYjtmzZgtatW9s2OnIarNwQkTMyV25yeQsGu9Lk5CYmJgYKhQIKhaLO7idPT0+sXLnSpsGR8zDPluKAYiJyJjV3Bi+DEAIKhULmiAiwIrk5d+4chBDo0KEDDhw4gJCQEOkxDw8PaLVaqFSc4kt1M1duOKCYiJyJ5SrFFWhVvagfyavJyU27du0AVN1qgcgaXJ2YiJyVeZXiq8UGZOvLmNzYiSYlN19++SVGjhwJd3d3fPnllw3uO2bMGJsERs6jqLwSZRVcnZiInFOIr7p6leJydA2TOxoCmpjc3HfffcjKyoJWq8V9991X734KhQJGo9FWsZGT4OrEROTMdH4anMwqkirUJL8mJTc3dkWxW4qsVXM3cHZJEZHz0fpWr3XD5MZu2OSu4EQNMS9upWOXFBE5oZoZU5wObi+aVLlZsWJFkw84e/bsWw6GnJNUueFgYiJyQuaxhOyWsh9NSm7+8Y9/NOlgCoWCyQ3VkqPnNHAicl7mL26s3NiPJiU3586da+44yIllF3EaOBE5L+n+UrwFg924rTE3QggIIWwVCzmpXFZuiMiJaW9apZjkd0vJzdtvv43u3btDo9FAo9Gge/fueOutt2wdGzkJqXLD2VJE5IRCblqlmOTX5BWKzebNm4dly5Zh1qxZiI+PBwCkpqbi6aefRkZGBl566SWbB0mOSwhRM+bGl5UbInI+Hm5KtPL2QH6xATlFXKXYHlid3KxevRpvvvkmJkyYIG0bM2YMevbsiVmzZjG5IQtF5ZUoraha2JGzpYjIWWl91cgvNiBbX46oULmjIau7pSoqKhAXF1dre2xsLCorK20SFDkPc9XGV+MGTw+uTkxEzkkad8Pp4HbB6uTmkUcewerVq2ttX7t2LR566CGbBEXOw/yHzvE2ROTMdOZVijkd3C5Y3S0FVA0o3rp1K+666y4AwP79+5GRkYGJEydizpw50n7Lli2zTZTksLK5OjERuQDzFzgu5GcfrE5ujh07hj59+gAAzp49CwAIDg5GcHAwjh07Ju2nUChsFCI5shyuTkxELkDLtW7sitXJzc6dO5sjDnJS2ZwpRUQuwPwFzlytJnnxxpnUrMwl2lB/Vm6IyHmZr3HZhUxu7IHVlZuysjKsXLkSO3fuRE5ODkwmk8XjaWlpNguOHF9mYSkAIJQDionIiZmvcdlF5TCaBFRKDs2Qk9XJzZQpU7B161aMHTsWffv25dgaapC5W4qVGyJyZiG+aqiUChhNAlevl0tTw0keVic3X3/9NTZv3oy77767OeIhJ2I0CalbKszfU+ZoiIiaj0qpQIiPGln6MmQWljG5kZnVY25at24NX1/f5oiFnMzV6+WoNAkoFUCwD5cjJyLnZq5QZ3E6uOysTm5ef/11PPvss7hw4UJzxENOxPwHrvXVwE3FsetE5NzCzMkNBxXLzupuqbi4OJSVlaFDhw7w8vKCu7u7xeP5+fk2C44cW2b1H7iO422IyAWYF/LLZHIjO6uTmwkTJuDy5ct49dVXodPpOKCY6iWNt2HfMxG5AHPlhqsUy8/q5OaHH35AamoqevXq1RzxkBMxf3vhTCkicgXma515CQySj9UDIaKiolBayn84alwWkxsiciHSWje8BYPsrE5uFi1ahD//+c/YtWsXrl69Cr1eb/FDZGZObsKY3BCRC7ixciOEkDka12Z1t9SIESMAAEOHDrXYLoSAQqGA0Wi0TWTk8MyzpXQcc0NELsB8rSurMKGwtAIBXlwCQy68cSY1CyEEKzdE5FI07ioEernjWkkFsvRlTG5kZHVyM2jQoHofO3bs2G0FQ85DX1qJ0oqqKh4rN0TkKkL9PXGtpAKZhWWICvWTOxyXddsrqxUVFWHt2rXo27cvZ1CRJFNfNeg80MsdGneVzNEQEbWMMN4d3C7ccnKzZ88eJCUlISwsDEuXLsWQIUPw448/2jI2cmA1M6V4Tykich1cyM8+WNUtlZWVhffeew9vv/029Ho9xo0bh/LycnzxxReIjo5urhjJAUnJjZ9a5kiIiFoOF/KzD02u3IwePRpdunTB0aNHsXz5cly5cgUrV65sztjIgWWyckNELiiUlRu70OTKzTfffIPZs2fjiSeeQOfOnZszJnIC5m8toRxMTEQuJJQ3z7QLTa7c7Nu3D0VFRYiNjUW/fv3wxhtvIC8vrzljIweWyWngROSCpOSG3VKyanJyc9ddd+HNN99EZmYmpk2bhk8//RTh4eEwmUzYtm0bioqKmjNOcjBS5YbJDRG5EPM1r7C0AqUGLmorF6tnS3l7e2Py5MnYt28ffv75Z/z5z3/GokWLoNVqMWbMmOaIkRwQb5pJRK7IV+0GL4+q5S9YvZHPba1z06VLFyxZsgSXLl3CJ598YquYyMGVGowoLK0AwOSGiFyLQqHg3cHtwG0v4gcAKpUK9913H7788ktbHI4cnPnbipeHCr5qqxfBJiJyaJwOLj+bJDdENzJ/Wwn110ChUMgcDRFRy+JCfvJjckM2x2ngROTKwjgdXHZMbsjmOJiYiFyZ+Ysdkxv5MLkhm8viGjdE5MLMK7NztpR8mNyQzdXcV4rJDRG5HlZu5MfkhmwuS1rAj/eVIiLXY+6Sz71ejgqjSeZoXBOTG7I5Vm6IyJUFeXvAXaWAEEBOUbnc4bgkJjdkUxVGE3KvV/0xc0AxEbkipVIBrS+7puTE5IZsKqeoHEIA7ioFgrw95A6HiEgWnA4uLyY3ZFNZ1Qv4aX01UCq5gB8RuSYdb8EgKyY3ZFOXrlX9IbcO5GBiInJdbQKqroGXC5jcyIHJDdmUOblpw+SGiFyY+RpoviZSy2JyQzZVk9x4yRwJEZF82rSqugYyuZEHkxuyqUvXSgAAEazcEJELM18DL+WXQAghczSuh8kN2RQrN0REQOuAqmtgUXkl9KWVMkfjepjckM2YTAKXOeaGiAieHioE+1Qth3GxuqJNLYfJDdlM7vVyGIwmqJQK3jSTiFxe60COu5ELkxuyGfN4m1A/DdxUfGsRkWurmTHFyk1L4ycQ2QyngRMR1Yhg5UY2TG7IZjiYmIioBis38mFyQzYjTQNvxcoNEREX8pOP7MnNqlWrEBkZCY1Gg379+uHAgQP17vvLL7/g/vvvR2RkJBQKBZYvX95ygVKjWLkhIqrR5oZuKa5107JkTW7Wr1+POXPmYP78+UhLS0OvXr2QmJiInJycOvcvKSlBhw4dsGjRIoSGhrZwtNSYi/lVlRuOuSEiqrkWXi+vRGFphczRuBZZk5tly5Zh6tSpSE5ORnR0NNasWQMvLy+88847de5/55134rXXXsODDz4ItVrdwtFSQ0wmId0gjskNERGgcVch2Kfqs4pdUy1LtuTGYDDg8OHDSEhIqAlGqURCQgJSU1Ntdp7y8nLo9XqLH7K9nKJyVBgFVEoFQv24xg0REVAzBpGDiluWbMlNXl4ejEYjdDqdxXadToesrCybnSclJQX+/v7ST0REhM2OTTXMf7hh/lzjhojIrA2ng8vC6T+F5s6di8LCQunn4sWLcofklLjGDRFRbeZronlMIrUMN7lOHBwcDJVKhezsbIvt2dnZNh0srFarOT6nBZgrN5wpRURUg9PB5SFb5cbDwwOxsbHYsWOHtM1kMmHHjh2Ij4+XKyy6ReY/3AgmN0REEnZLyUO2yg0AzJkzB0lJSYiLi0Pfvn2xfPlyFBcXIzk5GQAwceJEtG7dGikpKQCqBiEfP35c+u/Lly8jPT0dPj4+6NSpk2yvg9gtRURUlxtXKRZCQKFQyByRa5A1uRk/fjxyc3Mxb948ZGVlISYmBlu2bJEGGWdkZECprCkuXblyBb1795Z+X7p0KZYuXYpBgwZh165dLR0+3eDiNa5xQ0R0s9YBVdfEYoMRBSUVCPT2kDki1yBrcgMAM2fOxMyZM+t87OaEJTIykqs82iGjSeCKeY2bVuyWIiIy07iroPVVI6eoHJeulTK5aSFOP1uKml9OURkqjAJuSgV0vhy8TUR0I2nGFNe6aTFMbui2mcfbhAVwjRsiopvVDCpmctNS+ElEt02aBh7ALikioptxOnjLY3JDt+1SfvU08FYcTExEdDNOB295TG7ottVMA2flhojoZry/VMtjckO37VIBp4ETEdXnxsoNZ/y2DCY3dNsu5rNyQ0RUn/AADQCgxGBEfrFB5mhcA5Mbui3llUap1NouiMkNEdHN1G4qaTG/c3nFMkfjGpjc0G05n1cCkwB81W7Qco0bIqI6dQjxBgD8mnNd5khcA5Mbui1nc6v+UDtqfXjPFCKienTS+gCouWZS82JyQ7fF/C2kY4iPzJEQEdkv8zWSlZuWweSGbov5W4j5WwkREdVWU7nhmJuWwOSGbktN5cZb5kiIiOyXuXJz8VoJyiqMMkfj/Jjc0C0zmQR+q/4WwsoNEVH9gn084O/pDiE4Y6olMLmhW5apL0NphRHuKgUiWnEaOBFRfRQKhVTh5qDi5sfkhm6ZuUuqXZA33Hk3cCKiBnFQccvhJxLdsrPVf6CdOFOKiKhRHFTccpjc0C37VVrjhoOJiYgaw8pNy2FyQ7dMqtxwMDERUaPM18rfcq/DZOINNJsTkxu6ZdLqxOyWIiJqVJtAT3iolCivNOFyQanc4Tg1Jjd0SwpKDMi7XnV3WyY3RESNc1Mp0T64+h5TnDHVrJjc0C0xV23C/DXwVrvJHA0RkWMwj1E8y3E3zYrJDd2SszlVo/1ZtSEiajrzNZNr3TQvJjd0S37lPaWIiKxmvmZyxlTzYnJDt+Qs7ylFRGS1msoN17ppTkxu6JZIM6VYuSEiarIO1V8I84sNyC82yByN82JyQ1YrqzAiI78EAFcnJiKyhpeHG1oHeALguJvmxOSGrHbhaglMAvDVuCHEVy13OEREDsVc8eaMqebD5Ias9mtOzeJ9CoVC5miIiByLeawiBxU3HyY3ZDWuTExEdOuke0yxW6rZMLkhqx27XAgA6BLK5IaIyFpRob4AgF+u6CEE7zHVHJjckFWEEEi/WAAAiIkIlDcYIiIH1C3cHyqlArlF5bhSWCZ3OE6JyQ1ZJbOwDDlF5VApFejR2l/ucIiIHI6nh0qq3qRnFMgbjJNickNWMVdtuuh84emhkjcYIiIHFRMRAABIv3hN3kCcFJMbsorUJdU2QNY4iIgcWU1yUyBrHM6KyQ1ZpWa8TYCscRARObLe1V8Qf75ciEqjSd5gnBCTG2qySqMJP1+qminVm8kNEdEt6xDsA1+NG8oqTDiVXSR3OE6HyQ012ens6yitMMJX7cY1boiIboNSqUCvNgEA2DXVHJjcUJOZ/wB7RvhDqeTKxEREt0Mad8MZUzbH5IaazDyq3/xtg4iIbl0vDipuNkxuqMk4mJiIyHbM19Jfc6+jqKxC3mCcDJMbapKisgqcqb7JG6eBExHdvhBfNVoHeEII4Gj1ZA2yDSY31CQ/XyqEEEDrAE9ofTVyh0NE5BTMXxbZNWVbTG6oSY6wS4qIyObMy2oc4aBim2JyQ03C8TZERLZ340rFvEO47TC5oUZZ3Amc422IiGyme2t/uCkVyLtejssFpXKH4zSY3FCjrhSWIbf6TuDdw3kncCIiW9G4qxAVVn2HcI67sRkmN9SovadzAQDdw/14J3AiIhuLa9cKALD3dJ7MkTgPJjfUqK3HswEAw6J1MkdCROR8ErpWXVu3n8iG0cRxN7bA5IYadL28EvvOVH2bGN4tVOZoiIicT78OreCnccPVYgMOX7gmdzhOgckNNWjXqRwYjCa0D/ZGZy1vlklEZGvuKiWGVldvtv6SJXM0zoHJDTVo6y9VXVLDo3VQKHizTCKi5pDYrSq5+fZ4FqeE2wCTG6qXodKEnSdzALBLioioOQ28IwRqNyUu5pfiZFaR3OE4PCY3VK/U366iqLwSIb5qaRVNIiKyPS8PNwzoHAIA+JZdU7eNyQ3Vy/wHNixaB6WSXVJERM3J3DVlHg5At47JDdXJZBLYdrxmvA0RETWvoV11UCqA45l6XMwvkTsch8bkhup05GIBcovK4at2Q/+OwXKHQ0Tk9Fp5e6Bv+6oF/czri9GtYXJDdTJPRxwcpYWHG98mREQtYXh01eQNjru5PfzUoloqjSb87+dMADV9wERE1PyGV19zD53PxxXeSPOWMbmhWr786QouXStFoJc7hkRp5Q6HiMhltAn0QnyHIJgEsGb3WbnDcVhMbshCpdGEld/9CgCYOrADvDzcZI6IiMi1zB7aGQDw6YGLyCxk9eZWMLkhC18dvYJzecUI8HLHxPhIucMhInI58R2D0Ld9KxiMJqzZxerNrWByQxKjSWDljuqqzYAO8FGzakNEJIenEqqqN58cuIiswjKZo3E8TG5I8tVPV/BbddUmqX+k3OEQEbms+A5B6BtZXb3h2BurMbkhAFVVmxXfnQHAqg0RkdwUCoVUvfn4QAay9azeWIPJDQEANqZdwm+5xfD3dMfE+HZyh0NE5PLiOwbhzshAGCpNWL79jNzhOBQmN4SfLhbghf8eAwA8NrADfDXuMkdEREQKhQJPD7sDAPDJgQysP5ghc0SOg8mNi7tcUIpHPziEsgoTftclBNMGdpA7JCIiqta/YzCerJ4a/rdNx/DDr3kyR+QYmNy4sKKyCkx57yByi8oRFeqLlf/XB24qviWIiOzJUwmdMaZXOCpNAo+vO4yzudflDsnu8ZPMRZUYKjHrkyM4mVWEYB813p50JwcRExHZIYVCgSVje6JP2wDoyyox+b2DvDVDI5jcuKBdp3IwbNke7DqVC427Em8nxaF1gKfcYRERUT007iq8OTEOEa08ceFqCYb/Yw8+SD0Pk0nIHZpdsovkZtWqVYiMjIRGo0G/fv1w4MCBBvffsGEDoqKioNFo0KNHD2zevLmFInVsOUVleOrTI5j07kFcLihF6wBPvDPpTvSKCJA7NCIiakSQjxrrpvRDn7YBuF5eiXn//QVj1/yAE5l6uUOzOwohhKxp3/r16zFx4kSsWbMG/fr1w/Lly7FhwwacOnUKWm3tmzb+8MMPGDhwIFJSUvD73/8eH3/8MRYvXoy0tDR079690fPp9Xr4+/ujsLAQfn5+zfGS7MqVglJs/SULW37JwoFz+TAJQKkAJvVvjz8PvwPe7IoiInIoJpPAuv0XsGTLKVwvrwQARIX6YkT3UCR2C0VUqC8UCoXMUdqeNZ/fsic3/fr1w5133ok33ngDAGAymRAREYFZs2bhueeeq7X/+PHjUVxcjK+//lradtdddyEmJgZr1qxp9HzNldyUVxqRW1Rus+M1RAigrMKI0gojSgxGlBgqUVhaAX1p1f9fzC/BubxinMsrxtVig8Vz+7QNwPzR3VitISJycJmFpXj56+P49pdsGG/onvJRu6F9sDfaB3sjMtgbYf4a6PzU0Plp4KdxR0vkPR5uSmh9NTY9pjWf37J+bTcYDDh8+DDmzp0rbVMqlUhISEBqamqdz0lNTcWcOXMstiUmJuKLL76oc//y8nKUl9ckHXp985Tvfrmix5/+9UOzHPt2KBRAXLtAJHaryugjWnnJHRIREdlAmL8n/vVQLApKDNh+IgdbjmVhz5lcXC+vxM+XC/Hz5ULZYuvTNgAbp98t2/llTW7y8vJgNBqh0+kstut0Opw8ebLO52RlZdW5f1ZWVp37p6SkYMGCBbYJuAEKAGq3lhnCpFAAnu4qeLqroPFQwdvDDf6e7vDzdIOfxh1h/p5oH+KNDtVZO2dBERE5rwAvD4yNbYOxsW1QXmnExfwS/JZbVb0/f7UEOfoyZOnLkK0vQ1FZZYvE5C7zsiJO/6k3d+5ci0qPXq9HRESEzc/Tu20gTr0y0ubHJSIiaiq1mwqdtL7opPWVOxRZyZrcBAcHQ6VSITs722J7dnY2QkND63xOaGioVfur1Wqo1WrbBExERER2T9a6kYeHB2JjY7Fjxw5pm8lkwo4dOxAfH1/nc+Lj4y32B4Bt27bVuz8RERG5Ftm7pebMmYOkpCTExcWhb9++WL58OYqLi5GcnAwAmDhxIlq3bo2UlBQAwJNPPolBgwbh9ddfx6hRo/Dpp5/i0KFDWLt2rZwvg4iIiOyE7MnN+PHjkZubi3nz5iErKwsxMTHYsmWLNGg4IyMDSmVNgal///74+OOP8fe//x3PP/88OnfujC+++KJJa9wQERGR85N9nZuW5mqL+BERETkDaz6/7eL2C0RERES2wuSGiIiInAqTGyIiInIqTG6IiIjIqTC5ISIiIqfC5IaIiIicCpMbIiIicipMboiIiMipMLkhIiIipyL77RdamnlBZr1eL3MkRERE1FTmz+2m3FjB5ZKboqIiAEBERITMkRAREZG1ioqK4O/v3+A+LndvKZPJhCtXrsDX1xcKhcKmx9br9YiIiMDFixd536p6sI0axzZqGrZT49hGjWMbNY09tJMQAkVFRQgPD7e4oXZdXK5yo1Qq0aZNm2Y9h5+fH/9IGsE2ahzbqGnYTo1jGzWObdQ0crdTYxUbMw4oJiIiIqfC5IaIiIicCpMbG1Kr1Zg/fz7UarXcodgttlHj2EZNw3ZqHNuocWyjpnG0dnK5AcVERETk3Fi5ISIiIqfC5IaIiIicCpMbIiIicipMboiIiMipMLmxkVWrViEyMhIajQb9+vXDgQMH5A5JNikpKbjzzjvh6+sLrVaL++67D6dOnbLYp6ysDDNmzEBQUBB8fHxw//33Izs7W6aI5bdo0SIoFAo89dRT0ja2UZXLly/j4YcfRlBQEDw9PdGjRw8cOnRIelwIgXnz5iEsLAyenp5ISEjAmTNnZIy4ZRmNRrzwwgto3749PD090bFjR7z88ssW999xxTbas2cPRo8ejfDwcCgUCnzxxRcWjzelTfLz8/HQQw/Bz88PAQEBmDJlCq5fv96Cr6J5NdRGFRUVePbZZ9GjRw94e3sjPDwcEydOxJUrVyyOYa9txOTGBtavX485c+Zg/vz5SEtLQ69evZCYmIicnBy5Q5PF7t27MWPGDPz444/Ytm0bKioqMHz4cBQXF0v7PP300/jqq6+wYcMG7N69G1euXMGf/vQnGaOWz8GDB/Hvf/8bPXv2tNjONgKuXbuGu+++G+7u7vjmm29w/PhxvP766wgMDJT2WbJkCVasWIE1a9Zg//798Pb2RmJiIsrKymSMvOUsXrwYq1evxhtvvIETJ05g8eLFWLJkCVauXCnt44ptVFxcjF69emHVqlV1Pt6UNnnooYfwyy+/YNu2bfj666+xZ88ePPbYYy31EppdQ21UUlKCtLQ0vPDCC0hLS8PGjRtx6tQpjBkzxmI/u20jQbetb9++YsaMGdLvRqNRhIeHi5SUFBmjsh85OTkCgNi9e7cQQoiCggLh7u4uNmzYIO1z4sQJAUCkpqbKFaYsioqKROfOncW2bdvEoEGDxJNPPimEYBuZPfvss+Kee+6p93GTySRCQ0PFa6+9Jm0rKCgQarVafPLJJy0RouxGjRolJk+ebLHtT3/6k3jooYeEEGwjIYQAIDZt2iT93pQ2OX78uAAgDh48KO3zzTffCIVCIS5fvtxisbeUm9uoLgcOHBAAxIULF4QQ9t1GrNzcJoPBgMOHDyMhIUHaplQqkZCQgNTUVBkjsx+FhYUAgFatWgEADh8+jIqKCos2i4qKQtu2bV2uzWbMmIFRo0ZZtAXANjL78ssvERcXhwceeABarRa9e/fGm2++KT1+7tw5ZGVlWbSTv78/+vXr5zLt1L9/f+zYsQOnT58GAPz000/Yt28fRo4cCYBtVJemtElqaioCAgIQFxcn7ZOQkAClUon9+/e3eMz2oLCwEAqFAgEBAQDsu41c7saZtpaXlwej0QidTmexXafT4eTJkzJFZT9MJhOeeuop3H333ejevTsAICsrCx4eHtIfiJlOp0NWVpYMUcrj008/RVpaGg4ePFjrMbZRld9++w2rV6/GnDlz8Pzzz+PgwYOYPXs2PDw8kJSUJLVFXX9/rtJOzz33HPR6PaKioqBSqWA0GrFw4UI89NBDAMA2qkNT2iQrKwtardbicTc3N7Rq1col262srAzPPvssJkyYIN04057biMkNNasZM2bg2LFj2Ldvn9yh2JWLFy/iySefxLZt26DRaOQOx26ZTCbExcXh1VdfBQD07t0bx44dw5o1a5CUlCRzdPbhP//5Dz766CN8/PHH6NatG9LT0/HUU08hPDycbUQ2UVFRgXHjxkEIgdWrV8sdTpOwW+o2BQcHQ6VS1ZrFkp2djdDQUJmisg8zZ87E119/jZ07d6JNmzbS9tDQUBgMBhQUFFjs70ptdvjwYeTk5KBPnz5wc3ODm5sbdu/ejRUrVsDNzQ06nc7l2wgAwsLCEB0dbbGta9euyMjIAACpLVz57+8vf/kLnnvuOTz44IPo0aMHHnnkETz99NNISUkBwDaqS1PaJDQ0tNakkMrKSuTn57tUu5kTmwsXLmDbtm1S1Qaw7zZicnObPDw8EBsbix07dkjbTCYTduzYgfj4eBkjk48QAjNnzsSmTZvw3XffoX379haPx8bGwt3d3aLNTp06hYyMDJdps6FDh+Lnn39Genq69BMXF4eHHnpI+m9XbyMAuPvuu2stI3D69Gm0a9cOANC+fXuEhoZatJNer8f+/ftdpp1KSkqgVFpeylUqFUwmEwC2UV2a0ibx8fEoKCjA4cOHpX2+++47mEwm9OvXr8VjloM5sTlz5gy2b9+OoKAgi8ftuo1kHc7sJD799FOhVqvFe++9J44fPy4ee+wxERAQILKysuQOTRZPPPGE8Pf3F7t27RKZmZnST0lJibTP448/Ltq2bSu+++47cejQIREfHy/i4+NljFp+N86WEoJtJETV7Aw3NzexcOFCcebMGfHRRx8JLy8vsW7dOmmfRYsWiYCAAPHf//5XHD16VPzhD38Q7du3F6WlpTJG3nKSkpJE69atxddffy3OnTsnNm7cKIKDg8Vf//pXaR9XbKOioiJx5MgRceTIEQFALFu2TBw5ckSa6dOUNhkxYoTo3bu32L9/v9i3b5/o3LmzmDBhglwvyeYaaiODwSDGjBkj2rRpI9LT0y2u5eXl5dIx7LWNmNzYyMqVK0Xbtm2Fh4eH6Nu3r/jxxx/lDkk2AOr8effdd6V9SktLxfTp00VgYKDw8vISf/zjH0VmZqZ8QduBm5MbtlGVr776SnTv3l2o1WoRFRUl1q5da/G4yWQSL7zwgtDpdEKtVouhQ4eKU6dOyRRty9Pr9eLJJ58Ubdu2FRqNRnTo0EH87W9/s/gAcsU22rlzZ53XoaSkJCFE09rk6tWrYsKECcLHx0f4+fmJ5ORkUVRUJMOraR4NtdG5c+fqvZbv3LlTOoa9tpFCiBuWsSQiIiJycBxzQ0RERE6FyQ0RERE5FSY3RERE5FSY3BAREZFTYXJDREREToXJDRERETkVJjdERETkVJjcEBERkVNhckNELW7SpEm47777ZDv/I488It1p/HYZDAZERkbi0KFDNjkeEd0+rlBMRDalUCgafHz+/Pl4+umnIYRAQEBAywR1g59++glDhgzBhQsX4OPjY5NjvvHGG9i0aZPFjRiJSD5MbojIprKysqT/Xr9+PebNm2dxZ28fHx+bJRW34tFHH4WbmxvWrFljs2Neu3YNoaGhSEtLQ7du3Wx2XCK6NeyWIiKbCg0NlX78/f2hUCgstvn4+NTqlho8eDBmzZqFp556CoGBgdDpdHjzzTdRXFyM5ORk+Pr6olOnTvjmm28sznXs2DGMHDkSPj4+0Ol0eOSRR5CXl1dvbEajEZ999hlGjx5tsT0yMhKvvvoqJk+eDF9fX7Rt2xZr166VHjcYDJg5cybCwsKg0WjQrl07pKSkSI8HBgbi7rvvxqeffnqbrUdEtsDkhojswvvvv4/g4GAcOHAAs2bNwhNPPIEHHngA/fv3R1paGoYPH45HHnkEJSUlAICCggIMGTIEvXv3xqFDh7BlyxZkZ2dj3Lhx9Z7j6NGjKCwsRFxcXK3HXn/9dcTFxeHIkSOYPn06nnjiCanitGLFCnz55Zf4z3/+g1OnTuGjjz5CZGSkxfP79u2LvXv32q5BiOiWMbkhIrvQq1cv/P3vf0fnzp0xd+5caDQaBAcHY+rUqejcuTPmzZuHq1ev4ujRowCqxrn07t0br776KqKiotC7d2+888472LlzJ06fPl3nOS5cuACVSgWtVlvrsXvvvRfTp09Hp06d8OyzzyI4OBg7d+4EAGRkZKBz586455570K5dO9xzzz2YMGGCxfPDw8Nx4cIFG7cKEd0KJjdEZBd69uwp/bdKpUJQUBB69OghbdPpdACAnJwcAFUDg3fu3CmN4fHx8UFUVBQA4OzZs3Weo7S0FGq1us5Bzzee39yVZj7XpEmTkJ6eji5dumD27NnYunVrred7enpKVSUikpeb3AEQEQGAu7u7xe8KhcJimzkhMZlMAIDr169j9OjRWLx4ca1jhYWF1XmO4OBglJSUwGAwwMPDo9Hzm8/Vp08fnDt3Dt988w22b9+OcePGISEhAZ999pm0f35+PkJCQpr6comoGTG5ISKH1KdPH3z++eeIjIyEm1vTLmUxMTEAgOPHj0v/3VR+fn4YP348xo8fj7Fjx2LEiBHIz89Hq1atAFQNbu7du7dVxySi5sFuKSJySDNmzEB+fj4mTJiAgwcP4uzZs/j222+RnJwMo9FY53NCQkLQp08f7Nu3z6pzLVu2DJ988glOnjyJ06dPY8OGDQgNDbVYp2fv3r0YPnz47bwkIrIRJjdE5JDCw8Px/fffw2g0Yvjw4ejRoweeeuopBAQEQKms/9L26KOP4qOPPrLqXL6+vliyZAni4uJw55134vz589i8ebN0ntTUVBQWFmLs2LG39ZqIyDa4iB8RuZTS0lJ06dIF69evR3x8vE2OOX78ePTq1QvPP/+8TY5HRLeHlRsicimenp744IMPGlzszxoGgwE9evTA008/bZPjEdHtY+WGiIiInAorN0RERORUmNwQERGRU2FyQ0RERE6FyQ0RERE5FSY3RERE5FSY3BAREZFTYXJDREREToXJDRERETkVJjdERETkVP4fLamNmH9MwLIAAAAASUVORK5CYII=\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(np.arange(0, len(a_b_cz_wfm.amplitudes))*dt*1e9, a_b_cz_wfm.amplitudes)\n", + "plt.xlabel('Time (ns)')\n", + "plt.ylabel('Amplitude (a. u.)')\n", + "plt.title(f'Pulse on CZ frame between qubit {a} and {b}');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Playing the CZ waveform on a frame that is related to a fast-flux port enable a CZ interaction that causes the systems to oscillate between $|11\\rangle$ and $|20\\rangle$." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "a_rf_frame = device.frames[f'q{a}_rf_frame']\n", + "b_rf_frame = device.frames[f'q{b}_rf_frame']\n", + "frames = [a_rf_frame, b_rf_frame, a_b_cz_frame]\n", + "\n", + "cz_pulse_sequence = (\n", + " PulseSequence()\n", + " .barrier(frames)\n", + " .play(a_b_cz_frame, a_b_cz_wfm)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One side-effect of this pulse that that the mean qubit frequencies will be shifted during the process.\n", + "The qubit frames rotate at the different rates and a relative phase is acquired with respect to the all frames connected to these qubits. \n", + "\n", + "These phase shifts was measured via Ramsey sequences beforehand (and given here as hardcoded information via `phase_shift_a` and `phase_shift_b`). We apply corrections by using shift_phase instructions on RF and XY frames after the CZ pulse. (see Caldwell et all, https://arxiv.org/abs/1706.06562 for more information). " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "phase_shift_a=1.1733407221086924\n", + "phase_shift_b=6.269846678712192\n", + "\n", + "cz_pulse_sequence = (\n", + " cz_pulse_sequence\n", + " .delay(a_rf_frame, a_b_cz_wfm_duration)\n", + " .shift_phase(a_rf_frame, phase_shift_a)\n", + " .delay(b_rf_frame, a_b_cz_wfm_duration)\n", + " .shift_phase(b_rf_frame, phase_shift_b)\n", + " .barrier(frames)\n", + ")\n", + "for phase, q in [(phase_shift_a/2, a), (-phase_shift_b/2, b)]:\n", + " for neighbor in device.properties.paradigm.connectivity.connectivityGraph[str(q)]:\n", + " xy_frame_name = f\"q{min(q, int(neighbor))}_q{max(q, int(neighbor))}_xy_frame\"\n", + " if xy_frame_name in device.frames:\n", + " xy_frame = device.frames[xy_frame_name]\n", + " cz_pulse_sequence.shift_phase(xy_frame, phase)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pulse sequences can be exported as time series via the function `to_time_trace` for visualization. This method returns an object that contains all the numerical values of our pulse sequences, and can be used to plot the traces for each frames." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "data = cz_pulse_sequence.to_time_trace()\n", + "for frame_id in data.amplitudes:\n", + " f=plt.figure(figsize=(12,4))\n", + " plt.subplot(1,3,1)\n", + " plt.plot(data.amplitudes[frame_id].times(), np.real(data.amplitudes[frame_id].values()), label=\"Real\")\n", + " plt.plot(data.amplitudes[frame_id].times(), np.imag(data.amplitudes[frame_id].values()), label=\"Imag\")\n", + " plt.xlabel(\"Time (s)\")\n", + " plt.ylabel(\"Amplitude (norm.)\")\n", + " plt.legend(loc=\"upper right\")\n", + "\n", + " plt.subplot(1,3,2)\n", + " plt.title(frame_id)\n", + " plt.plot(data.frequencies[frame_id].times(), data.frequencies[frame_id].values())\n", + " plt.xlabel(\"Time (s)\")\n", + " plt.ylabel(\"Frequency (Hz)\")\n", + "\n", + " plt.subplot(1,3,3)\n", + " plt.plot(data.phases[frame_id].times(), data.phases[frame_id].values())\n", + " plt.xlabel(\"Time (s)\")\n", + " plt.ylabel(\"Phase (rad)\")\n", + " f.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can build our own implementation of the Bell circuit using a `pulse_gate` instruction that encapsulates the pulse sequence into a gate instructions. \n", + "\n", + "Pulse gates are strictly defined by the pulse sequence and the associated frames. The qubit or a list of qubits provided to `pulse_gate` are for representational purposes." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | 3 |4 | 5 | 6 | 7 | 8 |\n", + " \n", + "q10 : -Rz(3.14)-Rx(1.57)-Rz(1.57)-Rx(-1.57)-PG--------------------------------------\n", + " | \n", + "q113 : -Rz(3.14)-Rx(1.57)-Rz(1.57)-Rx(-1.57)-PG-Rz(3.14)-Rx(1.57)-Rz(1.57)-Rx(-1.57)-\n", + "\n", + "T : | 0 | 1 | 2 | 3 |4 | 5 | 6 | 7 | 8 |\n" + ] + } + ], + "source": [ + "bell_pair_with_pulse = (\n", + " Circuit()\n", + " .rigetti_native_h(a)\n", + " .rigetti_native_h(b)\n", + " .pulse_gate([a, b], cz_pulse_sequence)\n", + " .rigetti_native_h(b)\n", + ")\n", + "print(bell_pair_with_pulse)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Circuits with embedded pulse sequences can be executed normally.\n", + "\n", + "As pulse sequences are inherently hardware dependent since the timings and strength of the waveforms are tuned to be optimal for the frame they are played on, you can only use pulse gates with the flag `disable_qubit_rewiring=True` that prevents any compiler to remap qubits. Amazon Braket SDK toggles automatically the flag when it detects that pulse sequences are embedded in a circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Population')" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nb_shots = 500\n", + "task = device.run(bell_pair_with_pulse, shots=nb_shots, disable_qubit_rewiring=True)\n", + "counts = task.result().measurement_counts\n", + "plt.bar(sorted(counts), [counts[k]/nb_shots for k in sorted(counts)])\n", + "plt.xlabel(\"State\")\n", + "plt.ylabel(\"Population\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 600, 'tasks': {'COMPLETED': 2}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.810 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + }, + "vscode": { + "interpreter": { + "hash": "e8fe7b1d737818ec041fd05b4c8bbd1804e351a931e38c7cd860a34c69554183" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} \ No newline at end of file diff --git a/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/4_Build_single_qubit_gates.ipynb b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/4_Build_single_qubit_gates.ipynb new file mode 100644 index 000000000..95797d3ce --- /dev/null +++ b/modules/1_Continue_Exploring/A_qtm_hw/pulse_control/4_Build_single_qubit_gates.ipynb @@ -0,0 +1,548 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Construct single qubit quantum gates\n", + "\n", + "A quantum circuit is a powerful representation of an algorithm specifically designed to be executed on a gated-based universal quantum processor. While the usual way to define a circuit is using common gates, gates however abstract the underlying details of how qubits operate. \n", + "\n", + "A simple example of pulse-level control is using a parametric gate like $R_X$. An $R_X(θ)$ gate rotates the quantum state of a qubit by an angle θ with respect to an X axis defined by some properties of the pulse sequence. While this is equivalent to applying a pulse of a certain duration on a specific frame used to drive the qubit, it is not the most convenient implementation of the $R_X$ gate as it requires to calibrate and carefully map between the pulse duration and the angle.\n", + "\n", + "In this tutorial, we will describe how a method to create any single-qubit gate with pulses, based on a decomposition to a product of $R_X(\\pi/2)$ and $R_Z$ gates." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's first import some packages." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "from braket.aws import AwsDevice\n", + "from braket.pulse import PulseSequence, GaussianWaveform, ConstantWaveform, DragGaussianWaveform\n", + "from braket.parametric import FreeParameter\n", + "from braket.circuits import Circuit, circuit\n", + "\n", + "## Imports for function fitting\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import scipy.optimize\n", + "from scipy.fft import fft, fftfreq" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While we use Rigetti's Aspen M-3 device here, this notebooks can be easily adapted to OQC's Lucy device by changing the parameters of the $\\pi$/2 pulse." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We use qubit #4 and define a couple of frame to drive and readout the qubit" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "qubit = 4\n", + "drive_frame = device.frames[\"q4_rf_frame\"]\n", + "readout_frame = device.frames[\"q4_ro_rx_frame\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calibrating $\\pi$/2 pulses via Rabi spectroscopy \n", + "\n", + "As single-qubit gates are rotations around the Bloch sphere, we can get the intuition that any of them can be decomposed as a series of rotations around the X axis and the Z axis. Here, Z is defined as the axis along the measurement basis and X by the direction of the driving field with a phase equals to 0. We formalize the decomposition in more details below where we will see that it is only necessary to calibrate a single operation per qubit, namely a $\\pi$/2 pulse, to build any single-qubit gate.\n", + "\n", + "Let's optimize the pulse power to realize a $\\pi$/2 pulse. First we write the short sequence that will drive the qubit with a single pulse around the X axis (since the phase is set to 0). Unlike in the [tutorial](./1_Bringup_experiments.ipynb) where we presented a $\\pi/2$-pulse calibration based on a length sweep, here we will keep the pulse length fixed to 40ns and its width to 5ns and find the best pulse amplitude." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "width = 5e-9\n", + "length = 40e-9\n", + "waveform = GaussianWaveform(length, width, FreeParameter(\"amplitude\"), False)\n", + "\n", + "rabi_sequence = ( \n", + " PulseSequence()\n", + " .play(drive_frame, waveform)\n", + " .capture_v0(readout_frame)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We create the sweep range and execute the batch of pulse sequences" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "start_amp=0.01\n", + "end_amp=0.75\n", + "amps = np.arange(start_amp, end_amp, 0.02)\n", + "N_shots = 1000\n", + "\n", + "pulse_sequences = [rabi_sequence(amplitude=amplitude) for amplitude in amps]\n", + "\n", + "batch = device.run_batch(pulse_sequences, shots=N_shots)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define a fit function that is the product of an exponential and a sine function as we expect the qubit to oscillate between the state $|0\\rangle$ and the state $|1\\rangle$. The projected state after measurement must display this oscillatory dynamics." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rx(pi/2) amplitude: 0.16392 ns\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def damped_oscillation_fit(x, A, A0, Tau, f, x0):\n", + " return A*np.exp(-x/Tau)*np.cos(2*np.pi*(x-x0)*f)+A0\n", + "\n", + "population = [result.measurement_counts['0']/N_shots for result in batch.results()]\n", + "x, y = amps, population\n", + "\n", + "initial_guess=[0.5, 0.5, 1, 0.4, 0]\n", + "optimal_params, _ = scipy.optimize.curve_fit(damped_oscillation_fit, x, y, p0=initial_guess)\n", + "x_fit = np.arange(x[0],x[-1], np.diff(x)[0]/10)\n", + "y_fit = damped_oscillation_fit(x_fit, *optimal_params)\n", + "\n", + "plt.plot(x,y, 'o')\n", + "plt.plot(x_fit,y_fit)\n", + "plt.xlabel(\"Pulse width (s)\")\n", + "plt.ylabel(\"Population\")\n", + "\n", + "frequency = optimal_params[3]\n", + "phase_offset = optimal_params[4]\n", + "x90_amplitude=(np.pi/2)/(2*np.pi*frequency)+phase_offset\n", + "plt.plot(x90_amplitude, damped_oscillation_fit(x90_amplitude, *optimal_params), 'ks')\n", + "\n", + "print('rx(pi/2) amplitude: ', round(x90_amplitude, 5), ' ns')\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We save the $\\pi$/2 calibration to reuse it later." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "x90 = GaussianWaveform(length, width, x90_amplitude, False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Canonical decomposition of single-qubit gates\n", + "Native gates are directly related to the Hamiltonian of the qubits and do not require a complex design. Their implementation could essentially rely on the application of a single pulse. An example of a native gate is the $R_X(π/2)$ gate, also known as the V or SX gate (equivalent up to a global phase $e^{-i\\pi/4}$) that we just calibrated. \n", + "\n", + "On the other hand, non-native gates cannot be directly understood from a continuous Hamiltonian and usually requires a sequence of pulses with varying parameters. The concept of native gates is rather loose and gates that could be designed with a single pulse such as the Hadamard gate are often decomposed into a series of native gates during the compilation stage. \n", + "\n", + "As the state of a single qubit can be represented as a vector on the Bloch sphere, any gate operated on this qubit can be expressed via the following unitary matrix:\n", + "\n", + "$$\n", + " U(θ,ϕ,λ) = \n", + " \\begin{pmatrix}\n", + " \\cos⁡(\\theta/2) & -ie^{iλ} sin⁡(θ/2)\\\\\n", + " -ie^{iϕ} \\sin⁡(θ/2) & e^{i(ϕ+λ)} \\cos⁡(θ/2)\n", + " \\end{pmatrix}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is then convenient to decompose any 1-qubit gate (including the $R_X(\\theta)$ gate) into a sequence of three $R_Z$ gates, which will be [absorbed](https://aip.scitation.org/doi/10.1063/1.5089550) into an instantaneous and perfect shift of the phase of the frame, and two $R_X$ gates with a fixed angle of π/2. The result is that 1-qubit gates have all the same θ-independent duration (up to a global phase):\n", + "\n", + "$$U(θ,ϕ,λ)= R_Z (ϕ- π/2) R_X (π/2) R_Z (π-θ) R_X (π/2) R_Z (λ- π/2)$$\n", + "\n", + "We implement the parametric sequence by composing a sequence with `shift_phase` and `play` instructions\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "lambda_ = FreeParameter(\"lambda_\")\n", + "theta = FreeParameter(\"theta\")\n", + "phi = FreeParameter(\"phi\")\n", + "\n", + "U_sequence = (\n", + " PulseSequence()\n", + " .shift_phase(drive_frame, lambda_ - np.pi/2)\n", + " .play(drive_frame, x90)\n", + " .shift_phase(drive_frame, np.pi - theta)\n", + " .play(drive_frame, x90)\n", + " .shift_phase(drive_frame, phi - np.pi/2)\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "data = U_sequence(theta=np.pi/2, phi=0, lambda_=np.pi).to_time_trace()\n", + "for frame_id in data.amplitudes:\n", + " f, ax = plt.subplots(nrows=3, sharex=True)\n", + " f.subplots_adjust(hspace=0)\n", + "\n", + " ax[0].set_title(frame_id)\n", + " ax[0].plot(data.amplitudes[frame_id].times(), np.real(data.amplitudes[frame_id].values()), label=\"Real\")\n", + " ax[0].plot(data.amplitudes[frame_id].times(), np.imag(data.amplitudes[frame_id].values()), label=\"Imag\")\n", + " ax[0].set_ylabel(\"Amplitude\\n(a. u.)\")\n", + " ax[0].tick_params('x', labelbottom=False)\n", + "\n", + " ax[1].plot(data.frequencies[frame_id].times(), np.array(data.frequencies[frame_id].values())*1e-9)\n", + " ax[1].set_ylabel(\"Frequency\\n(GHz)\")\n", + " ax[1].tick_params('x', labelbottom=False)\n", + "\n", + " ax[2].plot(data.phases[frame_id].times(), data.phases[frame_id].values())\n", + " ax[2].set_xlabel(\"Time (s)\")\n", + " ax[2].set_ylabel(\"Phase\\n(rad)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this sequence, we can create the U Gate via the `pulse_gate` function. For instance, the Hadamard gate is implemented by:\n", + " \n", + "$$ U(π/2,0,π)=R_Z (-π/2) R_X (π/2) R_Z (π/2) R_X (π/2) R_Z (π/2) $$\n", + "\n", + "In the following, we test our implementation of the U gate by probing its behavior when we sweep the angle $\\theta$ fixing $\\phi$ and $\\lambda$ to zero. We expect to achieve the $R_X$ gate that makes the qubit oscillate between $|0\\rangle$ and $|1\\rangle$ around the X axis. We initialize the state along both the X and Y axis before applying the U gate, to confirm that the $R_X$ gate was created successfully. If we initialize the qubit along the X axis which should coincide with the rotation X, we should observe a flat line as the qubit remains in the same state. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "@circuit.subroutine(register=True)\n", + "def U_pulses(theta, phi, lambda_):\n", + " return (\n", + " Circuit()\n", + " .pulse_gate(\n", + " [qubit], \n", + " pulse_sequence=U_sequence(theta=theta, phi=phi, lambda_=lambda_)\n", + " )\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "nb_shots=500\n", + "thetas=np.linspace(0, 2*np.pi, 25)\n", + "\n", + "# initialization along the X axis\n", + "b_X=device.run_batch([Circuit().rx(4, np.pi/2).rz(4, np.pi/2).U_pulses(t, 0, 0) for t in thetas], shots=nb_shots, disable_qubit_rewiring=True)\n", + "\n", + "# initialization along the Y axis\n", + "b_Y=device.run_batch([Circuit().rx(4, np.pi/2).U_pulses(t, 0, 0) for t in thetas], shots=nb_shots, disable_qubit_rewiring=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "population_init_X = [result.measurement_counts['0']/nb_shots for result in b_X.results()]\n", + "plt.plot(thetas, population_init_X, label=\"Init along X\")\n", + "\n", + "population_init_Y = [result.measurement_counts['0']/nb_shots for result in b_Y.results()]\n", + "plt.plot(thetas, population_init_Y, label=\"Init along Y\")\n", + "\n", + "plt.xlabel(\"Angle (rad)\")\n", + "plt.ylabel(\"Population\")\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We observe that applying $U(\\theta, 0, 0)$ after initializing the qubit along the X axis does not seem to change the qubit state. On the other hand, the qubit undergoes a rotation of period $2\\pi$ if initialized on the Y axis. This indicates that we have construct an $R_X$ gate.\n", + "\n", + "The fidelity of the gate is noticibly low. This is mainly due to the $\\pi/2$ pulse characterization that is too simplistic. To go further, we could switch to DragGaussianWaveform that suppresses excitations in the second excited state during driving and implement a better calibration scheme that would optimize the detuning, phase and length of pulse and limit the impact of SPAM errors." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Construct a Hadamard gate with a single pulse\n", + "A trade-off to the previous construct is that any gate will have the same duration, i.e., the duration equivalent to a π-equivalent which is longest optimal duration for a 1-qubit gate. If you were able to use a single π/2-pulse, you would theoretically improve your gate duration and fidelity. In particular, let’s see that this decomposition is not the most performant for the Hadamard gate.\n", + "\n", + "The Hadamard gate is describable by a single rotation using the $U_2$ decomposition. \n", + "\n", + "$$ U(π/2,ϕ,λ)=U_2 (ϕ,λ)=R_Z (ϕ+π/2) R_X (π/2) R_Z (λ-π/2) $$\n", + "\n", + "Identifying that the Hadamard gate is given by $U_2(0, \\pi)$, we can write a sequence directly from this decomposition as the following pulse sequence:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "single_x90_sequence = ( \n", + " PulseSequence()\n", + " .shift_phase(drive_frame, lambda_ - np.pi/2)\n", + " .play(drive_frame, x90)\n", + " .shift_phase(drive_frame, phi + np.pi/2)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can visualize that we have only a single pulse." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "data = single_x90_sequence(phi=0, lambda_=np.pi).to_time_trace()\n", + "for frame_id in data.amplitudes:\n", + " f, ax = plt.subplots(nrows=3, sharex=True)\n", + " f.subplots_adjust(hspace=0)\n", + "\n", + " ax[0].set_title(frame_id)\n", + " ax[0].plot(data.amplitudes[frame_id].times(), np.real(data.amplitudes[frame_id].values()), label=\"Real\")\n", + " ax[0].plot(data.amplitudes[frame_id].times(), np.imag(data.amplitudes[frame_id].values()), label=\"Imag\")\n", + " ax[0].set_ylabel(\"Amplitude\\n(a. u.)\")\n", + " ax[0].tick_params('x', labelbottom=False)\n", + "\n", + " ax[1].plot(data.frequencies[frame_id].times(), np.array(data.frequencies[frame_id].values())*1e-9)\n", + " ax[1].set_ylabel(\"Frequency\\n(GHz)\")\n", + " ax[1].tick_params('x', labelbottom=False)\n", + "\n", + " ax[2].plot(data.phases[frame_id].times(), data.phases[frame_id].values())\n", + " ax[2].set_xlabel(\"Time (s)\")\n", + " ax[2].set_ylabel(\"Phase\\n(rad)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can register this gate with the subroutine decorated as follow. Executing the gate indicates that we have created an equal-weigth superposition of $|0\\rangle$ and $|1\\rangle$." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Counter({'0': 517, '1': 483})\n" + ] + } + ], + "source": [ + "@circuit.subroutine(register=True)\n", + "def short_h_4():\n", + " return (\n", + " Circuit()\n", + " .pulse_gate(\n", + " [qubit], \n", + " pulse_sequence=single_x90_sequence(phi=0, lambda_=np.pi)\n", + " )\n", + " )\n", + "\n", + "circ = Circuit().short_h_4()\n", + "print(device.run(circ, shots=1000).result().measurement_counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3': {'shots': 63000, 'tasks': {'COMPLETED': 88}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 48.450 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.9.14", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "e8fe7b1d737818ec041fd05b4c8bbd1804e351a931e38c7cd860a34c69554183" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} \ No newline at end of file diff --git a/modules/1_Continue_Exploring/B_qtm_sims/Simulating_Noise_On_Amazon_Braket.ipynb b/modules/1_Continue_Exploring/B_qtm_sims/Simulating_Noise_On_Amazon_Braket.ipynb new file mode 100644 index 000000000..bfffa293b --- /dev/null +++ b/modules/1_Continue_Exploring/B_qtm_sims/Simulating_Noise_On_Amazon_Braket.ipynb @@ -0,0 +1,1172 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulating noise on Amazon Braket" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook gives a detailed overview of noise simulations on Amazon Braket. Amazon Braket provides two noise simulators: a local noise simulator that you can use for free as part of the Braket SDK and an on-demand, high-performing noise simulator, DM1. Both simulators are based on the density matrix formalism. After this tutorial, you will be able to define noise channels, apply noise to new or existing circuits, and run those circuits on the Braket noise simulators. \n", + "\n", + "### Table of contents:\n", + "* [Background](#Background)\n", + " * [Noise simulation based on the density matrix formalism](#density_matrix)\n", + " * [Quantum channel and Kraus representation](#quantum_channel)\n", + "* [General imports](#imports)\n", + "* [Quick start](#start)\n", + "* [Defining noise channels](#noise_channels)\n", + " * [Pre-defined noise channels](#pre-defined)\n", + " * [Defining custom noise channels](#self-defined)\n", + "* [Adding noise to a circuit](#apply_noise)\n", + " * [Build noisy circuits bottom-up](#apply_noise_directly)\n", + " * [Applying noise to existing circuits with global methods](#apply_noise_globally)\n", + " * [Applying gate noise to the circuit](#gate-noise)\n", + " * [Applying initialization noise to the circuit](#initialization-noise)\n", + " * [Applying readout noise to the circuit](#readout-noise)\n", + " * [Using both the direct and global methods to apply noise](#both)\n", + "* [Running a noisy circuit](#run)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Background \n", + "\n", + "### Noise simulation based on the density matrix formalism \n", + "In an ideal case, a quantum state prepared by a noise-free circuit can be described by a state vector $|\\psi\\rangle$ -- we call it a 'pure state'. However, the presence of noise in realistic quantum devices will introduce classical uncertainty to the quantum state. For example, a bit flip error with 50% probability acting on a qubit flips the $|0\\rangle$ state into either $|0\\rangle$ or $|1\\rangle$ with a 50-50 chance. Note that this is different from an Hadamard-gate acting on $|0\\rangle$: The latter results in a coherent superposition of $|0\\rangle$ and $|1\\rangle$, whereas the former is a classical, so-called mixture of $|0\\rangle$ and $|1\\rangle$. The most general way of describing a quantum state in the presence of noise is through the so-called density matrix: $\\rho = \\sum_i p_i|\\psi_i\\rangle\\langle\\psi_i|$. It can be understood as a classical mixture of a series of pure states $|\\psi_i\\rangle$ (each of which could be highly entangled), where $p_i$ is the probability of the state being in $|\\psi_i\\rangle$. Because the $p_i$ are classical probabilities they have to sum up to 1: $\\sum_i p_i = 1$. The density matrix of a pure state is simply $\\rho = |\\psi\\rangle\\langle\\psi|$ and, in the bit-flip example from above, the density matrix would be $\\rho = 0.5|0\\rangle\\langle 0| + 0.5|1\\rangle\\langle 1|$. \n", + "\n", + "The density matrix formalism is a very useful way to describe a noisy system with probabilistic outcomes. It gives an exact description of a quantum system going through a quantum channel with noise. Besides, the expectation value of an observable $\\langle O\\rangle$ can be easily calculated by $\\rm{Tr}(O\\rho)$, where \"$\\rm{Tr}$\" is the trace operator. \n", + "\n", + "### Quantum channel and Kraus representation \n", + "\n", + "A [quantum channel](https://en.wikipedia.org/wiki/Quantum_channel) describes the time evolution of a quantum state which is expressed as a density matrix. For instance, to understand what a series of noisy gates does to the state of a quantum computer, you can apply a quantum channel corresponding to the different gate and noise operations. \n", + "Mathematically speaking, a quantum channel is a completely positive and trace-preserving (CPTP) linear map acting on a density matrix. Completely positive means the channel maps positive operators into positive operators (even if the operator is applied to part of a larger system) to make sure the density matrix describes a proper quantum state after the map. Trace-preserving means the trace of the density matrix remains unchanged during the mapping process (this is so that after the map the classical probabilities $p_i$ still sum to 1). \n", + "\n", + "The so-called _Kraus representation_ is a commonly used representation for CPTP maps. [Kraus's theorem](https://en.wikipedia.org/wiki/Quantum_operation#Kraus_operators) states that any quantum operation acting on a quantum state $\\rho$ can be expressed as a map $\\varepsilon(\\rho) = \\sum_i K_i\\rho K_i^{\\dagger}$, and it satisfies: $\\sum_i K_i^{\\dagger}K_i = \\mathbb{1}$, where $\\mathbb{1}$ is the Identity operator.\n", + "\n", + "Let's get started and have a look how you can define and simulate noisy circuits on Amazon Braket." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## General imports " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's begin with the usual imports." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from braket.circuits import Circuit, Observable, Gate, Noise, FreeParameter\n", + "from braket.devices import LocalSimulator\n", + "from braket.aws import AwsDevice\n", + "import numpy as np\n", + "from scipy.stats import unitary_group" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quick start \n", + "\n", + "Let's start with a simple example of running a noisy circuit on Amazon Braket. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "measurement results: Counter({'11': 441, '00': 381, '01': 94, '10': 84})\n" + ] + } + ], + "source": [ + "# build a simple circuit\n", + "circ = Circuit().h(0).cnot(0,1)\n", + "\n", + "# define a noise channel\n", + "noise = Noise.BitFlip(probability=0.1)\n", + "\n", + "# add noise to every gate in the circuit\n", + "circ.apply_gate_noise(noise)\n", + "\n", + "# select the local noise simulator\n", + "device = LocalSimulator('braket_dm')\n", + "\n", + "# run the circuit on the local simulator\n", + "task = device.run(circ, shots = 1000)\n", + "\n", + "# visualize the results\n", + "result = task.result()\n", + "measurement = result.measurement_counts\n", + "print('measurement results:', measurement)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ideally, in the noise-free case, the circuit we defined prepares a Bell-state, and we would expect to measure only '00' and '11' outcomes. However, the presence of noise, in our case a bit flip error, means that sometimes we find the state in '01' and '10' instead.\n", + "\n", + "The local simulator is suitable for fast prototyping on small circuits. If you want to run a noisy circuit with more than 10~12 qubits, we recommend using the on-demand simulator DM1. Using DM1, you can run circuits with up to 17 qubits, and benefit from parallel execution for a group of circuits. The code below shows an example of preparing a 13-qubit GHZ state in the presence of noise." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "measurement results: Counter({'0000000000000': 2, '1100111111111': 1, '0000000000001': 1, '1000001111100': 1, '1111100000000': 1, '0000000010000': 1, '1111111111111': 1, '1000010000001': 1, '0011111111111': 1})\n" + ] + } + ], + "source": [ + "def ghz_circuit(n_qubits: int) -> Circuit:\n", + " \"\"\"\n", + " Function to return simple GHZ circuit ansatz. Assumes all qubits in range(0, n_qubits-1)\n", + " are entangled.\n", + " \"\"\"\n", + " circuit = Circuit().h(0) \n", + "\n", + " for ii in range(0, n_qubits-1):\n", + " circuit.cnot(control=ii, target=ii+1) \n", + " return circuit\n", + "\n", + "# build a 13-qubit GHZ circuit\n", + "circ = ghz_circuit(13)\n", + "\n", + "# define a noise channel\n", + "noise = Noise.Depolarizing(probability=0.1)\n", + "\n", + "# add noise to every gate in the circuit\n", + "circ.apply_gate_noise(noise)\n", + "\n", + "# select the on-demand density matrix simulator DM1\n", + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/dm1\")\n", + "\n", + "# run the circuit on DM1\n", + "task = device.run(circ, shots = 10)\n", + "\n", + "# visualize the results\n", + "result = task.result()\n", + "measurement = result.measurement_counts\n", + "print('measurement results:', measurement)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now start exploring the detailed instructions and use cases of each step in the following sections." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Defining noise channels \n", + "\n", + "To apply noise to a quantum circuit, first, you need to define the noise channel, which is defined in Kraus representation. We offer many commonly-used noise channels in the `Noise` class of the [Amazon Braket SDK](https://amazon-braket-sdk-python.readthedocs.io/en/latest/_apidoc/braket.circuits.html). In addition, you can also define your own custom noise channel as a list of Kraus operators.\n", + "\n", + "### Pre-defined noise channels \n", + "\n", + "The pre-defined single-qubit noise channels include `BitFlip`, `PhaseFlip`, `Depolarizing`, `AmplitudeDamping`, `GeneralizedAmplitudeDamping`, `PhaseDamping` and `PauliChannel`. \n", + "The pre-defined two-qubit noise channels include `TwoQubitDepolarizing` and `TwoQubitDephasing`. The Kraus representations for all of the pre-defined channels are summarized in the following table.\n", + "\n", + "__single-qubit noise channels__\n", + "\n", + "| Noise channel |
    Kraus representation
    | Parameter |\n", + "|:-------------- |:-------------------------------------------------- |:------------|\n", + "| `BitFlip` | $(1-p)\\rho$ + $pX\\rho X$| $p$ is the probability of the bit flip noise. |\n", + "| `PhaseFlip` | $(1-p)\\rho$ + $pZ\\rho Z$| $p$ is the probability of the phase flip noise. |\n", + "| `Depolarizing` |$(1-p)\\rho$ + $p/3(X\\rho X$ + $Y\\rho Y$ + $Z\\rho Z)$|$p$ is the probability of the depolarizing noise (the three possible error cases share the same probability of $p/3$).|\n", + "|`AmplitudeDamping`|$K_0\\rho K_0^\\dagger$ + $K_1\\rho K_1^\\dagger$|$K_0=[1,0;0,\\sqrt{1-\\gamma}]$, $K_1=[0,\\sqrt{\\gamma};0,0]$, where $\\gamma$ is the rate of amplitude damping.|\n", + "|`GeneralizedAmplitudeDamping`|$K_0\\rho K_0^\\dagger$ + $K_1\\rho K_1^\\dagger$ + $K_2\\rho K_2^\\dagger$ + $K_3 \\rho K_3^\\dagger$|$K_0=\\sqrt{p}[1,0;0,\\sqrt{1-\\gamma}]$, $K_1=\\sqrt{p}[0,\\sqrt{\\gamma};0,0]$, $K_2=\\sqrt{1-p}[\\sqrt{1-\\gamma},0;0,1]$, $K_3=\\sqrt{1-p}[0,0;\\sqrt{\\gamma},0]$, where $\\gamma$ is the rate of amplitude damping, and $p$ is the probability of the system been excited by the environment [1].|\n", + "|`PhaseDamping`|$K_0\\rho K_0^\\dagger$ + $K_1 \\rho K_1^\\dagger$|$K_0=[1,0;0,\\sqrt{1-\\gamma}]$, $K_1=[0,0;0,\\sqrt{\\gamma}]$, where $\\gamma$ is the rate of phase damping.|\n", + "|`PauliChannel`|$(1-p_x-p_y-p_z)\\rho$ + $p_xX\\rho X$ + $p_yY\\rho Y$ + $p_zZ\\rho Z$|$p_x$, $p_y$ and $p_z$ are probabilities for the Pauli X, Y, Z noise respectively.|\n", + "\n", + "\n", + "__two-qubit noise channels__\n", + "\n", + "|
    Noise channel
    |
    Kraus representation
    | Parameter |\n", + "|:----------------------- |:-------------------------------------------------- |:------------|\n", + "| `TwoQubitDepolarizing`| $(1-p)\\rho$ + $p/15(IX\\rho IX$ + $IY\\rho IY$ + $IZ\\rho IZ$ + $XI\\rho XI$ +....+ $ZZ\\rho ZZ)$| $p$ is the probability of the two-qubit depolarizing noise (the 15 possible error combinations share the same probability of $p/15$).|\n", + "| `TwoQubitDephasing` | $(1-p)\\rho$ + $p/3(IZ\\rho IZ$ + $ZI\\rho ZI$ + $ZZ\\rho ZZ)$| $p$ is the probability of the two-qubit dephasing noise (the three possible error combinations share the same probability of $p/3$). |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following code block takes the example of the bit flip noise channel: $\\rho\\rightarrow(1-p)\\rho$ + $pX\\rho X$, where $p$ corresponds to the `probability` parameter when defining the noise. This noise channel is equivalent to applying a bit flip error (applying an X gate) with probability $p$ and doing nothing with probability $1-p$. You can check the target qubit count and the Kraus operators of the noise channel defined." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "name: BitFlip\n", + "qubit count: 1\n", + "Kraus operators: \n", + "[[0.9486833+0.j 0. +0.j]\n", + " [0. +0.j 0.9486833+0.j]] \n", + "\n", + "[[0. +0.j 0.31622777+0.j]\n", + " [0.31622777+0.j 0. +0.j]] \n", + "\n" + ] + } + ], + "source": [ + "# define a bit flip noise channel with probability = 0.1\n", + "noise = Noise.BitFlip(probability=0.1)\n", + "\n", + "print('name: ', noise.name)\n", + "print('qubit count: ', noise.qubit_count)\n", + "print('Kraus operators: ')\n", + "for matrix in noise.to_matrix():\n", + " print(matrix, '\\n')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Other pre-defined noise channels can be used in a similar way:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# define a phase flip noise channel\n", + "noise = Noise.PhaseFlip(probability=0.1)\n", + "# define a single-qubit depolarizing noise channel\n", + "noise = Noise.Depolarizing(probability=0.1)\n", + "# define a two-qubit depolarizing noise channel\n", + "noise = Noise.TwoQubitDepolarizing(probability=0.1)\n", + "# define a two-qubit dephasing noise channel\n", + "noise = Noise.TwoQubitDephasing(probability=0.1)\n", + "# define an amplitude damping noise channel\n", + "noise = Noise.AmplitudeDamping(gamma=0.1)\n", + "# define a generalized amplitude damping noise, where gamma is the amplitude damping rate, and\n", + "# probability is the probability of the system being excited by the environment.\n", + "noise = Noise.GeneralizedAmplitudeDamping(gamma=0.1, probability=0.1)\n", + "# define a phase damping noise channel\n", + "noise = Noise.PhaseDamping(gamma=0.1)\n", + "# define a Pauli noise channel\n", + "noise = Noise.PauliChannel(probX=0.1, probY=0.2, probZ=0.3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Defining custom noise channels \n", + "Apart from the pre-defined noise models, you can also define your own noise model by specifying a list of Kraus operators. The following code shows an example of defining a two-qubit Kraus channel with randomly generated unitary operators." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# create an arbitrary 2-qubit Kraus matrix\n", + "E0 = unitary_group.rvs(4) * np.sqrt(0.2) \n", + "E1 = unitary_group.rvs(4) * np.sqrt(0.8)\n", + "K = [E0, E1] \n", + "\n", + "# define a two-qubit noise channel with Kraus operators\n", + "noise = Noise.Kraus(K) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the noise channel you define needs to form a CPTP map. If the input matrices do not define a CPTP map, an error will be raised." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The input matrices do not define a completely-positive trace-preserving map.\n" + ] + } + ], + "source": [ + "K_invalid = [np.random.randn(2,2), np.random.randn(2,2)] \n", + "\n", + "try:\n", + " noise = Noise.Kraus(K_invalid)\n", + " pass\n", + "except ValueError as err:\n", + " print(err)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adding noise to a circuit \n", + "\n", + "There are two methods to build a 'noisy' circuit. First, you can add noise to the circuit 'bottom-up', by using the noise operations in the same way as you would add a gate to the circuit. Second, you can use the methods `apply_gate_noise()`, `apply_initialization_noise()` and `apply_readout_noise()` to apply gate error, qubit initialization error and measurement error globally to existing circuits. \n", + "\n", + "The direct method is more flexible as you can apply noise to any place in a circuit. But for an existing large circuit with lots of gates, you may want to use the global methods to conveniently apply noise to the circuit.\n", + "\n", + "\n", + "### Build noisy circuits bottom-up \n", + "Noise channels can be applied to the circuit the same way as gates. The following example shows how to apply single- and two-qubit noise channels directly to a circuit. The noise applied can be visualized in the circuit diagram with the `print()` method." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0| 1 | 2 |\n", + " \n", + "q0 : -X-C-----------X-DEPH(0.1)-\n", + " | | \n", + "q1 : -X-X-DEPO(0.2)---DEPH(0.1)-\n", + "\n", + "T : |0| 1 | 2 |\n" + ] + } + ], + "source": [ + "# apply depolarizing noise\n", + "circ = Circuit().x(0).x(1).cnot(0,1).depolarizing(1, probability=0.2).x(0).two_qubit_dephasing(target1=0, target2=1, probability=0.1)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Applying noise to existing circuits with global methods\n", + "\n", + "We offer three methods to apply noise globally to the circuit: `apply_gate_noise()`, `apply_initialization_noise()` and `apply_readout_noise()`. In the following, we explain in detail the usage of these three methods.\n", + "\n", + "#### Applying gate noise to the circuit \n", + "\n", + "`apply_gate_noise()` is the method to conveniently apply gate-noise to the circuit. It accepts the following input parameters:\n", + "\n", + "- __noise__: A single or a list of noise channel in `Noise` type.\n", + "- __target_unitary__: A single unitary gate in the form of a matrix in `numpy.ndarray` type. The noise will be applied to that unitary gate. \n", + "- __target_gates__: A single or a list of gates in `Gate` type. Note that `target_gates` and `target_unitary` can not be provided at the same time. If none of `target_gates` and `target_unitary` is given, noise will be applied to all the gates in the circuit. \n", + "- __target_qubits__: A single or a list of qubit indexes. If not given, noise will be applied to all the qubits in the circuit.\n", + "\n", + "When calling the method, the noise channel(s) will be applied right after all `target_gates` in `target_qubits`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note When you call this method, noise will be inserted right after the gate. If you like to apply more than one noise operation, be aware of the order. Alternatively, you can provide a list of noise operations in one call, and the noise will be applied in forward order. \n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The code below is an example of applying phase damping noise to all gates in the circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Noise is applied to every gate in the circuit:\n", + "\n", + "T : | 0 | 1 |\n", + " \n", + "q0 : -X-PD(0.1)-BF(0.1)-C-PD(0.1)-\n", + " | \n", + "q1 : -------------------X-PD(0.1)-\n", + "\n", + "T : | 0 | 1 |\n" + ] + } + ], + "source": [ + "noise = Noise.PhaseDamping(gamma=0.1)\n", + "\n", + "# the noise channel is applied to every gate in the circuit\n", + "circ = Circuit().x(0).bit_flip(0,0.1).cnot(0,1)\n", + "circ.apply_gate_noise(noise)\n", + "print('Noise is applied to every gate in the circuit:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to apply noise to some particular gates in the circuit, you can specify them as `target_gates`. Below is an example in which noise is applied to all X gates in the circuit." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note The target_gates must be a Gate type. You can find all available gates with the following commands:\n", + " \n", + "\n", + "from braket.circuits import Gate\n", + "gate_set = [attr for attr in dir(Gate) if attr[0] in string.ascii_uppercase]\n", + "print(gate_set)\n", + "\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Noise is applied to every X gate:\n", + "\n", + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -X-PD(0.1)-C-------------\n", + " | \n", + "q1 : -Y---------|-X-PD(0.1)---\n", + " | \n", + "q2 : -----------X-----------Z-\n", + "\n", + "T : | 0 | 1 |2|\n" + ] + } + ], + "source": [ + "# the noise channel is applied to all the X gates in the circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "circ.apply_gate_noise(noise, target_gates = Gate.X)\n", + "print('Noise is applied to every X gate:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you define custom unitary gates as part of your circuit, and you want to apply noise to them, you can use the `target_unitary` criterion." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Noise is applied to U2:\n", + "\n", + "T : |0|1| 2 |3| 4 |\n", + " \n", + "q0 : -X-U-C---------------\n", + " | | \n", + "q1 : -Y-U-|-X---U-PD(0.1)-\n", + " | | \n", + "q2 : -----X---Z-U-PD(0.1)-\n", + "\n", + "T : |0|1| 2 |3| 4 |\n" + ] + } + ], + "source": [ + "U1=unitary_group.rvs(4)\n", + "U2=unitary_group.rvs(4)\n", + "circ = Circuit().x(0).y(1).unitary((0,1),U1).cnot(0,2).x(1).z(2).unitary((1,2),U2)\n", + "circ.apply_gate_noise(noise, target_unitary = U2)\n", + "print('Noise is applied to U2:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to apply noise to some particular qubits in the circuit, you can specify them as `target_qubits`. Below is an example to apply noise to all gates in qubits 0 and 2 in the circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Noise is applied to every gate in qubits 0 and 2:\n", + "\n", + "T : | 0 | 1 | 2 |\n", + " \n", + "q0 : -X-PD(0.1)-C-PD(0.1)-----------\n", + " | \n", + "q1 : -Y---------|-X-----------------\n", + " | \n", + "q2 : -----------X-PD(0.1)-Z-PD(0.1)-\n", + "\n", + "T : | 0 | 1 | 2 |\n" + ] + } + ], + "source": [ + "# the noise channel is applied to every gate on qubits 0 and 2\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "circ.apply_gate_noise(noise, target_qubits = [0,2])\n", + "print('Noise is applied to every gate in qubits 0 and 2:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `target_qubits` and `target_gates` criteria can be used at the same time. The code block below applies the gate noise to all X gates in qubit 0." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Noise is applied to X gates in qubits 0:\n", + "\n", + "T : | 0 | 1 | 2 |\n", + " \n", + "q0 : -X-PD(0.1)-C---X-PD(0.1)-\n", + " | \n", + "q1 : -Y---------|-X-----------\n", + " | \n", + "q2 : -----------X---Z---------\n", + "\n", + "T : | 0 | 1 | 2 |\n" + ] + } + ], + "source": [ + "# the noise channel is applied to X gate on qubits 0\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(0).x(1).z(2)\n", + "circ.apply_gate_noise(noise, target_gates = Gate.X, target_qubits = 0)\n", + "print('Noise is applied to X gates in qubits 0:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If a list of noise channels is provided, the first noise channel in the list will be applied first, then the second. " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Noise channels are applied to every gate in qubits 0 and 1:\n", + "\n", + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -X-DEPO(0.1)-BF(0.2)-C-DEPO(0.1)-BF(0.2)-------------\n", + " | \n", + "q1 : -Y-DEPO(0.1)-BF(0.2)-|-X---------DEPO(0.1)-BF(0.2)---\n", + " | \n", + "q2 : ---------------------X-----------------------------Z-\n", + "\n", + "T : | 0 | 1 |2|\n" + ] + } + ], + "source": [ + "# define two noise channels\n", + "noise1 = Noise.Depolarizing(probability=0.1)\n", + "noise2 = Noise.BitFlip(probability=0.2)\n", + "\n", + "# apply a list of noise channels \n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "circ.apply_gate_noise([noise1, noise2], target_qubits = [0,1])\n", + "print('Noise channels are applied to every gate in qubits 0 and 1:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to apply multi-qubit noise channels to a gate, the number of qubits associated with the gate must equal to the number of qubits defined by the noise channel, or otherwise the noise will not be applied. Below shows an example." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The two-qubit noise channel is applied to all the two-qubit gates in the circuit:\n", + "\n", + "T : |0| 1 | 2 |\n", + " \n", + "q0 : -X-C-DEPH(0.1)---SWAP-DEPH(0.1)-\n", + " | | | | \n", + "q1 : -Y-|-|---------X-SWAP-DEPH(0.1)-\n", + " | | \n", + "q2 : ---X-DEPH(0.1)---Z--------------\n", + "\n", + "T : |0| 1 | 2 |\n" + ] + } + ], + "source": [ + "# define a two-qubit noise channel\n", + "noise = Noise.TwoQubitDephasing(probability=0.1)\n", + "\n", + "# apply the noise to the circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2).swap(1,0)\n", + "circ.apply_gate_noise(noise)\n", + "print('The two-qubit noise channel is applied to all the two-qubit gates in the circuit:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Applying initialization noise to the circuit \n", + "\n", + "`apply_initialization_noise()` is the method to apply initialization noise to the circuit. By using the method, the noise will be applied to every qubit at the beginning of a circuit. It accepts the following input parameters:\n", + "\n", + "- __noise__: a single or a list of noise channel in `Noise` type.\n", + "- __target_qubits__: a single or a list of qubit indexes. If not given, noise will be applied to all the qubits in the circuit.\n", + "\n", + "If you want to apply the initialization noise to an empty circuit, you need to provide `target_qubits` to the method. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note When you call this method, noise will be inserted at the very beginning of the circuit. If you like to apply more than one noise operation, be aware of the order. Alternatively, you can provide a list of noise operations in one call, and the noise will be applied in forward order. \n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initialization noise is applied to the circuit:\n", + "\n", + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -DEPO(0.1)-X-C-----\n", + " | \n", + "q1 : -DEPO(0.1)-Y-|-X---\n", + " | \n", + "q2 : -DEPO(0.1)---X---Z-\n", + "\n", + "T : | 0 | 1 |2|\n" + ] + } + ], + "source": [ + "# define a noise channel\n", + "noise = Noise.Depolarizing(probability=0.1)\n", + "\n", + "# the noise channel is applied as the initialization noise to the circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "circ.apply_initialization_noise(noise)\n", + "print('Initialization noise is applied to the circuit:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to apply a multi-qubit noise channel as the initialization noise to a circuit and if the number of the qubits in the existing circuit doesn't match the number of qubits as defined by the noise channel, you need to provide `target_qubits` with the number of qubits matching the noise channel. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initialization noise is applied to the circuit:\n", + "\n", + "T : | 0 |1|2|\n", + " \n", + "q0 : -DEPH(0.1)-X-C-Z-\n", + " | | \n", + "q1 : -DEPH(0.1)-Y-X-X-\n", + "\n", + "T : | 0 |1|2|\n" + ] + } + ], + "source": [ + "# define a two-qubit noise channel\n", + "noise = Noise.TwoQubitDephasing(probability=0.1)\n", + "\n", + "# the noise channel is applied as the initialization noise to the circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,1).x(1).z(0)\n", + "circ.apply_initialization_noise(noise)\n", + "print('Initialization noise is applied to the circuit:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Applying readout noise to the circuit \n", + "\n", + "The method of `apply_readout_noise()` is very similar to the method to apply initialization noise, except that the noise channel is applied to every qubit in the end of a circuit. It accepts the following input parameters:\n", + "\n", + "- __noise__: a single or a list of noise channel in `Noise` type.\n", + "- __target_qubits__: a single or a list of qubit indexes. If not given, noise will be applied to all the qubits in the circuit.\n", + "\n", + "If you want to apply the readout noise to an empty circuit, you need to provide `target_qubits` to the method. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + " Note When you call this method, noise will be inserted at the very end of the circuit. If you like to apply more than one noise operation, be aware of the order. You can also provide a list of noise operations in the one call, and the noise will be applied in forward order. \n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Read-out noise is applied to the circuit:\n", + "\n", + "T : |0| 1 | 2 |\n", + " \n", + "q0 : -X-C---DEPO(0.1)-----------\n", + " | \n", + "q1 : -Y-|-X-DEPO(0.1)-----------\n", + " | \n", + "q2 : ---X---Z---------DEPO(0.1)-\n", + "\n", + "T : |0| 1 | 2 |\n" + ] + } + ], + "source": [ + "# define a noise channel\n", + "noise = Noise.Depolarizing(probability=0.1)\n", + "\n", + "# the noise channel is applied as the readout noise to the circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "circ.apply_readout_noise(noise)\n", + "print('Read-out noise is applied to the circuit:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to apply a multi-qubit noise channel as the readout noise to a circuit and if the number of the qubits in the existing circuit doesn't match the number of qubits as defined by the noise channel, you need to provide `target_qubits` with the number of qubits matching the noise channel. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using both the direct and global methods to apply noise \n", + "You can apply noise to the circuit using both the direct and global methods. " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Noise channels are applied to the circuit:\n", + "\n", + "T : | 0 | 1 |2|\n", + " \n", + "q0 : -X-PF(0.2)-BF(0.1)---------------\n", + " \n", + "q1 : -Y-----------------C-DEPO(0.1)---\n", + " | | \n", + "q2 : -------------------X-DEPO(0.1)-Z-\n", + "\n", + "T : | 0 | 1 |2|\n" + ] + } + ], + "source": [ + "# define a noise channel\n", + "noise = Noise.PhaseFlip(probability=0.2)\n", + "\n", + "# create a circuit and add noise directly to the circuit\n", + "circ = Circuit().x(0).y(1).bit_flip(0,0.1).cnot(1,2).two_qubit_depolarizing(1, 2, probability=0.1).z(2)\n", + "circ.apply_gate_noise(noise, target_qubits=0)\n", + "print('Noise channels are applied to the circuit:\\n')\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running a noisy circuit \n", + "\n", + "Running a noisy circuit is like running any other task on Amazon Braket. In the example below we will pick the local simulator to run our circuit. \n", + "\n", + "With shots = 0, you can obtain the exact values of probability, density matrix and expectation values of the mixed state by attaching the corresponding result type. The reduced density matrix is also available if providing the targets qubits. If no target qubit is provided, the full density matrix will be returned. \n", + "\n", + "An example is shown in the code block below." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | Result Types |\n", + " \n", + "q0 : -X-AD(0.1)-C-AD(0.1)-----------Probability-Expectation(Z)-DensityMatrix-\n", + " | | | \n", + "q1 : -Y---------|-X-----------------Probability----------------DensityMatrix-\n", + " | | \n", + "q2 : -----------X-AD(0.1)-Z-AD(0.1)-Probability------------------------------\n", + "\n", + "T : | 0 | 1 | 2 | Result Types |\n", + "- Probability is: \n", + "[0.1171 0.0729 0. 0. 0.1539 0.6561 0. 0. ]\n", + "- Expectation value is: \n", + "-0.6199999999999997\n", + "- The reduced Density Matrix is: \n", + "[[0.19+0.j 0. +0.j 0. +0.j 0. +0.j]\n", + " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]\n", + " [0. +0.j 0. +0.j 0.81+0.j 0. +0.j]\n", + " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]]\n" + ] + } + ], + "source": [ + "# define the noise channel\n", + "noise = Noise.AmplitudeDamping(gamma=0.1)\n", + "# create a circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "# apply the noise to qubits 0 and 2 in the circuit \n", + "circ.apply_gate_noise(noise, target_qubits = [0,2])\n", + "\n", + "# attach the result types\n", + "circ.probability()\n", + "circ.expectation(observable = Observable.Z(),target=0)\n", + "# attach the density matrix with target=[0,1], and the reduced density matrix of qubits 0,1 will be returned\n", + "circ.density_matrix(target=[0,1])\n", + "print(circ)\n", + "\n", + "# choose the noise simulator, which is called \"braket_dm\"\n", + "device = LocalSimulator(\"braket_dm\")\n", + "# run the circuit\n", + "task = device.run(circ, shots=0)\n", + "result = task.result()\n", + "\n", + "\n", + "print('- Probability is: ')\n", + "print(result.values[0])\n", + "print('- Expectation value is: ')\n", + "print(result.values[1])\n", + "print('- The reduced Density Matrix is: ')\n", + "print(result.values[2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With shots > 0, the results are sampled from the probability distributions. The result type `density_matrix` is not available for shots > 0. \n", + "\n", + "The code below shows the expectation value $\\langle Z_0\\rangle$ and the probability that the mixed state collapsing into different states. We see those values here are different from the exact values obtained in the shots = 0 case." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | Result Types |\n", + " \n", + "q0 : -X-AD(0.1)-C-AD(0.1)-----------Probability-Expectation(Z)-\n", + " | | \n", + "q1 : -Y---------|-X-----------------Probability----------------\n", + " | | \n", + "q2 : -----------X-AD(0.1)-Z-AD(0.1)-Probability----------------\n", + "\n", + "T : | 0 | 1 | 2 | Result Types |\n", + "- Probability is: \n", + "[0.12 0.11 0. 0. 0.22 0.55 0. 0. ]\n", + "- Expectation value is: \n", + "-0.54\n" + ] + } + ], + "source": [ + "# create a circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "circ.apply_gate_noise(noise, target_qubits = [0,2])\n", + "\n", + "circ.probability()\n", + "circ.expectation(observable = Observable.Z(),target=0)\n", + "print(circ)\n", + "\n", + "# run the circuit\n", + "task = device.run(circ, shots=100)\n", + "result = task.result()\n", + "\n", + "print('- Probability is: ')\n", + "print(result.values[0])\n", + "print('- Expectation value is: ')\n", + "print(result.values[1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can also create circuits with parametrized noise operations and specify the parameter values later:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 | Result Types |\n", + " \n", + "q0 : -X-AD(gamma)-C-AD(gamma)-------------Probability-Expectation(Z)-\n", + " | | \n", + "q1 : -Y-----------|-X---------------------Probability----------------\n", + " | | \n", + "q2 : -------------X-AD(gamma)-Z-AD(gamma)-Probability----------------\n", + "\n", + "T : | 0 | 1 | 2 | Result Types |\n", + "- Probability when gamma=0.1 is: \n", + "[0.12 0.18 0. 0. 0.09 0.61 0. 0. ]\n", + "- Expectation value when gamma=0.1 is: \n", + "-0.4\n", + "- Probability when gamma=0.3 is: \n", + "[0.42 0.1 0. 0. 0.21 0.27 0. 0. ]\n", + "- Expectation value when gamma=0.3 is: \n", + "0.04\n" + ] + } + ], + "source": [ + "# define the free parameter\n", + "gamma = FreeParameter('gamma')\n", + "# define the noise channel\n", + "noise = Noise.AmplitudeDamping(gamma=gamma)\n", + "# create a circuit\n", + "circ = Circuit().x(0).y(1).cnot(0,2).x(1).z(2)\n", + "circ.apply_gate_noise(noise, target_qubits = [0,2])\n", + "\n", + "circ.probability()\n", + "circ.expectation(observable = Observable.Z(),target=0)\n", + "print(circ)\n", + "\n", + "# run the circuit with gamma = 0.1\n", + "task = device.run(circ(gamma=0.1), shots=100)\n", + "result = task.result()\n", + "\n", + "print('- Probability when gamma=0.1 is: ')\n", + "print(result.values[0])\n", + "print('- Expectation value when gamma=0.1 is: ')\n", + "print(result.values[1])\n", + "\n", + "# run the circuit with gamma = 0.3\n", + "task = device.run(circ(gamma=0.3), shots=100)\n", + "result = task.result()\n", + "\n", + "print('- Probability when gamma=0.3 is: ')\n", + "print(result.values[0])\n", + "print('- Expectation value when gamma=0.3 is: ')\n", + "print(result.values[1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reference\n", + "[1] Srikanth R, Banerjee S. \"Squeezed generalized amplitude damping channel\", Physical Review A, 2008, 77(1): 012318." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/dm1': {'shots': 10, 'tasks': {'COMPLETED': 1}, 'execution_duration': datetime.timedelta(microseconds=639000), 'billed_execution_duration': datetime.timedelta(seconds=3)}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.004 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.15" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/B_qtm_sims/TN1_demo_local_vs_non-local_random_circuits.ipynb b/modules/1_Continue_Exploring/B_qtm_sims/TN1_demo_local_vs_non-local_random_circuits.ipynb new file mode 100644 index 000000000..1743c0112 --- /dev/null +++ b/modules/1_Continue_Exploring/B_qtm_sims/TN1_demo_local_vs_non-local_random_circuits.ipynb @@ -0,0 +1,914 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Testing the tensor network simulator with 2-local Hayden-Preskill circuits\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Abstract:** We study a class of random quantum circuits known as Hayden-Preskill circuits using the tensor network simulator backend in Amazon Braket. The goal is to understand the degree to which the tensor network simulator is capable of detecting a hidden local structure in a quantum circuit, while simultaneously building experience with the Amazon Braket service and SDK. We find that the TN1 tensor network simulator can efficiently simulate local random quantum circuits, even when the local structure is obfuscated by permuting the qubit indices. Conversely, when running genuinely non-local versions of the quantum circuits, the simulator's performance is significantly degraded.\n", + "\n", + "This notebook is aimed at users who are familiar with Amazon Braket and have a working knowledge of quantum computing and quantum circuits." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from braket.circuits import Circuit\n", + "from braket.aws import AwsDevice\n", + "from braket.devices import LocalSimulator\n", + "\n", + "import numpy as np\n", + "import random\n", + "import matplotlib.pyplot as plt\n", + "import time\n", + "import os" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Setup the tensor network simulator:\n", + "In this notebook we will use the TN1 simulator on Amazon Braket [[1]](#References):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/tn1\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Local Hayden-Preskill Circuits" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Hayden-Preskill circuits are a class of unstructured, random quantum circuits. To produce a Hayden-Preskill circuit, one chooses a gate at random from some universal gate set at each time step and applies this gate to random target qubits. For example, one can choose to either apply a random single qubit rotation to a random qubit, or a CZ gate to a random pair of qubits at each time step. As a concrete example, consider the following pseudocode:\n", + "```\n", + "Choose either {single qubit, two qubit} gate w/ prob. {1/2, 1/2}\n", + " \n", + "If single qubit:\n", + " Choose either {Rx, Ry, Rz, H} randomly w/ prob. {1/4, 1/4, 1/4, 1/4} \n", + " Apply the chosen gate to a randomly chosen qubit\n", + " If the gate is Rx, Ry, or Rz, rotate by a randomly chosen angle\n", + " \n", + "If two qubit gate:\n", + " Choose (qubit 1, qubit 2) to be two randomly chosen qubits out of the set of N qubits\n", + " Apply CZ(qubit 1, qubit 2) # This means the couplings are long range, all-to-all\n", + "```\n", + "\n", + "Using the strategy above, one can quickly generate random circuits with all-to-all, long-range couplings. These circuits generate unitaries that rapidly converge to Haar random unitaries, and they are difficult to simulate. \n", + "\n", + "A much simpler class of random circuits, which we call **local Hayden-Preskill circuits**, can be generated using the same strategy as above, but in which the two qubit CZ gates are applied to nearest neighbour qubits instead of random pairs:\n", + "```\n", + "Choose a random qubit j from [0, N-2]\n", + "Apply CZ(qubit j, qubit j+1)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### In this notebook, we will focus on both local and non-local Hayden-Preskill circuits, defined using the helper functions below." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def CZtuple_generator(qubits):\n", + " \"\"\"Yields a CZ between a random qubit and its next nearest neighbor.\n", + " For simplicity, we choose a random qubit from the first N-1 qubits for\n", + " the control and we set the target to be qubit i+1, where i is the control.\"\"\"\n", + " a = np.random.choice(range(len(qubits)-1), 1, replace=True)[0]\n", + " yield Circuit().cz(qubits[a],qubits[a+1])\n", + "\n", + "def local_Hayden_Preskill_generator(qubits,numgates):\n", + " \"\"\"Yields the circuit elements for a scrambling unitary.\n", + " Generates a circuit with numgates gates by laying down a\n", + " random gate at each time step. Gates are chosen from single\n", + " qubit unitary rotations by a random angle, Hadamard, or a \n", + " controlled-Z between a qubit and its nearest neighbor (i.e.,\n", + " incremented by 1).\"\"\"\n", + " for i in range(numgates):\n", + " yield np.random.choice([\n", + " Circuit().rx(np.random.choice(qubits,1,replace=True),np.random.ranf()),\n", + " Circuit().ry(np.random.choice(qubits,1,replace=True),np.random.ranf()),\n", + " Circuit().rz(np.random.choice(qubits,1,replace=True),np.random.ranf()),\n", + " Circuit().h(np.random.choice(qubits,1,replace=True)),\n", + " CZtuple_generator(qubits), # For all-to-all: Circuit().cz(*np.random.choice(qubits,2,replace=False)),\n", + " ],1,replace=True,p=[1/8,1/8,1/8,1/8,1/2])\n", + " \n", + "def non_local_Hayden_Preskill_generator(qubits,numgates):\n", + " \"\"\"Yields the circuit elements for a scrambling unitary.\n", + " Generates a circuit with numgates gates by laying down a\n", + " random gate at each time step. Gates are chosen from single\n", + " qubit unitary rotations by a random angle, Hadamard, or a \n", + " controlled-Z between a qubit and its nearest neighbor (i.e.,\n", + " incremented by 1).\"\"\"\n", + " for i in range(numgates):\n", + " yield np.random.choice([\n", + " Circuit().rx(np.random.choice(qubits,1,replace=True),np.random.ranf()),\n", + " Circuit().ry(np.random.choice(qubits,1,replace=True),np.random.ranf()),\n", + " Circuit().rz(np.random.choice(qubits,1,replace=True),np.random.ranf()),\n", + " Circuit().h(np.random.choice(qubits,1,replace=True)),\n", + " Circuit().cz(*np.random.choice(qubits,2,replace=False)),\n", + " ],1,replace=True,p=[1/8,1/8,1/8,1/8,1/2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We use the helper functions above to generate local Hayden-Preskill (random) quantum circuits. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 |3| 4 |5|6|7|8|9|\n", + " \n", + "q0 : -H------------------C---------C-Rx(0.389)--C-C-C-----\n", + " | | | | | \n", + "q1 : -C--------Rx(0.37)--Z---------Z-Rx(0.464)--Z-Z-Z-----\n", + " | \n", + "q2 : -Z--------Ry(0.508)-Rz(0.562)-C------------------C---\n", + " | | \n", + "q3 : -Rx(0.26)---------------------Z-Ry(0.0278)-C-C-C-Z-C-\n", + " | | | | \n", + "q4 : -------------------------------------------Z-Z-Z---Z-\n", + "\n", + "T : | 0 | 1 | 2 |3| 4 |5|6|7|8|9|\n" + ] + } + ], + "source": [ + "# Generate an example of a local Hayden Preskill circuit\n", + "test_circuit = Circuit()\n", + "test_circuit.add(local_Hayden_Preskill_generator(range(5),20))\n", + "print(test_circuit)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : | 0 | 1 | 2 |3| 4 | 5 | 6 |7|8|9|10 | 11 |\n", + " \n", + "q0 : -Z---C-----------Rz(0.0273)---C---------Ry(0.634)-------------------------------\n", + " | | | \n", + "q1 : -|---|-----------C----------C-Z-----------------------------Z-------C-----------\n", + " | | | | | | \n", + "q2 : -|---|-----------|----------Z-Ry(0.435)-Rx(0.527)-Rz(0.172)-C-C---Z-|-Ry(0.643)-\n", + " | | | | | | \n", + "q3 : -|-H-|-Rz(0.375)-|--------------------------------------------Z-Z-|-Z-----------\n", + " | | | | | \n", + "q4 : -C---Z-----------Z----------H-Ry(0.921)-------------------------C-C-------------\n", + "\n", + "T : | 0 | 1 | 2 |3| 4 | 5 | 6 |7|8|9|10 | 11 |\n" + ] + } + ], + "source": [ + "# Generate an example of a non-local Hayden Preskill circuit\n", + "test_circuit = Circuit()\n", + "test_circuit.add(non_local_Hayden_Preskill_generator(range(5),20))\n", + "print(test_circuit)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulating _local_ random circuits using the TN1 tensor network simulator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Testing and timing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start with a reasonably sized circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "20 qubits, 10 layers = 200 total gates\n" + ] + } + ], + "source": [ + "num_qubits = 20 # Number of qubits\n", + "num_layers = 10 # Number of layers. A layer consists of num_qubits gates.\n", + "numgates = num_qubits * num_layers # Total number of gates.\n", + "print(f\"{num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "circ = Circuit()\n", + "circ.add(local_Hayden_Preskill_generator(range(num_qubits), numgates)); # Create the circuit with numgates gates." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Time this circuit using TN1. It should take about a minute or so." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running: 20 qubits, 10 layers = 200 total gates\n", + "ID of task: arn:aws:braket:us-west-2:586882978732:quantum-task/4e870cf6-c25b-4457-b03d-b40e6438e96f\n", + "Status of task: CREATED\n", + "Status: RUNNING\n", + "Status: RUNNING\n", + "Status: COMPLETED\n", + "CPU times: user 895 ms, sys: 7.99 ms, total: 903 ms\n", + "Wall time: 1min 1s\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "%%time\n", + "# define task\n", + "print(f\"Running: {num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "task = device.run(circ, shots=1000, poll_timeout_seconds = 1000)\n", + "\n", + "# get id and status of submitted task\n", + "task_id = task.id\n", + "status = task.state()\n", + "print('ID of task:', task_id)\n", + "print('Status of task:', status)\n", + "\n", + "# wait for job to complete\n", + "terminal_states = ['COMPLETED', 'FAILED', 'CANCELLED']\n", + "while status not in terminal_states:\n", + " time.sleep(20) # Update this for shorter circuits.\n", + " status = task.state()\n", + " print('Status:', status)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "counts = result.measurement_counts\n", + "plt.bar(counts.keys(), counts.values());" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The importance of locality in circuits" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The goal of this section is to understand the importance of a local structure in quantum circuits being simulated in the tensor network simulator. We will first generate and benchmark a local Hayden-Preskill circuit, and then we will re-run the exact same circuit with the qubits randomly permuted. By permuting the qubits, we produce a circuit that appears to be have non-local, long-range coupling, but for which we know that there exists an underlying local structure.\n", + "\n", + "An example of a circuit and its permuted version is shown below. A local Hayden-Preskill circuit is generated, and then a version of the same circuit is created in which the qubits are randomly permuted, according to the permutation [0,1,2,3,4,5]$\\mapsto$[5,2,4,1,0,3]." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": { + "image/png": { + "width": 400 + } + }, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "Image(filename='permuted_circuit.png', width=400)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these two circuits (that seem to have vastly different locality, but which are \"secretly\" the same), we can explore the tensor network simulator's ability to discern structure in a given circuit." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First generate a modest sized local Hayden-Preskill circuit. Then make a copy of that circuit by permuting the qubit indices randomly. We'll compare the runtime to sample from the outputs of these two circuits." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50 qubits, 10 layers = 500 total gates\n" + ] + } + ], + "source": [ + "num_qubits = 50 # Number of qubits\n", + "num_layers = 10 # Number of layers. A layer consists of num_qubits gates.\n", + "numgates = num_qubits * num_layers # Total number of gates.\n", + "qubits=range(num_qubits) # Generate the (1D) qubits\n", + "print(f\"{num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "\n", + "# Generate the circuit with numgates gates acting on qubits.\n", + "circ = Circuit()\n", + "circ.add(local_Hayden_Preskill_generator(qubits,numgates));\n", + "\n", + "# Choose a random permutation of the qubits\n", + "permuted_qubits=np.random.permutation(qubits)\n", + "\n", + "# Copy the circuit circ acting on the permuted qubits\n", + "perm = Circuit().add_circuit(circ, target_mapping=dict(zip(qubits, permuted_qubits)))\n", + "\n", + "##Uncomment for testing:\n", + "# print(permuted_qubits)\n", + "# print(circ)\n", + "# print(perm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Time both circuits using the tensor network simulator for a **single shot**." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running the local circuit with 50 qubits, 10 layers = 500 total gates\n", + "The sample was: 01011001101000001000011100110000001011010001100100.\n", + "CPU times: user 100 ms, sys: 2.76 ms, total: 103 ms\n", + "Wall time: 10.6 s\n" + ] + } + ], + "source": [ + "%%time\n", + "# define task\n", + "task = device.run(circ, shots=1, poll_timeout_seconds = 1000)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "print(f\"Running the local circuit with {num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "counts = result.measurement_counts\n", + "print(f\"The sample was: {next(iter(counts))}.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running the non-local circuit with 50 qubits, 10 layers = 500 total gates\n", + "The sample was: 11000010100100011011001010000100000110001000100001.\n", + "CPU times: user 161 ms, sys: 3.42 ms, total: 164 ms\n", + "Wall time: 28.2 s\n" + ] + } + ], + "source": [ + "%%time\n", + "# define task\n", + "task = device.run(perm, shots=1, poll_timeout_seconds = 1000)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "print(f\"Running the non-local circuit with {num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "counts = result.measurement_counts\n", + "print(f\"The sample was: {next(iter(counts))}.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you repeat these experiments, you'll find that the two runtimes are (typically) very similar! Even though the permuted circuit seems to be highly non-local at first glance, the simulator discovers the underlying local structure, and the total runtime is comparable to the manifestly local circuit. This similarity is due to the rehearsal phase of the tensor network simulation [[1]](#References). A sophisticated algorithm works behind the scenes to find an efficient path for contracting the tensor network. Thus, when the tensor network has an underlying structure, the tensor network simulator can often tease it out." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulating _non-local_ random circuits using the TN1 tensor network simulator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us now compare the efficiency of simulating local and genuinely non-local random quantum circuits. When using the non-local Hayden Preskill circuits above, the circuits we generate have no underlying structure, making them especially difficult for the tensor network simulator." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will generate one local random circuit and one non-local quantum circuit of the same size, and we will compare their runtimes. In this section, the we will not be comparing identical quantum circuits as we were above, so our results can be understood by repeating these experiments several times and noting that our claims are true on average." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50 qubits, 8 layers = 400 total gates\n" + ] + } + ], + "source": [ + "num_qubits = 50 # Number of qubits\n", + "num_layers = 8 # Number of layers. A layer consists of num_qubits gates.\n", + "numgates = num_qubits * num_layers # Total number of gates.\n", + "qubits=range(num_qubits) # Generate the (1D) qubits\n", + "print(f\"{num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "\n", + "# Generate the local circuit with numgates gates acting on qubits.\n", + "localcirc = Circuit()\n", + "localcirc.add(local_Hayden_Preskill_generator(qubits,numgates));\n", + "\n", + "# Generate the non-local circuit with numgates gates acting on qubits.\n", + "nonlocalcirc = Circuit()\n", + "nonlocalcirc.add(non_local_Hayden_Preskill_generator(qubits,numgates));\n", + "\n", + "##Uncomment for testing:\n", + "# print(permuted_qubits)\n", + "# print(circ)\n", + "# print(perm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run the local circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running the local circuit with 50 qubits, 8 layers = 400 total gates\n", + "The sample was: 01000011010100011111010010101101000000000000111010.\n", + "CPU times: user 99.7 ms, sys: 436 µs, total: 100 ms\n", + "Wall time: 10.5 s\n" + ] + } + ], + "source": [ + "%%time\n", + "# define task\n", + "task = device.run(localcirc, shots=1, poll_timeout_seconds = 1000)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "print(f\"Running the local circuit with {num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "counts = result.measurement_counts\n", + "print(f\"The sample was: {next(iter(counts))}.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run the non-local circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running the non-local circuit with 50 qubits, 8 layers = 400 total gates\n", + "The sample was: 01000110001010011000000001001010001000001000111100.\n", + "CPU times: user 118 ms, sys: 13 ms, total: 131 ms\n", + "Wall time: 20.3 s\n" + ] + } + ], + "source": [ + "%%time\n", + "# define task\n", + "task = device.run(nonlocalcirc, shots=1, poll_timeout_seconds = 1000)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "print(f\"Running the non-local circuit with {num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "counts = result.measurement_counts\n", + "print(f\"The sample was: {next(iter(counts))}.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When running this notebook several times, we find that the non-local circuit generally takes 2-3 times longer to run than the local circuit. However, on occasion the non-local circuit fails to run, for a reason we will explore below." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Non-local circuits quickly become too difficult for tensor network methods" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this section, we will compare larger circuits with and without locality. We will see that the local circuits execute very efficiently on the tensor network simulator, whereas the non-local circuits actually fail in the rehearsal phase.\n", + "\n", + "We start by generating these larger circuits:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50 qubits, 20 layers = 1000 total gates\n" + ] + } + ], + "source": [ + "num_qubits = 50 # Number of qubits\n", + "num_layers = 20 # Number of layers. A layer consists of num_qubits gates.\n", + "numgates = num_qubits * num_layers # Total number of gates.\n", + "qubits=range(num_qubits) # Generate the (1D) qubits\n", + "print(f\"{num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "\n", + "# Generate the circuit with numgates gates acting on qubits.\n", + "localcirc = Circuit()\n", + "localcirc.add(local_Hayden_Preskill_generator(qubits,numgates));\n", + "\n", + "# Generate the circuit with numgates gates acting on qubits.\n", + "nonlocalcirc = Circuit()\n", + "nonlocalcirc.add(non_local_Hayden_Preskill_generator(qubits,numgates));\n", + "\n", + "##Uncomment for testing:\n", + "# print(permuted_qubits)\n", + "# print(circ)\n", + "# print(perm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The local Hayden Preskill circuit executes in a reasonable amount of time, generally about a minute or so:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running the local circuit with 50 qubits, 20 layers = 1000 total gates\n", + "The sample was: 01010111001000001010000000100011110000110001110101.\n", + "CPU times: user 201 ms, sys: 7.95 ms, total: 209 ms\n", + "Wall time: 32.7 s\n" + ] + } + ], + "source": [ + "%%time\n", + "# define task\n", + "task = device.run(localcirc, shots=1, poll_timeout_seconds = 1000)\n", + "\n", + "# get results of task\n", + "result = task.result()\n", + "\n", + "# get measurement shots\n", + "print(f\"Running the local circuit with {num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "counts = result.measurement_counts\n", + "print(f\"The sample was: {next(iter(counts))}.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Conversely, the non-local Hayden Preskill circuit actually fails to execute:\n", + "\n", + "
    \n", + "Note: The following cell can take several minutes to run on TN1. It is only present to illustrate a task that will result in a FAILED state. To run this cell, uncomment it.\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Task is in terminal state FAILED and no result is available\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running the non-local circuit with 50 qubits, 20 layers = 1000 total gates\n", + "CPU times: user 411 ms, sys: 19.4 ms, total: 431 ms\n", + "Wall time: 1min 56s\n" + ] + } + ], + "source": [ + "#%%time\n", + "## define task\n", + "#task = device.run(nonlocalcirc, shots=1, poll_timeout_seconds = 1000)\n", + "\n", + "## get results of task\n", + "#result = task.result()\n", + "\n", + "## get measurement shots\n", + "#print(f\"Running the non-local circuit with {num_qubits} qubits, {num_layers} layers = {numgates} total gates\")\n", + "## counts = result.measurement_counts\n", + "## print(f\"The sample was: {next(iter(counts))}.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To see why this circuit `FAILED` to run, we can check the `failureReason` in the task's `_metadata`:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Predicted runtime based on best contraction path found exceeds TN1 limit. Single-shot FLOPS estimate = 2^105\n" + ] + } + ], + "source": [ + "#print(task._metadata['failureReason'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Evidently, without any structure to exploit, this tensor network would take too long to simulate, and the simulator returns with a `FAILED` state." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We saw that structured quantum circuits can be simulated much more efficiently than unstructured random quantum circuits. That said, structure in a quantum circuit may not be immediately evident, as the tensor network simulator was able to discover the hidden structure in our permuted quantum circuits, leading to efficiency on-par with their unpermuted, local counterparts. Note, however, that discovering this underlying structure is analogous to the graph isomorphism problem, and finding an efficient contraction path for a tensor network is a hard problem." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Appendix" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Version: 1.5.0\r\n" + ] + } + ], + "source": [ + "# Check SDK version\n", + "# alternative: braket.__version__\n", + "!pip show amazon-braket-sdk | grep Version" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "[1] [Amazon Braket Documentation: Tensor Network Simulator](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#braket-simulator-tn1)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/tn1': {'shots': 1006, 'tasks': {'COMPLETED': 6, 'FAILED': 1}, 'execution_duration': datetime.timedelta(seconds=124, microseconds=18000), 'billed_execution_duration': datetime.timedelta(seconds=124, microseconds=18000)}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "This estimate does not inclued the task which fails after rehersal, for which charges may apply. See https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html for more details.\n", + "Estimated cost to run this example: 0.568 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print('This estimate does not inclued the task which fails after rehersal, for which charges may apply. See https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html for more details.')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.10 ('venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/B_qtm_sims/Using_The_Adjoint_Gradient_Result_Type.ipynb b/modules/1_Continue_Exploring/B_qtm_sims/Using_The_Adjoint_Gradient_Result_Type.ipynb new file mode 100644 index 000000000..8b5dd7511 --- /dev/null +++ b/modules/1_Continue_Exploring/B_qtm_sims/Using_The_Adjoint_Gradient_Result_Type.ipynb @@ -0,0 +1,1300 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Using the Adjoint Gradient Result Type on Amazon Braket" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this tutorial we'll introduce the `AdjointGradient` result type, discuss what a gradient is and how to compute one on a quantum circuit, explain how they can be used to accelerate your workflows, and show an example of gradients in action on a hybrid quantum algorithm." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + "Note: This notebook requires amazon-braket-sdk-python>=1.35.0\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Table of Contents" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- [Background: What is a gradient?]()\n", + "- [Why compute gradients?]()\n", + "- [Computing gradients of parameters in a quantum circuit]()\n", + " - [Finite differences]()\n", + " - [Parameter shift]()\n", + " - [Adjoint gradient]()\n", + "- [The `AdjointGradient` result type]()\n", + "- [Accelerating QAOA with `AdjointGradient`]()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Background: What is a gradient?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A [gradient](https://en.wikipedia.org/wiki/Gradient) refers to a vector derivative of a scalar-valued function of multiple variables. If we have a function $f(x)$, which depends only on $x$ and maps $x \\to \\mathbb{R}$ (maps $x$ to a single real number), then $f$'s gradient is just its derivative with respect to $x$: $\\frac{df}{dx}$. The gradient is denoted $\\nabla$, so that $\\nabla f(x) = \\frac{df}{dx}$. However, if $f$ is a function of multiple variables, mapping $\\mathbb{R}^n \\to \\mathbb{R}$, we must take partial derivatives with respect to each variable. For example:\n", + "\n", + "$$ \\nabla f(x, y, z) = \\left[\\frac{\\partial f}{\\partial x}, \\frac{\\partial f}{\\partial y}, \\frac{\\partial f}{\\partial z}\\right] $$\n", + "\n", + "The gradient of $f$ is itself a function and can be evaluated on specific values of $x$, $y$, and $z$. In general, for a function $f$ of $n$ independent real variables, $\\nabla f$ is a length $n$ vector." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Why compute gradients?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Gradients are of interest to us because many quantum algorithms -- hybrid classical-quantum algorithms such as the quantum approximate optimization algorithm (QAOA) or the variational quantum eigensolver (VQE) especially -- can be formulated as a problem of optimizing parameters (i.e. variables) in a quantum circuit with respect to some cost function, for example an expectation value of a Hamiltonian. To efficiently perform this optimization it's common to use a gradient based optimization method, such as gradient descent (stochastic or not). An efficient means of computing gradients allows us to arrive at a good solution to the optimization problem in fewer circuit evaluations, and thus less cost." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computing gradients of parameters in a quantum circuit" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's make this a little more concrete. Suppose we have a quantum circuit which depends on a set of parameters $\\vec{p}$. We can compactly represent this circuit as $U(\\vec{p})$, where $U$ is the unitary that represents the action of all the gates in the circuit. Further suppose that after running this circuit, we will compute the expectation value of some operator $\\hat{O}$ (for example, a Hamiltonian) and use the result to determine how good our choice of parameters $\\vec{p}$ was. This situation arises often when running hybrid algorithms or quantum machine learning workflows. \n", + "\n", + "
    \n", + "Note Although, for the sake of simplicity, we will only discuss measuring expectation values to generate the function to differentiate, one can equally well compute variances or any other scalar valued function.\n", + "
    \n", + "\n", + "We can express this whole procedure as:\n", + "\n", + "$$ f(\\vec{p}) = \\left\\langle \\psi \\right| \\hat{O} \\left| \\psi \\right\\rangle = \\left\\langle 0 U^\\dagger(\\vec{p}) \\right| \\hat{O} \\left| U(\\vec{p}) 0 \\right\\rangle $$\n", + "\n", + "$f(\\vec{p})$ is a scalar valued function and we can compute its gradient -- all its partial derivatives with respect to the parameters $\\vec{p}$ -- in order to optimize those parameters. There are a variety of methods available to compute these derivatives, three of which will be discussed below. Of the three, the adjoint differentiation method is the fastest and most frugal in circuit executions and should be preferred when available, that is, when running on a state vector simulator in exact (`shots=0`) mode. We'll introduce these other two common approaches to better understand the benefit of using the adjoint differentiation method." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Finite differences" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [finite difference method](https://en.wikipedia.org/wiki/Finite_difference) is a common technique used to approximate derivatives. Suppose we have a function $f(\\vec{p})$ and we want to compute the $i$-th partial derivative of $f$, $\\frac{\\partial f}{\\partial p_i}$. We can do so by approximating:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} \\approx \\frac{f(p_1, p_2, ..., p_i + h, ..., p_n) - f(p_1, p_2, ..., p_i, ..., p_n)}{h} $$\n", + "\n", + "Where $h$ is some small real number. This formula might seem familiar from introductory calculus. The smaller $h$ is the better approximated the derivative is. By keeping all other parameters fixed, we can approximate the partial derivative with respect to $p_i$, but as we can see, computing *each* partial derivative would require *two* full circuit executions (one to compute each value of $f$). Thus, the total number of circuit executions needed to compute the gradient of $f$ for *one* set of values $\\vec{p}$ would be $2n$, if the length of $p$ is $n$.\n", + "\n", + "For a quantum circuit there can be additional problems. On a real quantum device, we can't compute the exact expectation value (or variance) of a circuit. We can only run many shots, each of which is a full circuit execution, and approximate the expectation value from the measurement statistics that result. This means that for very small $h$, it may be very difficult to approximate the gradient accurately." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Parameter shift rules" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's return to our original formula for the gradient of $f$:\n", + "\n", + "$$ \\nabla f(\\vec{p}) = \\left(\\frac{\\partial f}{\\partial p_1}, \\ldots , \\frac{\\partial f}{\\partial p_n}\\right) $$\n", + "\n", + "and examine one of the vector elements a little more closely:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = \\frac{\\partial}{\\partial p_i} \\left\\langle 0 U^\\dagger(\\vec{p}) \\right| \\hat{O} \\left| U(\\vec{p}) 0 \\right\\rangle = \\frac{\\partial}{\\partial p_i} \\left\\langle 0 \\right| U^\\dagger(\\vec{p}) \\hat{O} U(\\vec{p}) \\left| 0 \\right\\rangle $$\n", + "\n", + "We can pull the derivative operator inside the expectation value so that:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = \\left\\langle 0 \\left|\\frac{\\partial}{\\partial p_i} \\left( U^\\dagger(\\vec{p}) \\hat{O} U(\\vec{p})\\right) \\right| 0 \\right\\rangle $$\n", + "\n", + "We'll assume that each gate depends on at most one parameter, and each parameter appears in only one gate. What if we have repeated parameters? We can write down a mapping of each repeated parameter to a unique copy and sum the derivatives of those copies at the end using the [product rule](https://en.wikipedia.org/wiki/Product_rule). But for now, for simplicity we will assume that each parameter appears only once and each gate has at most one parameter. Further we'll state that gate $i$ is associated with the $i$-th parameter (every gate has a parameter). If non-parametrized gates are present, we can contract them into parametrized gates to achieve this, or assign them constant parameters (remember, the derivative of a constant is always 0).\n", + "\n", + "We can write that the overall circuit unitary $U$ is a product of individual gates:\n", + "\n", + "$$ U(\\vec{p}) = \\otimes_{i=1}^N U_{i}(p_i) $$\n", + "\n", + "if there are $N$ gates in the circuit.\n", + "\n", + "Then, using the product rule, we can write:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = \\left\\langle 0 \\left| \\otimes_{j=1}^{i-1} U^\\dagger_j \\otimes \\frac{\\partial U^\\dagger_i(p_i)}{\\partial p_i} \\otimes_{j=i+1}^{n} U^\\dagger_j \\hat{O} U(\\vec{p}) + U^\\dagger(\\vec{p}) \\hat{O}\\otimes_{j=i+1}^{n} U_j \\otimes \\frac{\\partial U_i(p_i)}{\\partial p_i}\\otimes_{j=1}^{i-1} U_j \\right| 0 \\right\\rangle $$\n", + "\n", + "We can absorb the non-differentiated products so that:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = \\left\\langle \\phi \\left| \\frac{\\partial U^\\dagger_i(p_i)}{\\partial p_i} \\hat{\\mathcal{O}}U_i(p_i) + U^\\dagger_i(p_i)\\hat{\\mathcal{O}}\\frac{\\partial U_i(p_i)}{\\partial p_i}\\right| \\phi \\right\\rangle $$\n", + "\n", + "where\n", + "\n", + "$$ \\phi = \\otimes_{j=1}^{i-1} U_j \\left| 0 \\right\\rangle $$\n", + "\n", + "and \n", + "\n", + "$$ \\hat{\\mathcal{O}} = \\otimes_{j=i+1}^{n} U^\\dagger_j \\hat{O} \\otimes_{j=i+1}^{n} U_j $$.\n", + "\n", + "Now we can see that\n", + "\n", + "$$ \\frac{\\partial U^\\dagger_i(p_i)}{\\partial p_i} \\hat{\\mathcal{O}}U_i(p_i) + U^\\dagger_i(p_i)\\hat{\\mathcal{O}}\\frac{\\partial U_i(p_i)}{\\partial p_i} = \\frac{\\partial}{\\partial p_i} \\left( U_i^\\dagger(p_i) \\hat{\\mathcal{O}} U_i(p_i)\\right) $$\n", + "\n", + "so, in sum:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = \\left\\langle \\phi \\left|\\frac{\\partial}{\\partial p_i} \\left( U_i^\\dagger(p_i) \\hat{\\mathcal{O}} U_i(p_i)\\right)\\right| \\phi \\right\\rangle $$\n", + "\n", + "and in many cases (but not all!) we can define a *shift* $s$ such that:\n", + "\n", + "$$ \\frac{\\partial}{\\partial p_i} \\left( U_i^\\dagger(p_i) \\hat{\\mathcal{O}} U_i(p_i)\\right) = U_i^\\dagger(p_i + s) \\hat{\\mathcal{O}} U_i(p_i + s) - U_i^\\dagger(p_i - s) \\hat{\\mathcal{O}} U_i(p_i - s) $$\n", + "\n", + "Thus the name \"parameter shift\". What makes this different from the finite differences method is that $s$ is not necessarily small. Detailed guides to choosing shifts and identifying which gates support the method can be found in Refs. [1](https://arxiv.org/abs/1803.00745) and [2](https://arxiv.org/abs/1811.11184). If a gate does *not* support a parameter shift rule, we can always fall back to the finite difference method.\n", + "\n", + "We can see that the parameter shift method *also* requires two circuit executions to compute the partial derivative of each parametrized gate. The advantage over finite difference is in numerical accuracy. Parameter shift can be used both when `shots=0` or when `shots>0`. Since the introduction of the method, many extensions and generalizations have been published, including Refs. [3](https://arxiv.org/abs/2107.12390), [4](https://arxiv.org/abs/2005.10299), and many more. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Adjoint differentiation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The two methods we've examined so far, finite differences and parameter shift, both require two full circuit executions per parameter to compute the gradient. This can become very expensive, in both time and charges, for deep circuits and/or circuits with many parameters. Is there a way to compute gradients in a more \"execution-frugal\" way? For `shots=0`, the answer is yes. First introduced in Ref. [5](https://arxiv.org/abs/2009.02823), the adjoint differentiation method allows us to compute all partial derivatives in \"1+1\" circuit executions. How does it work? Recall that:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = \\left\\langle 0 \\left| \\otimes_{j=1}^{i-1} U^\\dagger_j \\otimes \\frac{\\partial U^\\dagger_i(p_i)}{\\partial p_i} \\otimes_{j=i+1}^{n} U^\\dagger_j \\hat{O} U(\\vec{p}) + U^\\dagger(\\vec{p}) \\hat{O}\\otimes_{j=i+1}^{n} U_j \\otimes \\frac{\\partial U_i(p_i)}{\\partial p_i}\\otimes_{j=1}^{i-1} U_j \\right| 0 \\right\\rangle $$\n", + "\n", + "In the adjoint method, we take a different approach to computing this derivative. We realize that:\n", + "\n", + "$$ \\left( \\left \\langle 0 \\left| \\otimes_{j=1}^{i-1} U^\\dagger_j \\otimes \\frac{\\partial U^\\dagger_i(p_i)}{\\partial p_i} \\otimes_{j=i+1}^{n} U^\\dagger_j \\hat{O} U(\\vec{p}) \\right| 0 \\right\\rangle \\right)^\\dagger = \\left \\langle 0 \\left| U^\\dagger(\\vec{p}) \\hat{O}\\otimes_{j=i+1}^{n} U_j \\otimes \\frac{\\partial U_i(p_i)}{\\partial p_i}\\otimes_{j=1}^{i-1} U_j \\right| 0 \\right\\rangle$$\n", + "\n", + "and thus, because all the gates are unitaries and the operator $\\hat{O}$ is Hermitian,\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = 2\\Re \\left\\langle 0 \\left| U^\\dagger(\\vec{p}) \\hat{O}\\otimes_{j=i+1}^{n} U_j \\otimes \\frac{\\partial U_i(p_i)}{\\partial p_i}\\otimes_{j=1}^{i-1} U_j \\right| 0 \\right\\rangle $$\n", + "\n", + "where $\\Re$ denotes the real part. Now we can absorb some factors so that:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_i} = 2\\Re \\left\\langle b_i \\left| \\frac{\\partial U_i(p_i)}{\\partial p_i} \\right| k_i \\right\\rangle $$\n", + "\n", + "where\n", + "\n", + "$$ \\left\\langle b_i \\right| = \\left\\langle 0 \\right| U^\\dagger(\\vec{p}) \\hat{O}\\otimes_{j=i+1}^{n} U_j(p_j) $$\n", + "\n", + "and\n", + "\n", + "$$ \\left | k_i \\right\\rangle = \\otimes_{j=1}^{i-1} U_j(p_j) \\left| 0 \\right\\rangle $$\n", + "\n", + "The basis of the adjoint method is realizing that we can iteratively compute each partial derivative by \"back stepping\" through the circuit after having applied all its gates once. This is very similar to classical back propagation, if you're familiar with that technique from classical machine learning. We first apply all gates to compute $ \\left| k_n \\right\\rangle = \\otimes_{j=1}^{n} U_j \\left| 0 \\right\\rangle $, copy the state and apply $\\hat{O}$ to acquire:\n", + "\n", + "$$ \\left\\langle b_n \\right| = \\left\\langle 0 \\right| U^\\dagger(\\vec{p}) \\hat{O} $$\n", + "\n", + "then compute $\\frac{\\partial f}{\\partial p_n}$:\n", + "\n", + "$$ \\frac{\\partial f}{\\partial p_n} = \\left\\langle b_n \\left|\\frac{\\partial U_n(p_n)}{\\partial p_n}\\right| k_n \\right\\rangle $$\n", + "\n", + "In a moment we'll address how to find $\\frac{\\partial U_n(p_n)}{\\partial p_n}$. Once we've computed the first partial derivative, we update $\\left\\langle b_n\\right|$ and $ \\left| k_n \\right\\rangle$ to generate:\n", + "\n", + "$$ \\left\\langle b_{n-1} \\right| = \\left\\langle b_n \\right| U_n(p_n) $$\n", + "$$ \\left | k_{n-1} \\right\\rangle = U^\\dagger_{n-1} \\left| k_n \\right\\rangle $$\n", + "\n", + "By iteratively updating these two states, we can compute all partial derivatives with only one circuit execution plus one \"back step\" execution, significantly less than what is required by finite differences or parameter shift. The cost is that there is additional memory overhead, as we have to store an additional state vector and compute a third in the expectation value $\\left\\langle b_i \\left|\\frac{\\partial U_i(p_i)}{\\partial p_i}\\right| k_i \\right\\rangle$.\n", + "\n", + "How do we compute the derivative $\\frac{\\partial U_i(p_i)}{\\partial p_i}$? In many cases, if $U_i(p_i)$ is continually differentiable with respect to $p_i$, we can simply take a matrix derivative. In particular, many parametrizable gates can be written as exponentials of Paulis, so that:\n", + "\n", + "$$ \\frac{\\partial U_i(p_i)}{\\partial p_i} = \\frac{\\partial}{\\partial p_i}\\exp\\left\\{ i c p_i \\hat{P}\\right\\} = i c \\hat{P} \\exp\\left\\{ i c p_i \\hat{P}\\right\\} $$\n", + "\n", + "where $c$ is some constant, $\\hat{P}$ is some Pauli gate, and $i$ is the imaginary number $\\sqrt{-1}$. This is easily generalizable to exponents of sums of Paulis through the [chain rule](https://en.wikipedia.org/wiki/Chain_rule). In cases where $U(p_i)$ is *not* continuously differentiable, the derivative can be computed numerically, e.g. through finite differences as discussed above.\n", + "\n", + "
    \n", + "Note Because it is formulated only for exact computations, the adjoint method can only be used on simulators, such as SV1, when running with shots=0.\n", + "
    \n", + "\n", + "The adjoint differentiation method is available through the `AdjointGradient` result type on Amazon Braket, which we'll introduce in the next section. With this result type, all gradients are computed using the adjoint differentiation method." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The `AdjointGradient` Result Type" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Amazon Braket now supports a result type, `AdjointGradient`, which allows you to conveniently compute gradients of free parameters with respect to the expectation value of some observable on your circuits.\n", + "\n", + "
    \n", + "Note Currently, the AdjointGradient result type is only supported on SV1 when running in shots=0 mode. All gradients are computed using the adjoint differentiation method.\n", + "
    \n", + "\n", + "Let's see an example of this result type in action:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "! pip install seaborn\n", + "import numpy as np\n", + "from scipy.optimize import minimize\n", + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "import seaborn as sns\n", + "import time\n", + "from datetime import datetime\n", + "import pickle\n", + "import random\n", + "# magic line for producing visualizations in notebook\n", + "%matplotlib inline\n", + "\n", + "# AWS imports: Import Braket SDK modules\n", + "from braket.circuits import Circuit, Observable, FreeParameter\n", + "from braket.aws import AwsSession, AwsDevice" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "device_arn = \"arn:aws:braket:::device/quantum-simulator/amazon/sv1\"\n", + "device = AwsDevice(device_arn)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can prepare a simple parametrized circuit and compute its gradient with respect to some observable. Note that you supply the observable to the `AdjointGradient` result type. Supported observables are:\n", + " - Any of `Observable.Z()`, `Observable.X()`, `Observable.Y()`, `Observable.H()`, or `Observable.I()`\n", + " - A `TensorProduct`\n", + " - A `Hermitian`\n", + " - A `Sum`\n", + " \n", + "You can also supply the list of parameters to compute partial derivatives with respect to. If a parameter is present in the circuit, but not in the `parameters` argument to `adjoint_gradient`, its corresponding partial derivative will not be computed. If the list of `parameters` is empty, the gradient will be computed with respect to all free parameters present in the circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)])), Instruction('operator': Rx('angle': theta, 'qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': Rx('angle': theta, 'qubit_count': 1), 'target': QubitSet([Qubit(1)])), Instruction('operator': XX('angle': gamma, 'qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)]))], 'result_types': [AdjointGradient(observable=TensorProduct(Z('qubit_count': 1), Z('qubit_count': 1)), target=QubitSet([Qubit(0), Qubit(1)]), parameters=[])])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta = FreeParameter('theta')\n", + "gamma = FreeParameter('gamma')\n", + "circuit = Circuit().h(0).cnot(0, 1).rx(0, theta).rx(1, theta).xx(0, 1, gamma)\n", + "# add the adjoint gradient result type\n", + "#circuit.adjoint_gradient(observable = Observable.Z() @ Observable.Z(), target = [0, 1], parameters=['theta', gamma])\n", + "circuit.adjoint_gradient(observable = Observable.Z() @ Observable.Z(), target = [0, 1], parameters=[])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can compute the gradient of the circuit with respect to our two free parameters for a given set of parameter values, which we supply to `device.run` with the `inputs` argument:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gradient when theta = 0.1, gamma = 0.05: {'expectation': 0.9800665778412416, 'gradient': {'gamma': 6.938893903907228e-18, 'theta': -0.3973386615901225}}\n", + "Gradient when theta = 0.2, gamma = 0.1: {'expectation': 0.9210609940028854, 'gradient': {'gamma': -4.336808689942018e-19, 'theta': -0.7788366846173014}}\n" + ] + } + ], + "source": [ + "result_1 = device.run(circuit, shots=0, inputs = {'theta': 0.1, 'gamma': 0.05}).result()\n", + "result_2 = device.run(circuit, shots=0, inputs = {'theta': 0.2, 'gamma': 0.1}).result()\n", + "\n", + "print(f\"Gradient when theta = 0.1, gamma = 0.05: {result_1.values[0]}\")\n", + "print(f\"Gradient when theta = 0.2, gamma = 0.1: {result_2.values[0]}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can immediately see that although `theta` appears twice in the circuit (in two `Rx` gates), it only appears once in the result. `AdjointGradient` computes gradients **per parameter**, and **not** per-gate. We can also see that if `parameters` is empty, derivatives with respect to all free parameters will be computed. This is useful in cases when your circuit has a large number of free parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gradient when theta = 0.2, gamma = 0.1: {'expectation': 0.9210609940028854, 'gradient': {'gamma': -4.336808689942018e-19, 'theta': -0.7788366846173013}}\n" + ] + } + ], + "source": [ + "circuit = Circuit().h(0).cnot(0, 1).rx(0, theta).rx(1, theta).xx(0, 1, gamma)\n", + "# add the gradient result type\n", + "circuit.adjoint_gradient(observable = Observable.Z() @ Observable.Z(), target = [0, 1], parameters=[])\n", + "result_all = device.run(circuit, shots=0, inputs = {'theta': 0.2, 'gamma': 0.1}).result()\n", + "print(f\"Gradient when theta = 0.2, gamma = 0.1: {result_all.values[0]}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Accelerating QAOA with `AdjointGradient`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can see how using the `AdjointGradient` result type can improve performance for a hybrid algorithm such as QAOA. For an introduction to QAOA, see [its example notebook](../hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb). We'll modify the `train` function to use `AdjointGradient` and determine a Jacobian, and compare this approach with the Jacobian-free method used in the QAOA notebook. Much of the code here is further explained in that notebook, so we strongly suggest you review it before proceeding. We'll run the entire QAOA workflow in `shots=0` mode so that we can compare with `AdjointGradient`, which means we can directly compute the cost (energy). First, we set up the problem and import the circuit generator and training functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# setup Erdos Renyi graph\n", + "n = 10 # number of nodes/vertices\n", + "m = 20 # number of edges\n", + "seed = 2\n", + "\n", + "# define graph object\n", + "G = nx.gnm_random_graph(n, m, seed=seed)\n", + "# positions for all nodes\n", + "pos = nx.spring_layout(G)\n", + "\n", + "# choose random weights\n", + "for (u, v) in G.edges():\n", + " G.edges[u,v]['weight'] = random.uniform(0, 1)\n", + "\n", + "# draw graph\n", + "nx.draw(G, pos)\n", + "plt.show()\n", + "\n", + "# set Ising matrix \n", + "Jfull = nx.adjacency_matrix(G).todense()\n", + "Jfull = np.array(Jfull)\n", + "\n", + "# get off-diagonal upper triangular matrix\n", + "J = np.triu(Jfull, k=1).astype(np.float64)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "from utils_qaoa import circuit, train, train_adjoint\n", + "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n", + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we define hyperparameters. We'll use an optimization method that can benefit from information about the Jacobian, in this case `'BFGS'`, when running with the `AdjointGradient` result type. Without it, we'll use `'Powell'`, as we did in the other QAOA notebook, which uses the finite differences method to compute gradients and adjust the parameters. See the [scipy documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize) for more information about possible optimization methods." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit depth hyperparameter: 2\n", + "Problem size: 10\n" + ] + } + ], + "source": [ + "##################################################################################\n", + "# set up hyperparameters\n", + "##################################################################################\n", + "\n", + "# User-defined hypers\n", + "DEPTH = 2 # circuit depth for QAOA\n", + "OPT_METHOD = {'adjoint': 'BFGS', 'gradient-free': 'BFGS'}\n", + "\n", + "# set up the problem\n", + "n_qubits = J.shape[0]\n", + "\n", + "# initialize reference solution (simple guess)\n", + "energy_init = 0.0\n", + "\n", + "##################################################################################\n", + "# run QAOA optimization on graph \n", + "##################################################################################\n", + "\n", + "print('Circuit depth hyperparameter:', DEPTH)\n", + "print('Problem size:', n_qubits)\n", + "\n", + "# set options for classical optimization\n", + "options = {'disp': True, 'maxiter': 30}\n", + "verbose = True\n", + "\n", + "np.random.seed(2)\n", + "p = DEPTH\n", + "# randomly initialize variational parameters within appropriate bounds\n", + "gamma_initial = np.random.uniform(0, 2 * np.pi, p).tolist()\n", + "beta_initial = np.random.uniform(0, np.pi, p).tolist()\n", + "params0 = np.array(gamma_initial + beta_initial)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We're now ready to run the optimization. We'll set up separate cost trackers for each run to compare not only running time, but also billing incurred. First, using the adjoint differentiation method:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Starting the training.\n", + "====================================================================\n", + "OPTIMIZATION for circuit depth p=2\n", + "Initial energy: -0.05267587615473164\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 2\n", + "Energy expectation value (cost): -0.05267587615473156\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 3\n", + "Energy expectation value (cost): 0.3531762574841993\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 4\n", + "Energy expectation value (cost): -1.9354434136131804\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 5\n", + "Energy expectation value (cost): -0.3498090866453894\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 6\n", + "Energy expectation value (cost): -1.79710493450284\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 7\n", + "Energy expectation value (cost): -2.048613457094462\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 8\n", + "Energy expectation value (cost): -2.090456572339379\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 9\n", + "Energy expectation value (cost): -2.1335721563595507\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 10\n", + "Energy expectation value (cost): -2.1466520627954995\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 11\n", + "Energy expectation value (cost): -2.146589390426477\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 12\n", + "Energy expectation value (cost): -2.1548795821625237\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 13\n", + "Energy expectation value (cost): -2.158405687757965\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 14\n", + "Energy expectation value (cost): -2.160231466558164\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 15\n", + "Energy expectation value (cost): -2.170885714298184\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 16\n", + "Energy expectation value (cost): -2.2017257216438497\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 17\n", + "Energy expectation value (cost): -2.2204782717518112\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 18\n", + "Energy expectation value (cost): -2.231745254745078\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 19\n", + "Energy expectation value (cost): -2.272653720288545\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 20\n", + "Energy expectation value (cost): -2.338598305165878\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 21\n", + "Energy expectation value (cost): -2.406813607483334\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 22\n", + "Energy expectation value (cost): -2.4140539585680183\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 23\n", + "Energy expectation value (cost): -2.4226083364070496\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 24\n", + "Energy expectation value (cost): -2.425918124006462\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 25\n", + "Energy expectation value (cost): -2.42837089364217\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 26\n", + "Energy expectation value (cost): -2.428440753686318\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 27\n", + "Energy expectation value (cost): -2.4284433319360255\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 28\n", + "Energy expectation value (cost): -2.428443347240679\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 29\n", + "Energy expectation value (cost): -2.4284433472812954\n", + "Optimization terminated successfully.\n", + " Current function value: -2.428443\n", + " Iterations: 20\n", + " Function evaluations: 28\n", + " Gradient evaluations: 28\n", + "Final average energy (cost): -2.4284433472812954\n", + "Final angles: [2.65349514 0.60430877 1.10839027 1.38078709]\n", + "Training complete.\n", + "Code execution time using adjoint differentiation [sec]: 100.16227006912231\n", + "Optimal energy using adjoint differentiation: -2.4284433472812954\n" + ] + } + ], + "source": [ + "adjoint_costs = Tracker().start()\n", + "#set up trackers to keep track of results\n", + "adjoint_tracker = {\n", + " 'count': 1, # Elapsed optimization steps\n", + " 'optimal_energy': energy_init, # Global optimal energy\n", + " 'opt_energies': [], # Optimal energy at each step\n", + " 'global_energies': [], # Global optimal energy at each step\n", + " 'costs': [], # Cost (energy) at each step\n", + " 'res': None, # Quantum result object\n", + " 'params': [] # Track parameters\n", + "}\n", + "\n", + "# kick off training for adjoint\n", + "start = time.time()\n", + "result_energy, result_angle, adjoint_tracker = train_adjoint(\n", + " device = device, options=options, p=DEPTH, ising=J, n_qubits=n_qubits,\n", + " opt_method=OPT_METHOD['adjoint'], tracker=adjoint_tracker, params0=params0, verbose=verbose)\n", + "end = time.time()\n", + "\n", + "# print execution time\n", + "print('Code execution time using adjoint differentiation [sec]:', end - start)\n", + "\n", + "# print optimized results\n", + "print('Optimal energy using adjoint differentiation:', adjoint_tracker['optimal_energy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's also examine the costs incurred by running QAOA with the `AdjointGradient` result type and a gradient-aware optimization method:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Adjoint Gradient Aware Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 0, 'tasks': {'COMPLETED': 29}, 'execution_duration': datetime.timedelta(seconds=1, microseconds=860000), 'billed_execution_duration': datetime.timedelta(seconds=87)}}\n", + "Estimated cost to run this example: 0.109 USD\n" + ] + } + ], + "source": [ + "print(\"Adjoint Gradient Aware Task Summary\")\n", + "print(adjoint_costs.quantum_tasks_statistics())\n", + "print(f\"Estimated cost to run this example: {adjoint_costs.simulator_tasks_cost():.3f} USD\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we'll run without using the adjoint differentiation method to compute the gradient and compare the running time and costs:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Starting the training.\n", + "====================================================================\n", + "OPTIMIZATION for circuit depth p=2\n", + "Initial energy: -0.05267587615473153\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 2\n", + "Energy expectation value (cost): -0.05267587615473145\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 3\n", + "Energy expectation value (cost): -0.05267583401081515\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 4\n", + "Energy expectation value (cost): -0.052675832946504964\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 5\n", + "Energy expectation value (cost): -0.052675775205400364\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 6\n", + "Energy expectation value (cost): -0.05267578407188134\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 7\n", + "Energy expectation value (cost): 0.35317625639201633\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 8\n", + "Energy expectation value (cost): 0.35317635436937445\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 9\n", + "Energy expectation value (cost): 0.35317631990683873\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 10\n", + "Energy expectation value (cost): 0.35317628774530807\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 11\n", + "Energy expectation value (cost): 0.3531763197484072\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 12\n", + "Energy expectation value (cost): -1.9354434155579512\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 13\n", + "Energy expectation value (cost): -1.9354433768795676\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 14\n", + "Energy expectation value (cost): -1.9354433767431884\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 15\n", + "Energy expectation value (cost): -1.935443382335277\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 16\n", + "Energy expectation value (cost): -1.9354433899609917\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 17\n", + "Energy expectation value (cost): -0.34980910143980903\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 18\n", + "Energy expectation value (cost): -0.3498090652567156\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 19\n", + "Energy expectation value (cost): -0.34980906705689274\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 20\n", + "Energy expectation value (cost): -0.3498091824665031\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 21\n", + "Energy expectation value (cost): -0.34980906522353905\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 22\n", + "Energy expectation value (cost): -1.797105044442033\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 23\n", + "Energy expectation value (cost): -1.7971051019761821\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 24\n", + "Energy expectation value (cost): -1.7971051015680377\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 25\n", + "Energy expectation value (cost): -1.7971050144192944\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 26\n", + "Energy expectation value (cost): -1.797105015189591\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 27\n", + "Energy expectation value (cost): -2.0486134643105225\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 28\n", + "Energy expectation value (cost): -2.048613463165455\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 29\n", + "Energy expectation value (cost): -2.048613463165\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 30\n", + "Energy expectation value (cost): -2.048613433174286\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 31\n", + "Energy expectation value (cost): -2.048613434025501\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 32\n", + "Energy expectation value (cost): -2.0904565914685818\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 33\n", + "Energy expectation value (cost): -2.0904565917957267\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 34\n", + "Energy expectation value (cost): -2.090456594815293\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 35\n", + "Energy expectation value (cost): -2.0904566099986406\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 36\n", + "Energy expectation value (cost): -2.0904566127559843\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 37\n", + "Energy expectation value (cost): -2.133572157281146\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 38\n", + "Energy expectation value (cost): -2.1335721627107724\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 39\n", + "Energy expectation value (cost): -2.1335721621067916\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 40\n", + "Energy expectation value (cost): -2.1335721543128763\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 41\n", + "Energy expectation value (cost): -2.1335721553545866\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 42\n", + "Energy expectation value (cost): -2.1466520873072668\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 43\n", + "Energy expectation value (cost): -2.1466520963683533\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 44\n", + "Energy expectation value (cost): -2.1466520940265736\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 45\n", + "Energy expectation value (cost): -2.1466520819905996\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 46\n", + "Energy expectation value (cost): -2.146652080835302\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 47\n", + "Energy expectation value (cost): -2.146589380341281\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 48\n", + "Energy expectation value (cost): -2.146589379851874\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 49\n", + "Energy expectation value (cost): -2.1465893856205946\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 50\n", + "Energy expectation value (cost): -2.1465893820672637\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 51\n", + "Energy expectation value (cost): -2.146589378670433\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 52\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Energy expectation value (cost): -2.1548796100967627\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 53\n", + "Energy expectation value (cost): -2.1548796153793828\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 54\n", + "Energy expectation value (cost): -2.1548796166539845\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 55\n", + "Energy expectation value (cost): -2.1548796073363605\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 56\n", + "Energy expectation value (cost): -2.1548796054619683\n", + "====================================================================\n", + "Calling the quantum circuit. 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Cycle: 62\n", + "Energy expectation value (cost): -2.160231194220481\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 63\n", + "Energy expectation value (cost): -2.1602312040395066\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 64\n", + "Energy expectation value (cost): -2.160231202042433\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 65\n", + "Energy expectation value (cost): -2.1602311924177826\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 66\n", + "Energy expectation value (cost): -2.1602311872981423\n", + "====================================================================\n", + "Calling the quantum circuit. 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Cycle: 132\n", + "Energy expectation value (cost): -2.4284433472406057\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 133\n", + "Energy expectation value (cost): -2.428443347241153\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 134\n", + "Energy expectation value (cost): -2.428443347240252\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 135\n", + "Energy expectation value (cost): -2.4284433472406293\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 136\n", + "Energy expectation value (cost): -2.4284433472403757\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 137\n", + "Energy expectation value (cost): -2.428443347281297\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 138\n", + "Energy expectation value (cost): -2.428443347281339\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 139\n", + "Energy expectation value (cost): -2.428443347281304\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 140\n", + "Energy expectation value (cost): -2.4284433472813154\n", + "====================================================================\n", + "Calling the quantum circuit. Cycle: 141\n", + "Energy expectation value (cost): -2.4284433472812643\n", + "Optimization terminated successfully.\n", + " Current function value: -2.428443\n", + " Iterations: 20\n", + " Function evaluations: 140\n", + " Gradient evaluations: 28\n", + "Final average energy (cost): -2.428443347281297\n", + "Final angles: [2.65349514 0.60430877 1.10839025 1.38078708]\n", + "Training complete.\n", + "Code execution time without adjoint differentiation [sec]: 491.3400547504425\n", + "Optimal energy: -2.428443347281339\n" + ] + } + ], + "source": [ + "no_adjoint_costs = Tracker().start()\n", + "energy_init = 0.0\n", + "tracker = {\n", + " 'count': 1, # Elapsed optimization steps\n", + " 'optimal_energy': energy_init, # Global optimal energy\n", + " 'opt_energies': [], # Optimal energy at each step\n", + " 'global_energies': [], # Global optimal energy at each step\n", + " 'costs': [], # Cost (energy) at each step\n", + " 'res': None, # Quantum result object\n", + " 'params': [] # Track parameters\n", + "}\n", + "\n", + "# kick off training for gradient-free\n", + "start = time.time()\n", + "result_energy, result_angle, tracker = train(\n", + " device = device, options=options, p=DEPTH, ising=J, n_qubits=n_qubits, \n", + " opt_method=OPT_METHOD['gradient-free'], tracker=tracker, params0=params0, verbose=verbose)\n", + "end = time.time()\n", + "\n", + "# print execution time\n", + "print('Code execution time without adjoint differentiation [sec]:', end - start)\n", + "\n", + "# print optimized results\n", + "print('Optimal energy:', tracker['optimal_energy'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can examine the costs incurred by running QAOA without the `AdjointGradient` result type, using a finite-differences based optimization method:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gradient-Unaware Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 0, 'tasks': {'COMPLETED': 141}, 'execution_duration': datetime.timedelta(seconds=6, microseconds=22000), 'billed_execution_duration': datetime.timedelta(seconds=423)}}\n", + "Estimated cost to run this example: 0.529 USD\n" + ] + } + ], + "source": [ + "print(\"Gradient-Unaware Task Summary\")\n", + "print(no_adjoint_costs.quantum_tasks_statistics())\n", + "print(f\"Estimated cost to run this example: {no_adjoint_costs.simulator_tasks_cost():.3f} USD\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[1] Mitarai K., Negoro M., et al., \"Quantum Circuit Learning\", Physical Review A 98: 032309 (2018)\n", + "\n", + "[2] Schuld M., Bergholm V., et al., \"Evaluating analytic gradients on quantum hardware\", Physical Review A 99: 032331 (2019)\n", + "\n", + "[3] Weirechs D., Izaac J, et al., \"General parameter-shift rules for quantum gradients\", Quantum 6: 677 (2022)\n", + "\n", + "[4] Banchi L., Crooks G., \"Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule\", Quantum 5: 386 (2021)\n", + "\n", + "[5] Jones T., Gacon J., \"Efficient calculation of gradients in classical simulations of variational quantum algorithms\", arXiv:2009.02823" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 0, 'tasks': {'COMPLETED': 173}, 'execution_duration': datetime.timedelta(seconds=7, microseconds=958000), 'billed_execution_duration': datetime.timedelta(seconds=519)}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 0.649 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.15" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/B_qtm_sims/Using_the_tensor_network_simulator_TN1.ipynb b/modules/1_Continue_Exploring/B_qtm_sims/Using_the_tensor_network_simulator_TN1.ipynb new file mode 100644 index 000000000..b93b14dbb --- /dev/null +++ b/modules/1_Continue_Exploring/B_qtm_sims/Using_the_tensor_network_simulator_TN1.ipynb @@ -0,0 +1,923 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Using the Amazon Braket tensor network simulator TN1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", + "from braket.tracking import Tracker\n", + "t = Tracker().start()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This tutorial serves as an in-depth introduction to TN1, the Amazon Braket tensor network simulator. TN1 was previously introduced in [Running quantum circuits on simulators notebook](../getting_started/1_Running_quantum_circuits_on_simulators/1_Running_quantum_circuits_on_simulators.ipynb). This tutorial explains what makes TN1 different from SV1, Braket's state vector simulator, and it discusses which use cases are well suited for tensor network simulations. We examine what circuit properties affect TN1's performance and how TN1 can be used to simulate some types circuits for many more qubits than SV1 can handle." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## How TN1 Works\n", + "\n", + "A tensor network simulator models the execution of circuits on a quantum computer by representing each gate in the circuit as a *tensor*. Tensors generalize the concept of vectors and matrices to higher dimensions. The gates in the network form a graph. The simulator works by finding an efficient way to multiply all the different tensors on the graph during the _rehearsal_ stage and then, after a suitable multiplication sequence or _path_ is found, it performs these multiplications in the _contraction_ stage. For more information about TN1 and how it works, see the [TN1 docs](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#braket-simulator-tn1).\n", + "\n", + "## How is this different from SV1, the state vector simulator?\n", + "\n", + "SV1 works differently -- SV1 simulates all the evolution of all amplitudes as gates are applied. This means that SV1 cannot simulate large numbers of qubits for any circuit, because the memory required becomes infeasible. However, this restriction does not necessarily apply to TN1. Because TN1 works by contracting gates, it is able to work only with worldlines through the circuit which are relevant to the final outcome. However, TN1 can be slower than SV1 for circuits with complex geometry. In circuits which include multi-qubit gates, gates with long range, or circuits with few qubits (fewer than 28), SV1 is often the better choice. To use TN1 effectively it is important to understand that circuit geometry can pose more of a barrier than simple qubit number, as we will see below." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Can my circuit be simulated on TN1?\n", + "\n", + "While SV1 will simulate every circuit within the service limits (i.e., smaller or equal than 34 qubits), TN1 can only decide if a circuit can be contracted after it has the full information from the rehearsal stage. In the best case, this enables you to simulate circuits of much larger size than SV1 (up to 50 qubits) but, on the flip side, that means that in some cases you might find that TN1 will terminate the simulation after the rehearsal if it finds that the projected contraction time exceeds its runtime limit. In this case the `failureReason` for the task will be `Predicted runtime based on best contraction path found exceeds TN1 limit.` The rehearsal stage of TN1 is limited to 10 minutes, but in most cases you will find that TN1 will arrive at a decision much faster. \n", + " \n", + "As we will see below, if this situation occurs for a task for which you have requested a large number of shots, the task may be successful if you lower the shot count. It can also occur, albeit rarely, that the time to find a single contraction path candidate exceeds TN1's internal rehearsal runtime limit -- circuits for which this occurs are extremely unlikely to be contractable in reasonable time. In this case, the `failureReason` for the task will be `No viable contraction path found.`\n", + " \n", + "To learn more about why these two stages are present and what the simulator does in each, you can read the TN1 documentation [here](https://docs.aws.amazon.com/braket/latest/developerguide/braket-devices.html#braket-simulator-tn1)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + "Note: In the worst case, the TN1 runtime can scale linearly with the number of shots requested. It is strongly recommended to test your circuit or circuit class with a small number of shots first.\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "# general imports\n", + "import numpy as np\n", + "import math\n", + "\n", + "import boto3\n", + "# AWS imports: Import Braket SDK modules\n", + "from braket.circuits import Circuit, circuit, Gate, Instruction\n", + "from braket.aws import AwsDevice\n", + "\n", + "tn_device = AwsDevice('arn:aws:braket:::device/quantum-simulator/amazon/tn1')\n", + "sv_device = AwsDevice('arn:aws:braket:::device/quantum-simulator/amazon/sv1')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Two simple examples: The GHZ state and Quantum Fourier Transform\n", + "\n", + "We already presented the GHZ example circuit in the [Running quantum circuits on simulators notebook](../getting_started/1_Running_quantum_circuits_on_simulators/1_Running_quantum_circuits_on_simulators.ipynb). Here, we'll compare the performance of SV1 and TN1 for this relatively simple circuit. The GHZ state is simple to prepare:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def ghz_circuit(n_qubits: int) -> Circuit:\n", + " \"\"\"\n", + " Function to return simple GHZ circuit ansatz. Assumes all qubits in range(0, n_qubits-1)\n", + " are entangled.\n", + "\n", + " :param int n_qubits: number of qubits\n", + " :return: Constructed GHZ circuit\n", + " :rtype: Circuit\n", + " \"\"\"\n", + "\n", + " circuit = Circuit() # instantiate circuit object\n", + " circuit.h(0) # add Hadamard gate on first qubit\n", + "\n", + " for ii in range(0, n_qubits-1):\n", + " circuit.cnot(control=ii, target=ii+1) # apply series of CNOT gates\n", + " return circuit" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will simulate the measurement counts for this circuit on SV1 and TN1. SV1 can only simulate up to 34 qubits, but TN1 can work with substantially more in this case because of the circuit's geometry. In this case we will not run up to 34 qubits on SV1, because the runtime on that simulator can become quite long. 30 qubits is enough to see that TN1 can equal or outperform SV1 for circuits like GHZ, which has a simple, compact nearest-neighbor circuit geometry. Because the GHZ state is a \"cat state\", with only two possible measurement outcomes (all up or all down), it is easy for TN1 to explore all possible output bitstrings." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GHZ circuit:\n", + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|\n", + " \n", + "q0 : -H-C-----------------------------------------------\n", + " | \n", + "q1 : ---X-C---------------------------------------------\n", + " | \n", + "q2 : -----X-C-------------------------------------------\n", + " | \n", + "q3 : -------X-C-----------------------------------------\n", + " | \n", + "q4 : ---------X-C---------------------------------------\n", + " | \n", + "q5 : -----------X-C-------------------------------------\n", + " | \n", + "q6 : -------------X-C-----------------------------------\n", + " | \n", + "q7 : ---------------X-C---------------------------------\n", + " | \n", + "q8 : -----------------X-C-------------------------------\n", + " | \n", + "q9 : -------------------X-C-----------------------------\n", + " | \n", + "q10 : ---------------------X--C--------------------------\n", + " | \n", + "q11 : ------------------------X--C-----------------------\n", + " | \n", + "q12 : ---------------------------X--C--------------------\n", + " | \n", + "q13 : ------------------------------X--C-----------------\n", + " | \n", + "q14 : ---------------------------------X--C--------------\n", + " | \n", + "q15 : ------------------------------------X--C-----------\n", + " | \n", + "q16 : ---------------------------------------X--C--------\n", + " | \n", + "q17 : ------------------------------------------X--C-----\n", + " | \n", + "q18 : ---------------------------------------------X--C--\n", + " | \n", + "q19 : ------------------------------------------------X--\n", + "\n", + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|\n", + "20-qubit TN1 task COMPLETED.\n", + "Tensor network simulator:\n", + "This task ran 100 shots and the total runtime was 2364 ms\n", + "Measurement results: Counter({'11111111111111111111': 54, '00000000000000000000': 46})\n", + "\n", + "20-qubit SV1 task COMPLETED.\n", + "State vector simulator:\n", + "This task ran 100 shots and the total runtime was 177 ms\n", + "Measurement results: Counter({'00000000000000000000': 55, '11111111111111111111': 45})\n", + "\n", + "GHZ circuit:\n", + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|\n", + " \n", + "q0 : -H-C--------------------------------------------------------------\n", + " | \n", + "q1 : ---X-C------------------------------------------------------------\n", + " | \n", + "q2 : -----X-C----------------------------------------------------------\n", + " | \n", + "q3 : -------X-C--------------------------------------------------------\n", + " | \n", + "q4 : ---------X-C------------------------------------------------------\n", + " | \n", + "q5 : -----------X-C----------------------------------------------------\n", + " | \n", + "q6 : -------------X-C--------------------------------------------------\n", + " | \n", + "q7 : ---------------X-C------------------------------------------------\n", + " | \n", + "q8 : -----------------X-C----------------------------------------------\n", + " | \n", + "q9 : -------------------X-C--------------------------------------------\n", + " | \n", + "q10 : ---------------------X--C-----------------------------------------\n", + " | \n", + "q11 : ------------------------X--C--------------------------------------\n", + " | \n", + "q12 : ---------------------------X--C-----------------------------------\n", + " | \n", + "q13 : ------------------------------X--C--------------------------------\n", + " | \n", + "q14 : ---------------------------------X--C-----------------------------\n", + " | \n", + "q15 : ------------------------------------X--C--------------------------\n", + " | \n", + "q16 : ---------------------------------------X--C-----------------------\n", + " | \n", + "q17 : ------------------------------------------X--C--------------------\n", + " | \n", + "q18 : ---------------------------------------------X--C-----------------\n", + " | \n", + "q19 : ------------------------------------------------X--C--------------\n", + " | \n", + "q20 : ---------------------------------------------------X--C-----------\n", + " | \n", + "q21 : ------------------------------------------------------X--C--------\n", + " | \n", + "q22 : ---------------------------------------------------------X--C-----\n", + " | \n", + "q23 : ------------------------------------------------------------X--C--\n", + " | \n", + "q24 : ---------------------------------------------------------------X--\n", + "\n", + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|\n", + "25-qubit TN1 task COMPLETED.\n", + "Tensor network simulator:\n", + "This task ran 100 shots and the total runtime was 2441 ms\n", + "Measurement results: Counter({'1111111111111111111111111': 56, '0000000000000000000000000': 44})\n", + "\n", + "25-qubit SV1 task COMPLETED.\n", + "State vector simulator:\n", + "This task ran 100 shots and the total runtime was 604 ms\n", + "Measurement results: Counter({'0000000000000000000000000': 53, '1111111111111111111111111': 47})\n", + "\n", + "GHZ circuit:\n", + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|\n", + " \n", + "q0 : -H-C-----------------------------------------------------------------------------\n", + " | \n", + "q1 : ---X-C---------------------------------------------------------------------------\n", + " | \n", + "q2 : -----X-C-------------------------------------------------------------------------\n", + " | \n", + "q3 : -------X-C-----------------------------------------------------------------------\n", + " | \n", + "q4 : ---------X-C---------------------------------------------------------------------\n", + " | \n", + "q5 : -----------X-C-------------------------------------------------------------------\n", + " | \n", + "q6 : -------------X-C-----------------------------------------------------------------\n", + " | \n", + "q7 : ---------------X-C---------------------------------------------------------------\n", + " | \n", + "q8 : -----------------X-C-------------------------------------------------------------\n", + " | \n", + "q9 : -------------------X-C-----------------------------------------------------------\n", + " | \n", + "q10 : ---------------------X--C--------------------------------------------------------\n", + " | \n", + "q11 : ------------------------X--C-----------------------------------------------------\n", + " | \n", + "q12 : ---------------------------X--C--------------------------------------------------\n", + " | \n", + "q13 : ------------------------------X--C-----------------------------------------------\n", + " | \n", + "q14 : ---------------------------------X--C--------------------------------------------\n", + " | \n", + "q15 : ------------------------------------X--C-----------------------------------------\n", + " | \n", + "q16 : ---------------------------------------X--C--------------------------------------\n", + " | \n", + "q17 : ------------------------------------------X--C-----------------------------------\n", + " | \n", + "q18 : ---------------------------------------------X--C--------------------------------\n", + " | \n", + "q19 : ------------------------------------------------X--C-----------------------------\n", + " | \n", + "q20 : ---------------------------------------------------X--C--------------------------\n", + " | \n", + "q21 : ------------------------------------------------------X--C-----------------------\n", + " | \n", + "q22 : ---------------------------------------------------------X--C--------------------\n", + " | \n", + "q23 : ------------------------------------------------------------X--C-----------------\n", + " | \n", + "q24 : ---------------------------------------------------------------X--C--------------\n", + " | \n", + "q25 : ------------------------------------------------------------------X--C-----------\n", + " | \n", + "q26 : ---------------------------------------------------------------------X--C--------\n", + " | \n", + "q27 : ------------------------------------------------------------------------X--C-----\n", + " | \n", + "q28 : ---------------------------------------------------------------------------X--C--\n", + " | \n", + "q29 : ------------------------------------------------------------------------------X--\n", + "\n", + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|\n", + "30-qubit TN1 task COMPLETED.\n", + "Tensor network simulator:\n", + "This task ran 100 shots and the total runtime was 2649 ms\n", + "Measurement results: Counter({'111111111111111111111111111111': 54, '000000000000000000000000000000': 46})\n", + "\n", + "30-qubit SV1 task COMPLETED.\n", + "State vector simulator:\n", + "This task ran 100 shots and the total runtime was 17147 ms\n", + "Measurement results: Counter({'111111111111111111111111111111': 54, '000000000000000000000000000000': 46})\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "35-qubit TN1 task COMPLETED.\n", + "Tensor network simulator:\n", + "This task ran 100 shots and the total runtime was 2660 ms\n", + "Measurement results: Counter({'11111111111111111111111111111111111': 54, '00000000000000000000000000000000000': 46})\n", + "\n", + "40-qubit TN1 task COMPLETED.\n", + "Tensor network simulator:\n", + "This task ran 100 shots and the total runtime was 2899 ms\n", + "Measurement results: Counter({'0000000000000000000000000000000000000000': 53, '1111111111111111111111111111111111111111': 47})\n", + "\n", + "45-qubit TN1 task COMPLETED.\n", + "Tensor network simulator:\n", + "This task ran 100 shots and the total runtime was 2958 ms\n", + "Measurement results: Counter({'000000000000000000000000000000000000000000000': 51, '111111111111111111111111111111111111111111111': 49})\n", + "\n", + "50-qubit TN1 task COMPLETED.\n", + "Tensor network simulator:\n", + "This task ran 100 shots and the total runtime was 3198 ms\n", + "Measurement results: Counter({'11111111111111111111111111111111111111111111111111': 51, '00000000000000000000000000000000000000000000000000': 49})\n", + "\n" + ] + } + ], + "source": [ + "qubit_range = range(20, 31, 5)\n", + "tn_qubit_range = range(35, 51, 5)\n", + "n_shots = 100\n", + "ghz_circs = {}\n", + "sv_tasks = {}\n", + "tn_tasks = {}\n", + "sv_results = {}\n", + "tn_results = {}\n", + "for num_qubits in qubit_range:\n", + " ghz = ghz_circuit(num_qubits)\n", + " sv_tasks[num_qubits] = sv_device.run(ghz, shots=n_shots)\n", + " tn_tasks[num_qubits] = tn_device.run(ghz, shots=n_shots)\n", + " ghz_circs[num_qubits] = ghz\n", + "\n", + "# Run qubit numbers which only TN1 supports\n", + "for num_qubits in tn_qubit_range:\n", + " ghz = ghz_circuit(num_qubits)\n", + " tn_tasks[num_qubits] = tn_device.run(ghz, shots=n_shots)\n", + " ghz_circs[num_qubits] = ghz\n", + "\n", + "for num_qubits in qubit_range:\n", + " tn_status = tn_tasks[num_qubits].state()\n", + " sv_status = sv_tasks[num_qubits].state()\n", + " while tn_status != 'COMPLETED':\n", + " tn_status = tn_tasks[num_qubits].state()\n", + " while sv_status != 'COMPLETED':\n", + " sv_status = sv_tasks[num_qubits].state()\n", + "\n", + " tn_results[num_qubits] = tn_tasks[num_qubits].result()\n", + " sv_results[num_qubits] = sv_tasks[num_qubits].result()\n", + "\n", + " # get the running time of the tasks\n", + " sv_runtime = sv_results[num_qubits].additional_metadata.simulatorMetadata.executionDuration\n", + " tn_runtime = tn_results[num_qubits].additional_metadata.simulatorMetadata.executionDuration\n", + "\n", + " # get the 'shots' parameter from metadata\n", + " tn_num_shots = tn_results[num_qubits].task_metadata.shots\n", + " sv_num_shots = sv_results[num_qubits].task_metadata.shots\n", + "\n", + " # get the measurement counts\n", + " tn_counts = tn_results[num_qubits].measurement_counts\n", + " sv_counts = sv_results[num_qubits].measurement_counts\n", + " \n", + " print(\"GHZ circuit:\")\n", + " print(ghz_circs[num_qubits])\n", + " print('{}-qubit TN1 task {}.'.format(num_qubits,tn_status))\n", + " print('Tensor network simulator:')\n", + " print('This task ran {} shots and the total runtime was {} ms'.format(tn_num_shots,tn_runtime))\n", + " print(\"Measurement results: {}\\n\".format(tn_counts))\n", + " print('{}-qubit SV1 task {}.'.format(num_qubits,sv_status))\n", + " print('State vector simulator:')\n", + " print('This task ran {} shots and the total runtime was {} ms'.format(sv_num_shots,sv_runtime))\n", + " print(\"Measurement results: {}\\n\".format(sv_counts))\n", + "\n", + "for num_qubits in tn_qubit_range:\n", + " tn_status = tn_tasks[num_qubits].state()\n", + " while tn_status != 'COMPLETED':\n", + " tn_status = tn_tasks[num_qubits].state()\n", + "\n", + " tn_results[num_qubits] = tn_tasks[num_qubits].result()\n", + "\n", + " # get the running time of the tasks\n", + " tn_runtime = tn_results[num_qubits].additional_metadata.simulatorMetadata.executionDuration\n", + "\n", + " # get the 'shots' parameter from metadata\n", + " tn_num_shots = tn_results[num_qubits].task_metadata.shots\n", + "\n", + " # get the measurement counts\n", + " tn_counts = tn_results[num_qubits].measurement_counts\n", + " \n", + " # we will not print the circuits here as they are quite large\n", + " print('{}-qubit TN1 task {}.'.format(num_qubits,tn_status))\n", + " print('Tensor network simulator:')\n", + " print('This task ran {} shots and the total runtime was {} ms'.format(tn_num_shots,tn_runtime))\n", + " print(\"Measurement results: {}\\n\".format(tn_counts))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are many circuits which can be efficiently simulated by TN1 even up to very large qubit counts. Another example is the quantum Fourier transform (QFT) and its inverse, shown in [the QFT notebook](../advanced_circuits_algorithms/Quantum_Fourier_Transform/Quantum_Fourier_Transform.ipynb). TN1 is able to efficiently simulate the QFT on an input state of |00..00> because in this case it amounts to a simple rotation, even up to many qubits:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "@circuit.subroutine(register=True)\n", + "def qft(qubits): \n", + " \"\"\"\n", + " Construct a circuit object corresponding to the Quantum Fourier Transform (QFT)\n", + " algorithm, applied to the argument qubits. Does not use recursion to generate the QFT.\n", + " \n", + " Args:\n", + " qubits (int): The list of qubits on which to apply the QFT\n", + " \"\"\"\n", + " qftcirc = Circuit()\n", + "\n", + " # get number of qubits\n", + " num_qubits = len(qubits)\n", + " \n", + " for k in range(num_qubits):\n", + " # First add a Hadamard gate\n", + " qftcirc.h(qubits[k])\n", + " \n", + " # Then apply the controlled rotations, with weights (angles) defined by the distance to the control qubit.\n", + " # Start on the qubit after qubit k, and iterate until the end. When num_qubits==1, this loop does not run.\n", + " for j in range(1,num_qubits - k):\n", + " angle = 2*math.pi/(2**(j+1))\n", + " qftcirc.cphaseshift(qubits[k+j],qubits[k], angle)\n", + " \n", + " # Then add SWAP gates to reverse the order of the qubits:\n", + " for i in range(math.floor(num_qubits/2)):\n", + " qftcirc.swap(qubits[i], qubits[-i-1])\n", + " \n", + " return qftcirc" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "20-qubit task COMPLETED.\n", + "QFT:\n", + "This task ran 100 shots and the total runtime was 7408 ms\n", + "Measurement results: Counter({'00011011011110110110': 1, '11110101000111110010': 1, '00110011000001111111': 1, '10101011000111000110': 1, '10010000010001000011': 1, '00110110001011010101': 1, '01010111111111100100': 1, '11100111011110100011': 1, '00011011011010001011': 1, '01010000101011110000': 1, '10100011111111101011': 1, '10101001110110100000': 1, '01010011101100011110': 1, '10011001011101111000': 1, '01001111100011000011': 1, '00001011000000110000': 1, '11101111110010000001': 1, '01111111010111000101': 1, '01000111101111010011': 1, '10000101110111000011': 1, '01000110010111101101': 1, '11110010101000101010': 1, '01111110000000111101': 1, '00100110111000010100': 1, '00100100010101010101': 1, '01101010010010110011': 1, '11010101100111110001': 1, '10101010001100110001': 1, '11100010110101110101': 1, '10110110100010100001': 1, '01110110010001011110': 1, '01001110001101101000': 1, '00011100111010111111': 1, '10100011000001001100': 1, '00010110110011111000': 1, '01111101000000010110': 1, '01000010101110111101': 1, '10101101110011101001': 1, '01101000010001011010': 1, '01101010001001111000': 1, '01101010111010010001': 1, '01011111001001011011': 1, '10000010111001110110': 1, '01110001110100111110': 1, '11100010010001111010': 1, '11100111011000000001': 1, '10111010001110111100': 1, '11010001110111101001': 1, '10011010100010011101': 1, '11110000100001000011': 1, '11110001011100001101': 1, '00111100001010110010': 1, '10000100000100101000': 1, '11111001111001111010': 1, '01100000010010101100': 1, '01011110110011011001': 1, '00100111010110101101': 1, '10010001110001010111': 1, '11001010111110001101': 1, '10110111001110111011': 1, '11000111000111011111': 1, '11110011010110001011': 1, '10100101010000110010': 1, '01000110000111000010': 1, '11101100010001010010': 1, '01110100111111000000': 1, '01000010001101100101': 1, '10001000011000110111': 1, '11000100010111011100': 1, '00111000000110101111': 1, '01011101111011001010': 1, '10001001100010110010': 1, '00101010101011010111': 1, '00101111111001011010': 1, '10001010000100110010': 1, '10101100100111011100': 1, '00111011011000110110': 1, '11000010110011001001': 1, '01101110010010111011': 1, '11001001000111000000': 1, '01111010100001111000': 1, '11010100011100000101': 1, '11001110011001101100': 1, '11010110011001100111': 1, '11010100100000010000': 1, '11110010100110100100': 1, '11000000001000111001': 1, '11011111010001110010': 1, '00000110010101111001': 1, '01010111101100010001': 1, '11101011110100101000': 1, '10011111100001110001': 1, '11011111110011011010': 1, '01101100101000100100': 1, '11001111001110001100': 1, '10101000011110010100': 1, '10011110011011011011': 1, '11101001111001011001': 1, '01010011011100100111': 1, '00110110111001101001': 1})\n", + "\n", + "30-qubit task COMPLETED.\n", + "QFT:\n", + "This task ran 100 shots and the total runtime was 16040 ms\n", + "Measurement results: Counter({'110101100001110001110111101110': 1, '100000001001111111111100100110': 1, '111011001011001000110111110110': 1, '000010110010010100011101011101': 1, '010101100001001011011010010100': 1, '001000000011010100010111111000': 1, '101110110111000111010001100010': 1, '101001111010110011100100111010': 1, '111010100001110100100011100010': 1, '110110000010111010010000000101': 1, '101110111111001111101101100100': 1, '110010101010101000001100111111': 1, '111001101100110111111111100111': 1, '001000010111001101111100101000': 1, '000001110101111111001110011111': 1, '001111101101001000000010011010': 1, '111101000100111110100111010101': 1, '110011101010111001011100111110': 1, '001011111010000110111000001110': 1, '000111000010000010010010001111': 1, '110110101111010001011110110011': 1, '110110101101100010001111010101': 1, '111000101110001111010000110000': 1, '110110111111101011010001100011': 1, '100011010011100011001111001111': 1, '110001000011100011111110001010': 1, '000111000110101000111100101011': 1, '001101110010110111101010000100': 1, '011010101000001110001001000101': 1, '001000101000110000110110000110': 1, '111001111001100010101111110001': 1, '010110001111111110101000101001': 1, '001001110111100100001101000101': 1, '101000010111010100001010001001': 1, '110010101101010000001101100111': 1, '011101000011010000100001001110': 1, '111110011110100101101100000100': 1, '110111001101010111100010111101': 1, '010011111011000110000100010011': 1, '100000000111001000110001101001': 1, '000001101000110011111000000010': 1, '010111111101100101101001010110': 1, '100100011110011011011111110000': 1, '111011101000111110000101001101': 1, '101000011110000000111111111110': 1, '111010011001010001010111101001': 1, '100011000111111111110011111001': 1, '010101101011101001010111110110': 1, '001111111000001011010100101011': 1, '011000110101000010010010011011': 1, '011010011100111001011111011100': 1, '101000101000001110011111000010': 1, '011111111100111100010111101001': 1, '101010100100000001001011111000': 1, '000111101010110010101000100010': 1, '001000101110000011011111011010': 1, '000110101011101100111010110101': 1, '011001001010010101101111100001': 1, '000000010110110100000111100101': 1, '010100100001101010110001111011': 1, '010110101110010010111111101011': 1, '110111000001101001001110000110': 1, '100010100111000010000000010010': 1, '110100011111101111111010111101': 1, '100000010111000100010101111110': 1, '110010010000010111110010110001': 1, '001101000101000100001010110010': 1, '010001010011100011010011110011': 1, '011010110001000110011110100101': 1, '010100010111110011101111001111': 1, '011111100100001001000010011101': 1, '110110001110001100011000001011': 1, '101010010111001000100110100100': 1, '101010011110100100000000111000': 1, '100010101110110111010111010010': 1, '101000011011101101100001001101': 1, '101101000100010000111111111111': 1, '010100110001100101000101000011': 1, '001000101001001110110110011100': 1, '011000010010011010111000111010': 1, '101110011001011010011100000011': 1, '100101010000111101110101110010': 1, '001011101010110001000010110010': 1, '110100100011001010100111110000': 1, '100111011001010111000110001111': 1, '010001110011010111010011110010': 1, '100101000000110110110010000011': 1, '010110000100111101101111001111': 1, '011101001100001001001001110111': 1, '000011000100100110000011000010': 1, '110110000101000101000001010100': 1, '011110011100110011101110110011': 1, '011100110100100110101100010010': 1, '111101100011001111111010100000': 1, '011111011111011000111111111010': 1, '000110000000110101001011011011': 1, '101110110110110010101000011011': 1, '000100010001101011001001111011': 1, '000010101011100111100110001111': 1, '011010110111010111000101110101': 1})\n", + "\n", + "40-qubit task COMPLETED.\n", + "QFT:\n", + "This task ran 100 shots and the total runtime was 29304 ms\n", + "Measurement results: Counter({'0111101100100010100100000111011001110100': 1, '1110111000001001011001101100110010000001': 1, '1010000111110100011100010011100110011101': 1, '0101111100111000100110010111000101010000': 1, '1000001001101000010100101000111010001111': 1, '1110100101100010101101000100100000011010': 1, '1100001000100100011001010001001110100100': 1, '1000100101010110101101001010100010010000': 1, '1011010111101011111111010111011011100100': 1, '0110011100010101011011111110010010010001': 1, '1101100011011101001100111001011010110010': 1, '1001000110101001110010111001101101110110': 1, '0010110001111001110100011100111110010101': 1, '1111000010101010100111001011100011110110': 1, '1001011111001100010010111101000101011010': 1, '1011000001011001011100111101110111000000': 1, '0000110001010011011001101111110000010100': 1, '1000110111101010000000101111001100111000': 1, '1111110100111011001010010101011101101000': 1, '0000101100110001101110111011000111000010': 1, '1111010100010110101101001111101111111111': 1, '1100100010000111101111011001100110011010': 1, '1111011001111010010111001110111011001110': 1, '0111010111100101000111111111100000111010': 1, '0110110110011100011111010100011010100000': 1, '0011111001110110111001100011000011001100': 1, '1100110001111011000100000010000011011010': 1, '1110100001010011000001000000110100011011': 1, '0100100001010001000101111110101110111100': 1, '0001001001011101110010011000100010001110': 1, '0111011010100010011010101000000100111101': 1, '1101001100110000010000001011101100101010': 1, '1000001000101001101001000101011100000100': 1, '0010100011010001111010011101100011100000': 1, '0010110100101110111000000011111100110110': 1, '0000101111110101111110101010110101101000': 1, '1111111010000100001010100000101011111011': 1, '0110110101000111010111010011110011101100': 1, '0101001100011100110011110100001010001010': 1, '1011001001011110101101010101100010011010': 1, '0000111101110111101011111111111011001011': 1, '0101000101011110010101111000110011000000': 1, '1100011010101110000101100111111000011110': 1, '1001010101100000011011101100010111000111': 1, '1001001100011111010010101000010000110110': 1, '1011110100001010111010011111011001110111': 1, '0011111111101011000100001111111111011111': 1, '1101110100000100010100001110001110100101': 1, '1110110011011100000010100011110010111101': 1, '0111111011111000010111010000101001110010': 1, '0010100110100001100001100111101100011001': 1, '1100100101000011001010010101100100100100': 1, '0110111100110101101010000000000011011001': 1, '0111101001111011110100100101010001010000': 1, '1001111010001010000010110100111111111000': 1, '1000010100010101000000000110000010000110': 1, '0011011101100111101001110001100100101110': 1, '1110010111000101011100011000110100000111': 1, '1100001000110010010110100101101110000001': 1, '1010010100111000000000010101000101011011': 1, '0110111011000111001011000110010110001001': 1, '1101100111011111100001011000001001100100': 1, '0111001110101011001010000010000111001100': 1, '0000001000011001011110011110110110010101': 1, '0101110011101110000101010100000111100000': 1, '1010111001000010010011000000001010010111': 1, '0001010001101000000111101010011100110110': 1, '0001001000011011011100000011011100111000': 1, '1100101001000011111110101100010101001110': 1, '1100000001000110100110101011111111101110': 1, '1000010100110100100110110001011110100001': 1, '0100111000000000100110001101110111111001': 1, '0000011111000010000111010111000010100000': 1, '0010000100100100010000000000111001100111': 1, '1101101101100101000111111000110100100100': 1, '1001111100101101100101001110011101100011': 1, '0111100100011111010001011010101110111111': 1, '0001001100101000010110001010110110011011': 1, '1100100110101000001110100101010111010010': 1, '1101100010110001011001001010110000101010': 1, '0100011111111100101010011110001110001101': 1, '1000011000101111110001110101101110000011': 1, '0001010110111010010110011011110110101101': 1, '0011000001000011011111010111001010100110': 1, '0110000000001010001100100111001100101100': 1, '0010011000101101010001101101100010001100': 1, '1010101101010111001100001011111100110111': 1, '0010001100001100111111100101001000000001': 1, '1011010001101100111101111010101011001011': 1, '1110110111011001100001110001001100000001': 1, '0000010011101111000000000110000001001000': 1, '0010000111010011010001110011111111100101': 1, '0010010110001100000111110010010000011011': 1, '0111011101001000100000101111100111100100': 1, '1101100100101100111111101110110010011001': 1, '0100101010010111111100100110001011110101': 1, '0001011111001010001001100100110010100111': 1, '0011001100011101011110110000011110000110': 1, '0111010100001110010100111001010101000100': 1, '1101110011101101111011001100001100110010': 1})\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50-qubit task COMPLETED.\n", + "QFT:\n", + "This task ran 100 shots and the total runtime was 54215 ms\n", + "Measurement results: Counter({'01011100010101111100101011110011110000011011010110': 1, '10001100110100010110011100001010110001011000110101': 1, '00111001110000001011000110110110011010100110000011': 1, '10110001100100100101001001100100111001001100101110': 1, '10100011101000100101011001111110010010100011010010': 1, '00000011110001001110111001111010110100010001011010': 1, '10000001110001010000110101011100111111111111100110': 1, '11111100010110111000001111000010111000100110101010': 1, '11001111010100100010110111110100100110110111100011': 1, '10110000100011101000010100101000001101100100011000': 1, '00111110010111110100000001100010000100110001111110': 1, '11001001111010010010011100001000001001010001001011': 1, '10010100011011111010011000001111100011001001011111': 1, '01000111011100000100100101010001010001011111111001': 1, '01010001001100111101011000000101010101100100101001': 1, '00010011000011010010111100100011010110111101110100': 1, '00001100010000011101101111000010011010010011010000': 1, '10010111100100100010010101000110010110001110100011': 1, '01101000110000101111101101100000011100100010001011': 1, '01001010111011110000111000100110111011110001111100': 1, '10101101010000100101001101011110001001100001010001': 1, '11000011101100111110010100000111000010010100101101': 1, '00001011011000000101101100111111100110110100111100': 1, '11010111010001010010011011110011111111010010010011': 1, '10001101111000111000001001111011010100001000011010': 1, '10000110010111101100011001111001110000111110100010': 1, '01010000011100011110111001001010111001011010011001': 1, '10011111010011001011110010101111101011101111111101': 1, '01011011100100101111000101111111101101010110011010': 1, '00000110100010101111000110110111101111011111011010': 1, '00000010010010010100001000000101001001011110010100': 1, '01100100001100001111010000101000110100010110000110': 1, '11100010111001011100001001001010010110000011001111': 1, '11010011011010010100110101101010110110100010010100': 1, '10000000010001101111101101101110001001011001010011': 1, '01110011010111110101001001000001101010110000011001': 1, '01000001111000011001101110110101011111101011001111': 1, '10010101100100111000100000001010010011100010010100': 1, '01000000100110011100111110101100001001010011111010': 1, '00101011111110111110101100100000011100011100111101': 1, '11100100011111101100111000110011000001111101010000': 1, '11010011101001110100101010000101100101000111000010': 1, '11010111001001010101001011101110010101010000011100': 1, '11110100111111110110101011110011001100110110010010': 1, '01000011000111111111011111100010000111000001010001': 1, '10100101101000101111010011111001111010011100010001': 1, '01100011010001101010110000101011110101111101011000': 1, '01011000101110001010011110010010110001001100011010': 1, '01101100110110001100100000010110001111101010000001': 1, '00111100010000000111111110100101001100000110010001': 1, '01001100111001111100100101010011110110100011101000': 1, '01000011011011010110110000001000111010101111110101': 1, '10000100001010100011000100110100110110110101011101': 1, '01011100010010101011000110010110110011001100010111': 1, '00010000100010000010110111110101001111001000010001': 1, '11001110110011101110000011011000100010001010111000': 1, '00000000110101110110111101011000010011010100010101': 1, '00100000000010110001101100110001001110010111011100': 1, '00101101010100101010011011000000001001000000010010': 1, '01100011110100111111100101010001100101000010001100': 1, '10110010101110000001110101101011111010000111011111': 1, '11110011010111000100101110010111000001111001000011': 1, '01010000010000001101111111111111000000111100010100': 1, '11001100010101001100111101010110001010111011100000': 1, '10000000111011000111001000001011011011001101010011': 1, '00011000100100101010010001011010000101011011011100': 1, '01001101000110011001111100010010100111010100001010': 1, '10011000001000001000111001110010001111001110101011': 1, '00111011001010101111100000111011101111001110100111': 1, '01000001101110000011111011011001010101101010110001': 1, '01010001001111101111101111011010011001111001111011': 1, '00111110001110101100101011101101000110001010100001': 1, '00001010011000111100111001110011110110011100001101': 1, '01110101101111011010010011111010111110100011001010': 1, '10111011001101010010010010100110001000000010011110': 1, '11000101010010010111110010100110101011001010100000': 1, '11000101110011010101100001100011101110001001011010': 1, '10110101100000001111101001111010011100010100111100': 1, '00001000011110010100111000001101001100110100010101': 1, '00111000011000110001001000000101111111001001100011': 1, '00011001100011001000101111010001011100011111011110': 1, '10010001100100001111100111011001110110010001011100': 1, '01010011001101010001110100011001001100010010001111': 1, '00001001110100000011110010010001010010001101010100': 1, '01001101111011001010000000101001010110000001111001': 1, '01010110011010111110010100111101110000011111010010': 1, '11111011101111011010111001010100001001000110011011': 1, '10010011110100011110101110110010101111111100111011': 1, '01001001001000110010001111000111111100011010001010': 1, '11010100010100001000010110000100010110111010000001': 1, '10100011011111011110111101110001101001011010000110': 1, '01101011100011001100011011110111111000001001101110': 1, '01001010111011000011001011010010001111011101001011': 1, '11110110110000000111010001110101101100101110010101': 1, '01111010110111111110010110001011000000111100110101': 1, '01101110110110011010111100000100111110001110100111': 1, '01111001100001101011010000011001000101011011011000': 1, '01000000110100111000100000110100010010000010000010': 1, '01000011000100111010101110011101001100111000111000': 1, '01001100000111011100011001011110001110010100000011': 1})\n", + "\n" + ] + } + ], + "source": [ + "qubit_range = range(20, 51, 10)\n", + "tn_tasks = {}\n", + "tn_results = {}\n", + "for num_qubits in qubit_range:\n", + " # generate QFT circuit\n", + " qft_circ = qft(range(num_qubits))\n", + " tn_tasks[num_qubits] = tn_device.run(qft_circ, shots=n_shots)\n", + "\n", + "for num_qubits in qubit_range:\n", + " tn_status = tn_tasks[num_qubits].state()\n", + " while tn_status != 'COMPLETED':\n", + " tn_status = tn_tasks[num_qubits].state()\n", + "\n", + " tn_results[num_qubits] = tn_tasks[num_qubits].result()\n", + " # get the running time of the task\n", + " tn_runtime = tn_results[num_qubits].additional_metadata.simulatorMetadata.executionDuration\n", + "\n", + " # get the measurement counts\n", + " tn_counts = tn_results[num_qubits].measurement_counts\n", + " \n", + "\n", + " print('{}-qubit task {}.'.format(num_qubits,tn_status))\n", + " print('QFT:')\n", + " print('This task ran {} shots and the total runtime was {} ms'.format(tn_num_shots,tn_runtime))\n", + " print(\"Measurement results: {}\\n\".format(tn_counts))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Circuit geometry is extremely important for TN1\n", + "\n", + "We'll now examine a type of circuit that is harder for the tensor network simulator: local Hayden-Preskill circuits. \"Local\" here means that multi-qubit gates only act on qubits which are nearest-neighbors. In this case, we will simulate a one-dimensional chain, and so any 2-qubit gates will act on qubits `q` and `q+1`. These circuits are generated in the following way:\n", + "\n", + "For each of `N` gates:\n", + "- Choose a single qubit gate with 50% chance\n", + " - Choose between x-, y-, or z-rotations and Hadamard with equal likelihood.\n", + " - If a rotation is chosen, the angle is chosen from a uniform random distribution between `0` and `2*pi`.\n", + " - The qubit `q` to which to apply the gate is chosen randomly with equal likelihood from among all the available `N` qubits\n", + "- Choose a CZ gate with 50% chance\n", + " - The qubit `q` to which to apply the control is chosen randomly with equal likelihood from among `N-1` qubits. The `Z` gate is applied to `q+1`.\n", + "\n", + "Circuits of this type are effective at generating entanglement among qubits. We can see this by scaling the number of gates applied quadratically with the number of qubits. This is enough gates to spread entanglement throughout all the qubits. We see that the circuit becomes more time consuming to simulate as we apply more gates." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "@circuit.subroutine(register=True)\n", + "def local_Hayden_Preskill(num_qubits, num_gates):\n", + " hp_circ = Circuit()\n", + " \"\"\"Yields the circuit elements for a scrambling unitary.\n", + " Generates a circuit with numgates gates by laying down a\n", + " random gate at each time step. Gates are chosen from single\n", + " qubit unitary rotations by a random angle, Hadamard, or a \n", + " controlled-Z between a qubit and its nearest neighbor (i.e.,\n", + " incremented by 1).\"\"\"\n", + " qubits = range(num_qubits)\n", + " for i in range(num_gates):\n", + " if np.random.random_sample() > 0.5:\n", + " \"\"\"CZ between a random qubit and the next qubit to its left.\"\"\"\n", + " a = np.random.choice(range(len(qubits)-1), 1, replace=True)[0]\n", + " hp_circ.cz(qubits[a],qubits[a+1])\n", + " else:\n", + " \"\"\"Random single qubit rotation.\"\"\"\n", + " angle = np.random.uniform(0, 2 * math.pi)\n", + " qubit = np.random.choice(qubits,1,replace=True)[0]\n", + " gate = np.random.choice([Gate.Rx(angle), Gate.Ry(angle), Gate.Rz(angle), Gate.H()], 1, replace=True)[0]\n", + " hp_circ.add_instruction(Instruction(gate, qubit))\n", + " return hp_circ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Visualizing the Hayden-Preskill circuit\n", + "\n", + "Let's examine the geometry of some HP circuits of varying depths. We can see that the deeper the circuit, the more likely it is for (mediated) connections to exist among all qubits." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "HAYDEN PRESKILL CIRCUIT WITH 5 GATES:\n", + "T : | 0 |1|2|\n", + " \n", + "q0 : -Ry(4.4)-----\n", + " \n", + "q1 : -C-------C---\n", + " | | \n", + "q2 : -Z-------Z-H-\n", + " \n", + "q4 : -H-----------\n", + "\n", + "T : | 0 |1|2|\n", + "\n", + "HAYDEN PRESKILL CIRCUIT WITH 10 GATES:\n", + "T : | 0 | 1 | 2 | 3 | 4 |\n", + " \n", + "q0 : -Rx(2.55)-C--------Ry(2.69)-------------------\n", + " | \n", + "q1 : -Rz(3.43)-Z-----------------------------------\n", + " \n", + "q2 : -------------------C--------------------------\n", + " | \n", + "q3 : -C--------Rz(1.55)-Z--------Ry(1.85)-Ry(2.18)-\n", + " | \n", + "q4 : -Z--------Rz(4.75)----------------------------\n", + "\n", + "T : | 0 | 1 | 2 | 3 | 4 |\n", + "\n", + "HAYDEN PRESKILL CIRCUIT WITH 15 GATES:\n", + "T : | 0 | 1 | 2 | 3 | 4 |5|\n", + " \n", + "q0 : -Rx(5.92)-Rx(4.39)-Ry(4.23)---------------------\n", + " \n", + "q1 : -C-----------------C--------H-------------------\n", + " | | \n", + "q2 : -Z--------Ry(3.48)-Z--------Ry(4.12)-C--------C-\n", + " | | \n", + "q3 : ----------C--------------------------Z--------Z-\n", + " | \n", + "q4 : -Rz(3.71)-Z--------Rz(3.6)--Rz(5.85)-Ry(3.85)---\n", + "\n", + "T : | 0 | 1 | 2 | 3 | 4 |5|\n", + "\n", + "HAYDEN PRESKILL CIRCUIT WITH 20 GATES:\n", + "T : |0| 1 | 2 |3|4| 5 | 6 |7|8|9| 10 |11|12|\n", + " \n", + "q0 : -C-Rz(0.617)-Ry(5.44)-C-C-C--------H-----------------------------\n", + " | | | | \n", + "q1 : -Z-C---------C--------Z-Z-Z--------------------------------------\n", + " | | \n", + "q2 : ---Z---------Z--------C-C-Rz(3.42)------------C---------------C--\n", + " | | | | \n", + "q3 : ----------------------Z-Z-Ry(5.33)-Rx(4.68)-H-Z-C-Rx(4.48)-C--Z--\n", + " | | \n", + "q4 : ------------------------------------------------Z----------Z-----\n", + "\n", + "T : |0| 1 | 2 |3|4| 5 | 6 |7|8|9| 10 |11|12|\n", + "\n", + "HAYDEN PRESKILL CIRCUIT WITH 25 GATES:\n", + "T : | 0 | 1 | 2 | 3 | 4 |5| 6 | 7 | 8 | 9 |\n", + " \n", + "q0 : ----------C--------Rz(2.4)-Rz(2.91)-Ry(5.41)-C-Ry(1.73)----------------------------\n", + " | | \n", + "q1 : -C--------Z----------------------------------Z-C--------C--------------------------\n", + " | | | \n", + "q2 : -Z--------H--------H-------Ry(1.62)-C--------H-Z--------Z--------Ry(2.88)-Ry(1.73)-\n", + " | \n", + "q3 : -H----------------------------------Z--------C-Rx(1.78)-Ry(4.73)-Ry(3.26)----------\n", + " | \n", + "q4 : -Rz(0.39)-Rx(2.86)-H-------Ry(6.23)----------Z-------------------------------------\n", + "\n", + "T : | 0 | 1 | 2 | 3 | 4 |5| 6 | 7 | 8 | 9 |\n" + ] + } + ], + "source": [ + "num_qubits = 5\n", + "for num_gates in range(5, 26, 5):\n", + " print('')\n", + " print(f\"HAYDEN PRESKILL CIRCUIT WITH {num_gates} GATES:\")\n", + " my_hp_circ = local_Hayden_Preskill(num_qubits, num_gates)\n", + " print(my_hp_circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Experimenting with Hayden-Preskill circuits\n", + "\n", + "We will examine runtimes for various depths of circuits at relatively low (for TN1) qubit counts. This is to ensure that our job finishes in a reasonable amount of time. We'll examine the measurement counts at the end of each simulation. Because these are random circuits, we should not expect to see the measurement counts highly concentrated in a few outcomes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + "Caution: Running the following cell will take about 2 minutes. Only uncomment it if you are happy to wait.\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50-qubit 33-depth task COMPLETED.\n", + "Hayden-Preskill circuit:\n", + "This task ran 10 shots and the total runtime was 16752 ms\n", + "Measurement results: Counter({'10000011001011101000000100111011111110000010001010': 1, '00000111110011001110011101101011010101101111001000': 1, '01010111011111010110000100100011011101001111001101': 1, '10010011111110101000010010101010010010010110001000': 1, '10010111010010101111000011101011010110011100101000': 1, '10010111001000001110011100100010010110110101101001': 1, '10011110101011101101010100101011110110011010001001': 1, '10001011110000101101011111111111011111101101101000': 1, '11000011111101011001010111010010010111000111101000': 1, '10000111111111001111001000101101010111010101101000': 1})\n", + "\n", + "50-qubit 44-depth task COMPLETED.\n", + "Hayden-Preskill circuit:\n", + "This task ran 10 shots and the total runtime was 28063 ms\n", + "Measurement results: Counter({'01110001110011011110010000011001000000101101010011': 1, '10111011100100110111000110011000001000001010000001': 1, '10100001110011110011101100011000000011101100010010': 1, '01001001101101110111100010101101000011111011010011': 1, '11101011100000111000000000101001000010100011010011': 1, '01110001100001110011100101011001000000000100011011': 1, '10000001110101110101100110101011001010101100110011': 1, '00011001110101011011100110101100000011101001101000': 1, '00100001110001110001100010000110010000100001010011': 1, '10110011010011010010000010111000000011110010110011': 1})\n", + "\n", + "50-qubit 61-depth task COMPLETED.\n", + "Hayden-Preskill circuit:\n", + "This task ran 10 shots and the total runtime was 41970 ms\n", + "Measurement results: Counter({'01101001011011100001000111011010110000000111010111': 1, '01101100011000000000011100111111111000011101111011': 1, '01000011010111001100100111101111011000110001111101': 1, '01111011110111101000010000011010100101110001010111': 1, '01000001110111111100110010010000000010001001110010': 1, '01000110010111010000000101001110010010011011010111': 1, '01010111000111111100001110010101111110000100110111': 1, '01000100011010010010001111010000011101011001111011': 1, '11101000011011111100100100011000100100001111110111': 1, '01010111111011000001001111010100101100000101110111': 1})\n", + "\n" + ] + } + ], + "source": [ + "#num_qubits = 50\n", + "#n_shots = 10\n", + "#gate_range = range(500, 1001, 250)\n", + "#tn_tasks = {}\n", + "#tn_results = {}\n", + "#for gates in gate_range:\n", + "# # construct HP circuit\n", + "# circ = Circuit()\n", + "# # ensure the HP circuit is runnable -- circuits must have depth <= 100\n", + "# while True:\n", + "# circ = local_Hayden_Preskill(num_qubits, gates)\n", + "# if circ.depth <= 100:\n", + "# break\n", + "# tn_tasks[circ.depth] = tn_device.run(circ, shots=n_shots)\n", + "#\n", + "#for depth in tn_tasks.keys():\n", + "# tn_status = tn_tasks[depth].state()\n", + "# while tn_status != 'COMPLETED':\n", + "# tn_status = tn_tasks[depth].state()\n", + "#\n", + "# tn_results[depth] = tn_tasks[depth].result()\n", + "# # get the running time of the task\n", + "# tn_runtime = tn_results[depth].additional_metadata.simulatorMetadata.executionDuration\n", + "#\n", + "# # get the measurement counts\n", + "# tn_counts = tn_results[depth].measurement_counts\n", + "# \n", + "#\n", + "# print('{}-qubit {}-depth task {}.'.format(num_qubits,depth,tn_status))\n", + "# print('Hayden-Preskill circuit:')\n", + "# print('This task ran {} shots and the total runtime was {} ms'.format(n_shots,tn_runtime))\n", + "# print(\"Measurement results: {}\\n\".format(tn_counts))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The effect of shot counts on runtimes in TN1\n", + "\n", + "In order to generate samples from a quantum circuit, TN1 first partitions the qubits into groups, and then contracts each group in turn, generating a prediction for the current group's configuration based on the results of previously encountered groups. Because of this, in the worst case, the time to generate `n` shots may scale linearly with `n`. However, if the number of possible outcomes is small (as it is in the GHZ or QFT case), the runtime is effectively constant no matter the number of shots. We will examine this behavior below. It's therefore important to understand that your job may be rejected if the time to contract all the shots you have requested is too large. In this case your task will finish with a `FAILED` message, and the `failureReason` will be `Predicted runtime based on best contraction path found exceeds TN1 limit.` -- in this case you can attempt to retry the computation with fewer shots." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + "Note: Because the runtime of the task can scale linearly with the number of shots in the worst case, it is strongly advised that users run their circuits with a small number of shots (20 or fewer) to explore typical runtimes for their circuit before running the circuit for many shots.\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    \n", + "Caution: Running the following cell will take about 3 minutes. Only uncomment it if you are happy to wait.\n", + "
    " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GHZ task ran 10 shots and the total runtime was 2510 ms\n", + "QFT task ran 10 shots and the total runtime was 7197 ms\n", + "HP task ran 10 shots and the total runtime was 22564 ms\n", + "GHZ task ran 40 shots and the total runtime was 2545 ms\n", + "QFT task ran 40 shots and the total runtime was 10201 ms\n", + "HP task ran 40 shots and the total runtime was 36307 ms\n" + ] + } + ], + "source": [ + "#num_qubits = 30\n", + "#ghz_circ = ghz_circuit(num_qubits)\n", + "#qft_circ = qft(range(num_qubits))\n", + "#hp_circ = Circuit()\n", + "#while True:\n", + "# hp_circ = local_Hayden_Preskill(num_qubits, 750)\n", + "# if circ.depth <= 100:\n", + "# break\n", + "#ghz_tasks = {}\n", + "#ghz_results = {}\n", + "#qft_tasks = {}\n", + "#qft_results = {}\n", + "#hp_tasks = {}\n", + "#hp_results = {}\n", + "#for n_shots in [10, 40]:\n", + "# ghz_tasks[n_shots] = tn_device.run(ghz_circ, shots=n_shots)\n", + "# qft_tasks[n_shots] = tn_device.run(qft_circ, shots=n_shots)\n", + "# hp_tasks[n_shots] = tn_device.run(hp_circ, shots=n_shots)\n", + "#\n", + "#for n_shots in [10, 40]:\n", + "# ghz_status = ghz_tasks[n_shots].state()\n", + "# while ghz_status != 'COMPLETED':\n", + "# ghz_status = ghz_tasks[n_shots].state()\n", + "#\n", + "# qft_status = qft_tasks[n_shots].state()\n", + "# while qft_status != 'COMPLETED':\n", + "# qft_status = qft_tasks[n_shots].state()\n", + "#\n", + "# hp_status = hp_tasks[n_shots].state()\n", + "# while hp_status != 'COMPLETED':\n", + "# hp_status = hp_tasks[n_shots].state()\n", + "#\n", + "# ghz_results[n_shots] = ghz_tasks[n_shots].result()\n", + "# qft_results[n_shots] = qft_tasks[n_shots].result()\n", + "# hp_results[n_shots] = hp_tasks[n_shots].result()\n", + "# # get the running time of the task\n", + "# ghz_runtime = ghz_results[n_shots].additional_metadata.simulatorMetadata.executionDuration\n", + "# qft_runtime = qft_results[n_shots].additional_metadata.simulatorMetadata.executionDuration\n", + "# hp_runtime = hp_results[n_shots].additional_metadata.simulatorMetadata.executionDuration\n", + "#\n", + "# print('GHZ task ran {} shots and the total runtime was {} ms'.format(n_shots,ghz_runtime))\n", + "# print('QFT task ran {} shots and the total runtime was {} ms'.format(n_shots,qft_runtime))\n", + "# print('HP task ran {} shots and the total runtime was {} ms'.format(n_shots,hp_runtime))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:::device/quantum-simulator/amazon/sv1': {'shots': 300, 'tasks': {'COMPLETED': 3}, 'execution_duration': datetime.timedelta(seconds=20, microseconds=365000), 'billed_execution_duration': datetime.timedelta(seconds=25, microseconds=596000)}, 'arn:aws:braket:::device/quantum-simulator/amazon/tn1': {'shots': 1280, 'tasks': {'COMPLETED': 20}, 'execution_duration': datetime.timedelta(seconds=250, microseconds=608000), 'billed_execution_duration': datetime.timedelta(seconds=250, microseconds=608000)}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 1.181 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.3f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.10 ('venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/B_qtm_sims/permuted_circuit.png 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We show how to build the corresponding quantum circuit with simple modular building blocks using the Braket SDK. Specifically, we demonstrate how to build custom gates that are not part of the basic gate set provided by the SDK. A custom gate can used as a core quantum gate by registering it as a subroutine. \n", + "\n", + "After building the circuit, we will run it on two types of devices: 1) classical simulator, and 2) ion-based quantum machine provided by IonQ. For the latter, we will demonstrate how to recover quantum tasks that may be waiting in queue.\n", + "\n", + "1. [Introduction](#introduction)\n", + "2. [Background: What is a Quantum Oracle?](#background)\n", + "3. [Anatomy of Grover's Algorithm](#steps)\n", + "4. [Circuit Diagram](#diagram)\n", + "5. [Code](#code)\n", + " 1. [Libraries and Parameters](#setup)\n", + " 2. [Helper Functions](#wrappers)\n", + " 3. [Device: Classical Simulator](#sim_c)\n", + " 4. [Device: IonQ](#ionq)\n", + "6. [References](#ref)\n", + "\n", + "This tutorial is based on ion-trap experiments published as *C. Figgatt, D. Maslov, K. A. Landsman, N. M. Linke, S. Debnath & C. Monroe (2017), \"Complete 3-Qubit Grover search on a programmable quantum computer\", Nature Communications, Vol 8, Art 1918, doi:10.1038/s41467-017-01904-7, arXiv:1703.10535*. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Grover's algorithm is arguably one of the canonical quantum algorithms that kick-started the field of quantum computing. In the future, it could possibly serve as a hallmark application of quantum computing. Grover's algorithm allows us to find a particular register in an unordered database with $N$ entries in just $O(\\sqrt{N})$ steps, compared to the best classical algorithm taking on average $N/2$ steps, thereby providing a __quadratic speedup__.\n", + "\n", + "For large databases (with a large number of entries, $N$), a quadratic speedup can provide a significant advantage. For a database with one million entries, a quantum computer running Grover's algorithm would need about 1000 runs, while a classical computer would need, on average, $500$k runs.\n", + "\n", + "Research has been shown that any optimal quantum solution to an unstructured search problem has a speed limit of $O(\\sqrt{N})$ runtime. This research finding matches the performance of Grover's algorithm, thus proving that the algorithm is asymptotically optimal [2]. In fact, Grover's algorithm can be generalized to accelerate any type of search where one can construct a quantum oracle, as described in the next section. \n", + "\n", + "Consider the following problem [2]: \n", + "In a search space with $N$ elements, we are searching the index of those elements, which is a number in the range $0, 1, \\dots, N-1$. \n", + "We have $n$ bits at our disposal, with which we can store up to $2^{n}$ elements. \n", + "Our search problem can then be expressed with the help of a function $f$, which takes as input an element out of our set of indices (that is, an integer $x$) and generates two possible outputs: $f(x^{*})=1$, if $x^{*}$ is the solution to the search problem or $f(x)=0$ otherwise (if $N<2^{n}$ we can just set $f(x)=0$ for all extra unused elements). \n", + "This is done with the help of a quantum oracle, which recognizes solutions to the search problem. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Background: What is a Quantum Oracle? " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Grover's algorithm, like many other quantum algorithms, utilizes the concept of a quantum oracle which we will denote as $\\mathcal{O}$. In essence, an oracle $\\mathcal{O}$ is a black-box operation that serves as a subroutine to another algorithm. Typically, oracles are defined using a classical function $f:\\{0,1\\}^{n} \\rightarrow \\{0,1\\}^{m}$, that maps an $n$-input bitstring to an $m$-output bitstring. With $x \\in \\{0,1\\}^{n}$, i.e., $x=(x_{0}, x_{1}, \\dots, x_{n-1})$ is a bitstring vector, and $y \\in \\{0,1\\}^{m}$, the oracle $\\mathcal{O}$ is a unitary operator, commonly defined by its effect on an arbitrary computational basis state as:\n", + "\n", + "$$\\mathcal{O} (\\left|x\\right> \\otimes \\left|y\\right>) = \\left|x\\right> \\otimes \\left|y \\oplus f(x)\\right>,$$ where $\\oplus$ denotes addition modulo 2. \n", + "\n", + "This means that the second qubit register of size $m$ stores the result of the computation. \n", + "For $m=1$, which is the scenario we will focus on here, the second register $\\left|y\\right>$ is a single qubit that is flipped if (and only if) $f(x)=1$. \n", + "In short, the quantum oracle flips the ancilla qubit only if the function $f(x)$ evaluates to one. \n", + "Accordingly, we can check if $x$ is a solution to our search problem by first preparing the state $\\left|x\\right> \\otimes \\left|0\\right>$, then applying the oracle $\\mathcal{O}$ to that state, before finally measuring the state of the oracle qubit. \n", + "\n", + "In Grover's algorithm, it is useful to initialize the oracle qubit in a superposition, as $\\left|y\\right> = (\\left|0\\right> - \\left|1\\right>)/\\sqrt{2}$. \n", + "We can distinguish two cases: \n", + "(i) If $x$ is not a solution to our search problem (i.e., $f(x)=0$), then the application of the oracle operator $\\mathcal{O}$ to the input state $\\left|x\\right> \\otimes (\\left|0\\right> - \\left|1\\right>)/\\sqrt{2}$ leaves this state simply untouched. \n", + "(ii) Conversely, if $x$ is a solution to our search problem (i.e., $f(x)=1$), then the oracle states $\\left|0\\right>$ and $\\left|1\\right>$ are flipped, such that the state picks up a minus sign, giving the final output state $-\\left|x\\right> \\otimes (\\left|0\\right> - \\left|1\\right>)/\\sqrt{2}$. \n", + "Note that global phase factors do not matter in quantum computing, but the relative minus sign we encounter here does make all the difference for a superposition state, which would include the solution among all other possible input states. \n", + "\n", + "For both cases (i) and (ii), the action of the oracle can be summarized as: \n", + "\n", + "$$\\left|x\\right> \\otimes (\\left|0\\right> - \\left|1\\right>)/\\sqrt{2} \\longrightarrow (-1)^{f(x)} \\left|x\\right> \\otimes (\\left|0\\right> - \\left|1\\right>)/\\sqrt{2}.$$ \n", + "Accordingly, the solution to our search problem gets *marked* by shifting the corresponding phase. \n", + "Because the oracle qubit remains unchanged, one can omit this oracle qubit from further discussion and simply express the action of the oracle as: \n", + "\n", + "$$\\left|x\\right> \\longrightarrow (-1)^{f(x)}\\left|x\\right>.$$ \n", + "\n", + "This expression also captures the definition of a *phase oracle*, which will be used in our examples below. \n", + "If a phase oracle is applied on a computational basis state $\\left|x\\right>$, then we only get a global phase that is not observable. However, when applied to a superposition of computational basis states, this phase oracle becomes a powerful tool. As it turns out, the search oracle needs to be applied only $O(\\sqrt{N})$ times to obtain the solution with high probability [2]; more generally, if there are $G$ solutions, the oracle needs to be applied only $O(\\sqrt{N/G})$ times). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Anatomy of Grover's Algorithm " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this tutorial, we will be working with three bits $(n=3)$, leading to eight possible items $(N=2^{3}=8)$. \n", + "To find a given target item, Grover's algorithm uses the following steps:\n", + "\n", + "1. **Initialize**: Start with a uniform superposition of all possible bit strings by applying Hadamard gates. This will result in all inputs having the same amplitude. Since we do not have any prior knowledge about the solution, we initialize to an equal superposition of all possible candidate solutions. \n", + "\n", + "2. **Oracle**: Item bits are then passed through an oracle. The oracle produces only two results. If it detects the target item, its amplitude will be flipped to negative. For all other items, their amplitudes will remain positive. Because the oracle is specifically engineered to change amplitudes based on a certain bit pattern, each target item would have its own associated oracle.\n", + "\n", + "3. **Amplification**: While the oracle in step 2 distinguishes the target item by flipping its amplitude in the negative direction, this difference remains too small to detect. Hence, we use a trick to magnify the difference in amplitudes; by flipping every amplitude around the mean amplitude. Recall that only the target item's amplitude was flipped to negative. In other words, the mean amplitude would still be positive, and its value would only be slightly lower than the amplitudes of other items. By flipping all amplitudes about the mean, the amplitudes of non-target items would decrease only slightly. On the other hand, the amplitude of the target item, being much less than the mean value to start, would be reflected back up into the positive direction by a large margin.\n", + "\n", + "4. **Repeat**: By repeating steps 2 and 3, we can magnify the amplitude of the target item to a point where it can be identified with overwhelming probability. To get to this point, we need to repeat these steps approximately $\\sqrt{N}$ times (again assuming a single solution and large $N$). As discussed in more detail in our Quantum Amplification Algorithm (QAA) tutorial, to ensure we measure a solution with high probability, we apply the Grover iterator $\\left\\lfloor\\frac{\\pi}{4\\theta}\\right\\rfloor=\\left\\lfloor\\frac{\\pi}{4}\\sqrt{\\frac{N}{G}}\\right\\rfloor$ times, with $G$ denoting the number of solutions. Since we may not know $G$ in advance, we not know the ideal number of iterations a priori. To address this issue, however, we may use quantum counting techniques with the help of the phase estimation procedure (QPE); for details we refer to Ref.[2]. \n", + "\n", + "5. **Measurement**: Measure the resulting amplitudes to identify the target item." + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Circuit Diagram " + ] + }, + { + "attachments": { + "circuit.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Following Ref.[1], we will examine Grover's search algorithm for $n=3$ qubits, which corresponds to a search database of size $N = 2^{3} = 8$. Below we show the circuit used to find the item ```111```. To find other items, we can simply swap out the phase oracle, using the table given in Ref.[1].\n", + "\n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Code " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Libraries and Parameters " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Version: 1.0.0.post1\r\n" + ] + } + ], + "source": [ + "# Check SDK version\n", + "!pip show amazon-braket-sdk | grep Version" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Import Braket libraries\n", + "from braket.circuits import circuit, Circuit, Gate, Moments\n", + "from braket.circuits.instruction import Instruction\n", + "from braket.aws import AwsQuantumTask, AwsDevice\n", + "from braket.devices import LocalSimulator\n", + "import matplotlib.pyplot as plt\n", + "# magic word for producing visualizations in notebook\n", + "%matplotlib inline\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Helper Functions " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We develop a set of useful helper functions that we will explain in detail below. Specifically, we provide simple building blocks for the four core modules of Grover's search algorithm: 1) initialization, 2) oracle, 3) amplification, and 4) measurement. This approach allows us to solve the problem in a clean and modular way. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Helper function to build C-C-Z gate\n", + "@circuit.subroutine(register=True)\n", + "def ccz(targets=[0, 1, 2]):\n", + " \"\"\"\n", + " implementation of three-qubit gate CCZ\n", + " \"\"\"\n", + " # define three-qubit CCZ gate\n", + " ccz_gate = np.array([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0]],\n", + " dtype=complex)\n", + " \n", + " # instantiate circuit object\n", + " circ = Circuit()\n", + " \n", + " # add CCZ gate\n", + " circ.unitary(matrix=ccz_gate, targets=targets)\n", + " \n", + " return circ\n", + "\n", + "\n", + "# All possible items and their corresponding oracles\n", + "# define oracle dictionary using this CCZ gate\n", + "oracle_sim = {\"000\": Circuit().x([0,1,2]).ccz(targets=[0, 1, 2]).x([0,1,2]),\n", + " \"001\": Circuit().x([0,1]).ccz(targets=[0, 1, 2]).x([0,1]),\n", + " \"010\": Circuit().x([0,2]).ccz(targets=[0, 1, 2]).x([0,2]),\n", + " \"011\": Circuit().x([0]).ccz(targets=[0, 1, 2]).x([0]),\n", + " \"100\": Circuit().x([1,2]).ccz(targets=[0, 1, 2]).x([1,2]),\n", + " \"101\": Circuit().x([1]).ccz(targets=[0, 1, 2]).x([1]),\n", + " \"110\": Circuit().x([2]).ccz(targets=[0, 1, 2]).x([2]),\n", + " \"111\": Circuit().ccz(targets=[0, 1, 2])\n", + " }\n", + "\n", + "\n", + "# helper function for initialization\n", + "def initialize(n_qubits=3):\n", + " \"\"\"\n", + " function to apply hadamard to all qubits\n", + " \"\"\"\n", + " # Initialize with superposition\n", + " circ = Circuit();\n", + " circ.h(np.arange(n_qubits))\n", + " #print(circ)\n", + " return circ\n", + "\n", + "\n", + "# helper function for phase oracle\n", + "def oracle(item):\n", + " \"\"\"\n", + " function to apply oracle for given target item\n", + " \"\"\"\n", + " # instantiate circuit object\n", + " circ = Circuit()\n", + " \n", + " # add oracle\n", + " circ.add_circuit(oracle_sim[item])\n", + " \n", + " return circ\n", + "\n", + "\n", + "# helper function for amplification\n", + "def amplify(n_qubits=3):\n", + " \"\"\"\n", + " function for amplitude amplification\n", + " \"\"\"\n", + " # instantiate circuit object\n", + " circ = Circuit()\n", + " \n", + " # Amplification\n", + " circ.h(np.arange(n_qubits))\n", + " circ.add_circuit(oracle_sim['000'])\n", + " circ.h(np.arange(n_qubits))\n", + " \n", + " return circ\n", + "\n", + "\n", + "# helper function for grover algorithm\n", + "def grover(item, n_qubits=3, n_reps=1):\n", + " \"\"\"\n", + " function to put together individual modules of Grover algorithm\n", + " \"\"\"\n", + " # initialize\n", + " grover_circ = initialize()\n", + " # oracle and amplify\n", + " for ii in range(n_reps):\n", + " # get oracle\n", + " or_circ = oracle(item)\n", + " grover_circ.add(or_circ)\n", + " # amplify\n", + " amplification = amplify()\n", + " grover_circ.add(amplification)\n", + " \n", + " return grover_circ\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Function to run quantum task, check the status thereof, and collect results\n", + "def get_result(circ):\n", + " \n", + " # get number of qubits\n", + " num_qubits = circ.qubit_count\n", + "\n", + " # specify desired results_types\n", + " circ.probability()\n", + "\n", + " # submit task: define task (asynchronous)\n", + " task = device.run(circ, shots=1000)\n", + "\n", + " # Get ID of submitted task\n", + " task_id = task.id\n", + "# print('Task ID :', task_id)\n", + "\n", + " # Wait for job to complete\n", + " status_list = []\n", + " status = task.state()\n", + " status_list += [status]\n", + " print('Status:', status)\n", + "\n", + " # Only notify the user when there's a status change\n", + " while status != 'COMPLETED':\n", + " status = task.state()\n", + " if status != status_list[-1]:\n", + " print('Status:', status)\n", + " status_list += [status]\n", + "\n", + " # get result\n", + " result = task.result()\n", + "\n", + " # get metadata\n", + " metadata = result.task_metadata\n", + "\n", + " # get output probabilities\n", + " probs_values = result.values[0]\n", + "\n", + " # get measurement results\n", + " measurement_counts = result.measurement_counts\n", + "\n", + " # print measurement results\n", + " print('measurement_counts:', measurement_counts)\n", + "\n", + " # bitstrings\n", + " format_bitstring = '{0:0' + str(num_qubits) + 'b}'\n", + " bitstring_keys = [format_bitstring.format(ii) for ii in range(2**num_qubits)]\n", + "\n", + " # plot probabalities\n", + " plt.bar(bitstring_keys, probs_values);\n", + " plt.xlabel('bitstrings');\n", + " plt.ylabel('probability');\n", + " plt.xticks(rotation=90);\n", + " \n", + " return measurement_counts" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Device: Classical Simulator \n", + "We demonstrate Grover's algorithm on a classical simulator first. \n", + "You can choose between a local simulator or an on-demand simulator. \n", + "In the next section, we will run the same problem on a quantum IonQ device." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# Set up the cloud-based simulator \n", + "# device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n", + "\n", + "# set up the local simulator\n", + "device = LocalSimulator()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum Gates supported by StateVectorSimulator:\n", + "['ccnot', 'cnot', 'cphaseshift', 'cphaseshift00', 'cphaseshift01', 'cphaseshift10', 'cswap', 'cv', 'cy', 'cz', 'ecr', 'h', 'i', 'iswap', 'pswap', 'phaseshift', 'rx', 'ry', 'rz', 's', 'si', 'swap', 't', 'ti', 'unitary', 'v', 'vi', 'x', 'xx', 'xy', 'y', 'yy', 'z', 'zz']\n" + ] + } + ], + "source": [ + "# get device name\n", + "device_name = device.name\n", + "# show the properties of the device \n", + "device_properties = device.properties\n", + "# show supportedQuantumOperations (supported gates for a device)\n", + "device_operations = device_properties.dict()['action']['braket.ir.jaqcd.program']['supportedOperations']\n", + "# Note: This field also exists for other devices like the QPUs\n", + "print('Quantum Gates supported by {}:\\n {}'.format(device_name, device_operations))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since the ```CCZ``` gate is not part of the default gate set, we have used the ```unitary``` method to build a custom, doubly-controlled Z gate ```CCZ``` for the phase oracle operator. \n", + "We will leverage the Amazon Braket `circuit.subroutine` functionality, which allows us to use such a custom-built gate as if it were any other built-in gate. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we are ready to run our circuit for a few test cases. \n", + "To recap, the steps are as follows:\n", + "\n", + "1. Create a uniform superposition\n", + "2. Apply the phase oracle corresponding to our target item\n", + "3. Define the diffusion operator to magnify the amplitude difference created by the oracle\n", + "4. Collect the measurement counts for our target item" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4|5|6|\n", + " \n", + "q0 : -H-U-H-X-U-X-H-\n", + " | | \n", + "q1 : -H-U-H-X-U-X-H-\n", + " | | \n", + "q2 : -H-U-H-X-U-X-H-\n", + "\n", + "T : |0|1|2|3|4|5|6|\n", + "Status: COMPLETED\n", + "measurement_counts: Counter({'111': 776, '000': 39, '010': 35, '011': 33, '001': 33, '100': 31, '101': 28, '110': 25})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Select item to find. Let's start with '111' for now\n", + "item = \"111\"\n", + "\n", + "# get Grover circuit\n", + "circ = grover(item)\n", + "\n", + "# print circuit\n", + "print(circ)\n", + "\n", + "# Measurement\n", + "counts = get_result(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__DISCUSSION__: We observe a strong peak around the target solution given by the `111` bitstring, with all other bitstrings showing far smaller probabilities. \n", + "Let us try one more item: " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4|5|6|7|8|\n", + " \n", + "q0 : -H---U-H-X---U-X-H-\n", + " | | \n", + "q1 : -H-X-U-X-H-X-U-X-H-\n", + " | | \n", + "q2 : -H-X-U-X-H-X-U-X-H-\n", + "\n", + "T : |0|1|2|3|4|5|6|7|8|\n", + "Status: COMPLETED\n", + "measurement_counts: Counter({'100': 792, '111': 34, '011': 32, '010': 32, '001': 30, '110': 28, '000': 26, '101': 26})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Select item to find. Let's start with '111' for now\n", + "item = \"100\"\n", + "\n", + "# get Grover circuit\n", + "circ = grover(item)\n", + "\n", + "# print circuit\n", + "print(circ)\n", + "\n", + "# Measurement\n", + "counts = get_result(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__DISCUSSION__: By repeating steps 2 (oracle) and 3 (amplification), we can further magnify the amplitude of the target item, thus maximizing the single-shot probability of identifying the right answer. This repetition is demonstrated below." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|\n", + " \n", + "q0 : -H---U-H-X---U-X-H---U--H--X-----U--X--H--\n", + " | | | | \n", + "q1 : -H-X-U-X-H-X-U-X-H-X-U--X--H--X--U--X--H--\n", + " | | | | \n", + "q2 : -H-X-U-X-H-X-U-X-H-X-U--X--H--X--U--X--H--\n", + "\n", + "T : |0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|\n", + "Status: COMPLETED\n", + "measurement_counts: Counter({'100': 941, '011': 13, '010': 10, '000': 10, '111': 7, '101': 7, '110': 7, '001': 5})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Select item to find\n", + "item = \"100\"\n", + "\n", + "# get Grover circuit\n", + "circ = grover(item, n_reps=2)\n", + "\n", + "# print circuit\n", + "print(circ)\n", + "\n", + "# Measurement\n", + "counts = get_result(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__DISCUSSION__: We observed how repeated application of the Grover operator has amplified the occurrence of the desired bitstring, while further suppressing wrong answers to our search problem. We get the correct result with high probability. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Device: IonQ \n", + "\n", + "Finally, we check whether this scheme works on quantum hardware, by submitting our circuit to the IonQ device. To achieve this check, we first need to express the ```CCZ``` gate in terms of the native gate set of IonQ. In doing so, we build a custom gate that can be registered as a subroutine and then used as if it were any other native quantum gate within our SDK. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# Set up a QPU device\n", + "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum Gates supported by IonQ Device:\n", + " ['x', 'y', 'z', 'rx', 'ry', 'rz', 'h', 'cnot', 's', 'si', 't', 'ti', 'v', 'vi', 'xx', 'yy', 'zz', 'swap', 'i']\n" + ] + } + ], + "source": [ + "# get device name\n", + "device_name = device.name\n", + "# show the properties of the device \n", + "device_properties = device.properties\n", + "# show supportedQuantumOperations (supported gates for a device)\n", + "device_operations = device_properties.dict()['action']['braket.ir.jaqcd.program']['supportedOperations']\n", + "# Note: This field also exists for other devices like the QPUs\n", + "print('Quantum Gates supported by {}:\\n {}'.format(device_name, device_operations))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the 𝑁=8 Grover demonstration with three qubits shown in Figgatt et al. (2017), we need to implement the Controlled-Controlled-Z ```CCZ``` gate that is not natively provided on the IonQ device. We will construct this gate using native gates only such as ```CNOT``` and ```T```. Apart from our implementation, other alternative options are available (see [1] and references therein). " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "@circuit.subroutine(register=True)\n", + "def CCNot(controls=[0, 1], target=2):\n", + " \"\"\"\n", + " build CCNOT from H, CNOT, T, Ti\n", + " \"\"\"\n", + " cQb1, cQb2 = controls\n", + " circ = Circuit().h(target).cnot(cQb2,target).ti(target).cnot(cQb1,target).t(target).cnot(cQb2,target).ti(target).cnot(cQb1,target).t(target).h(target).t(cQb2).cnot(cQb1,cQb2).t(cQb1).ti(cQb2).cnot(cQb1,cQb2)\n", + " \n", + " return circ \n", + "\n", + "def CCZ_ionq(controls=[0, 1], target=2):\n", + " \"\"\"\n", + " build CCZ from H and CCNOT\n", + " \"\"\"\n", + " circ = Circuit().h(target).CCNot(controls, target).h(target)\n", + " return circ\n", + "\n", + "ccz_ionq = CCZ_ionq()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Following are oracles defined based on target items:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# Four possible items and their corresponding oracles\n", + "oracle_ionq = {\"000\": Circuit().x([0,1,2]).add(ccz_ionq).x([0,1,2]),\n", + " \"001\": Circuit().x([0,1]).add(ccz_ionq).x([0,1]),\n", + " \"010\": Circuit().x([0,2]).add(ccz_ionq).x([0,2]),\n", + " \"011\": Circuit().x([0]).add(ccz_ionq).x([0]),\n", + " \"100\": Circuit().x([1,2]).add(ccz_ionq).x([1,2]),\n", + " \"101\": Circuit().x([1]).add(ccz_ionq).x([1]),\n", + " \"110\": Circuit().x([2]).add(ccz_ionq).x([2]),\n", + " \"111\": Circuit().add(ccz_ionq)\n", + " }" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "# Select some example item to find\n", + "item = \"111\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Same as with the classical simulator, we first initialize the qubits by applying the Hadamard gate ```H``` to every qubit." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|\n", + " \n", + "q0 : -H-\n", + " \n", + "q1 : -H-\n", + " \n", + "q2 : -H-\n", + "\n", + "T : |0|\n" + ] + } + ], + "source": [ + "# Initialize with superposition\n", + "circ = Circuit();\n", + "circ.h(np.arange(3))\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we apply the phase oracle corresponding to our target item.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4 |5|6|7|8 |9|10|11|12|\n", + " \n", + "q0 : -H----------C--------C-C--T--C--\n", + " | | | | \n", + "q1 : -H-----C----|---C-T--|-X--Ti-X--\n", + " | | | | \n", + "q2 : -H-H-H-X-Ti-X-T-X-Ti-X-T--H--H--\n", + "\n", + "T : |0|1|2|3|4 |5|6|7|8 |9|10|11|12|\n" + ] + } + ], + "source": [ + "# Construct phase oracle\n", + "circ.add_circuit(oracle_ionq[item])\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To complete the circuit, we define the diffusion operator, whose job is to magnify the amplitude difference created by the oracle." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4 |5|6|7|8 |9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|25|26|27|28|\n", + " \n", + "q0 : -H----------C--------C-C--T--C--H--X--------------C-----------C--C--T--C--X--H--\n", + " | | | | | | | | \n", + "q1 : -H-----C----|---C-T--|-X--Ti-X--H--X--------C-----|-----C--T--|--X--Ti-X--X--H--\n", + " | | | | | | | | \n", + "q2 : -H-H-H-X-Ti-X-T-X-Ti-X-T--H--H--H--X--H--H--X--Ti-X--T--X--Ti-X--T--H--H--X--H--\n", + "\n", + "T : |0|1|2|3|4 |5|6|7|8 |9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|25|26|27|28|\n" + ] + } + ], + "source": [ + "# Amplification\n", + "circ.h(np.arange(3))\n", + "circ.add_circuit(oracle_ionq['000'])\n", + "circ.h(np.arange(3))\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This circuit could potentially be optimized, as detailed in Ref.[1], but we will use this version for simplicity. \n", + "\n", + "In the final step, we retrieve the probabilistic counts for our target item. \n", + "To this end, we submit our circuit to the IonQ device, by setting the device as ```AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")```. \n", + "\n", + "This task may not be executed immediately as it enters a queue for this machine. \n", + "Should we need to interrupt our kernel to work on something else, we can always recover our results using the unique ID of this task, as shown in the following lines. " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of task: CREATED\n" + ] + } + ], + "source": [ + "# set up device\n", + "ionq = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")\n", + "\n", + "# run circuit \n", + "ionq_task = ionq.run(circ, shots=1000)\n", + "\n", + "# get id and status of submitted task\n", + "ionq_task_id = ionq_task.id\n", + "ionq_status = ionq_task.state()\n", + "# print('ID of task:', ionq_task_id)\n", + "print('Status of task:', ionq_status)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: QUEUED\n" + ] + } + ], + "source": [ + "# print status\n", + "status = ionq_task.state()\n", + "print('Status of (reconstructed) task:', status)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: COMPLETED\n" + ] + } + ], + "source": [ + "# print status\n", + "status = ionq_task.state()\n", + "print('Status of (reconstructed) task:', status)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Status of (reconstructed) task: COMPLETED\n", + "1000 shots taken on machine arn:aws:braket:us-east-1::device/qpu/ionq/Harmony.\n", + "Measurement counts: Counter({'111': 354, '011': 166, '010': 103, '001': 93, '110': 87, '100': 72, '101': 69, '000': 56})\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# recover task\n", + "task_load = AwsQuantumTask(arn=ionq_task_id)\n", + "\n", + "# print status\n", + "status = task_load.state()\n", + "print('Status of (reconstructed) task:', status)\n", + "\n", + "# wait for job to complete\n", + "# terminal_states = ['COMPLETED', 'FAILED', 'CANCELLED']\n", + "if status == 'COMPLETED':\n", + " # get results\n", + " results = task_load.result()\n", + " \n", + " # get all metadata of submitted task\n", + " metadata = task_load.metadata()\n", + " # example for metadata\n", + " shots = metadata['shots']\n", + " machine = metadata['deviceArn']\n", + " # print example metadata\n", + " print(\"{} shots taken on machine {}.\".format(shots, machine))\n", + " \n", + " # get measurement counts\n", + " counts = results.measurement_counts\n", + " print('Measurement counts:', counts)\n", + "\n", + " # plot results: see effects of noise\n", + " plt.bar(counts.keys(), counts.values());\n", + " plt.xlabel('bitstrings');\n", + " plt.ylabel('counts');\n", + " plt.tight_layout();\n", + " plt.savefig('ionq.png', dpi=700);\n", + " \n", + "elif status in ['FAILED', 'CANCELLED']:\n", + " # print terminal message \n", + " print('Your task is in terminal status, but has not completed.')\n", + "\n", + "else:\n", + " # print current status\n", + " print('Sorry, your task is still being processed and has not been finalized yet.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output looks relatively noisy due to decoherence and gate errors in this relatively long gate sequence. However, we can still observe a dominant peak for the target item. \n", + "\n", + "In summary, we have shown how to implement Grover's search algorithm on a classical simulator, as well as on the IonQ device, using simple modular building blocks. We have also demonstrated how to build custom gates outside of the basic gate set provided by the SDK, and how to register these as subroutines that can be used as if they were any other pre-defined quantum gate. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "# References \n", + "\n", + "[1] C. Figgatt, D. Maslov, K. A. Landsman, N. M. Linke, S. Debnath & C. Monroe (2017), \"Complete 3-Qubit Grover search on a programmable quantum computer\", Nature Communications, Vol 8, Art 1918, doi:10.1038/s41467-017-01904-7, arXiv:1703.10535.\n", + "\n", + "[2] Nielsen, Michael A., Chuang, Isaac L. (2010). Quantum Computation and Quantum Information (2nd ed.). Cambridge: Cambridge University Press." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Summary\n", + "{'arn:aws:braket:us-east-1::device/qpu/ionq/Harmony': {'shots': 1000, 'tasks': {'QUEUED': 1}}}\n", + "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n", + "Estimated cost to run this example: 10.31 USD\n" + ] + } + ], + "source": [ + "print(\"Task Summary\")\n", + "print(t.quantum_tasks_statistics())\n", + "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n", + "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.10 ('venv': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "590fab68195cf107911461461f81d5c472d3d6127f579badfcfad30f03e5cab2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/C_qtm_algorithms/canonical_algorithms/Grover/anatomy.png b/modules/1_Continue_Exploring/C_qtm_algorithms/canonical_algorithms/Grover/anatomy.png new file mode 100644 index 0000000000000000000000000000000000000000..ef12832fac6bcc9b7e1633d4adc13f9096cad6b6 GIT binary patch literal 18105 zcmeHvWn9!v*FUV1f*>JCBhu2H3o0mG3P>ZJOG>jKB~l6^(kLY&A>AFKlz>u8$I`XL z0?Y3IhgaNQT+j3J|K|DJzSz$?%$%7yb86-zO%dA;iMMB362EPa6yC5(fB= z#>WLd9jhvxv9Pe^?e5;yRJwbYNz)BtZRco(g~jp8!pw|J={Cm~b8|DZFMZscgl=Bi z&!0zYn?c)Ju*0Q^ZbtTW;>2QO%gV75@zYTH*LStxzvo+j)>{@ip*82!2+Qx!>nk-s zHlkEL;0WSotrWlU0E0bWvH0vg87^)Y1(RWILk?EQ7FL&EJGo<{AI8WBApWrk{LJH>U`nX6sb<7g%plkh>BdYXK!I z(}YBGRvCwoO!mFjYt+gGgc&|PzLJEBxQcSz^5$2y&W>@#Z{O$?Cw-DENJO-p6!c6T z|8vECBBJ^-YHDvWmX47i^t{a17MG6qOrJTfZDDmmZg<*sDUymFJ;lZSX@|i;uiBWI zjar%^{mw9$nMn)=Qy(21e0=>*3)d$;apA<;CkI#0zn=;S-RMkl^DN zbO-GO1U0)Gzqz3pOu4L3V0V1MV+{N4Zewu}8WZ6O{IfY)wz7D~<@R&Ky# ze~$iZf&Y7tKWRzxowMsV_Wf}-zgmIAktLMo`}?3}2}u;V60or3u$1n}KlH}loWcvb z^(Y;=TU}osOnkd^gY3;MEjLBdYa{K=^N}t#azsoYVCmSGBJjO~U^nDt<}^w9na!j% zu_fYpKP(b~lu6(8^4_>EdImS#2~SB`%h<|TOIh364w>F6F7|zNP_UJ9()iHg&0)To zwj4GNh30P`!Nru+la+qUv7A{!AVQAcKICqi?QB!YU+m9I#gE+HyR@-&aRAWU>o>x` z#s&ZX?Y*+TcjkWdkNsfdNa~wSH~7r;uxF|snr)1sPu2y__>vC6-di~xqDT3;j{X>o z%A4B+3*ARykIQul6WG*zSKCF=4m&f7M&-Ky+yZrSOXa8u?Q(B2d7gSYO`d8pSyv1# z)f--8ny%>8Pb-;Dv3B3zD<}nbE%qd|Py21t>pr$hL~2cD5Thp*9lHL((I5~DWzEtX z!!`+c8oB6?M&^%8#!{O$bdMuUGwI#>#Vl9qw^_qq29 z74tR0%b6p`FiU*~rDpOqbK$gYc1ZV7uYGu+6GT-U8+s zmv-U=w!L%%goXo7RY2>ND{Zy#464AR`kAn%CbzZ4Z;w?p0z{@BUyzOWm+{}StEW+O zTz)GX;QN-}{EpV+I0IR7)3?-lhhF9@>)UObx<@!67%eGSvHm|L#Y`OA{_71o$nJb+ zPsq`ug5$W!R-wuJPc-jxA?0RRPae-Z7_#JYRXR2KS zA9yWUc`WY?W=w~B-v=3R3`#NwUe6pZG&4APh5lq*a=M-HKZv&C24hL(0J5vl|@>a-3eP|R~RQXdGmu(U8k<|fR z`1Br(;R1J+2|KdD&af+d4WwxFQ8Rlhrf$8MR&>f^IER$!I#~x?9Ahg>i;Bx@TE8Hb zEBM$TABIafSZ9f+M>9}p&1zn1JT_W%!Zw@V;pZoL#KQudpgy$Jyu-30*KaBf>^3?N zD_FXkE_$_-%0v}}X+|ya&BZ|cE%g01E8A;a7jU0JmkYIbAbn72H(Bm1Im63Mr&HVE zJk>BkI`>`yr=A&AN=>=orvyd;2S0j_*I5{kA9$av=1*4AARYm_Gr_yFssWX3Kp&Kl zO@RVA6AjhcufY@fq}L&P&4LiJK;`m3G{4z zPAKy@8Ye}K!3~5Q8v*}Z>^3}=IbKXqYW*60L#S=cl`m}6l_6tcolS52%{U-xZT5MD z9531BdN^>fl8oGxrn}X3fW>oh%k_bIu+*h@JH9$+)8+yE6295uNj+*|l$1V-!@ZIyFcf6g5^@T=$XrW%Jo4LN9*u*&YL|Unw;qClXZZ1| zW=Km&pR8nuq*3u0P{{5ClPqQki;bCuxUA+TT}=V=F)Dg41})3**33SW|F&H*tUi|n z2wIlixR_B|y8m9!cu&YQA<^eWeSrQn*!7WIKs^CK7bM zEAK?EaL~vkEv1J%oe4NHNS)gc#O~Kf%a=vXk&yi2zO+Qi_@4EmX@c_#uFG5)RrmlD zjc9)&jp!8;fv19@f#UPeS=syMs-6`-7Uw_>jHVZQ`u%M!h*r-tGF+(Hu=cJzwUFWIa;OhHz7yrMEWnp zh=u>qGnH}t+z8aPbl7r$9KG#1dYA$UVK}nO<_~7X)lpEk8W_EBi1$C zQI;0c;Hur;$rugA96?DKQL}h>(?Sy#lCGF;-`p=1_r#Z8>$Dv;9W~Y=wCXytO}-kA zI+&hLETR)&A%bV(fH<{R*bTeUkD2ni3?UFH;Ml1&{1DXJrBu8{wox^`MDf<{EVn(6w^2^t25cv+7s-R!jf1K_yVKNcBu+++-o~IITPW3r zb8nf6-p^lrQn;+j2X*~%TM(Ug}dvfrzTyaqXA5hnu*D;ghJsoj{IK_9+! 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Note that $|\\psi_{1}\\rangle$ and $|\\psi_{0}\\rangle$ are orthogonal, i.e., $ \\langle \\psi_{0}|\\psi_{1}\\rangle = \\langle B|G\\rangle \\langle 0|1\\rangle =0$, because $\\langle 0|1\\rangle =0$.\n", + "\n", + "__Goal of QAA__: The goal of the algorithm is then to evolve the initial state $|\\psi \\rangle \\in \\mathcal{H}$ into a state with a higher overlap with the _good_ subspace $\\mathcal{H}_{1}$ by _amplifying_ the amplitude of the $|\\psi_{1}\\rangle$ component of the state.\n", + "\n", + "The amplification process that follows boosts the amplitude of the good state $|G\\rangle$ from $\\sin(\\theta)$ to $\\sin((2m+1)\\theta)$ with $2m$ denoting the number of _queries_ or applications of the unitary $\\mathcal{A}$. The probability of finding a _good_ outcome is maximized when $m=\\left\\lfloor\\frac{\\pi}{4\\theta}\\right\\rfloor$.\n", + "\n", + "__Procedure of QAA__: Rather than directly taking measurements on $|\\psi\\rangle$ (as prepared by a _single_ application of $\\mathcal{A}$), QAA proceeds by applying the following operator $\\mathcal{Q}$ (that is derived from $\\mathcal{A}$, i.e., taking $\\mathcal{A}$ as an input), \n", + "\n", + "$$\\mathcal{Q}=\\mathcal{A} \\mathcal{R}_{0} \\mathcal{A}^{\\dagger} \\mathcal{R}_{B}.$$\n", + "\n", + "Here, \n", + "$\\mathcal{R}_{0}=2|0\\rangle_{n+1} \\langle 0| - \\mathbb{1}$\n", + "is a reflection about $|0\\rangle_{n+1}$ (leaving the all-zero state $|0\\rangle_{n+1}$ untouched while giving a minus sign to all other states) and similarly \n", + "$\\mathcal{R}_{B} = \\mathbb{1} - 2 |G\\rangle |1\\rangle \\langle 1|\\langle G|$ \n", + "is a reflection about $|B\\rangle |0\\rangle$, giving a negative sign on the good state, as $\\mathcal{R}_{B} |G\\rangle |1\\rangle = -1|G\\rangle |1\\rangle$, while leaving the bad state $|B\\rangle |0\\rangle$ untouched.\n", + "Finally, $\\mathcal{A}^{\\dagger}$ denotes the adjoint of $\\mathcal{A}$. \n", + "As demonstrated in Refs.[[2,3]](#References), repeated application of the operator $\\mathcal{Q}$ ($m$-times) on $|\\psi\\rangle = \\mathcal{A}|0\\rangle _{n+1}$ gives\n", + "\n", + "$$\\mathcal{Q}^{m} |\\psi\\rangle = \\mathcal{Q}^{m}\\mathcal{A}|0\\rangle _{n+1} = \\sin((2m+1)\\theta) |G\\rangle |1\\rangle + \\cos((2m+1)\\theta) |B\\rangle |0\\rangle.$$\n", + "\n", + "In a nutshell, this equation shows that, for small values of the unknown parameter $a$, the repeated application of $Q$ (involving $2m$ queries of $\\mathcal{A}$ in total) yields a state for which the desired good state would be measured with a probability at least $4m^{2}$ times larger than that of a naive strategy as obtained from $\\mathcal{A}|0\\rangle _{n+1}$. \n", + "This result is because the probability of measuring the good state $|G\\rangle |1\\rangle$ is $P_{1}=\\sin^{2}((2m+1)\\theta) \\approx (2m+1)^{2}\\theta^{2}>4m^{2} \\theta^{2}$. \n", + "Compare this to $2m$ naive queries, i.e., $2m$ measurements from copies of the state $\\mathcal{A}|0\\rangle _{n+1}$ which gives the good state with linear increase in probability $2m$. \n", + "This reasoning is at the heart of the quadratic speedup obtained with QAA: the probability of measuring the good state after QAA scales quadratically with $m$ instead of linearly, meaning we only need $O(\\sqrt{m})$ queries of $\\mathcal{A}$ to achieve the same probability of measuring $|G\\rangle$ compared to the classical strategy. \n", + "Specifically, if $(2m+1)\\theta \\approx \\pi/2$, we have amplified the success probability to $\\sin(...)^{2} \\approx 1$. \n", + "\n", + "Because $\\mathcal{A}$ is an input to QAA that we assume is given, our goal is to figure out how to implement $\\mathcal{R}_{B}$, $\\mathcal{R}_{0}$, and $\\mathcal{A}^{\\dagger}$ as unitaries in a quantum circuit.\n", + "This work is shown in detail in the lines that follow. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Intuition for QAA__: The previous discussion follows the canonical, formal introduction to QAA. \n", + "This section provides a pictorial derivation of the QAA routine, which helps to get an intuitive understanding of the definition and the role of the operator $\\mathcal{Q}$ introduced previously. \n", + "As shown previously, the two states $|\\psi_{1}\\rangle = |G\\rangle |1\\rangle$ and $|\\psi_{0}\\rangle = |B\\rangle |0\\rangle$ are orthogonal, and the whole problem can be analyzed in the two-dimensional subspace spanned by these two orthogonal vectors, with real amplitudes. \n", + "Since the length of the vectors involved are preserved (that is, the vectors remain normalized) we can visualize the whole QAA procedure as transformations of a point on a simple circle, as shown below, using the good and bad states $|G\\rangle |1\\rangle$ and $|B\\rangle |0\\rangle$ as basis vectors, respectively. " + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Going from left to right in the image above, the QAA routine proceeds as follows:\n", + "\n", + "1. __Original situation__: First, the original state prepared by $\\mathcal{A}$ as $|\\psi\\rangle = \\mathcal{A}|0\\rangle _{n+1} = \\sin(\\theta) |G\\rangle |1\\rangle + \\cos(\\theta) |B\\rangle |0\\rangle$ resides in the two-dimensional plane spanned by the basis vectors $|G\\rangle |1\\rangle$ and $|B\\rangle |0\\rangle$, respectively, with (typically small) projection $\\sin(\\theta)$ onto the $|G\\rangle |1\\rangle$ axis.\n", + "2. __Reflection about $|B\\rangle |0\\rangle$__: We then apply a reflection around $|B\\rangle |0\\rangle$, transforming $|\\psi\\rangle$ to $|\\psi'\\rangle$, keeping the projection along $|B\\rangle |0\\rangle$ unchanged, but adding a minus sign to the $|G\\rangle |1\\rangle$ component. Reflection about $|B\\rangle |0\\rangle$ means that all terms apart from $|B\\rangle |0\\rangle$ pick up a negative sign. Because there are only two terms, only $|G\\rangle |1\\rangle$ picks up a negative sign, which is accomplished by the operator $\\mathcal{R}_{B} = \\mathbb{1} - 2 |G\\rangle |1\\rangle \\langle 1|\\langle G|$, as defined previously. \n", + "3. __Reflection about $|\\psi\\rangle$__: Finally, we apply a reflection around the original state $|\\psi\\rangle$, giving the final state $|\\psi''\\rangle$, with an amplified $|G\\rangle |1\\rangle$ amplitude of $\\sin(3\\theta)$, adding an angle of $2\\theta$ from the rotation around $|\\psi\\rangle$ to the original angle $\\theta$.\n", + "Reflection about $|\\psi\\rangle$ means that all terms except for $|\\psi\\rangle$ pick up a minus sign, as can be done by applying the operator $\\mathcal{R}_{\\psi} = 2|\\psi\\rangle\\langle\\psi| - \\mathbb{1}$. \n", + "Using the definition $|\\psi\\rangle = \\mathcal{A}|\\vec{0}\\rangle$ and conversely $\\langle \\psi | = \\langle \\vec{0}|\\mathcal{A}^{\\dagger}$ as well as the unitarity condition $\\mathcal{A}\\mathcal{A}^{\\dagger}=\\mathbb{1}$, this reflection can be rewritten as $\\mathcal{R}_{\\psi} = \\mathcal{A}\\mathcal{R}_{0}\\mathcal{A}^{\\dagger}$, where $\\mathcal{R}_{0}=2|\\vec{0}\\rangle\\langle\\vec{0}| - \\mathbb{1}$ is a reflection about the all-zero state $|\\vec{0}\\rangle$ where all terms except for $|\\vec{0}\\rangle$ pick up a minus sign. \n", + "\n", + "This sequence completes one cycle of the QAA routine, that is one application of $\\mathcal{Q}$. \n", + "In total, each application of $Q$ involves two reflections, first through $|B\\rangle |0\\rangle$ and then through $|\\psi\\rangle$. \n", + "The product is a rotation with angle $2\\theta$. \n", + "Based on our analysis above we can write the rotation $\\mathcal{Q}$ as \n", + "\n", + "$$\\mathcal{Q} = \\mathcal{R}_{\\psi}\\mathcal{R}_{B} = \\mathcal{A}\\mathcal{R}_{0}\\mathcal{A}^{\\dagger}\\mathcal{R}_{B},$$\n", + "\n", + "thereby confirming the formal definition above. \n", + "Repeating this sequence, after $m$ iterations of $\\mathcal{Q}$ we get the generalized equation\n", + "\n", + "$$\\mathcal{Q}^{m} |\\psi\\rangle = \\sin((2m+1)\\theta) |G\\rangle |1\\rangle + \\cos((2m+1)\\theta) |B\\rangle |0\\rangle.$$\n", + "\n", + "\n", + "__Obtaining a quantum speedup__:\n", + "To see that QAA indeed provides a quantum speedup, suppose we use it to query an unsorted database with $N$ elements and $G$ _good_ elements. \n", + "The classical algorithm for finding good entries is to query each element in the database until a good one is found. Thus, the classical solution requires $O(N/G)$ queries. \n", + "A quantum solution would be to query the database in superposition using the state $1/\\sqrt{N}\\sum_i|j\\rangle$, where $j$ enumerates the $N$ elements of the database. \n", + "The oracle prepares the state\n", + "\n", + "$$|\\psi\\rangle = \\sqrt{\\frac{G}{N}} |G\\rangle |1\\rangle + \\sqrt{\\frac{N-G}{N}} |B\\rangle |0\\rangle.$$\n", + "\n", + "Thus, $\\sqrt{a}=\\sin(\\theta)=\\sqrt{G/N}$ and $\\theta \\approx \\sqrt{G/N}$ for the typical scenario where $\\theta \\ll 1$.\n", + "\n", + "We then apply the QAA algorithm to amplify the amplitude of the good states, such that the probability of obtaining a _good_ outcome is amplified. \n", + "To ensure that we measure a good outcome with high probability, we apply the Grover iterator $\\left\\lfloor\\frac{\\pi}{4\\theta}\\right\\rfloor=\\left\\lfloor\\frac{\\pi}{4}\\sqrt{\\frac{N}{G}}\\right\\rfloor$ times. \n", + "In other words, we only need to query the oracle $O(\\sqrt{N/G})$ times in order to find a good outcome to the search problem with high probability.\n", + "This outcome is a quadratic improvement over the $O(N/G)$ oracle calls required classically. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## CIRCUIT IMPLEMENTATION OF QAA" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Implementation of QAA on a QC__: Now that we have an intuitive understanding for QAA (after all, it is just a rotation, as illustrated previously), the final puzzle piece that remains to be solved is the actual implementation of the reflections $\\mathcal{R}_{B}$ and $\\mathcal{R}_{0}$ as a quantum circuit (since $\\mathcal{A}$ is given as input to the QAA problem). \n", + "Rather than implementing $\\mathcal{R}_{0}$ below, we will show how to implement \n", + "\n", + "$$-\\mathcal{R}_{0} = \\mathbb{1} - 2|0\\rangle_{n+1} \\langle 0|,$$ \n", + "\n", + "which gives a minus sign to $|0\\rangle_{n+1}$ only, leaving all other states untouched. \n", + "To compensate for this minus sign, overall we will show how to implement the unitary \n", + "$$\\mathcal{Q}=\\mathcal{A} (-\\mathcal{R}_{0}) \\mathcal{A}^{\\dagger} (-\\mathcal{R}_{B}).$$\n", + "\n", + "__Implementation of $-\\mathcal{R}_{B}$__: First, let us consider \n", + "\n", + "$$-\\mathcal{R}_{B} = 2 |G\\rangle |1\\rangle \\langle 1|\\langle G| - \\mathbb{1},$$ \n", + "\n", + "which is a reflection about $|G\\rangle |1\\rangle$, because $-\\mathcal{R}_{B} |G\\rangle |1\\rangle = +1|G\\rangle |1\\rangle$ and $-\\mathcal{R}_{B} |B\\rangle |0\\rangle = -1|B\\rangle |0\\rangle$. \n", + "This transformation can be achieved by applying $X_{n+1}Z_{n+1}X_{n+1}$ to the (last) ancilla qubit. \n", + "This way, we obtain a minus sign whenever the ancilla is in the $|0\\rangle$ state. \n", + "\n", + "__Implementation of $-\\mathcal{R}_{0}$__: We must implement the transformation $|0, \\dots, 0\\rangle \\rightarrow -|0, \\dots, 0\\rangle$, while leaving all other states untouched. \n", + "To this end, we can flip all the qubits (using single-qubit $X$ gates), flipping the sign of $|11...1\\rangle$, and flipping the qubits back. \n", + "Thus, the last operation that remains to be defined explicitly is flipping the sign of $|11...1\\rangle$ , which can be done with ancilla qubits. \n", + "One possible way to do this task is by using a multiply-controlled Toffoli gate:\n", + "First apply a Pauli-$X$ gate to each qubit. \n", + "Then apply the $N+1$ qubit Toffoli, controlled on all $N$ of the qubits we want to test, and targeted on a single ancilla qubit. \n", + "If (and only if) all of the qubits were in the zero state, then the ancilla qubit will be flipped to $|1\\rangle$. \n", + "We then apply a $Z$ gate to the ancilla qubit, so the overall wavefunction picks up a minus sign whenever all of the register qubits are in the $|0\\rangle$ state. \n", + "Finally, we uncompute the ancilla by applying another $N+1$ qubit Toffoli gate." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can decompose the $N+1$ qubit Toffoli gate into $N-1$ CCNOT (that is, 3 qubit Toffoli) gates and $N-1$ ancilla qubits, shown as follows for $N=4$ register qubits: " + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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RR0YP0jfccEMtxmYQBAgQIECAAAECBAgQINBdgenTp0d7xrvuuqu7g9I7AQIECBAgkISA8CWJaVTEcALCl+FknCdAgAABAgQIECBAgACB/fffPwpf7rzzTjAECBAgQIAAgXELCF/GTaiBOgsIX+o8O8ZGgAABAgQIECBAgACB7goccMABUfhyxx13dHdQeidAgAABAgSSEBC+JDGNihhO4IgjjogepG+88cbhLneeAAECBAgQIECAAAECBDISOOigg6I94+23356RgFIJECBAgACBdgkIX9olq91aCAhfajENBkGAAAECBAgQIECAAIFaCjzmMY+JwpfbbrutlmM1KAIECBAgQKBZAsKXZs2X0Y5SQPgySjCXEyBAgAABAgQIECBAICOBgw8+OApfBgYGMhJQKgECBAgQINAuAeFLu2S1WwuBww8/PHqQ/ulPf1qLsRkEAQIECBAgQIAAAQIECHRXYMaMGdGe8dZbb+3uoPROgAABAgQIJCEgfEliGhUxnIDwZTgZ5wkQIECAAAECBAgQIEDgkEMOicKXW265BQwBAgQIECBAYNwCwpdxE2qgzgLClzrPjrERIECAAAECBAgQIECguwKHHnpoFL78/Oc/7+6g9E6AAAECBAgkISB8SWIaFTGcgPBlOBnnCRAgQIAAAQIECBAgQOCwww6Lwpebb74ZDAECBAgQIEBg3ALCl3ETaqDOAo9//OOjB+mbbrqpzkM2NgIECBAgQIAAAQIECBDokIA9Y4egdUOAAAECBDIUEL5kOOk5lexBOqfZVisBAgQIECBAgAABAgRGJ+BvSxidl6sJECBAgACB1gWEL61bubKBAsKXBk6aIRMgQIAAAQIECBAgQKBDAkceeWT0tyXccMMNHepdNwQIECBAgEDKAsKXlGdXbYW/v9ciIECAAAECBAgQIECAAIHhBGbOnBmFL9dff/1wlztPgAABAgQIEGhZQPjSMpULmyggfGnirBkzAQIECBAgQIAAAQIEOiNw1FFHReHLunXrOtO5XggQIECAAIGkBYQvSU+v4oQv1gABAgQIECBAgAABAgQIDCdwzDHHROHL2rVrh7vceQIECBAgQIBAywLCl5apXNhEgcc97nHRg/TPfvazJpZizAQIECBAgAABAgQIECBQscCxxx4b7Rmvu+66invRHAECBAgQIJCjgPAlx1nPqGbhS0aTrVQCBAgQIECAAAECBAiMUuAJT3hCFL78+Mc/HmUrLidAgAABAgQIxALCl9jEmYQEhC8JTaZSCBAgQIAAAQIECBAgULHAcccdF4Uv1157bcW9aI4AAQIECBDIUUD4kuOsZ1TzoYceGj1I//znP89IQKkECBAgQIAAAQIECBAgMJzA7Nmzoz3jmjVrhrvceQIECBAgQIBAywLCl5apXNhEAeFLE2fNmAkQIECAAAECBAgQINAZgSc+8YlR+PLDH/6wM53rhQABAgQIEEhaQPiS9PQqTvhiDRAgQIAAAQIECBAgQIDAcALHH398FL5cc801w13uPAECBAgQIECgZQHhS8tULmyiwCGHHBI9SN9yyy1NLMWYCRAgQIAAAQIECBAgQKBigRNOOCHaM1599dUV96I5AgQIECBAIEcB4UuOs55RzcKXjCZbqQQIECBAgAABAgQIEBilwJOf/OQofLnqqqtG2YrLCRAgQIAAAQKxgPAlNnEmIQHhS0KTqRQCBAgQIECAAAECBAhULHDiiSdG4cv3v//9invRHAECBAgQIJCjgPAlx1nPqGbhS0aTrVQCBAgQIECAAAECBAiMUuCkk06Kwpcrr7xylK24nAABAgQIECAQCwhfYhNnEhKYMWNG9CB96623JlShUggQIECAAAECBAgQIEBgrAInn3xytGe84oorxtqc+wgQIECAAAECDwkIXx6i8E2KAsKXFGdVTQQIECBAgAABAgQIEKhG4KlPfWoUvnzve9+rpnGtECBAgAABAlkLCF+ynv70ixe+pD/HKiRAgAABAgQIECBAgMBYBU455ZQofFm1atVYm3MfAQIECBAgQOAhAeHLQxS+SVHgsY99bPQgvX79+hRLVRMBAgQIECBAgAABAgQIjFLg1FNPjfaMK1euHGUrLidAgAABAgQIxALCl9jEmYQEhC8JTaZSCBAgQIAAAQIECBAgULHA0572tCh8+c53vlNxL5ojQIAAAQIEchQQvuQ46xnVLHzJaLKVSoAAAQIECBAgQIAAgVEKPOMZz4jCl8svv3yUrbicAAECBAgQIBALCF9iE2cSEjj44IOjB+mBgYGEKlQKAQIECBAgQIAAAQIECIxV4LTTTov2jJdddtlYm3MfAQIECBAgQOAhAeHLQxS+SVFA+JLirKqJAAECBAgQIECAAAEC1Qg885nPjMKXb33rW9U0rhUCBAgQIEAgawHhS9bTn37xwpf051iFBAgQIECAAAECBAgQGKvA6aefHoUvK1asGGtz7iNAgAABAgQIPCQgfHmIwjcpCjzmMY+JHqRvu+22FEtVEwECBAgQIECAAAECBAiMUuCMM86I9oyXXnrpKFtxOQECBAgQIEAgFhC+xCbOJCQgfEloMpVCgAABAgQIECBAgACBigWe/exnR+HLN77xjYp70RwBAgQIECCQo4DwJcdZz6hm4UtGk61UAgQIECBAgAABAgQIjFLgzDPPjMKXSy65ZJStuJwAAQIECBAgEAsIX2ITZxISOOigg6IH6dtvvz2hCpVCgAABAgQIECBAgAABAmMVOOuss6I948UXXzzW5txHgAABAgQIEHhIQPjyEIVvUhQQvqQ4q2oiQIAAAQIECBAgQIBANQJz586Nwpevfe1r1TSuFQIECBAgQCBrAeFL1tOffvHCl/TnWIUECBAgQIAAAQIECBAYq8DZZ58dhS9f/epXx9qc+wgQIECAAAECDwkIXx6i8E2KAsKXFGdVTQQIECBAgAABAgQIEKhG4JxzzonCl4suuqiaxrVCgAABAgQIZC0gfMl6+tMv/sADD4wepH/xi1+kX7gKCRAgQIAAAQIECBAgQGBEgXPPPTfaM1544YUj3ucCAgQIECBAgMBIAsKXkYS83mgB4Uujp8/gCRAgQIAAAQIECBAg0FaB5z3veVH48uUvf7mtfWqcAAECBAgQyENA+JLHPGdbpfAl26lXOAECBAgQIECAAAECBEYUOO+886LwZfny5SPe5wICBAgQIECAwEgCwpeRhLzeaIEDDjggepC+4447Gl2TwRMgQIAAAQIECBAgQIBANQLnn39+tGfs7++vpnGtECBAgAABAlkLCF+ynv70ixe+pD/HKiRAgAABAgQIECBAgMBYBebNmxeFL1/84hfH2pz7CBAgQIAAAQIPCQhfHqLwTYoCwpcUZ1VNBAgQIECAAAECBAgQqEbghS98YRS+XHDBBdU0rhUCBAgQIEAgawHhS9bTn37x+++/f/Qgfeedd6ZfuAoJECBAgAABAgQIECBAIBLYtGlTsWzZsmL+/PnFrFmzil122SXaM5588slbrwnXOggQIECAAAECYxUQvoxVzn2NEBC+NGKaDJIAAQIECBAgQIAAAQJtFVi3bl0R/oqxSZMmRWHLhAkTSs+Fa8M94V4HAQIECBAgQGC0AsKX0Yq5vlECwpdGTZfBEiBAgAABAgQIECBAoFKBjRs3bv2US09PT2nAMlzwsu35cG/4pExoy0GAAAECBAgQaFVA+NKqlOsaKTB9+vToAfuuu+5qZC0GTYAAAQIECBAgQIAAAQKtC6xZs6Yo2xNuG6yM5vvQVmjTQYAAAQIECBBoRUD40oqSaxorUPagLXxp7HQaOAECBAgQIECAAAECBFoSWLFiRdHb2xv9YbzRhC1l14Y2Q9sOAgQIECBAgMBIAsKXkYS83mgB4Uujp8/gCRAgQIAAAQIECBAgMGqB1atXF5MnT648eBkMY0LboQ8HAQIECBAgQGBHAsKXHel4rfEC++23X/TA/ctf/rLxdSmAAAECBAgQIECAAAECBGKBDRs2FNOmTYv2gYPBSVVfQx+hLwcBAgQIECBAYDgB4ctwMs4nISB8SWIaFUGAAAECBAgQIECAAIGWBObOndv24GUwwAl9OQgQIECAAAECwwkIX4aTcT4JAeFLEtOoCAIECBAgQIAAAQIECIwosGrVqo4FL4MBTOjTQYAAAQIECBAoExC+lKk4l4yA8CWZqVQIAQIECBAgQIAAAQIEdigwZ86cjocvoU8HAQIECBAgQKBMQPhSpuJcowU2b95c9Pf3FwsWLCgmTZoUPXwfffTRxcKFC4vly5cX4VoHAQIECBAgQIAAAQIECDRbYGBgoOjp6Yn2f4OfUGnX19Bn6NtBgAABAgQIEBgqIHwZKuLnxgqsX7++6OvrK3p7e1t+4A7XhnvCvQ4CBAgQIECAAAECBAgQaKbA0qVLW94HVh3EhL4dBAgQIECAAIGhAsKXoSJ+bpzAli1bikWLFhUTJ04c88N2uDe0EdpyECBAgAABAgQIEKijwOLFi8f8vFv1m83am2AuJjDw/4E1YA1YA9aANWANpLsGlixZMu4tgfBl3IQa6KZA+Hj3zJkzK9v4hLZ8ZLybM6pvAgQIECBAgACB4QSEL+lu7r1xY26tAWvAGrAGrAFrwBqo1xoIz97jPYQv4xV0f9cE1q5dW0ydOrWy4GXwF7jQZmjbQYAAAQIECBAgQKBOAsKXem3IB/cPvpoXa8AasAasAWvAGrAG0lsDwpc67YSMpaMC4dMp7QheBn+hDG37BExHp1RnBAgQIECAAAECIwgIX9Lb1A/uP3w1t9aANWANWAPWgDVgDdRrDQhfRticeDlNgfDvslT5V40N9wtb6MO/AZPmGlIVAQIECBAgQKCJAsKXem3Ih9tHOG+erAFrwBqwBqwBa8AaaP4aEL40ccdkzOMWWLRoUeV/1dhwvyCGvhwECBAgQIAAAQIECBAgUG+BGTNmdGyfOHT/eMghh9Qbx+gIECBAgACBrgj4N1+6wq7TsQqsX7++mDhxYsceqkNfoU8HAQIECBAgQIAAAQIECNRXYO7cuR3bJw4NX0LfDgIECBAgQIDAUAHhy1ARP9daoK+vr+MP1KFPBwECBAgQIECAAAECBAjUV2Dp0qUd3ysOhjChbwcBAgQIECBAYKiA8GWoiJ9rK7B58+ait7e34w/Uoc/Qt4MAAQIECBAgQIAAAQIE6ikwMDBQ9PT0dHy/GPq87bbb6oliVAQIECBAgEBXBYQvXeXX+WgE+vv7O/4gPfgnmULfDgIECBAgQIAAAQIECBCor8CcOXM6vmcMfToIECBAgAABAmUCwpcyFedqKbBgwYKOP0gPhi8LFy6spYlBESBAgAABAgQIECBAgMCDAitXruz4nnHVqlX4CRAgQIAAAQKlAsKXUhYn6ygwe/bsjj9ID4YvoW8HAQIECBAgQIAAAQIECNRbYO7cuR3bN4a+HAQIECBAgACB4QSEL8PJOF87gSlTpnTsIXowdBn8utdee9XOw4AIECBAgAABAgQIECBAYHuBDRs2FNOmTWv73jH0EfpyECBAgAABAgSGE+h4+LJ48eK2PwQNvmHu6wTWExj4/6A7a2DJkiXD/brrPAECBAgQIECAAAECbRRYvXp1MXny5Lbth0PboQ8HAQIECBAgQGBHAsIXb8637YHUm/7dedOfez3cQ9DsIECAAAECBAgQIECgOwIrVqwoent7K9/vhjZD2w4CBAgQIECAwEgCwhfhS+UPo978r8eb/+ahu/MgfBnptx+vEyBAgAABAgQIEGivwJo1a4rp06dXtucNbYU2HQQIECBAgACBVgSEL8KXyh5Evdnf3Tf7+dfLX/jSym9BriFAgAABAgQIECDQXoGNGzcW8+fPL3p6esa89w33hjZCWw4CBAgQIECAQKsCwhfhy5gfQL3ZX683+81HveZD+NLqb0OuI0CAAAECBAgQINB+gXXr1hXz5s0rJk2a1PIeOFwb7gn3Oq4va5cAACAASURBVAgQIECAAAECoxXoePgy2gG6nsCgQH9/f8sPyVUHEcuXLx8chq8ECBAgQIAAAQIECBAg0FCB8OmVZcuWbf0ky6xZs0r/XZijjz566zU+6dLQSTZsAgQIECBQEwHhS00mwjBGFti8eXPpg3HVQcvQ9sI/qBj6dhAgQIAAAQIECBAgQIBAWgLveMc7oj/k97a3vS2tIlVDgAABAgQIdEVA+NIVdp2OVaCvry96MB4allT9c+jTQYAAAQIECBAgQIAAAQLpCbzzne+M9phvfetb0ytURQQIECBAgEDHBYQvHSfX4XgE1q9fX0ycODF6OK46cBlsL/QV+nQQIECAAAECBAgQIECAQHoC73rXu6L95Vve8pb0ClURAQIECBAg0HEB4UvHyXU4XoFFixZFD8eDYUnVX0NfDgIECBAgQIAAAQIECBBIU+Dd7353tL9885vfnGaxqiJAgAABAgQ6KiB86Si3zqoQ2LJlSzFz5szoAbnq4CX0EfpyECBAgAABAgQIECBAgECaAu95z3uiveWb3vSmNItVFQECBAgQINBRAeFLR7l1VpXAwMBAMXXq1OghuaoAJrQd+nAQIECAAAECBAgQIECAQLoC733ve6N95Rvf+MZ0C1YZAQIECBAg0DEB4UvHqHVUtcDatWvbEsCE4CW07SBAgAABAgQIECBAgACBtAXe9773ReHLG97whrSLVh0BAgQIECDQEQHhS0eYddIugfDplCr/CrLQlk+8tGu2tEuAAAECBAgQIECAAIF6CSxdujQKX17/+tfXa5BGQ4AAAQIECDRSQPjSyGkz6G0Fwr/LsmjRomLixInRQ3Orfw1ZuDe04d942VbW9wQIECBAgAABAgQIEEhb4P3vf3+0j3zd616XdtGqI0CAAAECBDoiIHzpCLNOOiGwfv36oq+vr+jt7Y0enocLYcK14Z5wr4MAAQIECBAgQIAAAQIE8hL4wAc+EO0fX/va1+aFoFoCBAgQIECgLQLCl7awarSbAps3by76+/uLBQsWFDvvvHP0IH3sscdufS1cE651ECBAgAABAgQIECBAgECeAh/84AejPeNrXvOaPDFUTYAAAQIECFQqIHyplFNjdRPYc889owfpjRs31m2YxkOAAAECBAgQIECAAAECXRD40Ic+FO0ZX/3qV3dhJLokQIAAAQIEUhMQvqQ2o+rZTkD4sh2HHwgQIECAAAECBAgQIEBgG4EPf/jDUfjyqle9apsrfEuAAAECBAgQGJuA8GVsbu5qiIDwpSETZZgECBAgQIAAAQIECBDogsBHPvKRKHz5h3/4hy6MRJcECBAgQIBAagLCl9RmVD3bCeyxxx7Rg/SmTZu2u8YPBAgQIECAAAECBAgQIJCnwEc/+tFoz/jKV74yTwxVEyBAgAABApUKCF8q5dRY3QSEL3WbEeMhQIAAAQIECBAgQIBAfQQ+9rGPReHLK17xivoM0EgIECBAgACBxgoIXxo7dQbeioDwpRUl1xAgQIAAAQIECBAgQCBPgU984hNR+LJw4cI8MVRNgAABAgQIVCogfKmUU2N1E3jkIx8ZPUj/8Y9/rNswjYcAAQIECBAgQIAAAQIEuiDwyU9+Mtoz9vX1dWEkuiRAgAABAgRSExC+pDaj6tlOQPiyHYcfCBAgQIAAAQIECBAgQGAbgU996lNR+PLyl798myt8S4AAAQIECBAYm4DwZWxu7mqIgPClIRNlmAQIECBAgAABAgQIEOiCwKc//ekofJk/f34XRqJLAgQIECBAIDUB4UtqM6qe7QR233336EH6nnvu2e4aPxAgQIAAAQIECBAgQIBAngKf+cxnoj3jy172sjwxVE2AAAECBAhUKiB8qZRTY3UTEL7UbUaMhwABAgQIECBAgAABAvUR+OxnPxuFLy996UvrM0AjIUCAAAECBBorIHxp7NQZeCsCwpdWlFxDgAABAgQIECBAgACBPAU+97nPReHLS17ykjwxVE2AAAECBAhUKiB8qZRTY3UT2G233aIH6XvvvbduwzQeAgQIECBAgAABAgQIEOiCwOc///loz/iiF72oCyPRJQECBAgQIJCagPAltRlVz3YCwpftOPxAgAABAgQIECBAgAABAtsIfOELX4jClxe+8IXbXOFbAgQIECBAgMDYBIQvY3NzV0MEhC8NmSjDJECAAAECBAgQIECAQBcELrjggih8ecELXtCFkeiSAAECBAgQSE1A+JLajKpnOwHhy3YcfiBAgAABAgQIECBAgACBbQT6+/uj8OX888/f5grfEiBAgAABAgTGJiB8GZubuxoisOuuu0YP0ps3b27I6A2TAAECBAgQIECAAAECBNopsHz58mjPeN5557WzS20TIECAAAECmQgIXzKZ6FzLFL7kOvPqJkCAAAECBAgQIECAwMgCX/rSl6Lw5fnPf/7IN7qCAAECBAgQIDCCgPBlBCAvN1tA+NLs+TN6AgQIECBAgAABAgQItFPgwgsvjMKXc889t51dapsAAQIECBDIRED4kslE51rmIx7xiOhB+k9/+lOuHOomQIAAAQIECBAgQIAAgW0ELrroomjPeM4552xzhW8JECBAgAABAmMTEL6Mzc1dDREQvjRkogyTAAECBAgQIECAAAECXRD4yle+EoUvz33uc7swEl0SIECAAAECqQkIX1KbUfVsJyB82Y7DDwQIECBAgAABAgQIECCwjcDXvva1KHw5++yzt7nCtwQIECBAgACBsQkIX8bm5q6GCPT29kYP0vfdd19DRm+YBAgQIECAAAECBAgQINBOgYsvvjjaM5511lnt7FLbBAgQIECAQCYCwpdMJjrXMoUvuc68ugkQIECAAAECBAgQIDCywNe//vUofHnOc54z8o2uIECAAAECBAiMICB8GQHIy80WEL40e/6MngABAgQIECBAgAABAu0UuOSSS6Lw5cwzz2xnl9omQIAAAQIEMhEQvmQy0bmW+fCHPzx6kP7zn/+cK4e6CRAgQIAAAQIECBAgQGAbgUsvvTTaM55xxhnbXOFbAgQIECBAgMDYBIQvY3NzV0MEhC8NmSjDJECAAAECBAgQIECAQBcEvvnNb0bhy7Oe9awujESXBAgQIECAQGoCwpfUZlQ92wkIX7bj8AMBAgQIECBAgAABAgQIbCOwYsWKKHw5/fTTt7nCtwQIECBAgACBsQkIX8bm5q6GCEyePDl6kN6yZUtDRm+YBAgQIECAAAECBAgQINBOgcsuuyzaM5522mnt7FLbBAgQIECAQCYCwpdMJjrXMoUvuc68ugkQIECAAAECBAgQIDCywLe//e0ofHnGM54x8o2uIECAAAECBAiMICB8GQHIy80WEL40e/6MngABAgQIECBAgAABAu0UuPzyy6Pw5elPf3o7u9Q2AQIECBAgkImA8CWTic61TOFLrjOvbgIECBAgQIAAAQIECIwssHLlyih8OfXUU0e+0RUECBAgQIAAgREEhC8jAHm52QK77LJL9CD9l7/8pdlFGT0BAgQIECBAgAABAgQIVCKwatWqaM94yimnVNK2RggQIECAAIG8BYQvec9/8tULX5KfYgUSIECAAAECBAgQIEBgzALf/e53o/Blzpw5Y27PjQQIECBAgACBQQHhy6CEr0kKCF+SnFZFESBAgAABAgQIECBAoBKBK664IgpfTj755Era1ggBAgQIECCQt4DwJe/5T776SZMmRQ/S999/f/J1K5AAAQIECBAgQIAAAQIERha48soroz3jSSedNPKNriBAgAABAgQIjCAgfBkByMvNFhC+NHv+jJ4AAQIECBAgQIAAAQLtFFi9enUUvjzlKU9pZ5faJkCAAAECBDIREL5kMtG5lil8yXXm1U2AAAECBAgQIECAAIGRBa666qoofDnxxBNHvtEVBAgQIECAAIERBIQvIwB5udkCEydOjB6k//rXvza7KKMnQIAAAQIECBAgQIAAgUoErr766mjPeMIJJ1TStkYIECBAgACBvAWEL3nPf/LVC1+Sn2IFEiBAgAABAgQIECBAYMwCP/jBD6Lw5UlPetKY23MjAQIECBAgQGBQQPgyKOFrkgLClySnVVEECBAgQIAAAQIECBCoROCaa66Jwpfjjz++krY1QoAAAQIECOQtIHzJe/6Tr37nnXeOHqQfeOCB5OtWIAECBAgQIECAAAECBAiMLLBmzZpozzh79uyRb3QFAQIECBAgQGAEAeHLCEBebraA8KXZ82f0BAgQIECAAAECBAgQaKfAj370oyh8mTVrVju71DYBAgQIECCQiYDwJZOJzrVM4UuuM69uAgQIECBAgAABAgQIjCxw7bXXRuHLcccdN/KNriBAgAABAgQIjCAgfBkByMvNFthpp52iB+m//e1vzS7K6AkQIECAAAECBAgQIECgEoHrrrsu2jMee+yxlbStEQIECBAgQCBvAeFL3vOffPXCl+SnWIEECBAgQIAAAQIECBAYs8BPfvKTKHw55phjxtyeGwkQIECAAAECgwLCl0EJX5MUEL4kOa2KIkCAAAECBAgQIECAQCUCa9eujcKXo48+upK2NUKAAAECBAjkLSB8yXv+k69e+JL8FCuQAAECBAgQIECAAAECYxa4/vrro/Bl5syZY27PjQQIECBAgACBQQHhy6CEr0kKPOxhD4sepJMsVFEECBAgQIAAAQIECBAgMGqBG264IdozHnnkkaNuxw0ECBAgQIAAgaECwpehIn5OSkD4ktR0KoYAAQIECBAgQIAAAQKVCtx4441R+HLEEUdU2ofGCBAgQIAAgTwFhC95zns2VQtfsplqhRIgQIAAAQIECBAgQGDUAjfddFMUvjz+8Y8fdTtuIECAAAECBAgMFRC+DBXxc1ICPT090YN0UgUqhgABAgQIECBAgAABAgTGLHDzzTdHe8bDDjtszO018cZNmzYVy5YtK+bPn1/MmjWrmDJlSjFp0qSt/4Xvw7nwWrgmXOsgQIAAAQIEWhMQvrTm5KqGCghfGjpxhk2AAAECBAgQIECAAIEOCPzsZz+LwpfHPe5xHei5+12sW7eumDdv3taQZcKECZFD2bkQyoR7wr0OAgQIECBAYMcCwpcd+3i14QLCl4ZPoOETIECAAAECBAgQIECgjQK33HJLFDoceuihbeyx+01v3Lhx6ydZyvbLZYFL2blwb/g0TGjLQYAAAQIECJQLCF/KXZxNRKDsITGR0pRBgAABAgQIECBAgAABAuMUuPXWW6PwZcaMGeNstb63r1mzppg+fXpUc9neuZVzoa3QpoMAAQIECBCIBYQvsYkzCQmUPSwmVJ5SCBAgQIAAAQIECBAgQGAcAuvXr4+CiMc+9rHjaLG+t65YsaLo7e2N6i3bN4/mXGgztO0gQIAAAQIEthcQvmzv4afEBMoeGBMrUTkECBAgQIAAAQIECBAgMEaBgYGBKIw4+OCDx9hafW9bvXp1MXny5KjWsj3zWM6FtkMfDgIECBAgQOD/BIQv/2fhuwQFyh4aEyxTSQQIECBAgAABAgQIECAwBoHbb789CiQOOuigMbRU31s2bNhQTJs2LaqzbL88nnOhj9CXgwABAgQIEHhQQPhiJSQtUPbgmHTBiiNAgAABAgQIECBAgACBlgV+8YtfRKHEgQce2PL9Tbhw7ty5UY1le+UqzoW+HAQIECBAgMCDAsIXKyFpgbKHx6QLVhwBAgQIECBAgAABAgQItCxwxx13RMHEAQcc0PL9db9w1apVUX1l++Qqz4U+HQQIECBAgEBRCF+sgqQFhj5A9vT0JF2v4ggQIECAAAECBAgQIECgdYG77rorCiemT5/eegM1v3LOnDlRfUP3yVX/HPp0ECBAgAABAsIXayBxgaEPkcKXxCdceQQIECBAgAABAgQIEBiFwC9/+csonNhvv/1G0UJ9Lx0YGCjCHnjovrjdP4c+Q98OAgQIECCQu4BPvuS+AhKvf+hDpfAl8QlXHgECBAgQIECAAAECBEYhcPfdd0fhxKMf/ehRtFDfS5cuXRrVNnSP3K6fQ98OAgQIECCQu4DwJfcVkHj9Qx8khS+JT7jyCBAgQIAAAQIECBAgMAqBDRs2RAHFPvvsM4oW6nvp3Llzo9qG7pHb9XPo20GAAAECBHIXEL7kvgISr3/og+TDHvawxCtWHgECBAgQIECAAAECBAi0KvDrX/86Cij23nvvVm+v9XUzZsyIahu6R27Xz6FvBwECBAgQyF1A+JL7Cki8/qEPksKXxCdceQQIECBAgAABAgQIEBiFwG9+85sooJg2bdooWqjvpbvttltU29A9crt+Dn07CBAgQIBA7gLCl9xXQIL1b9q0qVi2bFkxf/780gfNWbNmbX0tXBOudRAgQIAAAQIECBBogsDixYtLn2/b9eapdifwnsDA/wfWgDVgDVgD1oA1kOcaWLJkybi3CMKXcRNqoC4C69atK+bNm1dMmjSp5U1SuDbcE+51ECBAgAABAgQIEKizgPAlz42/N3zMuzVgDVgD1oA1YA1YA51fA+HZe7yH8GW8gu7vusDGjRu3fpKlp6en5dBl6C9Y4d7wSZnQloMAAQIECBAgQIBAHQWEL53fdA/dN/jZHFgD1oA1YA1YA9aANZDHGhC+1HFHZEwdFVizZk0xffr0MYcuQ3+xDG2FNh0ECBAgQIAAAQIE6iYgfMljoz90j+Jn824NWAPWgDVgDVgD1kDn14DwpW67IePpqMCKFSuK3t7eyoKXwV/EQpuhbQcBAgQIECBAgACBOgkIXzq/6R7cI/jK3hqwBqwBa8AasAasgbzWgPClTjshY+mowOrVq4vJkydXHrwM/iIa2g59OAgQIECAAAECBAgQIEAgXYE//vGP0b7ykY98ZBIFDwwMFOP567kH98ej/Rr6vO2225IwVAQBAgQIEBiPgH/zZTx67u2KwIYNG4pp06ZFD8ijfSAc6frQR+jLQYAAAQIECBAgQIAAAQJpCtxzzz3R3nL33XdPptg5c+ZE9Y20Fx7v66FPBwECBAgQIFAUwheroHECc+fO7djDY+jLQYAAAQIECBAgQIAAAQJpCmzevDnaX+66667JFLty5cqovvGGKyPdv2rVqmT8FEKAAAECBMYjIHwZj557Oy4QHuJGetCr+nUPjh2fZh0SIECAAAECBAgQIECgIwJ/+tOfoj3mIx7xiI703alO/AHGTknrhwABAgQIbC8gfNnew081F/CR6ZpPkOERIECAAAECBAgQIECgQQL33XdfFL709vY2qIKRh+qv7h7ZyBUECBAgQKAdAsKXdqhqsy0C3fzHAkPfDgIECBAgQIAAAQIECBBIS2DLli1R+DJ58uS0iiyKYvXq1UWoq+q/KWKwvdB26MNBgAABAgQI/J+A8OX/LHxXc4GlS5e27UFx8IFxuK+hbwcBAgQIECBAgAABAgQIpCXwl7/8Jdpn7rLLLmkV+b/VrFixogif6hlu3zvW86HN0LaDAAECBAgQ2F5A+LK9h59qLNDJv6d26ENn6NtBgAABAgQIECBAgAABAmkJ3H///VEYMWnSpLSK3KaaNWvWFNOnT49qHroHbvXn0FZo00GAAAECBAjEAsKX2MSZmgrMmDGjsgfEVh8kB68LfTsIECBAgAABAgQIECBAIC2BBx54INpn7rzzzmkVOaSajRs3FvPnzy96enqi2gf3wCN9DfeGNkJbDgIECBAgQKBcQPhS7uJsDQV22223MT8YjvTgONLroW8HAQIECBAgQIAAAQIECKQl8Le//S3aZ+60005pFTlMNevWrSvmzZtXhE/6jLQnHnw9XBvuCfc6CBAgQIAAgR0LdDx8Wbx4ccu/qQ/+5u7rBGYTGPj/oFlrYMmSJTv+1derBAgQIECAAAECBAjUQmDoXuthD3tYLcbVqUGET68sW7Zs6ydZZs2aVfr+Q/iUS7jGJ106NSv6IUCAAIEUBIQv3tQvfbAa+vDp52a98W++uj9fIWh2ECBAgAABAgQIECBQf4Gy/VP9R92+EfJon62WCRAgQCAvAeGL8EX4Yg1YA21YA8KXvH4zVS0BAgQIECBAgEBzBYQN288dj+09/ESAAAECBMYqIHxpw5uuZQ8qznX/kwjmwBx0cg0IX8b625L7CBAgQIAAAQIECHRWoOwfnu/sCOrVW9m+qV4jNBoCBAgQINAMAeGL8MWnHqwBa6ANa0D40ozfBI2SAAECBAgQIECAwE477RTtiXJWEb7kPPtqJ0CAAIEqBToevlQ5eG3lJTAwMFCU/YmksgfDKs+FPm+77ba8sFVLgAABAgQIECBAgACBTAR23nnnKHx54IEHMqk+LrNsPx1f5QwBAgQIECAwkoDwZSQhr9dKYM6cOdFDcdmDYZXnQp8OAgQIECBAgAABAgQIEEhTYOLEidE+869//WuaxbZQVdl+uoXbXEKAAAECBAgMERC+DAHxY70FVq5cGT0Ulz0YVnlu1apV9UYxOgIECBAgQIAAAQIECBAYs8CkSZOifeb9998/5vaafmPZfrrpNRk/AQIECBDohoDwpRvq+hyXwNy5c6MH47KHwyrOhb4cBAgQIECAAAECBAgQIJCuwOTJk6M95pYtW9IteITKyvbSI9ziZQIECBAgQKBEQPhSguJUvQU2bNhQTJs2LXo4LntAHM+50Efoy0GAAAECBAgQIECAAAEC6Qo8/OEPj/aXf/7zn9MteITKyvbRI9ziZQIECBAgQKBEQPhSguJU/QVWr15dlP3ppLKHxLGcC22HPhwECBAgQIAAAQIECBAgkLZAb29vFL7cd999aRe9g+rK9tA7uNxLBAgQIECAwDACwpdhYJyuv8CKFSuKsofksgfF0ZwLbYa2HQQIECBAgAABAgQIECCQvsCuu+4ahS+bN29Ov/BhKizbPw9zqdMECBAgQIDADgSELzvA8VL9BdasWVNMnz49elAue1hs5VxoK7TpIECAAAECBAgQIECAAIE8BHbbbbdoT3nvvffmUXxJlWV755LLnCJAgAABAgRGEBC+jADk5foLbNy4sZg/f37R09MTPTCXPTSWnQv3hjZCWw4CBAgQIECAAAECBAgQyEdg9913j/aS99xzTz4AQyot2zMPucSPBAgQIECAQAsCwpcWkFzSDIF169YV8+bNKyZNmhQ9OJc9PIZz4dpwT7jXQYAAAQIECBAgQIAAAQL5Ceyxxx7RHnLTpk35QfxvxWX752wxFE6AAAECBMYhIHwZB55b6ykQPr2ybNmy4sUvfnH0AB0+4TJr1qytn3IJ1/ikSz3n0KgIECBAgAABAgQIECDQKYE999wz2jvmvFcUvnRq5emHAAECBFIXEL6kPsMZ1xf+gcShD43hH1J0ECBAgAABAgQIECBAgACBQYFHPepR0d7xD3/4w+DL2X0duo8OPzsIECBAgACB0Qv4HXT0Zu5oiIDwpSETZZgECBAgQIAAAQIECBDoosCUKVOi8OX3v/99F0fU3a6FL9311zsBAgQIpCMgfElnLlUyRODee++NHqB32223IVf5kQABAgQIECBAgAABAgRyFthrr72ivePvfve7bEmEL9lOvcIJECBAoGIB4UvFoJqrj4DwpT5zYSQECBAgQIAAAQIECBCoq8DUqVOj8OW3v/1tXYfb9nEJX9pOrAMCBAgQyERA+JLJROdYpvAlx1lXMwECBAgQIECAAAECBEYnsPfee0fhy29+85vRNZLQ1cKXhCZTKQQIECDQVQHhS1f5dd5OgXvuuSd6gN59993b2aW2CRAgQIAAAQIECBAgQKBhAvvss0+0d9ywYUPDqqhuuMKX6iy1RIAAAQJ5Cwhf8p7/pKsXviQ9vYojQIAAAQIECBAgQIBAJQL77rtvFL786le/qqTtJjYifGnirBkzAQIECNRRQPhSx1kxpkoEhC+VMGqEAAECBAgQIECAAAECSQs8+tGPjsKXu+++O+mad1Sc8GVHOl4jQIAAAQKtCwhfWrdyZcME/vjHP0YP0I985CMbVoXhEiBAgAABAgQIECBAgEA7BaZPnx7tHe+66652dlnrtoUvtZ4egyNAgACBBgkIXxo0WYY6OgHhy+i8XE2AAAECBAgQIECAAIEcBfbff/8ofLnzzjtzpNhas/Al26lXOAECBAhULCB8qRhUc/UREL7UZy6MhAABAgQIECBAgAABAnUVOOCAA6Lw5Y477qjrcNs+LuFL24l1QIAAAQKZCAhfMpnoHMvctGlT9AC9xx575EihZgIECBAgQIAAAQIECBAYRuCggw6K9o633377MFenf1r4kv4cq5AAAQIEOiMgfOmMs166ICB86QK6LgkQIECAAAECBAgQINAwgcc85jFR+HLbbbc1rIrqhit8qc5SSwQIECCQt4DwJe/5T7p64UvS06s4AgQIECBAgAABAgQIVCJw8MEHR+HLwMBAJW03sRHhSxNnzZgJECBAoI4Cwpc6zooxVSIgfKmEUSMECBAgQIAAAQIECBBIWmDGjBlR+HLrrbcmXfOOihO+7EjHawQIECBAoHUB4UvrVq5smMDGjRujB+g999yzYVUYLgECBAgQIECAAAECBAi0U+CQQw6J9o633HJLO7usddvCl1pPj8ERIECAQIMEhC8NmixDHZ2A8GV0Xq4mQIAAAQIECBAgQIBAjgKHHnpoFL78/Oc/z5Fia83Cl2ynXuEECBAgULGA8KViUM3VR0D4Up+5MBICBAgQIECAAAECBAjUVeCwww6Lwpebb765rsNt+7iEL20n1gEBAgQIZCIgfMlkonMs8w9/+EP0AP2oRz0qRwo1EyBAgAABAgQIECBAgMAwAo9//OOjveNNN900zNXpnxa+pD/HKiRAgACBzggIXzrjrJcuCAhfuoCuSwIECBAgQIAAAQIECDRM4PDDD4/Cl5/+9KcNq6K64QpfqrPUEgECBAjkLSB8yXv+k65e+JL09CqOAAECBAgQIECAAAEClQgceeSRUfhy4403shTjGQAAIABJREFUVtJ2ExsRvjRx1oyZAAECBOooIHyp46wYUyUC//M//xM9QP/d3/1dJW1rhAABAgQIECBAgAABAgTSEJg5c2a0d7z++uvTKG4MVQhfxoDmFgIECBAgUCIgfClBcSoNAeFLGvOoCgIECBAgQIAAAQIECLRT4KijjorCl3Xr1rWzy1q3LXyp9fQYHAECBAg0SED40qDJMtTRCQhfRuflagIECBAgQIAAAQIECOQocPTRR0fhy9q1a3Ok2Fqz8CXbqVc4AQIECFQsIHypGFRz9RH4/e9/Hz1AT5kypT4DNBICBAgQIECAAAECBAgQ6LrAscceG+0dr7vuuq6Pq1sDEL50S16/BAgQIJCagPAltRlVz0MCwpeHKHxDgAABAgQIECBAgAABAsMIPOEJT4jClx//+MfDXJ3+aeFL+nOsQgIECBDojIDwpTPOeumCgPClC+i6JECAAAECBAgQIECAQMMEjjvuuCh8ufbaaxtWRXXDFb5UZ6klAgQIEMhbQPiS9/wnXf3vfve76AF6r732SrpmxREgQIAAAQIECBAgQIDA6ARmz54d7R3XrFkzukYSulr4ktBkKoUAAQIEuiogfOkqv87bKSB8aaeutgkQIECAAAECBAgQIJCGwBOf+MQofPnhD3+YRnFjqEL4MgY0txAgQIAAgRIB4UsJilNpCAhf0phHVRAgQIAAAQIECBAgQKCdAscff3wUvlxzzTXt7LLWbQtfaj09BkeAAAECDRIQvjRosgx1dALCl9F5uZoAAQIECBAgQIAAAQI5CpxwwglR+HL11VfnSLG1ZuFLtlOvcAIECBCoWED4UjGo5uoj8Nvf/jZ6gJ46dWp9BmgkBAgQIECAAAECBAgQINB1gSc/+cnR3vGqq67q+ri6NQDhS7fk9UuAAAECqQkIX1KbUfU8JCB8eYjCNwQIECBAgAABAgQIECAwjMCJJ54YhS/f//73h7k6/dPCl/TnWIUECBAg0BkB4UtnnPXSBQHhSxfQdUmAAAECBAgQIECAAIGGCZx00klR+HLllVc2rIrqhit8qc5SSwQIECCQt4DwJe/5T7r63/zmN9ED9LRp05KuWXEECBAgQIAAAQIECBAgMDqBk08+Odo7XnHFFaNrJKGrhS8JTaZSCBAgQKCrAsKXrvLrvJ0Cwpd26mqbAAECBAgQIECAAAECaQg89alPjcKX733ve2kUN4YqhC9jQHMLAQIECBAoERC+lKA4lYaA8CWNeVQFAQIECBAgQIAAAQIE2ilwyimnROHLd7/73XZ2Weu2hS+1nh6DI0CAAIEGCQhfGjRZhjo6gV//+tfRA/Tee+89ukZcTYAAAQIECBAgQIAAAQJJC5x66qnR3nHlypVJ17yj4oQvO9LxGgECBAgQaF1A+NK6lSsbJiB8adiEGS4BAgQIECBAgAABAgS6IPC0pz0tCl++853vdGEk9ehS+FKPeTAKAgQIEGi+gPCl+XOogmEEhC/DwDhNgAABAgQIECBAgAABAg8JPP3pT4/Cl8svv/yh13P7RviS24yrlwABAgTaJSB8aZesdrsusGHDhugBep999un6uAyAAAECBAgQIECAAAECBOojcNppp0V7x8suu6w+A+zwSIQvHQbXHQECBAgkKyB8SXZqFSZ8sQYIECBAgAABAgQIECBAYCSBZz7zmVH48q1vfWuk25J9XfiS7NQqjAABAgQ6LCB86TC47jonIHzpnLWeCBAgQIAAAQIECBAg0FSB008/PQpfVqxY0dRyxj1u4cu4CTVAgAABAgS2CghfLIRkBX71q19FD9D77rtvsvUqjAABAgQIECBAgAABAgRGL3DGGWdEe8dLL7109A0lcofwJZGJVAYBAgQIdF1A+NL1KTCAdgkIX9olq10CBAgQIECAAAECBAikI/DsZz87Cl++8Y1vpFPgKCsRvowSzOUECBAgQGAYAeHLMDBON19A+NL8OVQBAQIECBAgQIAAAQIE2i1w5plnRuHLJZdc0u5ua9u+8KW2U2NgBAgQINAwAeFLwybMcFsXEL60buVKAgQIECBAgAABAgQI5Cpw1llnReHLxRdfnCtHZBHCGAcBAgQIECAwegG/g47ezB0NEbj77rujh8ZHP/rRDRm9YRIgQIAAAQIECBAgQIBAJwTmzp0b7R2/9rWvdaLrWvbhky+1nBaDIkCAAIEGCghfGjhphtyagPClNSdXESBAgAABAgQIECBAIGeBs88+OwpfvvrVr2ZLInzJduoVToAAAQIVCwhfKgbVXH0EhC/1mQsjIUCAAAECBAgQIECAQF0FzjnnnCh8ueiii+o63LaPS/jSdmIdECBAgEAmAsKXTCY6xzJ/+ctfRg/Q++23X44UaiZAgAABAgQIECBAgACBYQTOPffcaO944YUXDnN1+qdzCF82bdpULFu2rJg/f34xa9asYsqUKcWkSZO2/he+D+fCa+GacK2DAAECBAiMRUD4MhY19zRCQPjSiGkySAIECBAgQIAAAQIECHRV4HnPe14Uvnz5y1/u6pi62XnK4cu6deuKefPmbQ1ZyuosOxdCmXBPuNdBgAABAgRGIyB8GY2WaxslIHxp1HQZLAECBAgQIECAAAECBLoicN5550Xhy5e+9KWujKUOnZYFEHUY13jGsHHjxq2fZOnp6YnmuqzesnPh3vBpmNCWgwABAgQItCIgfGlFyTWNFLjrrruih6rp06c3shaDJkCAAAECBAgQIECAAIH2CJx//vnR3rG/v789nTWg1bLgoQHDHnaIa9asKcJ7AWV1jeVcaCu06SBAgAABAiMJCF9GEvJ6YwWEL42dOgMnQIAAAQIECBAgQIBAxwTCXyk19E34L37xix3rv24dDbUIPzf1WLFiRdHb2xvNb1mNozkX2gxtOwgQIECAwI4Emvs76I6q8hqBoiiEL5YBAQIECBAgQIAAAQIECIwk8IIXvCB6c/6CCy4Y6bZkXy8LIZpY7OrVq4vJkydHc1tW31jOhbZDHw4CBAgQIDCcgPBlOBnnGy9w5513Rg9Z+++/f+PrUgABAgQIECBAgAABAgQIVCfwohe9KNo7fv7zn6+ug4a1VBZENKyEYsOGDcW0adOieS2rbTznQh+hLwcBAgQIECgTEL6UqTiXhIDwJYlpVAQBAgQIECBAgAABAgTaKvDiF784epN+2bJlbe2zzo2XhRF1Hm/Z2ObOnRvNaVldVZwLfTkIECBAgECZgPClTMW5JASEL0lMoyIIECBAgAABAgQIECDQVoGXvOQl0Rv1n/vc59raZ50bLwsk6jzeoWNbtWpVNJ9lNVV5LvTpIECAAAECQwWEL0NF/JyMwB133BE9cB1wwAHJ1KcQAgQIECBAgAABAgQIEBi/wMte9rJo7/iZz3xm/A03tIWyUKJJpcyZMyeaz7KaqjwX+nQQIECAAIGhAsKXoSJ+TkZA+JLMVCqEAAECBAgQIECAAAECbRP4+7//++jN+v/+7/9uW391b7gslKj7mAfHNzAwUPT09ETzWVZTledCn6FvBwECBAgQ2FZA+LKthu+TEhC+JDWdiiFAgAABAgQIECBAgEBbBObPnx+9Wf/pT3+6LX01odGyUKIJ4w5jXLp0aTSXZfW041zo20GAAAECBLYVEL5sq+H7pASEL0lNp2IIECBAgAABAgQIECDQFoG+vr7oDftPfvKTbemrCY2WBRNNGHcY49y5c6O5LKunHedC3w4CBAgQILCtgPBlWw3fJyXwi1/8InroOvDAA5OqUTEECBAgQIAAAQIECBAgMD6BBQsWRHvHT3ziE+NrtMF3lwUTTSlnxowZ0VyW1dOOc6FvBwECBAgQ2FZA+LKthu+TEhC+JDWdiiFAgAABAgQIECBAgEBbBBYuXBi9Yf/xj3+8LX01odGyYKIJ4w5j3G233aK5LKunHedC3w4CBAgQILCtgPBlWw3fJyUgfElqOhVDgAABAgQIECBAgACBtgi88pWvjN6w/+hHP9qWvprQaFkw0YRxhzHutNNO0VyW1dOOc6FvBwECBAgQ2FZA+LKthu+TErj99tujh66DDjooqRoVQ4AAAQIECBAgkI/A4sWLo+fbdryBqM0JnCcw8P+BNWANWAPWgDVgDeS9BpYsWTLujYbwZdyEGqirgPClrjNjXAQIECBAgAABAmMREL7k/QaAN4DMvzVgDVgD1oA1YA1YA51bA+HZe7yH8GW8gu6vncDmzZuL/v7+4vzzz4/+xFr4GPDs2bOL8Hf6Ll++vAjXOggQIECAAAECBAg0QUD40rnNtjc2WFsD1oA1YA1YA9aANZD3GhC+NGGHZIwdE1i/fn3R19dX9Pb2RqHLcL9YhmvDPeFeBwECBAgQIECAAIE6Cwhf8n4DYLg9jfPWhTVgDVgD1oA1YA1YA9WvAeFLnXdGxtYxgS1bthSLFi0qJk6c2HLoMvQXpHBvaCO05SBAgAABAgQIECBQRwHhS/Wb6qH7Aj8ztgasAWvAGrAGrAFrwBoIa0D4UscdkTF1VGBgYKCYOXPmmEOXob+YhrZCmw4CBAgQIECAAAECBAgQyEPgta99bbSn/MAHPpBH8SVVDt0nh5+bdMyZMyeaz7KaqjwX+nQQIECAAIGhAs36HXTo6P2ctcDatWuLqVOnVv5QFdoMbTsIECBAgAABAgQIECBAIH2B17/+9dG+cunSpekXPkyFZaHEMJfW8vTKlSuj+Syrqcpzq1atqqWFQREgQIBAdwWEL9311/sYBcKnU9oRvAw+fIW2fQJmjJPjNgIECBAgQIAAAQIECDRI4J/+6Z+iN+v/67/+q0EVVDvUwX3xtl+r7aH9rc2dOzea023rqfL70JeDAAECBAiUCQhfylScq7VA+HdZqvyrxoZ76Ap9+Ddgar0UDI4AAQIECBAgQIAAAQLjFnjDG94QvVH/vve9b9ztNrWBsj1y02rZsGFDMW3atGhey2obz7nQR+jLQYAAAQIEygSEL2UqztVaYNGiRW1/gBp8+Ap9OQgQIECAAAECBAgQIEAgXYE3velN0R7zPe95T7oFj1DZ4H54268j3FLLl1evXl1Mnjw5mttt6xrP96Ht0IeDAAECBAgMJyB8GU7G+VoKrF+/vpg4cWLbHp6GPniFvkKfDgIECBAgQIAAAQIECBBIU6DsD/j953/+Z5rFtlDV0H1x+Lmpx4oVK4re3t7K30MIbYa2HQQIECBAYEcCzf0ddEdVeS1Zgb6+vsofmsoeLLc9F/p0ECBAgAABAgQIECBAgECaAm9+85ujfea73/3uNIttoapt98OD37dwW20vWbNmTTF9+vRojgdrG+3X0FZo00GAAAECBEYSEL6MJOT12ghs3ry5LX9iZaQHrfAnWkLfDgIECBAgQIAAAQIECBBIT+Ctb31r9Mb8O9/5zvQKbbGisj1yi7fW9rKNGzcW8+fPL3p6eqK5Lqu37Fy4N7QR2nIQIECAAIFWBIQvrSi5phYC/f39Y35IKntwGs250LeDAAECBAgQIECAAAECBNIT+Od//udor/mOd7wjvUJbrKhsr9zirbW/bN26dcW8efOKSZMmRXNeVnc4F64N94R7HQQIECBAYDQCwpfRaLm2qwILFixo+eFouIemsZ5fuHBhV2vXOQECBAgQIECAAAECBAi0R+Btb3tbtNd8+9vf3p7OGtBq2b65AcMe1RDDp1eWLVu29ZMss2bNiuY/GIRPuYRrfNJlVLQuJkCAAIFtBIQv22D4tt4Cs2fPLn0gKnswrPpc6NtBgAABAgQIECBAgAABAukJ/Ou//mu01/z3f//39AptsaKy/XSLtzb2shxrbuxkGTgBAgQaJNDx8GXx4sXRQ03Zb3LOTeA0gYH/D5q7BpYsWdKg3woMlQABAgQIECBAgEC+Av/v//2/aP/9b//2b9mClO1DU8fIsebU51R9BAgQqIOA8MUb/NFDZtlDh3PNDQHMXXfmLgTNDgIECBAgQIAAAQIE6i9Q9odEc/7DVGV7yPrP4vhGmGPN4xNzNwECBAi0IiB8Eb4IX6wBa6ANa0D40spvQa4hQIAAAQIECBAg0H2B8CmXoW++5/w8P9Qi/Jz6kWPNqc+p+ggQIFAHgY7/Dlr2J0rKfpNzrjt/Wp87d2ugmjWQ82atDr+5GQMBAgQIECBAgACBVgXCv+8ydB8U/h2YXI+hFuHn1I8ca059TtVHgACBOgh0/HdQ4Us1b+yWPRg4x9YaqM8aEL7U4bc4YyBAgAABAgQIECAwssB//Md/ROHLv/zLv4x8Y6JXlO0rEy31obJyrPmh4n1DgAABAm0T6Hj40rZKNJy8wIIFC6IH4rIHpHacW7hwYfK+CiRAgAABAgQIECBAgECOAm9/+9ujvebb3va2HCm21ly2p04dI8eaU59T9REgQKAOAsKXOsyCMbQk0N/fHz0Qlz0gtePc8uXLWxqjiwgQIECAAAECBAgQIECgWQLvfOc7o73mW9/61mYVUeFoy/bUFTZfy6ZyrLmWE2FQBAgQSExA+JLYhKZczubNm4ve3t7oobjsIanKc6HP0LeDAAECBAgQIECAAAECBNITeNe73hXtM9/ylrekV2iLFZXtp1u8tbGX5VhzYyfLwAkQINAgAeFLgybLUIuir68veigue0iq8lzo00GAAAECBAgQIECAAAECaQq8+93vjvaZb37zm9MstoWqyvbTLdzW6EtyrLnRE2bwBAgQaIiA8KUhE2WYDwqsX7++mDhxYvRgXPagVMW50Ffo00GAAAECBAgQIECAAAECaQq85z3vifaYb3rTm9IstoWqyvbSLdzW6EtyrLnRE2bwBAgQaIiA8KUhE2WY/yewaNGi6MG47EGpinOhLwcBAgQIECBAgAABAgQIpCvw3ve+N9pjvvGNb0y34BEqK9tLj3BL41/OsebGT5oCCBAg0AAB4UsDJskQtxfYsmVLMXPmzOjhuOxhaTznQh+hLwcBAgQIECBAgAABAgQIpCvwvve9L9pfvuENb0i34BEqK9tHj3BL41/OsebGT5oCCBAg0AAB4UsDJskQY4GBgYFi6tSp0QNy2QPTWM6FtkMfDgIECBAgQIAAAQIECBBIW2Dp0qXR3vL1r3992kXvoLqyPfQOLk/ipRxrTmLiFEGAAIGaCwhfaj5Bhje8wNq1a9sSwITgJbTtIECAAAECBAgQIECAAIH0Bd7//vdH4cvrXve69AsfpsIcg4gcax5m+p0mQIAAgQoFhC8VYmqq8wLh0ylV/hVkoS2feOn8POqRAAECBAgQIECAAAEC3RL4wAc+EIUvr33ta7s1nK73m2MQkWPNXV9oBkCAAIEMBIQvGUxy6iWGf5dl0aJFxcSJE6MH5rIHqLJz4d7Qhn/jJfXVoj4CBAgQIECAAAECBAhsL/DBD34w2ku+5jWv2f6ijH4q2zOnXn6ONac+p+ojQIBAHQSEL3WYBWOoRGD9+vVFX19f0dvbGz04lz1IhXPh2nBPuNdBgAABAgQIECBAgAABAvkJfOhDH4r2kK9+9avzg/jfisv2z6lj5Fhz6nOqPgIECNRBQPhSh1kwhkoFNm/eXPT39xfnnntu9AC98847F7Nnzy4WLFiw9ZpwrYMAAQIECBAgQIAAAQIE8hX48Ic/HO0dX/WqV2ULkmMQkWPN2S5whRMgQKCDAsKXDmLrqrMCP/3pT6MH6MMPP7yzg9AbAQIECBAgQIAAAQIECNRa4CMf+Ui0d/zHf/zHWo+5nYPLMYjIseZ2riFtEyBAgMCDAsIXKyFZgRtvvDF6gD7iiCOSrVdhBAgQIECAAAECBAgQIDB6gY9+9KPR3vGVr3zl6BtK5I4cg4gca05kuSqDAAECtRYQvtR6egxuPALCl/HouZcAAQIECBAgQIAAAQJ5CHzsYx+LwpdXvOIVeRRfUmWOQUSONZdMvVMECBAgULGA8KViUM3VR0D4Up+5MBICBAgQIECAAAECBAjUVeDjH/94FL4sXLiwrsNt+7hyDCJyrLntC0kHBAgQIFAIXyyCZAVuuOGG6AH6yCOPTLZehREgQIAAAQIECBAgQIDA6AU++clPRnvHvr6+0TeUyB05BhE51pzIclUGAQIEai0gfKn19BjceASEL+PRcy8BAgQIECBAgAABAgTyEPjUpz4VhS8vf/nL8yi+pMocg4gcay6ZeqcIECBAoGIB4UvFoJqrj4DwpT5zYSQECBAgQIAAAQIECBCoq8CnP/3pKHyZP39+XYfb9nHlGETkWHPbF5IOCBAgQMBfO2YNpCtw/fXXRw/QM2fOTLdglREgQIAAAQIECBAgQIDAqAU+85nPRHvHl73sZaNuJ5Ubcgwicqw5lfWqDgIECNRZwCdf6jw7xjYuAeHLuPjcTIAAAQIECBAgQIAAgSwEPvvZz0bhy0tf+tIsai8rMscgIseay+beOQIECBCoVkD4Uq2n1mokIHyp0WQYCgECBAgQIECAAAECBGoq8LnPfS4KX17ykpfUdLTtH1aOQUSONbd/JemBAAECBIQv1kCyAsKXZKdWYQQIECBAgAABAgQIEKhM4POf/3wUvrzoRS+qrP2mNZRjEJFjzU1bl8ZLgACBJgoIX5o4a8bcksC6deuiB+ijjjqqpXtdRIAAAQIECBAgQIAAAQJ5CHzhC1+I9o4vfOEL8yi+pMocg4gcay6ZeqcIECBAoGIB4UvFoJqrj4DwpT5zYSQECBAgQIAAAQIECBCoq8AFF1wQhS8veMEL6jrcto8rxyAix5rbvpB0QIAAAQKF8MUiSFZA+JLs1CqMAAECBAgQIECAAAEClQn09/dH4cv5559fWftNayjHICLHmpu2Lo2XAAECTRQQvjRx1oy5JYG1a9dGD9BHH310S/e6iAABAgQIECBAgAABAgTyEFi+fHm0dzzvvPPyKL6kyhyDiBxrLpl6pwgQIECgYgHhS8WgmquPgPClPnNhJAQIECBAgAABAgQIEKirwJe+9KUofHn+859f1+G2fVw5BhE51tz2haQDAgQIEPDXjlkD6QoIX9KdW5URIECAAAECBAgQIECgKoELL7wwCl+e97znVdV849rJMYjIsebGLUwDJkCAQAMFfPKlgZNmyK0J/OQnP4keoI855pjWbnYVAQIECBAgQIAAAQIECGQhcNFFF0V7x3POOSeL2suKzDGIyLHmsrl3jgABAgSqFRC+VOuptRoJCF9qNBmGQoAAAQIECBAgQIAAgZoKfOUrX4nCl+c+97k1HW37h5VjEJFjze1fSXogQIAAAeGLNZCsgPAl2alVGAECBAgQIECAAAECBCoT+OpXvxqFL2effXZl7TetoRyDiBxrbtq6NF4CBAg0UUD40sRZM+aWBK677rroAfrYY49t6V4XESBAgAABAgQIECBAgEAeAhdffHG0dzzrrLPyKL6kyhyDiBxrLpl6pwgQIECgYgHhS8WgmquPgPClPnNhJAQIECBAgAABAgQIEKirwNe//vUofHnOc55T1+G2fVw5BhE51tz2haQDAgQIECiELxZBsgLCl2SnVmEECBAgQIAAAQIECBCoTOCSSy6Jwpczzzyzsvab1lCOQUSONTdtXRovAQIEmiggfGnirBlzSwI//vGPowfoJzzhCS3d6yICBAgQIECAAAECBAgQyEPg0ksvjfaOZ5xxRh7Fl1SZYxCRY80lU+8UAQIECFQsIHypGFRz9REQvtRnLoyEAAECBAgQIECAAAECdRX45je/GYUvz3rWs+o63LaPK8cgIsea276QdECAAAEC/toxayBdAeFLunOrMgIECBAgQIAAAQIECFQlsGLFiih8Of3006tqvnHt5BhE5Fhz4xamARMgQKCBAj750sBJM+TWBIQvrTm5igABAgQIECBAgAABAjkLXHbZZVH4ctppp2VLkmMQkWPN2S5whRMgQKCDAsKXDmLrqrMC1157bfQAfdxxx3V2EHojQIAAAQIECBAgQIAAgVoLfPvb3472js94xjNqPeZ2Di7HICLHmtu5hrRNgAABAg8KCF+shGQFhC/JTq3CCBAgQIAAAQIECBAgUJnA5ZdfHoUvT3/60ytrv2kN5RhE5Fhz09al8RIgQKCJAsKXJs6aMbckIHxpiclFBAgQIECAAAECBAgQyFpg5cqVUfhy6qmnZmuSYxCRY83ZLnCFEyBAoIMCwpcOYuuqswI/+tGPogfoWbNmdXYQeiNAgAABAgQIECBAgACBWgusWrUq2juecsoptR5zOweXYxCRY83tXEPaJkCAAIEHBYQvVkKyAsKXZKdWYQQIECBAgAABAgQIEKhM4Lvf/W4UvsyZM6ey9pvWUI5BRI41N21dGi8BAgSaKCB8aeKsGXNLAsKXlphcRIAAAQIECBAgQIAAgawFrrjiiih8eepTn5qtSY5BRI41Z7vAFU6AAIEOCghfOoitq84KrFmzJnqAnj17dmcHoTcCBAgQIECAAAECBAgQqLXAlVdeGe0dTzrppFqPuZ2DyzGIyLHmdq4hbRMgQIDAgwLCFyshWQHhS7JTqzACBAgQIECAAAECBAhUJrB69eoofHnKU55SWftNayjHICLHmpu2Lo2XAAECTRQQvjRx1oy5JQHhS0tMLiJAgAABAgQIECBAgEDWAt///vej8OXEE0/M1iTHICLHmrNd4AonQIBABwWELx3E1lVnBX74wx9GD9BPfOITOzsIvREgQIAAAQIECBAgQIBArQWuvvrqaO94wgkn1HrM7RxcjkFEjjW3cw1pmwABAgQeFBC+WAnJCghfkp1ahREgQIAAAQIECBAgQKAygR/84AdR+PKkJz2psvab1lCOQUSONTdtXRovAQIEmiggfGnirBlzSwLCl5aYXESAAAECBAgQIECAAIGsBa655poofDn++OOzNckxiMix5mwXuMIJECDQQQHhSwexddVZAQ/QnfXWGwECBAgQIECAAAECBJoo4N8L3X7Wcgwicqx5+1n3EwECBAi0Q0BznaQlAAAgAElEQVT40g5VbdZCQPhSi2kwCAIECBAgQIAAAQIECNRa4Ec/+lH0yZdZs2bVesztHFyOQUSONbdzDWmbAAECBB4UEL5YCckKCF+SnVqFESBAgAABAgQIECBAoDKBa6+9NgpfjjvuuMrab1pDOQYROdbctHVpvAQIEGiigPClibNmzC0JCF9aYnIRAQIECBAgQIAAAQIEsha47rrrovDl2GOPzdYkxyAix5qzXeAKJ0CAQAcFhC8dxNZVZwV+8IMfRA/QT3rSkzo7CL0RIECAAAECBAgQIECAQK0FfvKTn0R7x2OOOabWY27n4HIMInKsuZ1rSNsECBAg8KCA8MVKSFZA+JLs1CqMAAECBAgQIECAAAEClQmsXbs2Cl+OPvroytpvWkM5BhE51ty0dWm8BAgQaKKA8KWJs2bMLQkIX1pichEBAgQIECBAgAABAgSyFrj++uuj8GXmzJnZmuQYRORYc7YLXOEECBDooIDwpYPYuuqswNVXXx09QJ9wwgmdHYTeCBAgQIAAAQIECBAgQKDWAjfccEO0dzzyyCNrPeZ2Di7HICLHmtu5hrRNgAABAg8KCF+shGQFhC/JTq3CCBAgQIAAAQIECBAgUJnAjTfeGIUvRxxxRGXtN62hHIOIHGtu2ro0XgIECDRRQPjSxFkz5pYEhC8tMbmIAAECBAgQIECAAAECWQvcdNNNUfhy+OGHZ2uSYxCRY83ZLnCFEyBAoIMCwpcOYuuqswJXXXVV9AD95Cc/ubOD0BsBAgQIECBAgAABAgQI1Frg5ptvjvaOhx12WK3H3M7B5RhE5FhzO9eQtgkQIEDgQQHhi5WQrIDwJdmpVRgBAgQIECBAgAABAgQqE/jZz34WhS+Pe9zjKmv//7N3L3BWVvXi/x1kJhhRFBUs4yDHUDt6LDtB1imDc1JPeaM0jbw2AmYWKCje7zc0RTPNa5mk4iXNLOmiWMHp6IQe0FA7Mih5wQ4ahECI2Hl+ry//9v+1fdaambWf/VzWWt/Per18zexnP89a3+97re3ez/oyM6F1pLEQoTHn0NYl8SKAAAIhClB8CXHWiNlJgOKLExMnIYAAAggggAACCCCAAAKqBf7whz8YxZedd95ZrYnGQkSMOa9cuTKZOXNm0tHRkYwcOTLZZpttkra2to3/yfdyTJ6Tc+RcGgIIIIBA/gIUX/I3pUdPBObNm2d8gP7kJz/pSXSEgQACCCCAAAIIIIAAAggg4IPA888/b9w7jhgxwofQKokhxkJEb5Ax5bxw4cJk3LhxG4sstrxsx6QoI9fItTQEEEAAgfwEKL7kZ0lPnglQfPFsQggHAQQQQAABBBBAAAEEEPBQYPHixUbx5QMf+ICHkZYTkm1zvpyRqxslhpxXrFix8SdZWlpajPVsy892TK6Vn4aRvmgIIIAAAs0LUHxp3pAePBWg+OLpxBAWAggggAACCCCAAAIIIOCRQFdXl7FZveOOO3oUYbmh2Dbly42g/NFCz7mzszMZOnSosY5tebkck76kTxoCCCCAQHMCFF+a8+NqjwXmzp1rfPD41Kc+5XHEhIYAAggggAACCCCAAAIIIFC2wAsvvGDcOw4fPrzsMLwZz7Y5701wBQUScs6zZ89O2tvbjTVsy6mRY9Kn9E1DAAEEEMguQPElux1Xei5A8cXzCSI8BBBAAAEEEEAAAQQQQMADgRdffNHYuN5hhx08iKyaEGwb9NVEUt6ooeYs+x79+vUz1q8tnyzHpG8Zg4YAAgggkE2A4ks2N64KQIDiSwCTRIgIIIAAAggggAACCCCAQMUCS5cuNTavhw0bVnFU1Q1v26SvLppyRg4x52XLliVDhgwx1q4tl2aOyRgyFg0BBBBAoHEBii+Nm3FFIAIUXwKZKMJEAAEEEEAAAQQQQAABBCoUeOmll4wNbPmbF1qbbaM+dosQcx47dqyxbm155HFMxqIhgAACCDQuQPGlcTOuCETgN7/5jfFBZK+99gokesJEAAEEEEAAAQQQQAABBBAoQ+Dll1827h3f//73lzG0l2PYNuu9DDTHoELLec6cOcaateWQ5zEZk4YAAggg0JgAxZfGvDg7IAGKLwFNFqEigAACCCCAAAIIIIAAAhUJvPLKK8ZG9vbbb19RNNUPa9uwrz6qYiMILecxY8YYa9aWQ57HZEwaAggggEBjAhRfGvPi7IAEKL4ENFmEigACCCCAAAIIIIAAAghUJCB/zyK9Sf3e9763omiqHzZtIY9jbyHl3NXVlbS0tBhr1pZDnsdkTBmbhgACCCDgLhD/O6i7BWdGJvDrX//a+DDy6U9/OrIsSQcBBBBAAAEEEEAAAQQQQKAZgddee824d9xuu+2a6TLoa20b9kEn5BB8SDnPmDHDWK+2+Is4JmPTEEAAAQTcBSi+uFtxZmACFF8CmzDCRQABBBBAAAEEEOhR4Nxzz61sw62ITTz63IT53AQDXgesAdYAa4A1wBpgDfi5Bs4777weP5u7PEnxxUWJc4IUoPgS5LQRNAIIIIAAAggggEA3AhRf/LwxZ8OEeWENsAZYA6wB1gBrgDUQ3xqQz97NNoovzQpyvbcCv/rVr4x/STZ69Ghv4yUwBBBAAAEEEEAAAQR6EqD4Et9NPRs1zClrgDXAGmANsAZYA6wBP9cAxZee7kx4Tr0AxRf1SwAABBBAAAEEEEAgKgGKL37emLNhwrywBlgDrAHWAGuANcAaiG8NUHyJ6laKZPIWoPiStyj9IYAAAggggAACCFQpQPElvpt6NmqYU9YAa4A1wBpgDbAGWAN+rgGKL1Xe+TC2twIrV65MZs6cmXz2s581fu1Ya2trMnLkyKSjo2PjOXIuDQEEEEAAAQQQQAABBBBAQK+A3BemN7623HJLtSBpC3kcewsp5xEjRhjr1RZ/Ecd22mmn2JcC+SGAAAK5CsT/DporF535LLBw4cJk3LhxSVtbm/MHETlXrpFraQgggAACCCCAAAIIIIAAAvoE/vKXvxj3kAMHDtQH8feMbZv2sWOElPPYsWON9WqLv4hjMjYNAQQQQMBdgOKLuxVneiqwYsWKjT/J0tLSkvkDiFwrPw0jfdEQQAABBBBAAAEEEEAAAQT0CKxatcq4l9xiiy30AKQytW3ap06J7mFIOc+YMcNYr7b4izgmY9MQQAABBNwFKL64W3GmhwKdnZ3J0KFDc/vgIX1JnzQEEEAAAQQQQAABBBBAAAEdAqtXrzbuKQcMGKAjeUuWtk17y2lRHQop566urqSZf3xqy9XlmIy5ZMmSqOadZBBAAIGiBSi+FC1M/4UJzJ49O2lvbzc+JLt8aOjpHOlT+qYhgAACCCCAAAIIIIAAAgjEL7BmzRrjvnKzzTaLP/FuMrTdL3dzajSHQ8t5zJgxxpq15ZDnMRmThgACCCDQmADFl8a8ONsTgblz5yb9+vUr7MOG9C1j0BBAAAEEEEAAAQQQQAABBOIWWLt2rXFvKf8oT2uzbdjHbhFazo888oixZm055Hlszpw5sS8D8kMAAQRyF6D4kjspHRYtsGzZsmTIkCGFf9CQMWQsGgIIIIAAAggggAACCCCAQLwC69atM+4v5R/kaW22DfvYLULMeezYsca6teWRxzEZi4YAAggg0LgAxZfGzbiiYgE+YFQ8AQyPAAIIIIAAAggggAACCEQk8NZbbxmb2O95z3siyrCxVGyb9Y31EN7ZIebMP0wNb50RMQII6BOg+KJvzoPOWH7M1fahqMhj/Ght0EuG4BFAAAEEEEAAAQQQQACBHgXWr19v3Ge2tbX1eE3MT9rur2POV3ILNWd+JXvsK5P8EEAgdAGKL6HPoLL4+aNyyiacdBFAAAEEEEAAAQQQQACBggU2bNhgbL737du34FH97T7UQkQzoiHnPHv27ET+RpEth2aOSZ/SNw0BBBBAILsAxZfsdlxZskBXV1fS0tKS+weK3j6MyJgyNg0BBBBAAAEEEEAAAQQQQCA+gXfeece4z9x0003jS9QxI9s9suOlwZ4Wes6dnZ3J0KFDjXVsy8vlmPQlfdIQQAABBJoToPjSnB9XlygwY8aM3D5IuHzYqD9HxqYhgAACCCCAAAIIIIAAAgjEKVB//yff9+nTJ85EHbJKW8jj2FsMOa9YsSLp6Oho6h+tyj8+lT6kLxoCCCCAQPMC8b+DNm9ED54IjB07trLii4xNQwABBBBAAAEEEEAAAQQQiFMgvfkum9BaW9qC4ktYK2HhwoXJuHHjEvm7Rba5tB2Tc+UauZaGAAIIIJCfQOnFl3PPPdf5f/62NwSObYLfJhjwOvB/DZx33nn5/Z+anhBAAAEEEEAAAQQQQKBQAds9VqEDety5RosYc5afXpk5c+bGn2QZOXKkdS9JfspFzuEnXTx+QRIaAggELUDxhY186xuw7YMHx/zf8GeO/JkjKTTTEEAAAQQQQAABBBBAIAwB298XDSPy/KO03VfmP4pfPWrIWUOOfq0qokEAAQSShOILxReKL6wB1kABa4DiC2+xCCCAAAIIIIAAAgiEIyB/4yW9OR1O9PlGmnaQx7E3DTlryDH2dUp+CCAQnkDp76D82jF//mW+7Y2XY8wPayCfNUDxJbw3RCJGAAEEEEAAAQQQ0CvQt29fo/iyYcMGlSC2e8LYITTkrCHH2Ncp+SGAQHgCFF8K+Bfvtjc0juWzoY0jjqGsAYov4b0hEjECCCCAAAIIIICAXoHW1laj+PL222+rBLHdc8UOoSFnDTnGvk7JDwEEwhMovfgSHhER+yIwduxY48Ow7cNDEcdkbBoCCCCAAAIIIIAAAggggECcAm1tbcb95vr16+NMtpesbPfUvVwS/NMactaQY/ALkQQQQCA6AYov0U1pvAnNmDHD+DBs+/BQxDEZm4YAAggggAACCCCAAAIIIBCnQL9+/Yz7zXXr1sWZbC9Z2e6pe7kk+Kc15Kwhx+AXIgkggEB0AhRfopvSeBPq6upKWlpajA/Etg8QeR6TMZcsWRIvLJkhgAACCCCAAAIIIIAAAsoF+vfvb9xr/vWvf1WpYrufjh1CQ84acox9nZIfAgiEJ0DxJbw5Ux3xmDFjjA/Etg8QeR6TMWkIIIAAAggggAACCCCAAALxCrS3txv3mmvXro034R4ys91P93B6FE9pyFlDjlEsRpJAAIGoBCi+RDWd8SfzyCOPGB+IbR8g8jw2Z86c+GHJEAEEEEAAAQQQQAABBBBQLDBgwADjXnP16tUqRWz307FDaMhZQ46xr1PyQwCB8AQovoQ3Z+ojHjt2rPGh2PYhIo9jMhYNAQQQQAABBBBAAAEEEEAgboHNN9/cuM9888034066m+xs99LdnBrNYQ05a8gxmgVJIgggEI0AxZdoplJPIsuWLUuGDBlifDC2fZBo5piMIWPREEAAAQQQQAABBBBAAAEE4hbYYostjHvMVatWxZ10N9nZ7qO7OTWawxpy1pBjNAuSRBBAIBoBii/RTKWuRObOnZv069fP+HBs+zCR5Zj0LWPQEEAAAQQQQAABBBBAAAEE4hfYcsstjfvLlStXxp+4JUPbPbTltKgOachZQ45RLUqSQQCBKAQovkQxjTqTmD17dmL7o4i2DxSNHJM+pW8aAggggAACCCCAAAIIIICADoGtttrKKL6sWLFCR/KpLG33z6lTonuoIWcNOUa3MEkIAQSCF6D4EvwU6k6gs7MzGTp0qPEh2fahwuWY9CV90hBAAAEEEEAAAQQQQAABBPQIDBo0yLiv/POf/6wHoC5T271z3dNRfqshZw05Rrk4SQoBBIIWoPgS9PQRvAjIv0bq6OhIWlpajA/Ltg8XtmNyrfSh9V82sZIQQAABBBBAAAEEEEAAAc0C22yzjXE/+cYbb6gksd0zxw6hIWcNOca+TskPAQTCE6D4Et6cEXE3AgsXLkzGjRuXtLW1GR+abR8y5JicK9fItTQEEEAAAQQQQAABBBBAAAGdAttuu61xH7l8+XKVGLb759ghNOSsIcfY1yn5IYBAeAIUX8KbMyLuRUB+emXmzJnJPvvsY3x4lmLLyJEjN/6Ui5zDT7r0gsnTCCCAAAIIIIAAAggggIACgcGDBxv3j//7v/+rIHMzRY2b9Bpy1pCjuZo5ggACCFQrQPGlWn9GL1DgoYceMj48f+5znytwRLpGAAEEEEAAAQQQQAABBBAIUWDIkCHG/eOf/vSnEFNpOmaNm/QactaQY9OLnw4QQACBnAUovuQMSnf+CPz0pz81Pjzvt99+/gRIJAgggAACCCCAAAIIIIAAAl4IvPe97zXuH5ctW+ZFbGUHoXGTXkPOGnIs+7XCeAgggEBvAhRfehPi+WAFKL4EO3UEjgACCCCAAAIIIIAAAgiUKvC+973PKL68+uqrpcbgy2AaN+k15KwhR19eQ8SBAAII1AQovtQk+BqdAMWX6KaUhBBAAAEEEEAAAQQQQACBQgS23357o/jyyiuvFDKW751q3KTXkLOGHH1/bREfAgjoE6D4om/O1WT8k5/8xPjwvP/++6vJn0QRQAABBBBAAAEEEEAAAQTcBIYOHWrcP7700ktuF0d2lsZNeg05a8gxspci6SCAQAQCFF8imERSsAtQfLG7cBQBBBBAAAEEEEAAAQQQQODdAv/wD/9gFF/++Mc/vvskJY80btJryFlDjkpeoqSJAAIBCVB8CWiyCLUxAYovjXlxNgIIIIAAAggggAACCCCgVWDYsGFG8WXp0qUqOTRu0mvIWUOOKl+wJI0AAl4LUHzxenoIrhkBii/N6HEtAggggAACCCCAAAIIIKBHYPjw4Ubx5YUXXtADUJepxk16DTlryLFuGfMtAggg4IUAxRcvpoEgihB48MEHjQ/PBxxwQBFD0ScCCCCAAAIIIIAAAggggEDAAv/4j/9o3D8uWbIk4Iyyh65xk15DzhpyzL7quRIBBBAoRoDiSzGu9OqBAMUXDyaBEBBAAAEEEEAAAQQQQACBAAR23HFHo/jS1dUVQOT5h6hxk15DzhpyzP/VQI8IIIBAcwIUX5rz42qPBSi+eDw5hIYAAggggAACCCCAAAIIeCQwYsQIo/jy/PPPexRheaFo3KTXkLOGHMt7lTASAggg4CZA8cXNibMCFPjxj39sfHg+8MADA8yEkBFAAAEEEEAAAQQQQAABBIoU2GmnnYz7x//5n/8pckhv+9a4Sa8hZw05evuiIjAEEFArQPFF7dTHnzjFl/jnmAwRQAABBBBAAAEEEEAAgTwEdt55Z6P48oc//CGProPrQ+MmvYacNeQY3IuNgBFAIHoBii/RT7HeBCm+6J17MkcAAQQQQAABBBBAAAEEGhH44Ac/aBRfnnvuuUa6iOZcjZv0GnLWkGM0L0ISQQCBaAQovkQzlSSSFnjggQeMD88HHXRQ+jQeI4AAAggggAACCCCAAAIIKBf4p3/6J+P+8ZlnnlGponGTXkPOGnJU+YIlaQQQ8FqA4ovX00NwzQhQfGlGj2sRQAABBBBAAAEEEEAAAT0Cu+66q1F8WbRokR6Aukw1btJryFlDjnXLmG8RQAABLwQovngxDQRRhADFlyJU6RMBBBBAAAEEEEAAAQQQiE9gt912M4ovv//97+NL1CEjjZv0GnLWkKPD8uYUBBBAoFQBii+lcjNYmQI/+tGPjA/PY8eOLTMExkIAAQQQQAABBBBAAAEEEAhAYPfddzfuH5966qkAIs8/RI2b9Bpy1pBj/q8GekQAAQSaE6D40pwfV3ssQPHF48khNAQQQAABBBBAAAEEEEDAI4EPfehDRvFl4cKFHkVYXigaN+k15Kwhx/JeJYyEAAIIuAlQfHFz4qwABSi+BDhphIwAAggggAACCCCAAAIIVCDw4Q9/2Ci+LFiwoIJIqh9S4ya9hpw15Fj9q4cIEEAAgXcLUHx5twePIhK4//77jQ/Pn//85yPKkFQQQAABBBBAAAEEEEAAAQTyEPjIRz5i3D8++eSTeXQdXB8aN+k15Kwhx+BebASMAALRC1B8iX6K9SZI8UXv3JM5AggggAACCCCAAAIIINCIwL/8y78YxZcnnniikS6iOVfjJr2GnDXkGM2LkEQQQCAaAYov0UwliaQFKL6kRXiMAAIIIIAAAggggAACCCBgE/joRz9qFF/mz59vOzX6Yxo36TXkrCHH6F+cJIgAAsEJUHwJbsoI2FWA4ourFOchgAACCCCAAAIIIIAAAroFRo0aZRRfOjs7VaJo3KTXkLOGHFW+YEkaAQS8FqD44vX0EFwzAvfdd5/x4fkLX/hCM11yLQIIIIAAAggggAACCCCAQIQCH/vYx4z7x8cffzzCTHtPSeMmvYacNeTY++rmDAQQQKBcAYov5XozWokCFF9KxGYoBBBAAAEEEEAAAQQQQCBggT333NMovjz22GMBZ5Q9dI2b9Bpy1pBj9lXPlQgggEAxAhRfinGlVw8EKL54MAmEgAACCCCAAAIIIIAAAggEIPCJT3zCKL789re/DSDy/EPUuEmvIWcNOeb/aqBHBBBAoDkBii/N+XG1xwI//OEPjQ/PBx98sMcRExoCCCCAAAIIIIAAAggggEAVAv/6r/9q3D/+53/+ZxWhVD6mxk16DTlryLHyFw8BIIAAAikBii8pEB7GI0DxJZ65JBMEEEAAAQQQQAABBBBAoEiBT37yk0bxZd68eUUO6W3fGjfpNeSsIUdvX1QEhgACagUovqid+vgTp/gS/xyTIQIIIIAAAggggAACCCCQh8Bee+1lFF/mzp2bR9fB9aFxk15DzhpyDO7FRsAIIBC9AMWX6KdYb4L33nuv8eH5kEMO0QtC5ggggAACCCCAAAIIIIAAAlaBT3/608b9469//WvrubEf1LhJryFnDTnG/tokPwQQCE+A4kt4c0bEjgIUXxyhOA0BBBBAAAEEEEAAAQQQUC4wevRoo/jyq1/9SqWKxk16DTlryFHlC5akEUDAawGKL15PD8E1I0DxpRk9rkUAAQQQQAABBBBAAAEE9AiMGTPGKL48+uijegDqMtW4Sa8hZw051i1jvkUAAQS8EKD44sU0EEQRAvfcc4/x4fmLX/xiEUPRJwIIIIAAAggggAACCCCAQMAC//7v/27cPz7yyCMBZ5Q9dI2b9Bpy1pBj9lXPlQgggEAxAhRfinGlVw8EKL54MAmEgAACCCCAAAIIIIAAAggEIPCZz3zGKL48/PDDAUSef4gaN+k15Kwhx/xfDfSIAAIINCdA8aU5P672WIDii8eTQ2gIIIAAAggggAACCCCAgEcCe++9t1F8+eUvf+lRhOWFonGTXkPOGnIs71XCSAgggICbAMUXNyfOClDg7rvvNj48H3rooQFmQsgIIIAAAggggAACCCCAAAJFCuy7777G/ePPf/7zIof0tm+Nm/QactaQo7cvKgJDAAG1AhRf1E59/IlTfIl/jskQAQQQQAABBBBAAAEEEMhD4D/+4z+M4svPfvazPLoOrg+Nm/QactaQY3AvNgJGAIHoBSi+RD/FehOk+KJ37skcAQQQQAABBBBAAAEEEGhE4LOf/axRfJk9e3YjXURzrsZNeg05a8gxmhchiSCAQDQCFF+imUoSSQtQfEmL8BgBBBBAAAEEEEAAAQQQQMAmsN9++xnFl5/+9Ke2U6M/pnGTXkPOGnKM/sVJggggEJwAxZfgpoyAXQXuuusu48PzYYcd5no55yGAAAIIIIAAAggggAACCCgR2H///Y37x5/85CdKsn93mho36TXkrCHHd69kHiGAAALVC1B8qX4OiKAgAYovBcHSLQIIIIAAAggggAACCCAQmcABBxxgFF8efPDByLJ0S0fjJr2GnDXk6LbCOQsBBBAoT4DiS3nWjFSyAMWXksEZDgEEEEAAAQQQQAABBBAIVOCggw4yii8PPPBAoNk0F7bGTXoNOWvIsbmVz9UIIIBA/gIUX/I3pUdPBGbNmmV8eP7Sl77kSXSEgQACCCCAAAIIIIAAAggg4IvA2LFjjfvHH/3oR76EV2ocGjfpNeSsIcdSXygMhgACCDgIUHxxQOKUMAUovoQ5b0SNAAIIIIAAAggggAACCJQt8PnPf94ovtx///1lh+HFeBo36TXkrCFHL15ABIEAAgjUCVB8qcPg27gEKL7ENZ9kgwACCCCAAAIIIIAAAggUJXDwwQcbxZf77ruvqOG87lfjJr2GnDXk6PULi+AQQEClAMUXldOuI+k777zT+PA8btw4HcmTJQIIIIAAAggggAACCCCAgLPAIYccYtw/3nvvvc7Xx3Sixk16DTlryDGm1yG5IIBAHAIUX+KYR7KwCFB8saBwCAEEEEAAAQQQQAABBBBAwBD44he/aBRf7rnnHuM8DQc0btJryFlDjhpen+SIAAJhCVB8CWu+iLYBAYovDWBxKgIIIIAAAggggAACCCCgWODQQw81ii933323ShGNm/QactaQo8oXLEkjgIDXAhRfvJ4egmtG4I477jA+PH/5y19upkuuRQABBBBAAAEEEEAAAQQQiFDgS1/6knH/KH9HVGPTuEmvIWcNObq8XleuXJnMnDkz6ejoSEaOHJlss802SVtb28b/5Hs5Js/JOXIuDQEEEGhGgOJLM3pc67UAxRevp4fgEEAAAQQQQAABBBBAAAFvBOTvg6Y3p+W3KWhsaQd5HHvTkLOGHHtapwsXLkzkdS6FFpuF7ZicK9fItTQEEEAgi0D876BZVLgmCgGKL1FMI0kggAACCCCAAAIIIIAAAoULyG9JSG++yj2lxpZ2kMexNw05a8jRtk5XrFix8SdZWlpajNe4zcR2TK6Vn4aRvmgIIIBAIwLxv4M2osG5UQncfvvtxhvr4YcfHlWOJIMAAggggAACCCCAAAIIINC8wBFHHGHcP/7gBz9ovuMAe7BtPgeYRkMha8hZQ47pSe/s7EyGDh1qvLZtFi7HpC/pk4YAAgi4ClB8cZXivOAEKL4EN2UEjAACCCCAAAIIIIAAArwdfEMAACAASURBVAhUInDkkUcaG7TyNx80NtsmdOwOGnLWkGP9Op09e3bS3t5uvK5tDo0ckz6lbxoCCCDgIkDxxUWJc4IUoPgS5LQRNAIIIIAAAggggAACCCBQusBRRx1lbNLedtttpcfhw4C2jWgf4ioyBg05a8ixtkbmzp2b9OvXz3hN2wyyHJO+ZQwaAggg0JsAxZfehHg+WAGKL8FOHYEjgAACCCCAAAIIIIAAAqUKHHPMMcZG7a233lpqDL4MZtuM9iW2ouLQkLOGHGV9LFu2LBkyZIjxerbl38wxGUPGoiGAAAI9CVB86UmH54IWkN/Pm34jld/jS0MAAQQQQAABBBBAAAEEEECgXuArX/mKcf/4ve99r/4UNd+n76PlcexNQ84acpR1OnbsWOO1bMs9j2MyFg0BBBDoSSD+d9Cesue5qAUovkQ9vSSHAAIIIIAAAggggAACCOQm0NHRYWzYfve7382t/5A6sm1KhxR/llg15Kwhxzlz5hivY1veeR6TMWkIIIBAdwIUX7qT4XjwAhRfgp9CEkAAAQQQQAABBBBAAAEEShEYP368sWl78803lzK2b4PYNqZ9izHveDTkrCHHMWPGGK9jW955HpMxaQgggEB3AhRfupPhePACM2fONN50jzzyyODzIgEEEEAAAQQQQAABBBBAAIF8BSZMmGDcP9500035DhJIb7aN6UBCzxymhpxjz7GrqytpaWkxXse2vPM8JmPK2DQEEEDAJkDxxabCsSgEKL5EMY0kgQACCCCAAAIIIIAAAggULjBx4kRj0/bGG28sfFwfB7BtTPsYZ54xacg59hxnzJhhvIZtORdxTMamIYAAAjYBii82FY5FIUDxJYppJAkEEEAAAQQQQACBvwuce+65lW0sFbFZRZ+bMJ+bYMDrgDXAGmANsAZYA6wBP9fAeeed1/R9CMWXpgnpwFeB2267zbiZOeqoo3wNl7gQQAABBCoQWL9+ffLWW2/xn4PB3/72twpmiCERQKBegOKLnzfmbJgwL6wB1gBrgDXAGmANsAbiWwPy2bvZRvGlWUGu91aA4ou3U0NgCCCAgBcCixYtMor0fGDu/gPzlClTvJg3gkBAswDFl+7/H8X/v7FhDbAGWAOsAdYAa4A1wBrIcw1QfNF850XuvQpQfOmViBMQQAAB1QLz58+n+NLAr3s5/vjjVa8XkkfABwGKL2wo5LmhQF+sJ9YAa4A1wBpgDbAGWAPdrwGKLz7cARGDtwLf//73jU21o48+2tt4CQwBBBBAoFwBii/df8i0fQCn+FLu+mQ0BGwCFF8a+/+W7f9lHMOQNcAaYA2wBlgDrAHWAGvAZQ1QfLHdkXAMgb8LUHxhKSCAAAII9CRA8aWxD9wUX3paTTyHAAIIIBC6wKRJk4x/vPetb30r9LQyxW/bkMrUUUAXacg59hxHjBhhvIZtORdxbKeddgpotRMqAgiUKcDffClTm7FKFaD4Uio3gyGAAALBCVB8ofgS3KIlYAQQQACBwgQmT55sbNxeffXVhY3nc8e2zWmf480jNg05x57j2LFjjdewLecijsnYNAQQQMAmQPHFpsKxoAVWrlyZzJw5M/nUpz5lvPH269cvGTlyZNLR0bHxHDmXhgACCCCgU4DiC8UXnSufrBFAAAEEbAInnXSScf84Y8YM26nRH7NtTseetIacY89RXq+2HMs4pvX/FbH/f4H8EMhDgOJLHor04YXAwoULk3HjxiVtbW3Ob7hyrlwj19IQQAABBHQJUHyh+KJrxZMtAggggEBPAlOmTDHuI6+88sqeLon2OdtmdbTJ/j0xDTnHnmNXV1fS0tJivI5teed5TMZcsmRJ7C8R8kMAgYwCFF8ywnGZPwIrVqzY+JMszbzJyrXy0zDSFw0BBBBAQIcAxReKLzpWOlkigAACCLgITJ061di0veKKK1wuje4c28Z0dEmmEtKQs4Ycx4wZY7yObXnneUzGpCGAAALdCVB86U6G40EIdHZ2JkOHDs3tzVX6kj5pCCCAAALxCyxbtiyR38980EEH8Z+DwQ9+8IP4FwUZIoAAAgioFTjllFOM+8rLL79cpYdtYzp2CA05a8jxkUceMV7HtrzzPDZnzpzYXx7khwACTQhQfGkCj0urFZg9e3bS3t6e+xur9Cl90xBAAAEEEEAAAQQQQAABBHQITJs2zbi3vOyyy3Qkn8rStjGdOiW6hxpy1pCjLEz5x1W2XIs4JmPREEAAgZ4EKL70pMNz3grMnTs36devX2FvqNK3jEFDAAEEEEAAAQQQQAABBBCIX+DUU0817i+nT58ef+KWDG2b1JbTojqkIWcNOcqilJ9uHzJkiPF6tuXfzDEZQ8aiIYAAAj0JUHzpSYfnvBTgjdTLaSEoBBBAAAEEEEAAAQQQQCBYgdNPP93YrL3kkkuCzaeZwG0b0s30F8K1GnLWkGNtrfEPdmsSfEUAgaoFKL5UPQOM37AAP0LaMBkXIIAAAggggAACCCCAAAII9CBwxhlnGMWXiy++uIcr4n1K0yZ9bRY15Kwhx9p8yld+VX29Bt8jgEBVAhRfqpJn3EwC8ofMbB8YijzGH0/LNFVchAACCCCAAAIIIIAAAggEI3DmmWca95oXXXRRMPHnGajt/jrP/n3sS0POGnJMr63Ozs5k6NChxmvbZuFyTPqSPmkIIICAqwDFF1cpzvNCYMyYMbm9abq8sco5MiYNAQQQQAABBBBAAAEEEEAgXoGzzz7buNe88MIL4024h8xs98o9nB7FUxpy1pCjbTGuWLEi6ejoSFpaWozXuM3EdkyulT6kLxoCCCDQiADFl0a0OLdSga6urqbeLG1voC7H5E1WxqYhgAACCCCAAAIIIIAAAgjEKXDOOecYG7Pnn39+nMn2kpXtPrmXS4J/WkPOGnLsaSEuXLgwGTduXNLW1ma81m02ckzOlWvkWhoCCCCQRYDiSxY1rqlEYMaMGc5vkN29cWY9LmPTEEAAAQQQQAABBBBAAAEE4hQ499xzjfvN8847L85ke8nKdt/cyyXBP60hZw05uixE+emVmTNnbvxJlpEjRxqve3GSn3KRc/hJFxdRzkEAgZ4ESi++2D7Q2N4AOLaJ9Q0AF1xYA2GsAa03aj294fAcAggggAACCCCAAAK+Csjn9/S9luxfaGxpB3kce9OQs4Ycs6xTXLKocQ0CCLgKlP4OSvEljI1j25sPx5g71oD7GtB6o+b65sN5CCCAAAIIIIAAAgj4JHDBBRcYxRf5OzAam+2+L3YHDTlryDHLOsUlixrXIICAqwDFl03cN1Nt/0PmGH6sAdaAbQ1QfHF9G+I8BBBAAAEEEEAAAQSqF7jwwguN4stZZ51VfWAVRGC7v6kgjFKH1JCzhhyzLBpcsqhxDQIIuApQfKH4YnzAtL3xcIwCA2ugsTVA8cX1bYjzEEAAAQQQQAABBBCoXuCiiy4y7o3PPPPM6gOrIALbvV8FYZQ6pIacNeSYZdHgkkWNaxBAwFWA4gvFF+MDpu2Nh2ONbbzjhRfFF9e3Ic5DAAEEEEAAAQQQQKB6gUsuucS4Nz799NOrD6yCCGz3sxWEUeqQGnLWkGOWRYNLFjWuQQABV4HSiy+ugXEeAmmBESNGGB+GbW+SRRzbaaed0uHwGAEEEEAAAQQQQAABBBBAIBKBSy+91LjfPO200yLJrrE0bPfUjfUQ3tkactaQY5aVh0sWNa5BAAFXAYovrlKcV7nA2LFjjQ/DtjfJIo7J2DQEEEAAAQQQQAABBBBAAIE4BaZPn27cb5566qlxJttLVrZ76l4uCf5pDTlryDHLQsQlixrXIICAqwDFF1cpzqtcYMaMGcaHYdubZBHHZGwaAggggAACCCCAAAIIIIBAnAKXX365cb95yimnxJlsL1nZ7ql7uST4pzXkrCHHLAsRlyxqXIMAAq4CFF9cpTivcoGurq6kpaXF+EBse6PM85iMuWTJksrzJwAEEEAAgXwFXn311eTAAw9M9t9/f/5zMLjtttvynQB6QwABBBBAwCOBb37zm8a95sknn+xRhOWFYrufLm/0akbSkLOGHLOsHlyyqHENAgi4ClB8cZXiPC8ExowZY3wgtr1R5nlMxqQhgAACCMQnMH/+/NLfU/J8fyq7r+OPPz6+RUBGCCCAAAII/F3giiuuMD4XTJ06VaWP7TNG7BAactaQY5Z1iksWNa5BAAFXAYovrlKc54XAI488Ynwgtr1R5nlszpw5XuROEAgggAAC+QpQfNmkofdUii/5rj96QwABBBDwS8D2a65POukkv4IsKRrb/XRJQ1c2jIacNeSYZQHhkkWNaxBAwFWA4ourFOd5IzB27NiGNotsb6Sux2QsGgIIIIBAnAIUXyi+xLmyyQoBBBBAIIvAVVddZdxnnnjiiVm6Cv4a2/1y8En1koCGnDXk2Ms0W5/GxcrCQQQQyEmA4ktOkHRTnsCyZcuSIUOGGB+MbW+YzRyTMWQsGgIIIIBAnAIUXyi+xLmyyQoBBBBAIIvA1VdfbdxjTp48OUtXwV9ju48OPqleEtCQs4Yce5lm69O4WFk4iAACOQlQfMkJkm7KFZg7d27Sr18/48Ox7U0zyzHpW8agIYAAAgjEK0DxheJLvKubzBBAAAEEGhW45pprjPvLSZMmNdpNFOfb7qGjSKyHJDTkrCHHHqa426dw6ZaGJxBAIAcBii85INJFNQKzZ89O2tvbjQ/ItjfORo5Jn9I3DQEEEEAgbgGKLxRf4l7hZIcAAggg0IjAt7/9bePe8utf/3ojXURzru3+OZrkuklEQ84acuxmens8jEuPPDyJAAJNClB8aRKQy6sV6OzsTIYOHWp8SLa9ebock76kTxoCCCCAQPwCFF8ovsS/yskQAQQQQMBV4NprrzXuK0844QTXy6M6z3bvHFWClmQ05KwhR8vU9noIl16JOAEBBJoQoPjSBB6X+iGwYsWKpKOjI2lpaTE+LNveRG3H5FrpQ/qiIYAAAgjoEFi0aFHm9w3be0nsx6ZOnapjYZAlAggggIBKgeuuu874XPC1r31NpYXtM03sEBpy1pBjlnWKSxY1rkEAAVcBii+uUpznvcDChQuTcePGJW1tbcaHZtubqRyTc+UauZaGAAIIIKBPYMOGDQn/uRn83//9n74FQsYIIIAAAmoErr/+euM+8qtf/aqa/OsTtd0/1z8f4/cactaQY5a1iUsWNa5BAAFXAYovrlKcF4yA/PTKzJkzk0984hPGh+d+/folI0eO3PhTLnIOP+kSzLQSKAIIIIAAAggggAACCCBQmMANN9xg3D8ed9xxhY3nc8caN6M15KwhxyyvK1yyqHENAgi4ClB8cZXivOAEvvOd7xgfno8//vjg8iBgBBBAAAEEEEAAAQQQQACBYgVuvPFG4/5x4sSJxQ7qae8aN6M15KwhxywvKVyyqHENAgi4ClB8cZXivOAE+J29wU0ZASOAAAIIIIAAAggggAAClQjcfPPNRvFl/PjxlcRS9aAaN6M15KwhxyyvHVyyqHENAgi4ClB8cZXivOAEKL4EN2UEjAACCCCAAAIIIIAAAghUInDLLbcYxZdjjz22kliqHlTjZrSGnDXkmOW1g0sWNa5BAAFXAYovrlKcF5wAxZfgpoyAEUAAAQQQQAABBBBAAIFKBL773e8axZeOjo5KYql6UI2b0Rpy1pBjltcOLlnUuAYBBFwFKL64SnFecAIUX4KbMgJGAAEEEEAAAQQQQAABBCoRuPXWW43iyzHHHFNJLFUPqnEzWkPOGnLM8trBJYsa1yCAgKsAxRdXKc4LTuDaa681PjyfcMIJweVBwAgggAACCCCAAAIIIIAAAsUKfP/73zfuH48++uhiB/W0d42b0Rpy1pBjlpcULlnUuAYBBFwFKL64SnFecAIUX4KbMgJGAAEEEEAAAQQQQAABBCoRuO2224ziy1FHHVVJLFUPqnEzWkPOGnLM8trBJYsa1yCAgKsAxRdXKc4LToDiS3BTRsAIIIAAAggggAACCCCAQCUCP/jBD4ziyxFHHFFJLFUPqnEzWkPOGnLM8trBJYsa1yCAgKsAxRdXKc4LTuDb3/628eH561//enB5EDACCCCAAAIIIIAAAggggECxArfffrtx/3j44YcXO6invWvcjNaQs4Ycs7ykcMmixjUIIOAqQPHFVYrzghOg+BLclBEwAggggAACCCCAAAIIIFCJwB133GEUX7785S9XEkvVg2rcjNaQs4Ycs7x2cMmixjUIIOAqQPHFVYrzghOg+BLclBEwAggggAACCCCAAAIIIFCJwKxZs4ziy7hx4yqJpepBNW5Ga8hZQ45ZXju4ZFHjGgQQcBWg+OIqxXnBCVxzzTXGh+dvfOMbweVBwAgggAACCCCAAAIIIIAAAsUK3HXXXcb942GHHVbsoJ72rnEzWkPOGnLM8pLCJYsa1yCAgKsAxRdXKc4LToDiS3BTRsAIIIAAAggggAACCCCAQCUCd999t1F8OfTQQyuJpepBNW5Ga8hZQ45ZXju4ZFHjGgQQcBWg+OIqxXnBCVB8CW7KCBgBBBBAAAEEEEAAAQQQqETgnnvuMYovX/ziFyuJpepBNW5Ga8hZQ45ZXju4ZFHjGgQQcBWg+OIqxXnBCXzrW98yPjxPmjQpuDwIGAEEEEAAAQQQQAABBBBAoFiBH/7wh8b948EHH1zsoJ72rnEzWkPOGnLM8pLCJYsa1yCAgKsAxRdXKc4LToDiS3BTRsAIIIAAAggggAACCCCAQCUC9913n1F8+cIXvlBJLFUPqnEzWkPOGnLM8trBJYsa1yCAgKsAxRdXKc4LToDiS3BTRsAIIIAAAggggAACCCCAQCUC999/v1F8+fznP19JLFUPqnEzWkPOGnLM8trBJYsa1yCAgKsAxRdXKc4LTuDqq682PjxPnjw5uDwIGAEEEEAAAQQQQAABBBBAoFiBBx54wLh/POigg4od1NPeNW5Ga8hZQ45ZXlK4ZFHjGgQQcBWg+OIqxXnBCVB8CW7KCBgBBBBAAAEEEEAAAQQQqETgxz/+sVF8OfDAAyuJpepBNW5Ga8hZQ45ZXju4ZFHjGgQQcBWg+OIqxXnBCVB8CW7KCBgBBBBAAAEEEEAAAQQQqETgwQcfNIovBxxwQCWxVD2oxs1oDTlryDHLaweXLGpcgwACrgIUX1ylOC84AYovwU0ZASOAAAIIIIAAAggggAAClQj89Kc/NYov++23XyWxVD2oxs1oDTlryDHLaweXLGpcgwACrgIUX1ylOC84gauuusr48HziiScGlwcBI4AAAggggAACCCCAAAIIFCvw0EMPGfePn/vc54od1NPeNW5Ga8hZQ45ZXlK4ZFHjGgQQcBWg+OIqxXnBCVB8CW7KCBgBBBBAAAEEEEAAAQQQqERg9uzZRvHls5/9bCWxVD2oxs1oDTlryDHLaweXLGpcgwACrgIUX1ylOC84AYovwU0ZASOAAAIIIIAAAggggAAClQj8/Oc/N4ov++67byWxVD2oxs1oDTlryDHLaweXLGpcgwACrgIUX1ylOC84gRkzZhgfnk866aTg8iBgBBBAAAEEEEAAAQQQQACBYgV+8YtfGPeP++yzT7GDetq7xs1oDTlryDHLSwqXLGpcgwACrgIUX1ylOC84AYovwU0ZASOAAAIIIIAAAggggAAClQj88pe/NIove++9dyWxVD2oxs1oDTlryDHLaweXLGpcgwACrgIUX1ylOC84AYovwU0ZASOAAAIIIIAAAggggAAClQg88sgjRvHlM5/5TCWxVD2oxs1oDTlryDHLaweXLGpcgwACrgIUX1ylOC84gSuvvNL48DxlypTg8iBgBBBAAAEEEEAAAQQQQACBYgXmzJlj3D/+27/9W7GDetq7xs1oDTlryDHLSwqXLGpcgwACrgIUX1ylOC84AYovwU0ZASOAAAIIIIAAAggggAACpQgsXbo0uf3225OzzjorOfTQQ5MRI0YYxZfW1tZk2LBhyR577LHxHDlXrpFrY24aN6M15KwhxyyvS1yyqHENAgi4ClB8cZXivOAEKL4EN2UEjAACCCCAAAIIIIAAAggUIrBhw4bkoYceSjo6OpLhw4cbhRbbBmxPx6QP6Uv6lL5jara8Y8rPlouGnDXkaJvb3o7h0psQzyOAQDMCFF+a0eNarwWuuOIK4wP11KlTvY6Z4BBAAAEEEEAAAQQQQAABBPITeP7555NJkyYlgwcPNu4PbZuuWY5J3zKGjBVDsxnEkFdPOWjIWUOOPc1xd8/h0p0MxxFAIA8Bii95KNKHlwIUX7ycFoJCAAEEEEAAAQTUCqxb/06y9LU1ye+efSP52WOvJHf8fEly/X3/k1w2c1Fy9o0LkqlXz0+Ov+zxpOPC/0oOP2deMu7Mucmhp/8mOXjar5OxJ/8qufMXL6i1I3EEGhVYsGDBxl8V1qdPn8KKLulNWxlLfoWZjB1yS+clj2NvGnLWkGOWdYpLFjWuQQABV4H430FdJTgvOgGKL9FNKQkhgAACCCCAAALBCPxl9frkP59antz6k8XJ2TcsSI45/7cbiyjHXfr4xsdXzXo2ue2hruSB37yU/OqJ15L5z76RPPvCyo3FmT/9+a/JyjfXJ2v+uiH561vvJOs3/C1552//F0zuBIpAlQLLly/f+OvAWlpaSiu6pDdvZWz5lWQSS4gtnY88jr1pyFlDjlnWKS5Z1LgGAQRcBeJ/B3WV4LzoBL75zW8aH7ZPPvnk6PIkIQQQQAABBBBAAAE/BKRY8qNfv5ScdNX85Cvn/3bjT7Tc9+gfkyeeeyP53xXr/AiSKBCIWODGG29MttxyS+M+0La52rdv3+TjH/94IveIt9xyS3L99dcb140aNSp58cUXk3nz5m08R86Va+RaW5/pYxKLxBRaS+chj2NvGnLWkGOWdYpLFjWuQQABV4H430FdJTgvOgGKL9FNKQkhgAACCCCAAALeCnQ+83oy4eLHktt/tiT545/WeBsngSEQo8DKlSuTgw8+uNeCSP/+/ZPDDjssefDBB5M1a979Ov2v//ov43optNja6tWrN/YhfUmfts3b+mMSm8QYSquPvfZ9KLFnjbOWZ/3XrH35el19brXvfY21zLhqFvVfyxyfsRBAIG4Bii9xz6/q7Ci+qJ5+kkcAAQQQQAABBEoVOOyM3/DTLaWKMxgC/5/AU089lQwbNqzHAsj222+fzJgxI3nzzTe7ZXvssceMPvbcc89uz689sWrVquTKK69MZIz6zdv09xKjxBpCS8cuj2NvGnLWkGOWdYpLFjWuQQABV4H430FdJTgvOgGKL9FNKQkhgAACCCCAAALeChw45VFvYyMwBGIVePTRR5Mtttii26LHoEGDkuuuuy5Zv359rwSdnZ1GP/Jrx1ybjHHttdcmMqZtM1eODRw4MJGYfW+2+H2Pudn4NOSsIccs6wCXLGpcgwACrgIUX1ylOC84gcsvv9z40HvKKacElwcBI4AAAggggAACCPgvQPHF/zkiwrgE7r///qStrc2456ttpB577LHJ66+/7pz07373O6OvkSNHOl9fO1HGlLFrcaS/SswSu88tHbM8jr1pyFlDjlnWKS5Z1LgGAQRcBeJ/B3WV4LzoBCi+RDelJIQAAggggAACCHgrQPHF26khsAgFHn744W4LL1tttVWm4sb8+fONgslHP/rRzHpSYJFYbBu7UoCRHHxttph9jTWvuDTkrCHHLOsBlyxqXIMAAq4CFF9cpTgvOAGKL8FNGQEjgAACCCCAAALBClB8CXbqCDwwAfkJlQEDBliLGrvuumuydOnSTBk9+eSTRp8f+chHMvVVu0hikZhsm7uSg+TiY7PF62OcecakIWcNOWZZE7hkUeMaBBBwFaD44irFecEJXHbZZcaH3GnTpgWXBwEjgAACCCCAAAII+C9A8cX/OSLC8AWWL1/e7R+232uvvZKVK1dmTvK///u/jfvHPfbYI3N/tQslJonNtsG7/fbbJ5KTb80Wq28x5h2Phpw15JhlXeCSRY1rEEDAVYDii6sU5wUnQPEluCkjYAQQQAABBBBAIFgBii/BTh2BBySw9957W4sYUtxYt25dU5ksWLDA6PvDH/5wU33WLpbYuivA7LPPPrXTvPmqcTNaQ84acszyIsIlixrXIICAqwDFF1cpzgtOgOJLcFNGwAgggAACCCCAQLACFF+CnToCD0TAdn8nm6by0ymrVq1qOounnnrKKL586EMfarrfWgcSo8Rq2+iV3Hxqthh9iq+IWDTkrCHHLGsDlyxqXIMAAq4CFF9cpTgvOIHp06cbH2xPPfXU4PIgYAQQQAABBBBAAAH/BSi++D9HRBiuwIsvvpi0t7cb93eDBw9OXn311VwSe/rpp43+//mf/zmXvmudSKzbbrutMY7kJjn60jRuRmvIWUOOWV5DuGRR4xoEEHAVoPjiKsV5wQlQfAluyggYAQQQQAABBBAIVoDiS7BTR+ABCOy3335GwaJPnz7Jww8/nFv0v//9740xdtttt9z6r3UkMUvs6Q1fydGXlo5NHsfeNOSsIccs6xSXLGpcgwACrgLxv4O6SnBedAIUX6KbUhJCAAEEEEAAAQS8FaD44u3UEFjgAnPmzDEKFbJZOnXq1FwzW7RokTHOrrvumusYtc6mTJlijCU5Sa5VtdWrVyezZs1KJkyYYI1t1KhRycSJE5O77rorkXNjaxo24DXkmGVd4pJFjWsQQMBVgOKLqxTnBSdw6aWXGh8aTzvttODyIGAEEEAAAQQQQAAB/wUovvg/R0QYpsDo0aON+7qhQ4cma9asyTWhZ5991hjngx/8YK5j1DqT4oXkkN70lVzLbosXL07Gjx9v/bVu6fhqj+XXpMk1cm0srZZb/ddYcqvlUZ9b7fvac5q/1izqv2r2IHcEEMhXgOJLvp705pEAxRePJoNQEEAAAQQQQACByAUovkQ+waRXG7YZhwAAIABJREFUicC8efOMAoVskN599925x/Pcc88ZY+2yyy65j1PrUHKo3+ytfS85l9HWrVuXTJs2LWltbbXGUYunp69yrfQhfYXebHmGnlM6fg05pnN2eYyLixLnIIBAVgGKL1nluM57AYov3k8RASKAAAIIIIAAAtEIUHyJZipJxCOBcePGGYWBon4V2B/+8AdjrJ133rlQDcklvfErORfdurq6kt13390YOx2L62PpS/oMudlyDTkfW+wacrTl3dsxXHoT4nkEEGhGgOJLM3pc67XAJZdcYnyYPP30072OmeAQQAABBBBAAAEEwhSg+BLmvBG1vwKrVq1K+vfvb9zT3XnnnYUE/fzzzxtjjRgxopCxap1KLumNX8lZci+qLViwIBk8eLAxbjqORh9Ln9J3qM2Wb6i5dBe3hhy7y72n47j0pMNzCCDQrADFl2YFud5bAYov3k4NgSGAAAIIIIAAAtEJUHyJbkpJqGKBm2++2SgQbLvttsnbb79dSGTy90vSm7Af+MAHChmr1qnkIjmlx5Xci2jy0ylFFF5q8Uvfof4ETC2H+q9FzEGVfdbnVvu+ynh8GbtmUf/Vl9iIAwEEwheg+BL+HJJBNwIUX7qB4TACCCCAAAIIIIBA7gIUX3InpUPlAgcddJBRlJg8eXJhKlI0qN98le933HHHwsardSw5pceV3PNu8ndZ8vxVY+mYa49ljBD/Bkwt/vqvec9B1f3V51b7vuqYfBi/ZlH/1Ye4iAEBBOIQoPgSxzyShUWA4osFhUMIIIAAAggggAAChQhQfCmElU6VCrzzzjvJwIEDjaLE448/XpjICy+8YIw3fPjwwsardSw51W/6yveSuxjk2aZNm2aMkx43r8cyVmjNlntoOfQWr4YcezOwPY+LTYVjCCCQlwDFl7wk6cc7gYsvvtj4cHnGGWd4FycBIYAAAggggAACCIQvQPEl/DkkA38EOjs7jXu5IgoS9Rm/+OKLxpg77LBD/SmFfN9doUkM8mryK9VaW1uN/Gybznkck7FkzJCaLe+Q4neJVUOOLg7pc3BJi/AYAQTyFKD4kqcmfXklQPHFq+kgGAQQQAABBBBAIGoBii9RTy/JlSxw3XXXGYWCIn4VV31aS5cuNcYcNmxY/SmFfW/7FWtikFcbP368kZttwznPYzJmSM2We0jxu8SqIUcXh/Q5uKRFeIwAAnkKUHzJU5O+vBKg+OLVdBAMAggggAACCCAQtQDFl6inl+RKFpg0aZJRLLjwwgsLjeKll14yxhw6dGihY9Y6l9zSG8BikEdbvXp10t7ebvSfHi/vxzKmjB1Ks+UfSuyucWrI0dWi/jxc6jX4HgEE8hag+JK3KP15I3DRRRcZHzDPPPNMb+IjEAQQQAABBBBAAIF4BCi+xDOXZFK9wD777GPcy917772FBvbyyy8bY77//e8vdMxa55JbegNYDPJos2bNMvpOj1XUYxk7lGYzCCV21zg15OhqUX8eLvUafI8AAnkLUHzJW5T+vBGg+OLNVBAIAggggAACCCAQvQDFl+inmARLFNh5552NgsHTTz9daASvvPKKMeb2229f6Ji1ziW39AawGOTRJkyYYPSdHquoxxMnTswjhVL6sBmUMnCJg2jIMQsnLlnUuAYBBFwFKL64SnFecAIUX4KbMgJGAAEEEEAAAQSCFSij+HLHz5ckMg7/YRD7Gug3YJvKCga2jdgqjolBHvO85XYfrMxSxs4jhzL6sM1xGeOWOYaGHLN44sJ7apZ1wzU61s2dv3ih6XsTii9NE9KBrwK235t71lln+RoucSGAAAIIIIAAAggELCA34UU3ii86bvTZ0Hk02bSt/L9RYtuArfKYGOSxFtr6D6ys+CJj55FDGX3Y5rqMccscQ0OOWTxx4b01y7rhGh3rRj57N9sovjQryPXeClB88XZqCAwBBBBAAAEEEIhOQG7Ci24UX3Tc6LOh82jS0tKnsoKBbSO2imNikMda6LNpa2WWMnYeOZTRh22Oyxi3zDE05JjFExfeW7OsG67RsW4ovhR9d0P/QQtQfAl6+ggeAQQQQAABBBAISkBuwotuFF903OizocNPvshmcF4/+ULxxe3/Gxo24DXkmOX/n7i4vUay2HINtqGvAYovRd/d0H/QAhdccIHxL3zOPvvsoHMieAQQQAABBBBAAAE/BeTmsuhG8YVNjNA3MVzj52++bJLk9Tdf+LVjbv/f0LABryFH1//H1J+Hi9trpN6M7zHTsgYovhR9d0P/QQtQfAl6+ggeAQQQQAABBBAISkBuQmkIIJCPwM4772z8Q7qnn346n8676eWNN94wxtx66627OTvfw5JbegNYDPJoo0aNMvpOj1XUYxk7lGYzCCV21zg15OhqUX8eLvUafI8AAnkL8Ddf8halP28EKL54MxUEggACCCCAAAIIRC9A8SX6KSbBEgX22Wcfo2Bw7733FhrBn//8Z2PMQYMGFTpmrXPJLb0BLAZ5tAkTJhh9p8cq6vHEiRPzSKGUPmwGpQxc4iAacszCiUsWNa5BAAFXAYovrlKcF5zA+eefb3zIPOecc4LLg4ARQAABBBBAAAEE/Beg+OL/HBFhOAKTJk0y7uXkb3oW2VauXGmMueWWWxY55P/ft+3vlYpBHm3WrFlGXrbN5iKO3XXXXXmkUEoftvxLGbjEQTTkmIUTlyxqXIMAAq4CFF9cpTgvOAGKL8FNGQEjgAACCCCAAALBClB8CXbqCNxDgeuuu84oGBx00EGFRvqXv/zFGHPgwIGFjlnrXHJLbwCLQR5t9erVSXt7u9F/ery8H8uYMnYozZZ/KLG7xqkhR1eL+vNwqdfgewQQyFuA4kveovTnjQDFF2+mgkAQQAABBBBAAIHoBSi+RD/FJFiiQGdnp1EskELIO++8U1gUq1atMsbcYostChuv1rHkJLmlN4DFIK82fvx4o//0eHk/ljFDarb8Q4rfJVYNObo4pM/BJS3CYwQQyFOA4kuemvTllQDFF6+mg2AQQAABBBBAAIGoBSi+RD29JFeyQHcFiccff7ywSOSnNNKbsAMGDChsvFrHjz32mDFu3oWmxYsXJ62trcY46XzzeixjyZghNVvuIcXvEquGHF0c0ufgkhbhMQII5ClA8SVPTfrySuC8884zPlyee+65XsVIMAgggAACCCCAAAJxCFB8iWMeycIfAduv4po8eXJhAa5Zs8a4f9xss80KG6/WseSU3vwt4lesTZs2zRgnPW5ej2Ws0Jot99By6C1eDTn2ZmB7HhebCscQQCAvAYoveUnSj3cCFF+8mxICQgABBBBAAAEEohWg+BLt1JJYRQK33HKLUSzYdtttk7fffruQiNauXWuMJ3+3pMgmuUhO6c1fyT3vtm7dumT33Xc3xkqP3exjGUPGCq3Z8g4th97i1ZBjbwa253GxqXAMAQTyEqD4kpck/XgnQPHFuykhIAQQQAABBBBAIFoBii/RTi2JVSQgf4Olf//+RrHgzjvvLCQiKRikN2H79etXyFi1TiWX9JiSs+ReROvq6koGDx5sjJmOIetj6VvGCLHZcg4xj55i1pBjT/l39xwu3clwHAEE8hCg+JKHIn14KSC/Yiz9JioFGRoCCCCAAAIIIIAAAnkLUHzJW5T+EEiScePGGfd0u+66ayE0b731ljHWe97znkLGqnUquaTvWSXnItuCBQsKKcBI4UX6DrWl50Eex9Y05JhlznDJosY1CCDgKhDfu4lr5pwXvQDFl+inmAQRQAABBBBAAAFvBCi+eDMVBBKRwLx584zihGyU3n333blnuX79emOstra23MepdSg52DZ9Jeeim/x0Sp6/gkz6CvUnXmrWtrmoPRfLVw05ZpkrXLKocQ0CCLgKUHxxleK84AQovgQ3ZQSMAAIIIIAAAggEK0DxJdipI3DPBUaPHm0UKYYOHZqsWbMm18g3bNhgjNPa2prrGLXOVq9enUgO6U1fybWsJr9mbdq0aYnkmI7D9bFcK32E+Dde0s62nNPnhP5YQ45Z5giXLGpcgwACrgIUX1ylOC84gXPOOcf4EHn++ecHlwcBI4AAAggggAACCPgvQPHF/zkiwjAF5syZY9zXyWbplClTck3onXfeMcbZdNNNcx2j1pnEbtvwffTRR2unlPZ18eLFyfjx45P29nZrTLY45Vy5Rq6NpdnyjCW3Wh4acqzl2shXXBrR4lwEEGhUgOJLo2KcH4wAxZdgpopAEUAAAQQQQACB4AUovgQ/hSTgscB+++1nFAb69OmTPPzww7lGnd6ElTHybhKz9JseS3KssslP48yaNSuZMGGCEZvEOmrUqI3PyTlybmwtPR/yOLamIccsc4ZLFjWuQQABV4H43k1cM+e86AUovkQ/xSSIAAIIIIAAAgh4I0DxxZupIJAIBV588UXrT2Zsu+22yauvvppbxulN2JaWltz6lo4kVok5PY78JInk6EtLxyePY28actaQY5Z1iksWNa5BAAFXgfjfQV0lOC86gbPPPtv4UHvBBRdElycJIYAAAggggAACCFQvQPGl+jkggrgFLrvsMuP+TjZN99hjj2TVqlW5JF/kJqzEKLHaxpDcfGq2GH2Kr4hYNOSsIccsawOXLGpcgwACrgIUX1ylOC84AYovwU0ZASOAAAIIIIAAAsEKUHwJduoIPCCBvffe21q82GuvvXL5o+/yky7pjdg8eOQP0kuM6b7lseTkW7PF6VuMecejIWcNOWZZF7hkUeMaBBBwFaD44irFecEJUHwJbsoIGAEEEEAAAQQQCFaA4kuwU0fgAQksX7482X777a1FDClurFy5sqlsbH+LpakOk2RjTN0VXiQXycm3pnEzWkPOGnLM8lrCJYsa1yCAgKsAxRdXKc4LTuCss84yPpRfeOGFweVBwAgggAACCCCAAAL+C1B88X+OiDAOgd/97nfJgAEDjHs92UDdddddk6VLl2ZOtG/fvka/GzZsyNyfxCIx2TZ3JQfJxcdmi9fHOPOMSUPOGnLMsiZwyaLGNQgg4CpA8cVVivOCE6D4EtyUETACCCCAAAIIIBCsAMWXYKeOwAMUePjhh5O2tjZrUWOrrbZK7r///kxZtba2Gn2+/fbbmfqSGCQW28auxC45+NpsMfsaa15xachZQ45Z1gMuWdS4BgEEXAUovrhKcV5wAhRfgpsyAkYAAQQQQAABBIIVoPgS7NQReKACUtzorgAjm6nHHnts8sYbbzSUna2/9evXN9TH66+/vnFs24auHJMxshaHGgqkiZNtsTfRXRCXashZQ45ZFhsuWdS4BgEEXAUovrhKcV5wAhRfgpsyAkYAAQQQQAABBIIVoPgS7NQReMACjz76aDJw4EDrT5fIhuqgQYOS6667LnEtoPTr18/oa926dU5CMoaMJWPaNnPlmMQqMfvebPH7HnOz8WnIWUOOWdYBLlnUuAYBBFwFKL64SnFecAJnnnmm8aH3oosuCi4PAkYAAQQQQAABBBDwX4Dii/9zRIRxCjz11FPJsGHDjHu/+g1V+cP2M2bMSN58880eEfr372/089e//rXHa1atWrWxbxmjfsz09xKjxBpCS8cuj2NvGnLWkGOWdYpLFjWuQQABV4H430FdJTgvOgGKL9FNKQkhgAACCCCAAALeClB88XZqCEyBwMqVK5ODDz64x+KHbLBKceWwww5LHnzwwWTNmjWGTHt7u9HH2rVrjfPkWulD+rIVbNKbuRKbxBhKS8cvj2NvGnLWkGOWdYpLFjWuQQABV4H430FdJTgvOgGKL9FNKQkhgAACCCCAAALeClB88XZqCEyRwI033phsueWWRgHFtrnat2/f5OMf/3hy8sknJ7fccksyb968ZLPNNjOufeaZZzY+J+fIuXKNXGvrM31MYpGYQmvpPORx7E1DzhpyzLJOccmixjUIIOAqEP87qKsE50UncMYZZxgfiC+++OLo8iQhBBBAAAEEEEAAgeoFKL5UPwdEgIAILF++POno6EhaWlqM+0HbJmsRx2RsiUFiCbHZTELMo5GYNeSsIcdG5rx2Li41Cb4igEARAhRfilClTy8EKL54MQ0EgQACCCCAAAIIqBCg+KJimkkyIIEFCxYkhx56aNKnT5/SijAylowpY4fcNG5Ga8hZQ45ZXne4ZFHjGgQQcBWg+OIqxXnBCVB8CW7KCBgBBBBAAAEEEAhWgOJLsFNH4JELPP/888mkSZOSwYMHF1aEkb5lDBkrhqZxM1pDzhpyzPL6wyWLGtcggICrAMUXVynOC07g9NNPNz5cX3LJJcHlQcAIIIAAAggggAAC/gtQfPF/johQt8CGDRuShx56aOOvA9thhx2Me0XbBmxPx6QP+dVi0qf0HVOz5R1TfrZcNOSsIUfb3PZ2DJfehHgeAQSaEaD40owe13otQPHF6+khOAQQQAABBBBAICoBii9RTSfJKBBYunRpcvvttydnnXXWxl8VtsceeyTDhg1Ltt5666StrW3jf/K9HJPn5NeJyblyjVwbc9O4Ga0hZw05Znld4pJFjWsQQMBVgOKLqxTnBSdA8SW4KSNgBBBAAAEEEEAgWAGKL8FOHYEjgEBKQONmtIacNeSYWspOD3FxYuIkBBDIKEDxJSMcl/kvcNpppxk/Sn7ppZf6HzgRIoAAAggggAACCAQnQPEluCkjYAQQ6EZA42a0hpw15NjNku7xMC498vAkAgg0KUDxpUlALvdXgOKLv3NDZAgggAACCCCAQGwCFF9im1HyQUCvgMbNaA05a8gxy6sWlyxqXIMAAq4CFF9cpTgvOAGKL8FNGQEjgAACCCCAAALBClB8CXbqCBwBBFICGjejNeSsIcfUUnZ6iIsTEychgEBGAYovGeG4zH+BU0891fi1Y9OnT/c/cCJEAAEEEEAAAQQQCE6A4ktwU0bACCDQjYDGzWgNOWvIsZsl3eNhXHrk4UkEEGhSgOJLk4Bc7q8AxRd/54bIEEAAAQQQQACB2AQovsQ2o+SDgF4BjZvRGnLWkGOWVy0uWdS4BgEEXAUovrhKcV5wAhRfgpsyAkYAAQQQQAABBIIVoPgS7NQROAIIpAQ0bkZryFlDjqml7PQQFycmTkIAgYwCFF8ywnGZ/wIUX/yfIyJEAAEEEEAAAQRiEaD4EstMkgcCCGjcjNaQs4Ycs7x6ccmixjUIIOAqQPHFVYrzghOYNm2a8TdfLrvssuDyIGAEEEAAAQQQQAAB/wUovvg/R0SIAAJuAho3ozXkrCFHtxX+7rNwebcHjxBAIF8Bii/5etKbRwIUXzyaDEJBAAEEEEAAAQQiF6D4EvkEkx4CigQ0bkZryFlDjlleprhkUeMaBBBwFaD44irFecEJUHwJbsoIGAEEEEAAAQQQCFaA4kuwU0fgCCCQEtC4Ga0hZw05ppay00NcnJg4CQEEMgpQfMkIx2X+C5xyyinGrx27/PLL/Q+cCBFAAAEEEEAAAQSCE6D4EtyUETACCHQjoHEzWkPOGnLsZkn3eBiXHnl4EgEEmhSg+NIkIJf7K0Dxxd+5ITIEEEAAAQQQQCA2AYovsc0o+SCgV0DjZrSGnDXkmOVVi0sWNa5BAAFXAYovrlKcF5wAxZfgpoyAEUAAAQQQQACBYAUovgQ7dQSOAAIpAY2b0Rpy1pBjaik7PcTFiYmTEEAgowDFl4xwXOa/wMknn2z82rFvfvOb/gdOhAgggAACCCCAAALBCVB8CW7KCBgBBLoR0LgZrSFnDTl2s6R7PIxLjzw8iQACTQpQfGkSkMv9FaD44u/cEBkCCCCAAAIIIBCbAMWX2GaUfBDQK6BxM1pDzhpyzPKqxSWLGtcggICrAMUXVynOC06A4ktwU0bACCCAAAIIIIBAsAIUX4KdOgJHAIGUgMbNaA05a8gxtZSdHuLixMRJCCCQUYDiS0Y4LvNfYOrUqcavHbviiiv8D5wIEUAAAQQQQAABBIIToPgS3JQRMAIIdCOgcTNaQ84acuxmSfd4GJceeXgSAQSaFKD40iQgl/srQPHF37khMgQQQAABBBBAIDYBii+xzSj5IKBXQONmtIacNeSY5VWLSxY1rkEAAVcBii+uUpwXnADFl+CmjIARQAABBBBAAIFgBSi+BDt1BI4AAikBjZvRGnLWkGNqKTs9xMWJiZMQQCCjAMWXjHBc5r/AlClTjF87duWVV/ofOBEigAACCCCAAAIIBCdA8SW4KSNgBBDoRkDjZrSGnDXk2M2S7vEwLj3y8CQCCDQpQPGlSUAu91eA4ou/c0NkCCCAAAIIIIBAbAIUX2KbUfJBQK+Axs1oDTlryDHLqxaXLGpcgwACrgIUX1ylOC84AYovwU0ZASOAAAIIIIAAAsEKUHwJduoIHAEEUgIaN6M15Kwhx9RSdnqIixMTJyGAQEYBii8Z4bjMfwGKL/7PEREigAACCCCAAAKxCFB8iWUmyQMBBDRuRmvIWUOOWV69uGRR4xoEEHAVoPjiKsV5wQmcdNJJxt98mTFjRnB5EDACCCCAAAIIIICA/wIUX/yfIyJEAAE3AY2b0Rpy1pCj2wp/91m4vNuDRwggkK8AxZd8PenNIwGKLx5NBqEggAACCCCAAAKRC1B8iXyCSQ8BRQIaN6M15KwhxywvU1yyqHENAgi4ClB8cZXivOAEKL4EN2UEjAACCCCAAAIIBCtA8SXYqSNwBBBICWjcjNaQs4YcU0vZ6SEuTkychAACGQUovmSE4zL/BU488UTj145dddVV/gdOhAgggAACCCCAAALBCVB8CW7KCBgBBLoR0LgZrSFnDTl2s6R7PIxLjzw8iQACTQpQfGkSkMv9FaD44u/cEBkCCCCAAAIIIBCbAMWX2GaUfBDQK6BxM1pDzhpyzPKqxSWLGtcggICrAMUXVynOC06A4ktwU0bACCCAAAIIIIBAsAIUX4KdOgJHAIGUgMbNaA05a8gxtZSdHuLixMRJCCCQUYDiS0Y4LvNfYPLkycavHbv66qv9D5wIEUAAAQQQQAABBIIToPgS3JQRMAIIdCOgcTNaQ84acuxmSfd4GJceeXgSAQSaFKD40iQgl/srQPHF37khMgQQQAABBBBAIDYBii+xzSj5IBC/wJo1a5Jf/OIXyRVXXJFMnDgxGT16dDJixAjjHzHK5rQcl+flPDlfrpPrY2kaNuA15JhlPeKSRY1rEEDAVYDii6sU5wUnQPEluCkjYAQQQAABBBBAIFgBii/BTh2BI6BKYNGiRclZZ52V7Lnnnknfvn2thRbbZrTtmFwv/Uh/0m/IzZZfyPnYYteQoy3v3o7h0psQzyOAQDMCFF+a0eNarwUmTZpkfJD81re+5XXMBIcAAggggAACCCAQpgDFlzDnjagR0CCwatWq5Morr0w+9KEPGffIto3nrMekfxlHxgut2XIOLYfe4tWQY28GtudxsalwDAEE8hKg+JKXJP14J0DxxbspISAEEEAAAQQQQCBaAYov0U4tiSEQrMCf/vSn5LTTTksGDhxYaNElvXkt48m4Mn4oLZ2DPI6tacgxy5zhkkWNaxBAwFUgvncT18w5L3oBii/RTzEJIoAAAggggAAC3ghQfPFmKggEAfUC69evT6ZPn54MGDCg1KJLehNbxpc4JB7fWzp2eRxb05BjljnDJYsa1yCAgKtAfO8mrplzXvQC3/jGN4wPmtdcc030eZMgAggggAACCCCAQPkCFF/KN2dEBBAwBebMmZOMGDHCuBe2bTDLseHDhydHH310csUVVyQPPvhg8uyzz1qvlePyvJwn58t13fWZPi7xSFw+t3TM8ji2piHHLHOGSxY1rkEAAVeB+N5NXDPnvOgFKL5EP8UkiAACCCCAAAIIeCNA8cWbqSAQBFQKbNiwYeOv+urTp0+vRZGPf/zjybXXXpv88Y9/tFq5bkbL9dKP9Ge7pv6YxCW/ikzi9LHVx1r73sc4m4mpllf912b6i+Xaeo/a97HkRh4IIFC9AMWX6ueACAoSoPhSECzdIoAAAggggAACCBgCFF8MEg4ggEBJAq+99lrysY99rMcCSP/+/ZMTTjgh6erq6jWq2gZ0/dfeLpJ+v/a1ryUyTv116e/33HPPROL1raXjlMexNQ05ZpkzXLKocQ0CCLgKxPdu4po550UvQPEl+ikmQQQQQAABBBBAwBsBii/eTAWBIKBK4Lnnnkt22GGHbgseffv2TU488cRk+fLlzi7NbEbLODKejGvrR45JvBK3T80Wq0/x5RGLhhyzOOGSRY1rEEDAVYDii6sU5wUn8PWvf934sPftb387uDwIGAEEEEAAAQQQQMB/AYov/s8RESIQm8Djjz+eDBo0yLjvrW0mjx49OnnmmWcaTrt2ff3XRjuRcWX8+j7qv5e4Ozs7G+22sPPrY6t9X9hgFXVcy6v+a0WheDVsvUfte68CJBgEEAhagOJL0NNH8D0JUHzpSYfnEEAAAQQQQAABBPIUoPiSpyZ9IYBAbwJPP/10stVWW1mLG62trcn06dN766Lb52sb0PVfuz25lyckDomnvq/a9xK/5OFDq8VU/9WHuPKMoT632vd59h9qXzWL+q+h5kLcCCDgnwDFF//mhIhyEqD4khMk3SCAAAIIIIAAAgj0KkDxpVciTkAAgZwE5O+rbLfddtaCxuDBgxP5iZhmWv0mdO37Zvp77LHHEomr1lf9V8nD5e/QNDO+y7X1MdW+d7kupHNqedV/DSn+omKt96h9X9RY9IsAAvoEKL7om3M1GcsfE6y9cda+XnvttWryJ1EEEEAAAQQQQACB8gQovpRnzUgIaBZYu3Ztsttuuxn3unLPu9NOOyVLlixpmqd2/1z/tdlOJS6Jr77P2veSj+RVZavFUv+1yniKGLs+t9r3RYwTWp81i/qvoeVAvAgg4K8AxRd/54bImhSg+NIkIJcjgAACCCCAAAIIOAtQfHGm4kQEEGhC4IgjjrAWMHbZZZdE/th9Hq1+E7r2fR79SnwnoGKuAAAgAElEQVQSZ63P+q+SV5WtPpba91XGU8TYtbzqvxYxTmh91nvUvg8tB+JFAAF/BSi++Ds3RNakAMWXJgG5HAEEEEAAAQQQQMBZgOKLMxUnIoBARoHvfe971sLFsGHDkpdffjljr+ZltQ3o+q/mWdmOSJwSb33fte8lv6paLYb6r1XFUtS49bnVvi9qrJD6rVnUfw0pfmJFAAG/BSi++D0/RNeEwNe+9jXjA911113XRI9cigACCCCAAAIIIICAXYDii92FowggkI+A/NTIoEGDjHvczTbbLFm0aFE+g/y9l/pN6Nr3eQ4g8Urctb5rXyW/vH56p9F4azHUf220D9/Pr8+t9r3vMZcRX82i/msZ4zIGAgjoEKD4omOeVWZJ8UXltJM0AggggAACCCBQiQDFl0rYGRQBNQLd/bqxO+64I3eD+k3o2vd5DyJx1/qu/1rVrx+rj6H2fd45V91fLa/6r1XH5MP49R61732IixgQQCAOAYovccwjWVgEKL5YUDiEAAIIIIAAAgggUIgAxZdCWOkUAQSSJJk/f761UHHUUUcV4lPbgK7/WsRARx55pDUvybeMtnr16mTWrFnJhAkTrHGMGjUqmThxYnLXXXclcm7orX4+a9+HnlMe8dcs6r/m0S99IIAAAiJA8YV1EK3A8ccfb3yA+s53vhNtviSGAAIIIIAAAgggUJ0AxZfq7BkZgdgFDjjgAOPeduutt05ef/31QlKv34SufV/EQBK/5FEbo/ZV8i2yLV68OBk/fnzS3t5ujF2LIf1VzpVr5NpQWzoneUxLrGsAFwQQQCAvAf5Pm5ck/XgnQPHFuykhIAQQQAABBBBAIFoBii/RTi2JIVCpwJNPPmndHL7pppsKi6vMTXrJwzae5J13W7duXTJt2rSktbXVOqYtjvQxuVb6kL5Ca+lc5DGN4gtrAAEEihXg/7TF+tJ7hQIUXyrEZ2gEEEAAAQQQQECZAMUXZRNOugiUJNDR0WEUCoYPH55s2LChsAjK3KSXPCSf9JiSd56tq6sr2X333Y1x0uO6Ppa+pM+Qmi23kOIvKlZcipKlXwQQEAGKL6yDaAW++tWvGh+srr/++mjzJTEEEEAAAQQQQACB6gQovlRnz8gIxCqwdu3aZPPNNzfua2+++eZCUy57M1rySY8peUv+ebQFCxYkgwcPNsZIj9noY+lT+g6l2fILJfYi48SlSF36RgABii+sgWgFKL5EO7UkhgACCCCAAAIIeCdA8cW7KSEgBIIXmDlzplEwGDhwYOG/8qrszWj5FV6SV3pcyb/ZJj+dUkThpRar9B3KT8DUYq7/2qxvDNfXe9S+jyEvckAAAT8EKL74MQ9EUYAAxZcCUOkSAQQQQAABBBBAwCpA8cXKwkEEEGhC4JBDDjEKEscdd1wTPbpdWtuArv/qdmX2sySv+vHke8m/mSZFnTx/1Vg6vtpjGSOEvwFTi7f+azO+sVxb71H7PpbcyAMBBKoXoPhS/RwQQUECFF8KgqVbBBBAAAEEEEAAAUOA4otBwgEEEGhSYNCgQUZBYu7cuU322vvltQ3o+q+9X9XcGZJX/XjyveTfTJs2bZrRZ3qMvB7LWL43W66+x1xGfLiUocwYCOgVoPiid+6jz9z2L2duuOGG6PMmQQQQQAABBBBAAIHyBSi+lG/OiAjELPDEE08YhQP5OyjyB+qLblVsRktetr9vIw5Z2uLFi5PW1lbD0JZbHsdkLBnT52bL0+d4y4oNl7KkGQcBnQIUX3TOu4qsKb6omGaSRAABBBBAAAEEvBCg+OLFNBAEAtEIXH/99UbhYP/99y8lv6o2oyW/9NjikKWNHz/e6Cvdd96PZUyfmy1fn+MtKzZcypJmHAR0ClB80TnvKrKm+KJimkkSAQQQQAABBBDwQoDiixfTQBAIRCMwefJko3hw/vnnl5JfVZvRkl96bHFotK1evTppb283+kr3nfdjGVPG9rXZ8vU11jLjwqVMbcZCQJ8AxRd9c64m44kTJxoftm688UY1+ZMoAggggAACCCCAQHkCFF/Ks2YkBDQI7Lvvvsb97D333FNK6lVtRkt+6bHFodE2a9Yso590v0U9lrF9bbacfY21zLhwKVObsRDQJ0DxRd+cq8mY4ouaqSZRBBBAAAEEEECgcgGKL5VPAQEgEJXALrvsYhQQnnrqqVJyrGozWvJLjy0OjbYJEyYY/aT7Leqx7EP42mw5+xprmXHhUqY2YyGgT4Dii745V5MxxRc1U02iCCCAAAIIIIBA5QIUXyqfAgJAICqB973vfZUVEGyb0VUdE4dG26hRoyqzk7F9bbY59DXWMuPCpUxtxkJAnwDFF31zriZj2792uemmm9TkT6IIIIAAAggggAAC5QmUUXy54+dLEhmH/zBgDcS/BjZtK/9vltg2oas+Jg6Nrve2/gMrK77I2I3GW9b5trksa2yfx8El/v+f+rz+iM3v9XfnL15o+maC4kvThHTgqwDFF19nhrgQQAABBBBAAIH4BOTmuehG8cXvG3Q2UJifPNdAS0ufygoIts3oqo6JQ6OufTZtrcxOxm403rLOt81hWWP7PA4u/L/b5/VJbNWuT/ns3Wyj+NKsINd7K0DxxdupITAEEEAAAQQQQCA6Abk5LrpRfKn2BpwNEPzLXAP85MsmGwsoWX7yheKL/bVKkQGXMv8fxlj29YZLWC4UX4q+u6H/oAXGjx9v/GuXm2++OeicCB4BBBBAAAEEEEDATwG5mS66UXwJ64adDRbmq5k10G/ANsb9rG3zPPZj4tCoI792zP7as62VRm1jPB8X+3qJca7JibludA1QfCn67ob+gxag+BL09BE8AggggAACCCAQlIDczBXdKL6wadDopgHnh7tmNh/0D0bxZfSRtzRciMiyBqrajJb80mOLQ6M5bLndB41+0v0W9VjGbjTess635VzW2D6Pg0u4/5/0eV0RWxzriuJL0Xc39B+0AMWXoKeP4BFAAAEEEEAAgaAE5CabhgACCOQlsO+++xoFhHvuuSev7nvsx7YZ3eMFOT0p+aXHFodGm+1XkKf7LerxxIkTGw23tPNtOZc2uMcD4eLx5BAaAhEI8DdfIphEUrALHHvsscYHt1tuucV+MkcRQAABBBBAAAEEEGhCgOJLE3hcigAChsDkyZON+9nzzz/fOK+IA1VtRkt+6bHFodE2a9Yso590v0U9vuuuuxoNt7TzbTmXNrjHA+Hi8eQQGgIRCFB8iWASScEuQPHF7sJRBBBAAAEEEEAAgfwFKL7kb0qPCGgWuOGGG4wCwv77718KSVWb0ZJfemxxaLStXr06aW9vN/pK9533YxlTxva12fL1NdYy48KlTG3GQkCfAMUXfXOuJmOKL2qmmkQRQAABBBBAAIHKBSi+VD4FBIBAVAJPPPGEUTzYfPPNkw0bNhSeZxWb0ZKX5JceWxyyNNuvIU/3nfdjGdPnZsvX53jLig2XsqQZBwGdAhRfdM67iqwpvqiYZpJEAAEEEEAAAQS8EKD44sU0EAQCUQkMGjTIKEbMnTu38Byr2IyWvNLjSv5Z2+LFi5PW1lajz/QYeT2WsWRMn5stV5/jLSs2XMqSZhwEdApQfNE57yqy7ujoMD5offe731WRO0kigAACCCCAAAIIlCtA8aVcb0ZDQIPAIYccYtzTHnfccYWnXsVmtOSVHlfyb6ZNmzbN6DM9Rl6PZSzfmy1X32MuIz5cylBmDAT0ClB80Tv30WdO8SX6KSZBBBBAAAEEEEDAGwGKL95MBYEgEI3AzJkzjeLBwIEDk3Xr1hWaY9mb0ZKP5JUeV/Jvpkm/u+++u9FvepxmH8sYRc9JMw61a2151p7T/BUXzbNP7ggUL0DxpXhjRqhIgOJLRfAMiwACCCCAAAIIKBSg+KJw0kkZgYIF1qxZY/07KDfffHOhI5e9GS35pMeUv/+ydu3apvPs6upKBg8ebPSfHi/rY+lbxgih2XIMIe6iY8SlaGH6R0C3AMUX3fMfdfZf+cpXjA9Y3/ve96LOmeQQQAABBBBAAAEEqhGg+FKNO6MiELuA7R8VDh8+PJE/UF9UK3MzWvKQfNJjSt55tQULFhRSgJHCi/QdSksby2NaYqw9XFgVCCCQpwD/p81Tk768EqD44tV0EAwCCCCAAAIIIBC1AMWXqKeX5BCoTODJJ5+0bg7fdNNNhcVU5ia95GEbT/LOs8lPp+T5K8ikr1B+4qXmaHOuPaf5Ky6aZ5/cEShegOJL8caMUJEAxZeK4BkWAQQQQAABBBBQKEDxReGkkzICJQkccMABRoFi6623Tl5//fVCIihrM1rilzzS40m+RTT5uyzTpk1LWltbjTHTMXT3WK6VPkL4Gy9pQ1tO6XM0PsZF46yTMwLlCVB8Kc+akUoWOOaYY4wPVLfeemvJUTAcAggggAACCCCAgAYBii8aZpkcEahGYP78+ca9rWwYH3nkkYUEVNZmtMRvG0vyLbItXrw4GT9+fNLe3m4d3xaTnCvXyLWhNlteoeaSZ9y45KlJXwggkBag+JIW4XE0AhRfoplKEkEAAQQQQAABBLwXoPji/RQRIAJBCxxxxBHWQsEdd9yRe15lbEZL3LZxJM+y2urVq5NZs2YlEyZMsMYyatSojc/JOXJu6M3mHXpOecSPSx6K9IEAAt0JUHzpTobjwQtQfAl+CkkAAQQQQAABBBAIRoDiSzBTRaAIBCmwfPnyZNCgQUaRYLPNNksWLVqUa05Fb0ZLvBJ3ehzJT/KsoqVjkcexNQ05ZpkzXLKocQ0CCLgKxPdu4po550UvcPTRRxsf5r7//e9HnzcJIoAAAggggAACCJQvQPGlfHNGRECbgPwabdtG8bBhw5KXX345Nw7bGHl1LnFKvLYxqvw14bZ48srZl3405JjFGpcsalyDAAKuAhRfXKU4LzgBii/BTRkBI4AAAggggAACwQpQfAl26ggcgaAEDj/8cGvhYpdddsntp0aK2oyWn2rZeeedrfGX+evGbBNeVM62sao6piHHLLa4ZFHjGgQQcBWg+OIqxXnBCVB8CW7KCBgBBBBAAAEEEAhWgOJLsFNH4AgEJbB27dpkt912sxYwpLDxwgsvNJ1PEZvREtdOO+1kjVvykbyqbEXkXGU+trE15GjLu7djuPQmxPMIINCMAMWXZvS41muBo446yvhgd9ttt3kdM8EhgAACCCCAAAIIhClA8SXMeSNqBEIU6OrqSrbbbjvjflc2kQcPHpw8/vjjTaWV92a0xCNx2fqVPCSfqpsttqpjynt8DTlmMcMlixrXIICAqwDFF1cpzgtOgOJLcFNGwAgggAACCCCAQLACFF+CnToCRyBIgaeffjrZaqutrAWN1tbWZPr06ZnzynMzWuKQeGx9SvyShw/NFp8PceUZg4Ycs3jhkkWNaxBAwFWA4ourFOcFJ0DxJbgpI2AEEEAAAQQQQCBYAYovwU4dgSMQrID8REl3BRjZUB49enTyzDPPNJxfHpvRMq6Mb+tLjg0aNCjp7OxsOLaiLrDFWdRYVfWrIccstrhkUeMaBBBwFaD44irFecEJUHwJbsoIGAEEEEAAAQQQCFaA4kuwU0fgCAQt8NxzzyU77LBDt0WOvn37JieeeGIif+zetTWzGS3jyHgyrq0fOSbxStw+NVusPsWXRywacszihEsWNa5BAAFXAYovrlKcF5zAkUceaXzYmzlzZnB5EDACCCCAAAIIIICA/wIUX/yfIyJEIFaB1157LfnYxz5m3P/Wbyr3798/OeGEE5z+vkr9dbXve7OTv9si/cs4tWtsX/fcc89E4vWt2WL1Lcb/1969QNlVnvfBj2RFQbKMQFjCsUJkWmO3kVNbaWhMmhJIA2lKHHBxpFCnaSpWm0tXhYv52iQf8arLShx1FTldRXWJlaahGAeTYAdXvlSRbCPbILDNxTaOCViCmIsFRtbFVoRkv996pt8Zzpy9R3PmnL332ZffXos1c/bZ+32f5/cedGb2f2bPuPV0ocdRjLiMouYcAgSGFRC+DCvluMYJCF8at2QKJkCAAAECBAg0VkD40tilUziBVggcP348/fqv/3pauHDhScOPuNB83nnnpRtuuCE99thjub0PezE6zo9xYry8c/r3RV1RX9RZx62/1t7ndaxznJp6ffV/HGe8tpzb79H7vC296YMAgckLCF8mvwYqKElA+FISrGEJECBAgAABAgQyAsKXDIkdBAhMQGDnzp3pnHPOmTMM6V1kPvvss9Mv/dIvpeuvvz7dcccd6aGHHso9N/bH83FcHB/n9caY62PUE3XVecvroc71jlJbF3rkMoqAcwgQKFNA+FKmrrEnKvALv/ALmS8G/9f/+l8TrcnkBAgQIECAAAEC7RQQvrRzXXVFoIkCx44dS+94xzvSsmXLMt8T512AL2tfzB91RD113/IM6l7zfOvrQo/zNYnjuYyi5hwCBIYVEL4MK+W4xgkIXxq3ZAomQIAAAQIECDRWQPjS2KVTOIHWCjz99NNTt/pavnx57gXmvIvOReyL+eIWYzF/U7a8vptS+7B1dqHHYS36j+PSr+FzAgSKFhC+FC1qvNoICF9qsxQKIUCAAAECBAi0XkD40vol1iCBxgocPHhw6nZhr33ta0sNYWL8uC1ZzNe0rQsX4LvQ4yivOy6jqDmHAIFhBYQvw0o5rnECb37zmzNfWN58882N60PBBAgQIECAAAEC9RcQvtR/jVRIgEBKX/jCF9K1116bXv/616dFixZlvmfOuxA92744P8aJ8WLcJm95PTa5n7zau9BjXt9z7eMyl5DnCRAYR0D4Mo6ec2stIHyp9fIojgABAgQIECDQKgHhS6uWUzMEOiFw+PDh9NGPfjT95//8n9O/+lf/Kl1wwQXpnHPOSS972cum/l7Mi170oqmP8Tj2x/NxXBwf5x05cqQ1Tl24AN+FHkd5QXIZRc05BAgMKyB8GVbKcY0TEL40bskUTIAAAQIECBBorIDwpbFLp3ACBAjk/gZQ21iEDPkryiXfxV4CBIoREL4U42iUGgr803/6TzNfQL3nPe+pYaVKIkCAAAECBAgQaLqA8KXpK6h+AgS6LNCFC/Bd6HGU1zCXUdScQ4DAsALCl2GlHNc4AeFL45ZMwQQIECBAgACBxgoIXxq7dAonQIBA5gc344J82zYhQ/6Kcsl3sZcAgWIE2vduUoyLUVogIHxpwSJqgQABAgQIECDQEAHhS0MWSpkECBDIEejCBfgu9JiztHPu4jInkQMIEBhDQPgyBp5T6y1wxRVXZH565ZZbbql30aojQIAAAQIECBBopIDwpZHLpmgCBAhMCXThAnwXehzl5cxlFDXnECAwrIDwZVgpxzVOQPjSuCVTMAECBAgQIECgsQLCl8YuncIJECCQ+cHNuCDftk3IkL+iXPJd7CVAoBiB9r2bFONilBYICF9asIhaIECAAAECBAg0RED40pCFUiYBAgRyBLpwAb4LPeYs7Zy7uMxJ5AACBMYQEL6MgefUegsIX+q9PqojQIAAAQIECLRJQPjSptXUCwECXRPowgX4LvQ4yuuWyyhqziFAYFgB4cuwUo5rnMDP//zPZ351+L3vfW/j+lAwAQIECBAgQIBA/QWEL/VfIxUSIEBgNoEuXIDvQo+zre/J9nM5mY7nCBAYV0D4Mq6g82srIHyp7dIojAABAgQIECDQOgHhS+uWVEMECHRIoAsX4LvQ4ygvWS6jqDmHAIFhBYQvw0o5rnECwpfGLZmCCRAgQIAAAQKNFRC+NHbpFE6AAIHMXTPignzbNiFD/opyyXexlwCBYgTa925SjItRWiCwYcOGzBdQf/zHf9yCzrRAgAABAgQIECBQNwHhS91WRD0ECBAYXqALF+C70OPwK/7CkVxesPAZAQLFCwhfijc1Yk0EhC81WQhlECBAgAABAgQ6ICB86cAia5EAgdYKdOECfBd6HOUFymUUNecQIDCsgPBlWCnHNU5A+NK4JVMwAQIECBAgQKCxAsKXxi6dwgkQIJC5a0ZckG/bJmTIX1Eu+S72EiBQjED73k2KcTFKCwTWr1+f+QLq1ltvbUFnWiBAgAABAgQIEKibgPClbiuiHgIECAwv0IUL8F3ocfgVf+FILi9Y+IwAgeIFhC/FmxqxJgLCl5oshDIIECBAgAABAh0QEL50YJG1SIBAawW6cAG+Cz2O8gLlMoqacwgQGFZA+DKslOMaJyB8adySKZgAAQIECBAg0FgB4Utjl07hBAgQyNw1Iy7It20TMuSvKJd8F3sJEChGoH3vJsW4GKUFAj/3cz+X+QLqfe97Xws60wIBAgQIECBAgEDdBIQvdVsR9RAgQGB4gS5cgO9Cj8Ov+AtHcnnBwmcECBQvIHwp3tSINREQvtRkIZRBgAABAgQIEOiAgPClA4usRQIEWivQhQvwXehxlBcol1HUnEOAwLACwpdhpRzXOAHhS+OWTMEECBAgQIAAgcYKCF8au3QKJ0CAQOauGXFBvm2bkCF/Rbnku9hLgEAxAu17NynGxSgtEHjTm96U+QLqtttua0FnWiBAgAABAgQIEKibgPClbiuiHgIECAwv0IUL8F3ocfgVf+FILi9Y+IwAgeIFhC/FmxqxJgLCl5oshDIIECBAgAABAh0QEL50YJG1SIBAawW6cAG+Cz2O8gLlMoqacwgQGFZA+DKslOMaJyB8adySKZgAAQIECBAg0FgB4Utjl07hBAgQyNw1Iy7It20TMuSvKJd8F3sJEChGoH3vJsW4GKUFAsKXFiyiFggQIECAAAECDREQvjRkoZRJgACBHIEuXIDvQo85SzvnLi5zEjmAAIExBIQvY+A5td4Cl19+eeanV/7kT/6k3kWrjgABAgQIECBAoJECwpdGLpuiCRAgMCXQhQvwXehxlJczl1HUnEOAwLACwpdhpRzXOAHhS+OWTMEECBAgQIAAgcYKCF8au3QKJ0CAQOYHN+OCfNs2IUP+inLJd7GXAIFiBNr3blKMi1FaICB8acEiaoEAAQIECBAg0BAB4UtDFkqZBAgQyBHowgX4LvSYs7Rz7uIyJ5EDCBAYQ0D4MgaeU+st8E/+yT/J/PTKn/7pn9a7aNURIECAAAECBAg0UkD40shlUzQBAgSmBLpwAb4LPY7ycuYyippzCBAYVkD4MqyU4xonIHxp3JIpmAABAgQIECDQWAHhS2OXTuEECBDI/OBmXJBv2yZkyF9RLvku9hIgUIxA+95NinExSgsEhC8tWEQtECBAgAABAgQaIiB8achCKZMAAQI5Al24AN+FHnOWds5dXOYkcgABAmMICF/GwHNqvQXe+MY3Zn565fbbb6930aojQIAAAQIECBBopIDwpZHLpmgCBAhMCXThAnwXehzl5cxlFDXnECAwrIDwZVgpxzVOQPjSuCVTMAECBAgQIECgsQLCl8YuncIJECCQ+cHNuCDftk3IkL+iXPJd7CVAoBiB9r2bFONilBYICF9asIhaIECAAAECBAg0RED40pCFUiYBAgRyBLpwAb4LPeYs7Zy7uMxJ5AACBMYQEL6MgefUegtcdtllmZ9eef/731/volVHgAABAgQIECDQSAHhSyOXTdEECHRQYN++fenmm29O1157bVq/fn1at25d5tpBXJBfs2bN1HNxTBwb58S5Td2EDPkrxyXfxV4CBIoREL4U42iUGgoIX2q4KEoiQIAAAQIECLRUQPjS0oXVFgECjRc4fvx42r59e9q4cWM6++yzc4OWvAvws+2LMWKsGDPGbsqW109Tai+zTi5l6hqbAAHhi9dAawWEL61dWo0RIECAAAECBGonIHyp3ZIoiACBjgs8/PDDadOmTWnVqlVjBy55F+hjX4wdc8Rcdd/yeqh7zVXUx6UKZXMQ6K6A8KW7a9/6zi+99NLMF1gf+MAHWt+3BgkQIECAAAECBKoXEL5Ub25GAgQI5Ancd999U7cTW7hwYeaaQN6F9iL2xVxxe7KYu65bXp91rbXKurhUqW0uAt0TEL50b80707HwpTNLrVECBAgQIECAwMQFhC8TXwIFECDQcYH9+/dP3Q5swYIFlYUugxfuY+64JVnUUrdtsNZ4bEu5rxUuBAgQKErAv7RFSRqndgLCl9otiYIIECBAgAABAq0VEL60dmk1RoBAAwRuvPHGdNppp+VeSB8MHRYtWpTOO++8dM0116Rt27al3bt35563d+/eqefimDg2zolzB8fLexy1RE112vLqrFN9k6qFy6TkzUugGwLCl26scye7FL50ctk1TYAAAQIECBCYiIDwZSLsJiVAoOMCBw4cSJdffvmcgciSJUvShg0b0h133JGOHDmSURv2Avzhw4enxoixYsy88/r3RW1RYx22/rp6n9ehrknX0LPo/zjpmsxPgEB7BIQv7VlLnQwI/OzP/mzmC6E/+7M/GzjKQwIECBAgQIAAAQLjCwhfxjc0AgECBOYj8MADD6Q1a9Zkvu/vv4i+evXqtGXLlnTo0KGTDt1/Tu/zk56QUjp48GC6/vrrU8zROyfvY9QYtU56y6tt0jXVYX4udVgFNRBor4Dwpb1r2/nOhC+dfwkAIECAAAECBAhUJiB8qYzaRAQIEEi7du1Kp5566qyhx4oVK9LWrVvTsWPHhtIa5wJ8zHHDDTekmDNvnNi3fPnyqZqHKqakg/JqK2mqRg3LpVHLpVgCjRMQvjRuyRQ8rIDwZVgpxxEgQIAAAQIECIwrIHwZV9D5BAgQGE7g9ttvT4sXL5416LjyyivTM888M9xg//9RRVyAjzlj7ryxYl/UHLVPasura1K11GleLnVaDbUQaJ+A8KV9a6qj/1/gDW94Q+aLnri/q40AAQIECBAgQIBA0QLCl6JFjUeAAIGswI4dO2YNXk4//fSRw40iL8BHwBK15I0ZAUz0MIktr55J1FG3ObnUbUXUQ6BdAsKXdq2nbvoEhC99GD4lQIAAAQIECBAoVUD4UrV8IqQAACAASURBVCqvwQkQIJDuueeetGzZstxQY+3atWnfvn0jKxV9AT5qiZryxo0eopeqt7xaqq6hjvNxqeOqqIlAewSEL+1ZS50MCAhfBkA8JECAAAECBAgQKE1A+FIarYEJECCQ9u/fP+sftj///PPTgQMHxlIq4wJ81BS15Y29evXqqZ7GKnqeJ+fVMc8hWnk4l1Yuq6YI1EZA+FKbpVBI0QI/8zM/k/ki54Mf/GDR0xiPAAECBAgQIECAQBK+eBEQIECgPIGLLroo8/19XDSPcOPo0aNjT1zWBfiobbYA5uKLLx677vkMUFaP86mhjsdyqeOqqIlAewSEL+1ZS50MCAhfBkA8JECAAAECBAgQKE1A+FIarYEJEOi4wObNm3ODl3Xr1qWDBw8WolPmBfioMWrNmyN6q2rLm7+ques8D5c6r47aCDRfQPjS/DXUwSwCwpdZYOwmQIAAAQIECBAoXED4UjipAQkQIJD27t2bli5dmgkuVq1alZ544onChMq+AB+1rly5MtNH9BY9VrGV3WMVPZQxB5cyVI1JgEBPQPjSk/CxdQKXXHJJ5gub//2//3fr+tQQAQIECBAgQIDA5AWEL5NfAxUQINA+gbzv6xcuXJh27NhRaLNVXICPmqP2wbmixyq2wXnjsS1l1oOLVwUBAkUK+Je2SE1j1Uog74s04UutlkgxBAgQIECAQIUCx44dS3feeWf68Ic/nD772c/mzjzMMbkn2ulvvngNECBAoGCBnTt35l4Yf+tb31rwTNVdgL/66qtze4pey96EL/nCXPJd7CVAoBgB4UsxjkapoYDwpYaLoiQCBAgQIECgVIFDhw6l73znO7lz/NEf/dGMCz5f/epXM8cNc0zmJDumBPzmixcCAQIEihW44IILZrxvxUXys846Kx05cqTYiVJ14cvhw4enehi84B+9lrEdOHAg3XTTTWnjxo0Zy6jh3HPPnXoujolju7gNrkU8thEgQKAoAf+iFCVpnNoJ/ON//I8zX1xs3769dnUqiAABAgQIEJiMwDe+8Y3027/92yl+CjX++93f/d0UF0WauL3//e9Pq1evnvraJ+6D//jjj2fa+B//43/M+NroscceG+mYzEl2TAkIX7wQCBAgUJzA7t27Z7xn9S6Q33rrrcVN0jdSb/z+j31PF/pp9NA/T+/z6Lmo7f77709XXHFFWrx4ce5cvTn7P8axcU6c26Wt36D3eZf61ysBAuUKCF/K9TX6BAWELxPENzUBAgQIEGiAwNvf/vbMBYnf+Z3faUDl2RLf+MY3zuglfoJ1cBO+DIoU+1j4Uqyn0QgQ6LZAhAC9C+G9j2vXri0NpTdH/8fSJkspRS/9c8Xn0fO423PPPTf1mywLFizIjD8432yP49z4TZkYqwtbnkMX+tYjAQLVCAhfqnE2ywQEhC8TQDclAQIECBBokMA555yTuTDxAz/wAw3q4IVS3/SmN83oJYKWwU34MihS7GPhS7GeRiNAoLsCBw8eTEuWLJnxvhYXyG+55ZbSUKq+AB+9DM4ZPUfvo2579uzJvaXZ4DzDPo5bvMWYbd/yPNres/4IEKhOQPhSnbWZKhYQvlQMbjoCBAgQINAggbvvvjtz0aP3zfdsf4y+zu3dfvvtU7cdi59Wfd3rXpf+6q/+KlOu8CVDUugO4UuhnAYjQKDDAu9+97sz79ErV65Mzz//fGkqva8B+j+WNllKU71ET/3zxefR+yjbhz70obR06dLMeIPjz/dxjBljt3nLM2lzv3ojQKBaAeFLtd5mq1Dgp3/6pzNfeLT9i4YKeU1FgAABAgQaLfCv//W/znyd0Pvm+y1veUtjezt69OistQtfZqUp5AnhSyGMBiFAgEC69NJLM+/RV111Vakyva8B+j+WOmFKKXrqny8+j97nu915553plFNOyYw1OPaoj2PsmKOtW55LW3vVFwEC1QsIX6o3N2NFAsKXiqBNQ4AAAQIEGiYQPzn70pe+dPoixS//8i+nM888c/rxy172snTixImGdTV3ucKXuY3GOUL4Mo6ecwkQIPB/BeL9d/ny5dPvyb0L4/Ebq2VuvXn6P5Y5X4yd91u40ft8vgZ58sknZ3wN019/kZ/H10kxVxu3PKc29qknAgQmIyB8mYy7WSsQEL5UgGwKAgQIECDQQIEPfvCDMy7q7N69O/2bf/NvZuz7yEc+Mmdn3/nOd9KXv/zl9PnPfz4dOHBgxvFxz/Y77rgjvetd70qf/OQn0ze/+c0Zzw/7IG4fFr+5+9/+239Lf/zHf5w+97nPpZh3cIt9X/nKV6Zqme3iSNHhS1wcuvfee9Ott96abrjhhvRf/+t/TR/4wAfSI488klvjYM1teyx8aduK6ocAgUkIxN8YGbwYPt9AYpS6B+eMx2VvswVN8/k7K5dddlnGK6+XIvbFXG3c8mza2KeeCBCYjED57yaT6cusBNI/+kf/KPNFyIc//GEyBAgQIECAQMcF1q9fP/01Qvwx2Qgu7rrrrul98U34m9/85jmV3vOe90yf88M//MNTx3/84x9Pr3/969OLXvSi6edivHj8cz/3c+nw4cNzjhv1bN26NZ1xxhkzxuhdHFi9enX6vd/7vRk/Gdtfy8KFC9NTTz2Vmaeo8OX+++9P//yf//N06qmn5tYXdYbHpz/96UwNbd4hfGnz6uqNAIGqBOL9r/d+1/s4yq245ltvb67+j/MdY5Tj826xFgbDbDt37sxY9ddfxucxZ9u2PKe29agfAgQmJyB8mZy9mUsWEL6UDGx4AgQIECDQQIH4jZT++6Jfc801012cffbZ0xcxXvziF6cjR45MP5f3SX+Y8YM/+IPpd37nd1L8wfu8b+J7++K4Z555Jm+4qX3xWys/+ZM/edIxemNdccUV0+P01xLPP/bYY9PP9T4p4pj/+T//ZyZY6tUz+DEs4rdiurIJX7qy0vokQKBMgU2bNmXeA6+77royp5wae/A9LB5XsUVvg3OHwTDbhRdemDl3cKyiH8ecbdvyjNrWo34IEJicQDXvJpPrz8wdFhC+dHjxtU6AAAECBGYR+IM/+IMZFyo++9nPTh/5m7/5mzOeu+mmm6afy/tkMMzo/+Z9xYoV6fzzz0/xWyr9++Pza6+9Nm+4qX15PwH7qle9Kr3hDW9Ir3vd69KiRYumx1u8ePH0OIO1lBW+vPGNb5yeP3o555xz0oYNG9Jb3vKW9PM///Np5cqVM56P3ywa9ZZr08015BPhS0MWSpkECNRa4OKLL57xPhLvNbfddlvpNQ++V8fjKrbobXDuMJhri1t8zvUDH4PjFvE45oy527TlubSpP70QIDBZgWreTSbbo9k7KvBTP/VTmS9ihrl/e0e5tE2AAAECBDoh0P9TohEc9G9f+MIXZnztMNfFj8HAo/fN+9VXXz3jt2b+03/6TzMukEQwkxdIDN4+JI6LvxfTv8UFj7h9Wcz1kpe8ZPqpwVrKCl/+2T/7Z1Nz/8zP/Ez61Kc+NT1/75PnnnsuXXDBBTMc3/e+9/WebvVH4Uurl1dzBAhUJPDqV796xntIvN89+OCDpc/eew/v/1j6pClN9dY/Z3weBnNtW7ZsyTgNjlPW45i7TVueU5v60wsBApMVEL5M1t/sJQoIX0rENTQBAgQIEGigwOOPP57i76H0vsl+29velukibgvWez7+Tkve307pnTQYeMR5/+E//Ife0zM+RljRGzc+9v/GTe/A+M2W/mPij9nPtv3Jn/zJ1N+F6T0/WEtZ4cvXv/719Oijj/amzf34wAMPzOhj8+bNuce1aefXnjuaNvzmJ0pv6T0feTRFyOM/Bl4DXgNtfQ2csuylM95D+t8Xu/J5GMy1vi975Y9NzCnmnqu+Jj2f97pqUv1q9X7gNVDea+CWj35l7K/vhS9jExqgrgLCl7qujLoIECBAgMBkBH73d393xoWKhx56KFPIO97xjhnHXH/99ZljejsGA4/Zgpc4/vbbb58x7gc/+MHeMFMfv/GNb8x4Pn57ZD7bYC1lhS/D1hR/M6d3MeNXfuVXhj2tccc99vSRdPOHH03/8rfvSnu+OPvf8imqMeFLed9cu3DB1mugHq+BFy1eOv3+0Xsf6drHMJjr9fji07O3Na3KKeaeq74mPZ/n1qT61VqPf7usQzvXIb72HncTvowr6PzaCuTdK/ajH/1obetVGAECBAgQIFCuwGte85rpCzqvfe1rcyfbt2/fjFuErVu3Lve42DlM4NE7+f7775+eO77J//3f//3eU1MfP/OZz8x4ftu2bTOen+vBMLUUdcxctcTzr3zlK6f7+YVf+IVhTqn9MfHbLZ/50rPpT3c9ljbf9IX0L97+qfRv33lvev/HH09Hjp6opH7hSzu/sXfBxrp6DbzwGliw4IXfUM27KN6FfWEw12tikiHVMOHQXPXX6fm811Sd6lPLC/8+sGBR9WtA+FLJtzgmaaqA8KWpK6duAgQIECBQvMBg+BG/4TLb9qM/+qPTwUF8Q/7FL34x99BhwozeiU8//fSMMd/5znf2npr6+N73vnfG8/H3X+azDVNLUcf06nryySfTH/7hH6b/+B//Y/rVX/3VdNlll6X4zeP4b9GiRdP91CV8OfHt76Rjx7+dvvXXJ9KRbx1PBw4dS09//Vtp31NH0kNfOZDufejZ9LHPPJU+8InH0x9tfyS9870Ppd/67/elX37H3enyf/fx9Etv/9TU4z/84F+mTz6wP33j8LEeRWUfhS8uOlR90cF8XnNVvwYmGSrkXYSfxL5hwo1JhlTDhENVv27GmS9vjccZz7n+3fQaaM9rQPhS2bc5JmqigPCliaumZgIECBAgUI7AW9/61ukwIL7JvuGGG9L27dtz/3vDG94w49hf//Vfzy1qmDCjd+KBAwdmjDkYvlx33XUznv/Sl77UO3Woj8PUUtQx8TddfuInfmLG38/Ju3DR21eH8GW+ocUb/5+PpbdsuTdtve0v0ic+99RUUDPUQpR80Hz78M1/e775t5bWsiuvAX/z5bvSMH/zZZIh1TDhUJNer72vV/o/Nql+tXp/8Boo7zUgfCn5mxvDN1vgoosumnERI95I/8//+T/Nbkr1BAgQIECAwLwFTpw4kV7+8pdnvi7o/yb7ZJ9///d/f/rOd76TmXeYMKN30lzhy2/8xm/MqC/v79H0xsr7OEwtRRzz+c9/Pp1xxhkzau3ZLV68OK1YsWLqv96++FiH8CXM2vCbL3lrbx8BAgTaJPDqV7868x7z4IMPlt5i//tW7/PSJ00pRW+9+Xofw2Cu7Zxzzsmc1zu/7I+vetWr5iqvUc/neTWqAcUSIFBrAX/zpdbLo7hxBIQv4+g5lwABAgQItEcgfvgi7xvr+ez72Mc+lgEZJszonTRX+PKud71rRo07duzonTrUx2FqGfeYCLG+93u/d0adP/uzP5ui1q9//esz6uy/eFaX8GVGgSM8qMPffBmhbKcQIECgUQJ5d7C47bbbSu8h72uC0idNKUVvg3OHwVxb3Opz8LyqHsfcbdry3NrUn14IEJisgPBlsv5mL1FA+FIirqEJECBAgECDBH7xF39xxgWKSy65JEVocLL/fuRHfmTGOVdeeWWm42HCjN5Jc4UvH/nIR2bMd+ONN/ZOHerjMLWMe8xnPvOZGTVu3Lhx1traGL7kNfvY00fSzR9+NP3L374r7fniM3mH2EeAAAEC8xDYtGnTjPeauDAet+Yse5vUBfjB245GHWEw17Zly5aMU14PZeyLudu05Rm1qT+9ECAwWQHhy2T9zV6igPClRFxDEyBAgACBhgh885vfTMuWLZu+QPGa17xmqMq/9rWvzfij8cuXL09Hjx6dce4wYUbvhLnCly9/+cvTNcZFgAh/5rMNU8u4x/yX//JfZtR47733zlpiV8KXHkD8VsyG3/xE76GPBAgQIDCiwNatW2e818R74qWXXjriaMOfNqkL8NHb4NxhMNf2yCOPpAULFmTOHRyr6Mcx56OPPjpXeY16Ps+oUQ0olgCBWgsIX2q9PIobR+Anf/InM1+IzPcWHuPM71wCBAgQIEBg8gLvec97Znw9MJ+fnv2pn/qpGee+733vm9HQMGFG74S5wpfnn38+fd/3fd+M+Wb7W3XHjx9Pb3vb26b+6H3vb9EMU8u4x2zevHlGfXfffXevvRkf47d2Fi1aNH1sW247NqPJnAfxx05tBAgQIDCewJ49e6bfP3oXxeMHIOLWl2Vuvbn6P5Y5X4wdPUVv/XPG52EwzHbhhRdmzh0cq+jHMWfbtjyjtvWoHwIEJicgfJmcvZlLFhC+lAxseAIECBAg0ACBn/7pn55xYeLhhx8euuqbbrppxrlxm7L+bZgwo3f8XOFLHDf4d19OOeWUFDVEMBNbBC0RyKxbt26qrvgD973fxhmmlnGP+ehHPzrDI+5J/9xzz/VaTBEK/ft//+9nHBMXNIQv00Q+IUCAAIE5BGYLJGYL/OcYbuinJ3EB/q677sq8Z84naPrzP//zzPl5fRS5b+fOnUObNuXAPJ+m1K5OAgTqLyB8qf8aqXBEAeHLiHBOI0CAAAECLRF4+umnZ/wGxg/90A/Nq7NDhw6lJUuWTF/Y+O7v/u707LPPTo8xTJjRO3iY8CVClle84hXT8/UuBnzP93zP1G/FvPjFL848961vfWtqimFqGfeY6GHFihUzagiTCGEimDr11FNnPNerX/jSexX4SIAAAQLDCOTdiuuqq64a5tSRj+m9Z/V/HHmwIU+Mnvrni8/ne4u1yy67LDPG4JhFPY652rjl+bSxTz0RIDAZAeHLZNzNWoHAP/yH/zDzRUj8ZIiNAAECBAgQ6IbA4H3j47ZZ893Wr18/4+uJ3//9358eYpgwo3fwMOFLHPvQQw+l+Ls0eRcCBvf1X4gappYijvmzP/uzOWs788wz0yWXXDJ9nPCl9yrwkQABAgSGEdi2bdv0e0jvvW/lypXTvwk6zBjzPaY3T//H+Y4xn+PjBy6ip/754vPofT7bk08+meJ9d3Ccoh/HHDFXG7c8qzb2qScCBCYjIHyZjLtZKxAQvlSAbAoCBAgQIFBjgd/6rd+avhgRvzXy+OOPz7vaj3zkIzP+oG38rZXedtttt02PH78B8rWvfa33VObjN7/5zRS3Eet9g/8Hf/AHmWN6O+K3WX7t134t92JK/C2V+Bpn8O/BDFNLUcd87GMfS+eee+50L72e4lYpb3rTm9JTTz2Vor/e/l/5lV/ptdbqj/7mS6uXV3MECFQocPDgwRm/edp7P7nllltKq6I3R//H0iZLKUUv/XPF5/HbttH7fLc777xzxtcYg+OO+zi+fok52rrl+bS1V30RIFC9gPClenMzViQgfKkI2jQECBAgQKCmAvE3UuLWY0888cT030YZpdS4EPLVr351aqzeH7jvjRN/8ySei3Blri2OiWO//vWvz3Xo9PMRZETQ8qEPfSjt3r07xW/QzLYNU0tRx0QNUVtcjNm+fXv6/Oc/n7797W/PKC3CqDhmcP+Mg1r0QPjSosXUCgECExe44oorMuHE2rVrS6ur6gvw0cvgnNHzqFt8nbB06dLMmINzzPdxjBljt3nLM2lzv3ojQKBaAeFLtd5mq1DgJ37iJzJfeLTxj8NVSGoqAgQIECBAgACBWQSEL7PA2E2AAIERBOIHDvIuit96660jjDb3KXlzzX3WaEdED3nzRc/jbHv27ElnnXVW7th58821L8aKMdu+5Tm0vWf9ESBQnYDwpTprM1UsIHypGNx0BAgQIECAAIEOCwhfOrz4WidAoBSBCy64IBMkRCBw5MiRwuer6gL84cOHcwOS6LWILX7DdePGjTNumZrX28n2LViwYGqMGKsLW55FF/rWIwEC1QgIX6pxNssEBIQvE0A3JQECBAgQIECgowLCl44uvLYJEChNIO5ckXdh/Oqrry58zrx5Cp8kpRS15821a9euQqe7//77U9zGbPHixbnz5dUQx8Y5cW6XtjyLLvWvVwIEyhUQvpTra/QJClx44YWZLzKK/oJmgu2ZmgABAgQIECBAoEYCwpcaLYZSCBBojcAll1yS+b5+4cKFaceOHYX2WMUF+Kg5ah+cK3osa4vfXrnpppumfpNlcN54fO655049F8d05TddBq3zXAaP8ZgAAQKjCghfRpVzXu0FhC+1XyIFEiBAgAABAgRaIyB8ac1SaoQAgRoJ7N27N/cPya9cuTI98cQThVVa9gX4qDVqHpwn/qB99FjFNjh3PLalzJpw8aogQKBIAf/SFqlprFoJCF9qtRyKIUCAAAECBAi0WkD40url1RwBAhMU2Lx5c+4F8nXr1qWDBw8WUlmZwUTUGLXmzRG9VbXlzV/V3HWeh0udV0dtBJovIHxp/hrqYBaBvD/O97GPfWyWo+0mQIAAAQIECBAgMLqA8GV0O2cSIEBgLoGLLrooN7w4//zz09GjR+c6fc7ny7oAH7VFjXnjR09Vbnk1VDl/XefiUteVUReBdggIX9qxjrrIERC+5KDYRYAAAQIECBAgUIqA8KUUVoMSIEBgSmD//v1p9erVuSFGhBsHDhwYS6qMC/BR02zBS/QSPVW5ldFjlfWXNReXsmSNS4BACAhfvA5aKyB8ae3SaowAAQIECBAgUDsB4UvtlkRBBAi0TOCee+5Jy5Ytyw1g1q5dm/bt2zdyx0VfgI9aoqa8caOH6KXqLa+Wqmuo43xc6rgqaiLQHgHhS3vWUicDAsKXARAPCRAgQIAAAQIEShMQvpRGa2ACBAhMC+zYsSMtXrw4N9Q4/fTT0+233z597Hw+KfICfNQQteSNGbVHD5PY8uqZRB11m5NL3VZEPQTaJSB8add66qZP4Md//MczX+x8/OMf7zvCpwQIECBAgAABAgSKERC+FONoFAIECMwlEOHGbAFMXEi/8sor07PPPjvXMDOeL+IC/DPPPDM1d95YsS9qHjUcmlHsiA/y6hpxqFadxqVVy6kZArUTEL7UbkkUVJSA8KUoSeMQIECAAAECBAjMJSB8mUvI8wQIEChOYNeuXWn58uWZH7jsXUhfsWJF2rp1azp27NhQk/bO6/841IkpTc0Rc8Wc/ef3fx61Rs2T3Prr6X0+yXrqMnfPov9jXWpTBwECzRcQvjR/DXUwi4DwZRYYuwkQIECAAAECBAoXEL4UTmpAAgQInFTggQceSGvWrJk18IiL6fGH7bds2ZIOHTp00rH6L7z3Pj/pCSmlgwcPTo0dc/TOyfsYNUatk97yapt0TXWYn0sdVkENBNorIHxp79p2vrPzzz8/8wXQJz7xic67ACBAgAABAgQIECheQPhSvKkRCRAgMJfAgQMH0uWXX5753n/wgvqSJUvShg0b0h133JGOHDmSGXbw+Hict8W5MUaMFWPmnde/L2qLGuuw9dfV+7wOdU26hp5F/8dJ12R+AgTaI5D/btKe/nTSYQHhS4cXX+sECBAgQIAAgYoFhC8Vg5uOAAECfQI33nhjOu200+YMQ+IC+6JFi9J5552XrrnmmrRt27a0e/fu3PP27t079VwcE8fGOXFu/0X62T6PWqKmOm15tdapvknVwmVS8uYl0A0B4Us31rmTXQpfOrnsmiZAgAABAgQITERA+DIRdpMSIEBgWmD//v1p48aNacGCBUMFJHkX3cfdF3NHDVFL3ba83upW4yTq4TIJdXMS6I6A8KU7a925Tv/BP/gHmS+47rzzzs45aJgAAQIECBAgQKB8AeFL+cZmIECAwDAC9913X1q/fn1auHBh5ppA3oX2IvbFXDFnzF3XLa/PutZaZV1cqtQ2F4HuCQhfurfmnelY+NKZpdYoAQIECBAgQGDiAsKXiS+BAggQIDBD4OGHH06bNm1Kq1atKi2EibFjjpir7puQIX+FuOS72EuAQDECwpdiHI1SQwHhSw0XRUkECBAgQIAAgZYKCF9aurDaIkCg8QLHjx9P27dvn7od2Cte8Yqxg5gYI24tFmPG2E3ZhAz5K8Ul38VeAgSKERC+FONolBoK/NiP/Vjmi6r4Q3o2AgQIECBAgAABAkULCF+KFjUeAQIEyhHYt29fuvnmm9O11147dauwdevWpTVr1qQzzjgjLV68eOq/+Dz2xXNxO7E4Ns6Jc5u6CRnyV45Lvou9BAgUIyB8KcbRKDUUEL7UcFGURIAAAQIECBBoqYDwpaULqy0CBAi0REDIkL+QXPJd7CVAoBgB4UsxjkapoYDwpYaLoiQCBAgQIECAQEsFhC8tXVhtESBAoCUCQob8heSS72IvAQLFCAhfinE0Sg0F/v7f//uZ24598pOfrGGlSiJAgAABAgQIEGi6gPCl6SuofgIECLRbQMiQv75c8l3sJUCgGAHhSzGORqmhgPClhouiJAIECBAgQIBASwWELy1dWG0RIECgJQJChvyF5JLvYi8BAsUICF+KcTRKDQWELzVcFCURIECAAAECBFoqIHxp6cJqiwABAi0REDLkLySXfBd7CRAoRkD4UoyjUWooIHyp4aIoiQABAgQIECDQUgHhS0sXVlsECBBoiYCQIX8hueS72EuAQDECwpdiHI1SQ4Ef/dEfzfzNl0996lM1rFRJBAgQIECAAAECTRcQvjR9BdVPgACBdgsIGfLXl0u+i70ECBQjIHwpxtEoNRQQvtRwUZREgAABAgQIEGipgPClpQurLQIECLREQMiQv5Bc8l3sJUCgGAHhSzGORqmhgPClhouiJAIECBAgQIBASwWELy1dWG0RIECgJQJChvyF5JLvYi8BAsUICF+KcTRKDQXOO++8zG3HPv3pT9ewUiURIECAAAECBAg0XUD40vQVVD8BAgTaLSBkyF9fLvku9hIgUIyA8KUYR6PUUED4UsNFURIBAgQIECBAoKUCwpeWLqy2CBAg0BIBIUP+QnLJd7GXAIFiBIQvxTgapYYCwpcaLoqSCBAgQIAAAQItFRC+tHRhtUWAAIGWCAgZULRRVwAAIABJREFU8heSS76LvQQIFCMgfCnG0Sg1FHj961+fue3YXXfdVcNKlUSAAAECBAgQINB0AeFL01dQ/QQIEGi3gJAhf3255LvYS4BAMQLCl2IcjVJDAeFLDRdFSQQIECBAgACBlgoIX1q6sNoiQIBASwSEDPkLySXfxV4CBIoREL4U42iUGgoIX2q4KEoiQIAAAQIECLRUQPjS0oXVFgECBFoiIGTIX0gu+S72EiBQjIDwpRhHo9RQ4Ed+5Ecytx27++67a1ipkggQIECAAAECBJouIHxp+gqqnwABAu0WEDLkry+XfBd7CRAoRkD4UoyjUWooIHyp4aIoiQABAgQIECDQUgHhS0sXVlsECBBoiYCQIX8hueS72EuAQDECwpdiHI1SQwHhSw0XRUkECBAgQIAAgZYKCF9aurDaIkCAQEsEhAz5C8kl38VeAgSKERC+FONolBoK/L2/9/cytx3bs2dPDStVEgECBAgQIECAQNMFhC9NX0H1EyBAoN0CQob89eWS72IvAQLFCAhfinE0Sg0FhC81XBQlESBAgAABAgRaKiB8aenCaosAAQItERAy5C8kl3wXewkQKEZA+FKMo1FqKCB8qeGiKIkAAQIECBAg0FIB4UtLF1ZbBAgQaImAkCF/Ibnku9hLgEAxAsKXYhyNUkMB4UsNF0VJBAgQIECAAIGWCghfWrqw2iJAgEBLBIQM+QvJJd/FXgIEihEQvhTjaJQaCpx77rmZv/lyzz331LBSJREgQIAAAQIECDRdQPjS9BVUPwECBNotIGTIX18u+S72EiBQjIDwpRhHo9RQQPhSw0VREgECBAgQIECgpQLCl5YurLYIECDQEgEhQ/5Ccsl3sZcAgWIEhC/FOBqlhgLClxouipIIECBAgAABAi0VEL60dGG1RYAAgZYICBnyF5JLvou9BAgUIyB8KcbRKDUU+OEf/uHMbcfuvffeGlaqJAIECBAgQIAAgaYLCF+avoLqJ0CAQLsFhAz568sl38VeAgSKERC+FONolBoKCF9quChKIkCAAAECBAi0VED40tKF1RYBAgRaIiBkyF9ILvku9hIgUIyA8KUYR6PUUED4UsNFURIBAgQIECBAoKUCwpeWLqy2CBAg0BIBIUP+QnLJd7GXAIFiBIQvxTgapYYCf/fv/t3Mbcc+85nP1LBSJREgQIAAAQIECDRdQPjS9BVUPwECBNotIGTIX18u+S72EiBQjIDwpRhHo9RQQPhSw0VREgECBAgQIECgpQLCl5YurLYIECDQEgEhQ/5Ccsl3sZcAgWIEhC/FOBqlhgLClxouipIIECBAgAABAi0VEL60dGG1RYAAgZYICBnyF5JLvou9BAgUIyB8KcbRKDUU+KEf+qHMbcc++9nP1rBSJREgQIAAAQIECDRdQPjS9BVUPwECBNotIGTIX18u+S72EiBQjIDwpRhHo9RQQPhSw0VREgECBAgQIECgpQLCl5YurLYIECDQMIF9+/alm2++OV177bVp/fr1ad26dWnNmjWZH06N0CGei2Pi2Dgnzu3aJnzp2orrl0C1AsKXar3NVqGA8KVCbFMRIECAAAECBDouIHzp+AtA+wQIEJiQwPHjx9P27dvTxo0b09lnn50bsuQFDLPtizFirBgzxm77lufQ9p71R4BAdQLCl+qszVSxQPwEx+Cb6Oc+97mKqzAdAQIECBAgQIBAFwSEL11YZT0SIECgPgIPP/xw2rRpU1q1alXm2sfgtZBRH8fYMUfM1dYtz6atveqLAIHqBYQv1ZubsSIB4UtF0KYhQIAAAQIECBBIwhcvAgIECBCoQuC+++6bulXYwoULSwtdBgOJmCtuTxZzt20b7DUe2wgQIFCUgH9RipI0Tu0EhC+1WxIFESBAgAABAgRaKyB8ae3SaowAAQK1ENi/f//U7cAWLFhQWegyGEzE3HFLsqilLdtgj8KXtqysPgjUQ0D4Uo91UEUJAsKXElANSYAAAQIECBAgkCsgfMllsZMAAQIEChC48cYb02mnnTZU6LJo0aJ03nnnpWuuuSZt27Yt7d69O+3duzf33Hgujolj45w4Ny+MGNwXtURNbdgGexO+tGFV9UCgPgLCl/qshUoKFnjd616X+aKhjb8iWzCb4QgQIECAAAECBEYQEL6MgOYUAgQIEDipwIEDB9Lll1+eubYxGBgsWbIkbdiwId1xxx3pyJEjuWMOnpMXMhw+fHhqjBgrxsw7p39f1BY1Nnnr76f3eZP7UTsBAvUSEL7Uaz1UU6CA8KVATEMRIECAAAECBAicVED4clIeTxIgQIDAPAUeeOCBtGbNmpMGIKtXr05btmxJhw4dmnP0XrDQ//FkJx08eDBdf/31KeboP2fw86gxam3qNthPPLYRIECgKAH/ohQlaZzaCQhfarckCiJAgAABAgQItFZA+NLapdUYAQIEKhfYtWtXOvXUU2cNPVasWJG2bt2ajh07NnRto4YMMccNN9yQYs68MWLf8uXLU9TcxC2vpyb2oWYCBOopIHyp57qoqgCB1772tZkvDO6///4CRjYEAQIECBAgQIAAgZkCwpeZHh4RIECAwGgCt99+e1q8eHHmekYvJLjyyivTM888M+/Be+f3f5zPIDFnzN1/fv/nUXPU3rStv4fe503rQb0ECNRXQPhS37VR2ZgCwpcxAZ1OgAABAgQIECAwtIDwZWgqBxIgQIDALAI7duyYNXg5/fTTxwo3esFC/8dZyjjp7ghYopb+cXqfRwATPTRp69Xe/7FJ9auVAIF6Cwhf6r0+qhtDQPgyBp5TCRAgQIAAAQIE5iUgfJkXl4MJECBAYEDgnnvuScuWLcsNNdauXZv27ds3cMb8HvaHC73P5zfCC0dHLVFTb5z+j9FD9NKUrb/23udNqV2dBAjUX0D4Uv81UuGIAn/n7/ydzBcCTf4jcCMyOI0AAQIECBAgQKACAeFLBcimIECAQEsF9u/fP+sftj///PPTgQMHxu68Fyz0fxxn0Kgpausfr/f56tWrU/TUhK1Xc//HJtStRgIEmiEgfGnGOqlyBAHhywhoTiFAgAABAgQIEBhJQPgyEpuTCBAgQCCldNFFF+WGGBFuHD16tBCj/nCh9/m4A0dtswUwF1988bjDV3J+z6L/YyUTm4QAgU4ICF86sczdbFL40s111zUBAgQIECBAYBICwpdJqJuTAAECzRfYvHlzbvCybt26dPDgwcIa7A8Xep8XMXjUGLX2xuz/GL3Vfeuvt/d53WtWHwECzREQvjRnrVQ6T4Ef/MEfzLz5P/jgg/McxeEECBAgQIAAAQIE5hYQvsxt5AgCBAgQmCmwd+/etHTp0sy1i1WrVqUnnnhi5sFjPuoFC/0fxxxy+vSodeXKlZk+orfosc5bv0fv8zrXqzYCBJolIHxp1nqpdh4Cwpd5YDmUAAECBAgQIEBgLAHhy1h8TiZAgEAnBS655JJMYLFw4cK0Y8eOwj16wUL/xyIniZqj9v7x4/Posc7bYL3x2EaAAIGiBPyLUpSkcWonIHyp3ZIoiAABAgQIECDQWgHhS2uXVmMECBAoRWDnzp2ZoCIu/L/1rW8tZb4qQoarr746t6fota5bFS517V1dBAiULyB8Kd/YDBMSeM1rXpN50//85z8/oWpMS4AAAQIECBAg0GYB4UubV1dvBAgQKF7gggsuyFyzOOuss9KRI0eKnyylzFxl/IbH4cOHU/QwGGhEr3XaDhw4kG666aa0cePGTK1R+7nnnjv1XBwTx9oIECAwqoDwZVQ559VeQPhS+yVSIAECBAgQIECgNQLCl9YspUYIECBQusDu3btzL/rfeuutpc09GIiUEb5E8dFD3lzR86S3+++/P11xxRVp8eLFuTXm1R3Hxjlxro0AAQLzFRC+zFfM8Y0REL40ZqkUSoAAAQIECBBovIDwpfFLqAECBAhUJhAX8wcv9K9du7bU+Qfni8dlbdHL4HzR86S25557buo3WRYsWJCpa7DO2R7HufGbMjGWjQABAsMKlPcv7bAVOI5ASQLCl5JgDUuAAAECBAgQIJAREL5kSOwgQIAAgRyBgwcPpiVLlmRCgFtuuSXn6OJ25YUKxY0+c6ToZXC+6Dl6r3rbs2dP7q3QBusb9nHcVi3GtBEgQGAYAeHLMEqOaaRA3k9afOELX2hkL4omQIAAAQIECBCot4Dwpd7rozoCBAjUReDd7353JphYuXJlev7550stMS9cKGvC6CV6Gpwzeq9y+9CHPpSWLl2aqWOwrvk+jjFjbBsBAgTmEhC+zCXk+cYKCF8au3QKJ0CAAAECBAg0TkD40rglUzABAgQmInDppZdmwoCrrrqq9FryAoYyJ42eBueM3qva7rzzznTKKadkahisadTHMXbMYSNAgMDJBIQvJ9PxXKMFhC+NXj7FEyBAgAABAgQaJSB8adRyKZYAAQITEThx4kRavnx5JhC4++67S68nL2Qoc9LoaXDO6D0Myt6efPLJdOaZZ2bmH6xn3McxR8xlI0CAwGwCwpfZZOxvvMAP/MAPZN5ov/jFLza+Lw0QIECAAAECBAjUT0D4Ur81UREBAgTqJhB/K2Twgn9VgcTgvPG4zG22oKmKv5dy2WWXZZzz+i9iX8xlI0CAwGwC5f5LO9us9hOoQED4UgGyKQgQIECAAAECBKYEhC9eCAQIECAwl8DWrVszoUBVt+LKCxrmqnfc5/NusRYGZW47d+7MGOf1XuS+mNNGgACBPAHhS56Kfa0QEL60Yhk1QYAAAQIECBBohIDwpRHLpEgCBAhMVGDTpk2ZYOC6666rpKa8sKHsiaO3wXnDoMztwgsvzMw5WEPRj2NOGwECBPIEhC95Kva1QuBv/+2/nXnDfeihh1rRmyYIECBAgAABAgTqJSB8qdd6qIYAAQJ1FLj44osz1yluu+22SkrNCxzKnjh6G5w3DMraHnnkkbRgwYLMnIM1FP045oy5bQQIEBgUEL4MinjcGgHhS2uWUiMECBAgQIAAgdoLVBG+vOcjj6aYx38MvAa8BrwGmvkaePHpZ2WCgQt+cVsl/67nBQ5lv46it8F5w6Csedf++K9l5hucv6zHMXdZfRm3mf+/W7fmr9stH/3K2N+DCF/GJjRAXQWEL3VdGXURIECAAAECBNonEN9gl70JX5r/TbwLMdbQa6Dbr4FTlr10YuFAWaHDfMcNg7L+P3jZK39sYr4xd1l9Gbfb/25Y/8mtf3ztPe4mfBlX0Pm1Ffhbf+tvZd50v/SlL9W2XoURIECAAAECBAg0VyC+MS57E75M7ptvFz7Yew14DRTxGnjR4qWZ6xTzDS+afnwYFGGZN8aLT189Md+YO68m+/zb4TXQ3NeA8KXs726M32gB4Uujl0/xBAgQIECAAIFGCcQ31mVvwpfmfvPuwou18xrwGojXwIIFCycWDtQltAmDsv5/mGS4VWaoVJaXcf275DVw8teA8KXs726M32gB4Uujl0/xBAgQIECAAIFGCcQ3r2VvwpeTf4PsAgIfrwGvgbq/BiYZDtQlfCkzpJhkuFVmqFT317X6/Nvb1teA8KXs726M32iBV7/61ZmfKPmLv/iLRvekeAIECBAgQIAAgXoKxDedNgIECBAgcDKBl7/85ZnrFHUJRaqqIwzK2l7ykpdMzDfmthEgQGBQwN98GRTxuDUCwpfWLKVGCBAgQIAAAQK1FxC+1H6JFEiAAIGJC+Rdp3jwwQcrqSsvXCl74uhtcN4wKGs755xzMvMNzl/W41e96lVltWVcAgQaLCB8afDiKf3kAnlf1PjNl5ObeZYAAQIECBAgQGA0AeHLaG7OIkCAQJcELr744kw4cNttt1VCkBc6lD1x9DY4bxiUtV122WWZ+QbnL+txzG0jQIDAoIDwZVDE49YICF9as5QaIUCAAAECBAjUXkD4UvslUiABAgQmLrBp06ZMOHDddddVUlde6FD2xNHb4LxhUNa2ZcuWzHyD85f1OOa2ESBAYFBA+DIo4nFrBOJXPgffVL/85S+3pj+NECBAgAABAgQI1EdA+FKftVAJAQIE6iqwdevWzHWKSy+9tJJyB6+PxOOyt+htcN4wKGt75JFH0oIFCzJzDtZQ9OOY89FHHy2rLeMSINBggfL/pW0wjtKbLSB8afb6qZ4AAQIECBAg0CQB4UuTVkutBAgQmIzAnj17MsHA8uXL04kTJ0ovKC9wKHPS6Cl6G5w3DMrcLrzwwsycgzUU/TjmtBEgQCBPQPiSp2JfKwSEL61YRk0QIECAAAECBBohIHxpxDIpkgABAhMVmC2QuPvuu0uvKy9wKHPSu+66KxOCVBE0/fmf/3lm3rzei9y3c+fOMimNTYBAgwWELw1ePKWfXOCcc87JvOE+/PDDJz/JswQIECBAgAABAgRGEBC+jIDmFAIECHRQIO9WXFdddVXpEnlhQ5mTRk+Dc1Z1i7XLLrssM/dgLUU9jrlsBAgQmE1A+DKbjP2NFxC+NH4JNUCAAAECBAgQaIyA8KUxS6VQAgQITFRg27ZtmWBg5cqV6fnnny+1rrywoawJo5foaXDO6L2K7cknn0xnnnlmZv7BesZ9HHPEXDYCBAjMJiB8mU3G/sYLCF8av4QaIECAAAECBAg0RkD40pilUigBAgQmKnDw4MG0ZMmSTDBwyy23lFpXXtBQ1oTRy+B80XP0XtV25513plNOOSVTx2Bdoz6OsWMOGwECBE4mIHw5mY7nGi3wyle+MvMm+5d/+ZeN7knxBAgQIECAAAEC9RQQvtRzXVRFgACBOgpcccUVmesVa9euLbXUvJChrAmjl8H5oueqtw996ENp6dKlmVoGa5vv4xgzxrYRIEBgLgHhy1xCnm+sgPClsUuncAIECBAgQIBA4wSEL41bMgUTIEBgYgK7d+/ODQRuvfXW0mrKCxjKmCx6yJsrep7EtmfPnnTWWWfl1pRX51z7YqwY00aAAIFhBIQvwyg5ppECwpdGLpuiCRAgQIAAAQKNFBC+NHLZFE2AAIGJCVxwwQWZQCAu7B85cqSUmvJChaInOnz4cG7QEb1OcnvuuefSxo0b04IFCzLmeS55++LcGCPGshEgQGBYAeHLsFKOa5zA3/ybfzPzpvrII480rg8FEyBAgAABAgQI1F9A+FL/NVIhAQIE6iSwc+fOzDWLuOh/9dVXl1JmXqBQ9ERRe948u3btKnqqkca7//77U9z+bPHixbl15tUex8Y5ca6NAAEC8xUQvsxXzPGNERC+NGapFEqAAAECBAgQaLyA8KXxS6gBAgQIVC5wySWXZEKAhQsXph07dhReS16wUOQkUXPUPjhP9Fi3LX575aabbpr6TZbBeuPxueeeO/VcHOM3Xeq2euoh0CwB4Uuz1ku18xAQvswDy6EECBAgQIAAAQJjCQhfxuJzMgECBDopsHfv3tw/CL9y5cr0xBNPFGqSFzIUNUHUGjUPzhF/mD56rPM2WHM8thEgQKAoAf+iFCVpnNoJ/I2/8Tcyb/yPPvpo7epUEAECBAgQIECAQPMFhC/NX0MdECBAYBICmzdvzly7iABg3bp16eDBg4WVVFbIEDVGrXnjR2913/LqrnvN6iNAoDkCwpfmrJVK5ykgfJknmMMJECBAgAABAgRGFhC+jEznRAIECHRe4KKLLsoNL84///x09OjRQnzKCBmitqgxb+zoqQlbXu1NqFuNBAg0Q0D40ox1UuUIAsKXEdCcQoAAAQIECBAgMJKA8GUkNicRIECAQEpp//79afXq1bkhRoQbBw4cGNup6JAhapoteIleoqcmbEW7NKFnNRIgUJ2A8KU6azNVLCB8qRjcdAQIECBAgACBDgsIXzq8+FonQIBAAQL33HNPWrZsWW4As3bt2rRv376xZikyZIhaoqa8MaOH6KUpW14PTaldnQQI1F9A+FL/NVLhiAJnn3125guBr3zlKyOO5jQCBAgQIECAAAECswsIX2a38QwBAgQIDCewY8eOtHjx4sy1jAgITj/99HT77bcPN1DOUUWFDFFD1JI3XtQePTRpy+ujSfWrlQCBegsIX+q9PqobQ0D4MgaeUwkQIECAAAECBOYlIHyZF5eDCRAgQGAWgQg3ZgtgIii48sor07PPPjvL2bPvHjdkeOaZZ6bmzhsn9kXN44RDs1de7jN5/ZQ7o9EJEOiSgPClS6vdsV6FLx1bcO0SIECAAAECBCYoIHyZIL6pCRAg0DKBXbt2peXLl+f+dkmEBStWrEhbt25Nx44dG7rzUUOGmCPmijnzxoh9UWvU3MQtr6cm9qFmAgTqKSB8qee6qKoAgVe84hWZLwz27t1bwMiGIECAAAECBAgQIDBTQPgy08MjAgQIEBhP4IEHHkhr1qzJXNfoDwviD9tv2bIlHTp0aM7J+s/rfX6ykw4ePDg1dszROz7vY9QYtTZ1y+upqb2omwCB+gkIX+q3JioqSED4UhCkYQgQIECAAAECBOYUEL7MSeQAAgQIEJinwIEDB9Lll19+0vAjwoMlS5akDRs2pDvuuCMdOXIkd5ZhQoY4N8aIsWLMvHP690VtUWOTt/5+ep83uR+1EyBQLwHhS73WQzUFCghfCsQ0FAECBAgQIECAwEkFhC8n5fEkAQIECIwhcOONN6bTTjttzjAkwoNFixal8847L11zzTVp27Ztaffu3Wnfvn2558ZzcUwcG+fEub0A4mQfo5aoqQ1bXp9t6EsPBAjUQ0D4Uo91UEUJAnm/nhtfcNgIECBAgAABAgQIFC0gfCla1HgECBAg0C+wf//+tHHjxrRgwYKhApK8UGHcfTF31BC1tGXLM2lLb/ogQGDyAsKXya+BCkoSEL6UBGtYAgQIECBAgACBjIDwJUNiBwECBAiUIHDfffel9evXp4ULF1YWwsRcMWfM3bZN+NK2FdUPgXoJCF/qtR6qKVBA+FIgpqEIECBAgAABAgROKiB8OSmPJwkQIECgYIGHH344bdq0Ka1ataq0ECbGjjlirrZuwpe2rqy+CNRDQPhSj3VQRQkC3//935/5AuSxxx4rYSZDEiBAgAABAgQIdF1A+NL1V4D+CRAgMBmB48ePp+3bt0/dDizvb9/mhQsn2xdjxK3FYswYu+1bnkXbe9YfAQLVCQhfqrM2U8UCwpeKwU1HgAABAgQIEOiwgPClw4uvdQIECNRIIP7W7c0335yuvfbaqVuFrVu3LsWdQc4444y0ePHiqf/i89gXz8XtxOLYOKeLfydX+FKjF69SCLRQQPjSwkXV0v8VEL54JRAgQIAAAQIECFQlIHypSto8BAgQIECgOAHhS3GWRiJAICsgfMma2NMSgbPOOitz27HHH3+8Jd1pgwABAgQIECBAoE4Cwpc6rYZaCBAgQIDAcALCl+GcHEWAwGgCwpfR3JzVAAHhSwMWSYkECBAgQIAAgZYICF9aspDaIECAAIFOCQhfOrXcmiVQuYDwpXJyE1YlIHypSto8BAgQIECAAAECwhevAQIECBAg0DwB4Uvz1kzFBJokIHxp0mqpdV4Cwpd5cTmYAAECBAgQIEBgDAHhyxh4TiVAgAABAhMSEL5MCN60BDoiIHzpyEJ3sc3v+77vy/zNl7/6q7/qIoWeCRAgQIAAAQIEShYQvpQMbHgCBAgQIFCCgPClBFRDEiAwLSB8mabwSdsEhC9tW1H9ECBAgAABAgTqKyB8qe/aqIwAAQIECMwmIHyZTcZ+AgSKEBC+FKFojFoKCF9quSyKIkCAAAECBAi0UkD40spl1RQBAgQItFxA+NLyBdYegQkLCF8mvACmL09g9erVmduOffWrXy1vQiMTIECAAAECBAh0VkD40tml1zgBAgQINFhA+NLgxVM6gQYICF8asEhKHE1A+DKam7MIECBAgAABAgTmLyB8mb+ZMwgQIECAwKQFhC+TXgHzE2i3gPCl3evb6e6EL51efs0TIECAAAECBCoVEL5Uym0yAgQIECBQiIDwpRBGgxAgMIuA8GUWGLubL/Dyl788c9uxJ554ovmN6YAAAQIECBAgQKB2AsKX2i2JgggQIECAwJwCwpc5iRxAgMAYAsKXMfCcWm8B4Uu910d1BAgQIECAAIE2CQhf2rSaeiFAgACBrggIX7qy0vokMBkB4ctk3M1agYDwpQJkUxAgQIAAAQIECEwJCF+8EAgQIECAQPMEhC/NWzMVE2iSgPClSaul1nkJfO/3fm/mtmNPPvnkvMZwMAECBAgQIECAAIFhBIQvwyg5hgABAgQI1EtA+FKv9VANgbYJCF/atqL6mRYQvkxT+IQAAQIECBAgQKBkAeFLycCGJ0CAAAECJQgIX0pANSQBAtMCwpdpCp+0TUD40rYV1Q8BAgQIECBAoL4Cwpf6ro3KCBAgQIDAbALCl9lk7CdAoAgB4UsRisaopcDLXvayzG3HnnrqqVrWqigCBAgQIECAAIFmCwhfmr1+qidAgACBbgoIX7q57romUJWA8KUqafNULiB8qZzchAQIECBAgACBzgoIXzq79BonQIAAgQYLCF8avHhKJ9AAAeFLAxZJiaMJCF9Gc3MWAQIECBAgQIDA/AWEL/M3cwYBAgQIEJi0gPBl0itgfgLtFhC+tHt9O92d8KXTy695AgQIECBAgEClAsKXSrlNRoAAAQIEChEQvhTCaBACBGYREL7MAmN38wXOPPPMzN98efrpp5vfmA4IECBAgAABAgRqJyB8qd2SKIgAAQIECMwpIHyZk8gBBAiMISB8GQPPqfUWEL7Ue31UR4AAAQIECBBok4DwpU2rqRcCBAgQ6IqA8KUrK61PApMREL5Mxt2sFQgIXypANgUBAgQIECBAgMCUgPDFC4EAAQIECDRPQPjSvDVTMYEmCQhfmrRaap2XwKpVqzK3Hfva1742rzEcTIAAAQIECBAgQGAYAeHLMEqOIUCAAAEC9RIQvtRrPVRDoG0Cwpe2rah+pgWEL9MUPiFAgAABAgQIEChZQPhSMrA6coptAAAZ7ElEQVThCRAgQIBACQLClxJQDUmAwLSA8GWawidtExC+tG1F9UOAAAECBAgQqK+A8KW+a6MyAgQIECAwm4DwZTYZ+wkQKEJA+FKEojFqKbBy5crMbcf2799fy1oVRYAAAQIECBAg0GwB4Uuz10/1BAgQINBNAeFLN9dd1wSqEhC+VCVtnsoFhC+Vk5uQAAECBAgQINBZAeFLZ5de4wQIECDQYAHhS4MXT+kEGiAgfGnAIilxNAHhy2huziJAgAABAgQIEJi/gPBl/mbOIECAAAECkxYQvkx6BcxPoN0Cwpd2r2+nu3vpS1+aue3YM88802kTzRMgQIAAAQIECJQjIHwpx9WoBAgQIECgTAHhS5m6xiZAQPjiNdBaAeFLa5dWYwQIECBAgACB2gkIX2q3JAoiQIAAAQLTAvv27Us333xzuvbaa9P69evTunXr0po1azI/tBthTDwXx8SxcU6cayNAgMAoAsKXUdSc0wgB4UsjlkmRBAgQIECAAIFWCAhfWrGMmiBAgACBlggcP348bd++PW3cuDGdffbZuSFL3m+9zLYvxoixYswY20aAAIFhBIQvwyg5ppECZ5xxRubN9dlnn21kL4omQIAAAQIECBCot4Dwpd7rozoCBAgQ6IbAww8/nDZt2pRWrVqVuSY0W7Ay3/0xdswRc9kIECBwMgHhy8l0PNdoAeFLo5dP8QQIECBAgACBRgkIXxq1XIolQIAAgZYJ3HfffVO3Clu4cGFpoctgSBNzxe3JYm4bAQIE8gSEL3kq9jVOIO/enXlvuGeddZZ7dzZudRVMgAABAgQIEKi/gPCl/mukQgIECBBon8D+/funbge2YMGCykKXwRAm5o5bkkUtNgIECPQLCF/6NXzeGAH37mzMUimUAAECBAgQINAJAeFLJ5ZZkwQIECBQI4Ebb7wxnXbaaUOFLosWLUrnnXdeuuaaa9K2bdvS7t270969e3PPjefimDg2zolzBwOXvMdRS9RkI0CAQE9A+NKT8LERAu7d2YhlUiQBAgQIECBAoHMCwpfOLbmGCRAgQGBCAgcOHEiXX375nIHIkiVL0oYNG9Idd9yRjhw5klttXogyeODhw4enxoixYsy8c/r3RW1Ro40AAQLCF6+BRgi4d2cjlkmRBAgQIECAAIHOCghfOrv0GidAgACBCgUeeOCBtGbNmpMGIKtXr05btmxJhw4dmrOy/tCk9/nJTjp48GC6/vrrU8zROz7vY9QYtdoIEOi2gPCl2+tf++7du7P2S6RAAgQIECBAgACBlJLwxcuAAAECBAiUK7Br16506qmnzhp6rFixIm3dujUdO3Zs6ELygpNhTo45brjhhhRz5o0R+5YvX56iZhsBAt0VEL50d+1r3/m49+6MN7nBN8D7779/6r6e7t1Z++VXIAECBAgQIECgUQLCl0Ytl2IJECBAoGECt99+e1q8eHHmOk/vus+VV16ZnnnmmXl31Tu//+N8Bok5Y+7+8/s/j5qjdhsBAt0UEL50c91r3XVR9+48/fTTM29+zz33XKZ39+7MkNhBgAABAgQIECAwTwHhyzzBHE6AAAECBIYU2LFjx6zBS1z7GSfc6A9Kep8PWdaMw6KGvOtQMWYEMNGDjQCB7gkIX7q35rXuuMh7d+a96eWFL/0g7t3Zr+FzAgQIECBAgACBYQWEL8NKOY4AAQIECAwvcM8996Rly5Zlfrg2Qo21a9emffv2DT9YzpG9wKX/Y85hQ+2KWqKm/rF6n0cP0YuNAIFuCQhfurXete626Ht3nnbaaZk3vPitmmE29+4cRskxBAgQIECAAAECPQHhS0/CRwIECBAgUIxA/B3g2f6w/fnnn5+GvcZzsmp64Uj/x5MdP9dzUVPU1j9e7/PoJXqyESDQHQHhS3fWutadlnHvznHClx6We3f2JHwkQIAAAQIECBA4mYDw5WQ6niNAgAABAvMXuOiii3JDjAg3jh49Ov8Bc87oBSP9H3MOm9euqG22AObiiy+e11gOJkCg2QLCl2avXyuqL+venUWELz1g9+7sSfhIgAABAgQIECCQJyB8yVOxjwABAgQIjCawefPm3OBl3bp1KW4ZX9TWH7r0Pi9i7Kgxau2N2f8xerMRINANAeFLN9a5tl2Wee/O5cuXZ97kvvGNb4xs4d6dI9M5kQABAgQIECDQegHhS+uXWIMECBAgUJHA3r1709KlSzPXdFatWpWeeOKJQqvoD0V6nxc1QdS6cuXKTB/RW/RoI0Cg/QLCl/avcW07LPvenUWHLwHp3p21fTkpjAABAgQIECAwUQHhy0T5TU6AAAECLRK45JJLMoHFwoULU9w5peitF7j0fyxyjqg5au8fPz6PHm0ECLRfQPjS/jWubYdl37uzjPAlMN27s7YvKYURIECAAAECBCYmIHyZGL2JCRAgQKBFAjt37swEFRFWvPWtby2ly8FQJB4XvV199dW5PUWvNgIE2i1Q/L8o7fbSXUECVdy789RTT828uRV1X1D37izohWAYAgQIECBAgEBLBIQvLVlIbRAgQIDARAUuuOCCzLWcs846Kx05cqSUuqoIXw4fPpyih8G5olcbAQLtFhC+tHt9a9ldVffuLDN8CVj37qzly0tRBAgQIECAAIGJCAhfJsJuUgIECBBokcDu3bszAUUEFrfeemtpXQ4GIvG4jC16yJsrerYRINBegXL+RWmvl84KEKjq3p1lhy9B4d6dBbwgDEGAAAECBAgQaIGA8KUFi6gFAgQIEJiowBVXXJEJKNauXVtqTXmBSFkTRi+D80XPNgIE2isgfGnv2taysyrv3VlF+BLI7t1Zy5eaoggQIECAAAEClQoIXyrlNhkBAgQItEwgbu++ZMmSTDhxyy23lNrpYBgSj8vaopfB+aLnom6RX1bdxiVAYHSB8v5FGb0mZ7ZYoMp7d77kJS/JvKkdOnSocF337iyc1IAECBAgQIAAgcYJCF8at2QKJkCAAIEaCbz73e/OXMNZuXJlev7550utcjAMKTN8iV6ip8E5o3cbAQLtFBC+tHNda9lV1ffurCp8CWz37qzlS05RBAgQIECAAIHKBIQvlVGbiAABAgRaKHDppZdmQomrrrqq9E4Hg5Ayw5doJnoanDN6txEg0E4B4Us717WWXVV9784qw5cAd+/OWr7sFEWAAAECBAgQqERA+FIJs0kIECBAoIUCJ06cSMuXL8+EEnfffXfp3Q4GIWWHL9HT4JzRexjYCBBon4DwpX1rWsuOJnHvzmXLlmXe0OIWYWVt7t1ZlqxxCRAgQIAAAQL1FxC+1H+NVEiAAAEC9RTYs2dP5vpNVYHEYBBSdvgyW9AUBjYCBNonIHxp35rWsqNJ3Luz6vDFvTtr+dJTFAECBAgQIECgEgHhSyXMJiFAgACBFgps3bo1E75UdSuuqsOXWL68W6yFgY0AgfYJCF/at6a17CjvjaXse3dWHb4EvHt31vLlpygCBAgQIECAQOkCwpfSiU1AgAABAi0V2LRpUyZ8ue666yrpdhLhS/Q2OG8Y2AgQaJ+A8KV9a1q7jmb7lcqy79354he/OPNmduTIkVJ93LuzVF6DEyBAgAABAgRqKyB8qe3SKIwAAQIEai5w8cUXZ67f3HbbbZVUPRiCxOOyt+htcN4wsBEg0D6B8v9FaZ+ZjuYpMKl7d04ifJktaHLvznm+aBxOgAABAgQIEGiYgPClYQumXAIECBCojcCrX/3qTBjx4IMPVlLfYAhSRfgSvQ3OGwY2AgTaJyB8ad+a1q6jSd27cxLhS+Dn3WLNvTtr97JUEAECBAgQIECgUIEqwpf3fOTRFPP4j4HXgNeA14DXQJteA6cse2kmjBgMJ9r+OAzatKZ68W9UG14Dt3z0K2N/vyB8GZvQAHMJTOrenUuXLs28eX/zm9+cq9yxn3fvzrEJDUCAAAECBAgQaJxAfINZ9iZ8cSGjDRcy9OB17DXgNTD4GnjR4uz1m7aHLYP9hcGgi8f+X/EamOxrIL72HncTvowr6Pw5BSZ1785JhS/u3TnnS8IBBAgQIECAAIHWCcQ3x2VvwpfJfgPuAgh/rwGvAa+Bcl4DCxYszPzw7GA40fbHYeD1Vc7riyvXUV8Dwpeyv7sxfiECk7p356TCF/fuLORlYxACBAgQIECAQKME4pu6sjfhi4sHo148cJ7XjteA10CdXwN+8+W7kt988f9onf8f7WptjQxffMPQvX9M3Lvzu5J7d3bvdV/EfSHLvoBjfAIECBAgQKA4gfimtOzN91Ld+5qyqxc79O217jXQrdeA60auG/l/vlv/zzdlvYUv/thkI34l0U8w+AmGpvyjWmSdRfwDXfYFHOMTIECAAAECxQnE1xE2AgQIECBAYP4Ck7pjSlSadzuz+XcwvzPcMWV+Xo4m0GSByv/mi5/W6l6S6d6d35Xcu7N7r3vhS5PfGtVOgAABAgTmLyB8mb+ZMwgQIECAQAhM6m8Fx9yTCF/8rWCvewLdERC++O2Z0n97xm+++M2XIn+jpCljCV+680aqUwIECBAgEALCF68DAgQIECAwmsCmTZsyIch111032mDzPGsS4Uv0NjhvGNgIEGifgPBF+FJ6+OLene7d2ZTApMg6hS/te8PUEQECBAgQOJmA8OVkOp4jQIAAAQKzC2zdujUTRlx66aWzn1DgM4MhSDwue4veBucNAxsBAu0TKP9flPaZ6WieApO6d+cpp5ySeTM7evToPKuf/+Hu3Tl/M2cQIECAAAECBJouIHxp+gqqnwABAgQmJbBnz57M9Zvly5enEydOlF7SYAhSdvgSPUVvg/OGgY0AgfYJCF/at6a162hS9+6cVPji3p21ewkqiAABAgQIECBQuoDwpXRiExAgQIBASwVmCyTuvvvu0jseDEHKDl/uuuuuTPBSVdBUOqYJCBDICAhfMiR2FC0wqXt3fs/3fE/mDe2v//qvi24vM557d2ZI7CBAgAABAgQItF5A+NL6JdYgAQIECJQokHcrrquuuqrEGf/v0FWHL9HT4JxV3WKtdEwTECCQERC+ZEjsKFpgUvfunFT4kvcFg3t3Fv2qMh4BAgQIECBAoF4Cwpd6rYdqCBAgQKBZAtu2bcuEEitXrkzPP/98qY0MBiFl/uZL9BI9Dc4ZvdsIEGingPClnetaq64mde/OSYQvs/2qrHt31uolqRgCBAgQIECAQOECwpfCSQ1IgAABAh0SOHjwYFqyZEkmmLjllltKVRgMQsoMX6KXwfmi5+jdRoBAOwWEL+1c11p1NVsgUfa9OxcvXpx5Uzt27FipNu7dWSqvwQkQIECAAAECtRUQvtR2aRRGgAABAg0RuOKKKzLXcdauXVtq9YNhSJnhS/QyOF/0bCNAoL0Cwpf2rm2tOsu7FVfZ9+6cRPji3p21etkphgABAgQIECBQmYDwpTJqExEgQIBASwV2796dCScirLj11ltL63gwDCkrfIke8uaKnm0ECLRXQPjS3rWtVWeTuHdn1eGLe3fW6iWnGAIECBAgQIBApQLCl0q5TUaAAAECLRW44IILMiHFWWedlY4cOVJKx3mBSNETHT58OEUPg3NFrzYCBNotIHxp9/rWprtJ3Lvzu7/7uzNvbGX+oTb37qzNy00hBAgQIECAAIHKBYQvlZObkAABAgRaKLBz587MtZwILa6++upSuh0MROJx0VvUnjfPrl27ip7KeAQI1Eyg+H9RatagcuojUPW9O6sOX9y7sz6vNZUQIECAAAECBKoWEL5ULW4+AgQIEGirwCWXXJIJKxYuXJh27NhReMt5oUiRk0TNUfvgPNGjjQCB9gsIX9q/xrXpsOp7d1YZvrh3Z21eZgohQIAAAQIECExEQPgyEXaTEiBAgEALBfbu3ZuWLl2aCSxWrlyZnnjiiUI7HgxF4nFRW9QaNQ/OEb1FjzYCBNovUNy/KO230mEBAlXeu3PRokWZN7jjx48X0MXMIdy7c6aHRwQIECBAgACBLgoIX7q46nomQIAAgbIENm/enLmmEyHGunXrUtzavqhtMBgpKnyJGqPWvPGjNxsBAt0QEL50Y51r02WV9+6sKnxx787avLwUQoAAAQIECBCYmIDwZWL0JiZAgACBlgpcdNFFueHF+eefn44ePVpI13nhyLgDR21RY97Y0ZONAIHuCAhfurPWtem0qnt3VhG+uHdnbV5WCiFAgAABAgQITFRA+DJRfpMTIECAQAsF9u/fn1avXp0bYkS4ceDAgbG7zgtIxhk0apoteIleoicbAQLdERC+dGeta9NpVffuLDt8ce/O2rykFEKAAAECBAgQmLiA8GXiS6AAAgQIEGihwD333JOWLVuWG8CsXbs27du3b6yuiwxfopaoKW/M6CF6sREg0C0B4Uu31rs23VZx784XvehFmTe8EydOFGLg3p2FMBqEAAECBAgQINAaAeFLa5ZSIwQIECBQM4G468jixYsz13gi5Dj99NPT7bffPnLFeUHJKINFDVFL3nhRe/RgI0CgewLCl+6teW06LvvenWWFL+7dWZuXkEIIECBAgAABArUREL7UZikUQoAAAQItFIhwY7YAJgKPK6+8Mj377LPz7jwvLJnPIM8888zU3HnjxL6oeZxwaD61OJYAgfoJCF/qtyadqajse3eWEb64d2dnXp4aJUCAAAECBAjMS0D4Mi8uBxMgQIAAgXkL7Nq1Ky1fvjz3t0si6FixYkXaunVrOnbs2NBj54Umw5wcc8RcMWfeGLEvao2abQQIdFdA+NLdta9F52Xeu3PhwoWZN8BxmnbvznH0nEuAAAECBAgQaLeA8KXd66s7AgQIEKiHwAMPPJDWrFmTud7TH4DEH7bfsmVLOnTo0JxF95/X+/xkJ8Vt6GPsmKN3fN7HqDFqtREg0G0B4Uu3178W3Zd1784iwxf37qzFS0URBAgQIECAAIHaCghfars0CiNAgACBlgnEXUkuv/zyk4YfEYgsWbIkbdiwId1xxx3pyJEjuQp5wcnggXFujBFjxZh55/Tvi9qiRhsBAgSEL14DtRAo496dRYQv7t1Zi5eHIggQIECAAAECtRcQvtR+iRRIgAABAi0TuPHGG9Npp502ZxgSwciiRYvSeeedl6655pq0bdu2tHv37hR3OOkPTXqfx3NxTBwb58S5vedO9jFqiZpsBAgQ6AkIX3oSPk5coOh7dy5YsCDz5jhsk+7dOayU4wgQIECAAAECBEJA+OJ1QIAAAQIEqheIvye8cePGlHcN6GRBSZHPxdxRQ9RiI0CAQL+A8KVfw+cTFyjy3p15b7xzNejenXMJeZ4AAQIECBAgQCBPQPiSp2IfAQIECBCoRuC+++5L69evT3l3QSkyaOkfK+aKOWNuGwECBPIEhC95KvZNVKCoe3cOG764d+dEl9vkBAgQIECAAIFWCGz4zU+krz13tBW9aIIAAQIECDRV4OGHH06bNm1Kq1atytwNpT84GefzGDvmiLlsBAgQOJmA8OVkOp6bqMC49+7MeyPdu3fv1H093btzoktrcgIECBAgQIBA6wT2fPGZ9C9/+65084cfTY89nf9HfVvXtIYIECBAgEBNBY4fP562b98+dTuwV7ziFWMHMTFG3FosxoyxbQQIEBhGQPgyjJJjJibg3p0TozcxAQIECBAgQIDAPAWOfOt4ev/HH0//9p33pn/x9k+lzTd9If3prsfSZ770rN+KmaelwwkQIECAQJEC+/btSzfffHO69tprp24Vtm7durRmzZp0xhlnpMWLF0/9F5/HvngubicWx8Y5ca6NAAECowgIX0ZRc07lAu7dWTm5CQkQIECAAAECBMYQ+MbhY+mTD+xPf/jBv0y/9d/vS7/09k+ly//dx9Mvv+PuqcfvfO9D6Y+2P5I+8InH08c+81S696Fn00NfOZD2PXUkPf31b6UDh46lCHO+9dcn0rHj304nvv2dMapxKgECBAgQIECAAAECVQsIX6oWN99YAu7dORafkwkQIECAAAECBCYocPTYialw5Z6Hnk0fvuur6T0feTS960+/PPUbMhHQvPX37k2/uvnutPG6T6c3v213uuL/vTOt/41PTIU2l13zsXTLR78ywepNTYAAAQIECBAgQIDAfASEL/PRcmxtBNy7szZLoRACBAgQIECAAAECBAgQIECAAAECBAgQGBAQvgyAeNhMAffubOa6qZoAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTED4MjF6ExMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTED4MjF6ExMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTED4MjF6ExMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTED4MjF6ExMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTED4MjF6ExMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTED4MjF6ExMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTED4MjF6ExMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJtFBC+tHFV9USAAAECBAgQIECAAAECBAgQIECAAAECBAhMTOD/AwZ2jZsWGQQEAAAAAElFTkSuQmCC" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Thus, the final circuit can be implemented using ancilla qubits as" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## IMPORTS and SETUP" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# general imports\n", + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "# magic word for producing visualizations in notebook\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# AWS imports: Import Braket SDK modules\n", + "from braket.circuits import Circuit, circuit\n", + "from braket.devices import LocalSimulator\n", + "from braket.aws import AwsSession, AwsDevice" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# local imports\n", + "from utils_circuit import get_unitary, adjoint\n", + "from utils_qaa import qaa\n", + "\n", + "# monkey patch get_unitary() and adjoint() to the Circuit class\n", + "Circuit.get_unitary = get_unitary\n", + "Circuit.adjoint = adjoint" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# set up device: Local Schroedinger Simulator\n", + "device = LocalSimulator()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## IMPLEMENTATION OF REFLECTION OPERATORS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In ```utils_qaa.py``` we provide a set of simple helper functions to implement the quantum circuit for the QAA algorithm. \n", + "Specifically, we demonstrate how such modular building blocks can be registered as subroutines, using ```@circuit.subroutine(register=True)```. \n", + "Here we first highlight the implementation of the reflections $-\\mathcal{R}_{B}$ and $-\\mathcal{R}_{0}$ as discussed previously. The functions defined as follows comprise the ```utiles_qaa.py``` module." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### REFLECTION AROUND $|B\\rangle |0\\rangle$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We need to apply a minus sign to $|B\\rangle |0\\rangle$ only. We achieve this goal by applying $XZX$ to the ancilla qubit, so that we obtain a minus sign whenever the ancilla is in the $|0\\rangle$ state." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```python\n", + "# helper function to apply XZX to given qubit\n", + "@circuit.subroutine(register=True)\n", + "def minus_R_B(qubit):\n", + " \"\"\"\n", + " Function to apply a minus sign to |B>|0>. This goal is achieved by applying XZX to the ancilla qubit.\n", + "\n", + " Args:\n", + " qubit: the ancilla qubit on which we apply XZX.\n", + " \"\"\"\n", + " # instantiate circuit object\n", + " circ = Circuit()\n", + " \n", + " # Apply sequence XZX to given qubit\n", + " circ.x(qubit).z(qubit).x(qubit)\n", + " \n", + " return circ\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### REFLECTION AROUND $|0\\rangle^{\\otimes n+1}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We must implement $-\\mathcal{R}_{0}$, which gives a minus sign to $|0\\rangle_{n+1}$ only, leaving all other states untouched. \n", + "To this end, we implement the circuit visualized previously using ancilla qubits; alternatively, as controlled by the flag ```use_explicit_unitary```, one can evolve the system with the the unitary $\\mathrm{diag}(-1,1,1,...,1)$.\n", + "This way, we can run QAA on _classical_ simulators without the need to resort to ancilla qubits. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```python\n", + "# Helper function to apply rotation -R0\n", + "@circuit.subroutine(register=True)\n", + "def minus_R_zero(qubits, use_explicit_unitary=False):\n", + " \"\"\"\n", + " Function to implement transformation: |0,0,...0> -> -|0,0,...0>, all others unchanged. \n", + "\n", + " Args:\n", + " qubits: list of qubits on which to apply the gates\n", + " use_explicit_unitary (default False): Flag to specify that we could instead implement\n", + " the desired gate using a custom gate defined by the unitary diag(-1,1,...,1).\n", + " \"\"\"\n", + "\n", + " circ = Circuit()\n", + " \n", + " # If the use_explicit_matrix flag is True, we just apply the unitary defined by |0,0,...0> -> -|0,0,...0>\n", + " if use_explicit_unitary:\n", + " # Create the matrix diag(-1,1,1,...,1)\n", + " unitary = np.eye(2**len(qubits))\n", + " unitary[0][0]=-1\n", + " # Add a gate defined by this matrix\n", + " circ.unitary(matrix=unitary, targets=qubits)\n", + " \n", + " # Otherwise implement the unitary using ancilla qubits:\n", + " else:\n", + " # Flip all qubits. We now must check whether all qubits are |1>, rather than |0>.\n", + " circ.x(qubits)\n", + "\n", + " # If we have only 1 qubit, we only must apply XZX to that qubit to pick up a minus sign on |0>\n", + " if len(qubits) < 2:\n", + " circ.z(qubits)\n", + "\n", + " # For more qubits, we use Toffoli (or CCNOT) gates to verify the qubits are in |1> (after applying X)\n", + " else:\n", + "\n", + " # Dynamically add ancilla qubits, starting on the next unused qubit in the circuit\n", + " # NOTE: if this subroutine is being applied to a subset of qubits in a circuit, these ancilla\n", + " # registers may already be used. We could pass in circ as an argument and add ancillas outside of\n", + " # circ.targets instead, if desired.\n", + " ancilla_start = max(qubits) + 1\n", + "\n", + " # Check that the first two register qubits are both 1's using a CCNOT on a new ancilla qubit.\n", + " circ.ccnot(qubits[0],qubits[1],ancilla_start)\n", + "\n", + " # Now add a CCNOT from each of the next register qubits, comparing with the ancilla we just added.\n", + " # Target on a new ancilla. If len(qubits) is 2, this does not execute.\n", + " for ii,qubit in enumerate(qubits[2:]):\n", + " circ.ccnot(qubit,ancilla_start+ii, ancilla_start+ii+1)\n", + "\n", + " # A Z gate applied to the last ancilla qubit gives a minus sign if all register qubits are |1>\n", + " ancilla_end = ancilla_start + len(qubits[2:])\n", + " circ.z(ancilla_end)\n", + "\n", + " # Now uncompute to disentangle the ancilla qubits by applying CCNOTs in the reverse order to the previous.\n", + " for jj,qubit in enumerate(reversed(qubits[2:])):\n", + " circ.ccnot(qubit,ancilla_end-jj-1, ancilla_end-jj)\n", + "\n", + " # Finally undo the last CCNOT on the first two register qubits.\n", + " circ.ccnot(qubits[0],qubits[1],ancilla_start)\n", + "\n", + " # Flip all qubits back\n", + " circ.x(qubits)\n", + " \n", + " return circ\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## VISUALIZATION OF THE CIRCUIT FOR THE REFLECTION $\\mathcal{R}_{0}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To check our implementation of the $-\\mathcal{R}_{0}$ circuit discussed previously, let us visualize this circuit for small number of qubits. \n", + "Note that our implementation accepts a list of qubit indices with arbitrary index ordering. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example circuit with four qubits and simple index ordering:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4|5| 6 | 7 |8|\n", + " \n", + "q0 : -X-C-------------C---X-\n", + " | | \n", + "q1 : -X-C-------------C---X-\n", + " | | \n", + "q2 : -X-|-C-------C---|-X---\n", + " | | | | \n", + "q3 : -X-|-|-C---C-|-X-|-----\n", + " | | | | | | \n", + "q4 : ---X-C-|---|-C---X-----\n", + " | | | | \n", + "q5 : -----X-C---C-X---------\n", + " | | \n", + "q6 : -------X-Z-X-----------\n", + "\n", + "T : |0|1|2|3|4|5| 6 | 7 |8|\n" + ] + } + ], + "source": [ + "qubits = [0,1,2,3]\n", + "circ = Circuit()\n", + "circ.minus_R_zero(qubits)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example with four qubits and arbitrary index ordering:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the simulators require contiguous qubit indexing, while our algorithm does not." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T : |0|1|2|3|4|5|6| 7 |8|\n", + " \n", + "q0 : -X-C-----------C---X-\n", + " | | \n", + "q1 : -X-C-----------C---X-\n", + " | | \n", + "q4 : -X-|---C---C-X-|-----\n", + " | | | | \n", + "q5 : -X-|-C-|---|-C-|-X---\n", + " | | | | | | \n", + "q6 : ---X-C-|---|-C-X-----\n", + " | | | | \n", + "q7 : -----X-C---C-X-------\n", + " | | \n", + "q8 : -------X-Z-X---------\n", + "\n", + "T : |0|1|2|3|4|5|6| 7 |8|\n" + ] + } + ], + "source": [ + "qubits = [1, 0, 5, 4]\n", + "circ = Circuit()\n", + "circ.minus_R_zero(qubits)\n", + "print(circ)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## IMPLEMENTATION OF QAA " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This section puts everything together and shows how to implement QAA using the subroutines given previously. \n", + "We first build a function ```grover_iterator(...)``` that implements the Grover iterator $\\mathcal{Q}=\\mathcal{A} \\mathcal{R}_{0} \\mathcal{A}^{\\dagger} \\mathcal{R}_{B}$, given the unitary $\\mathcal{A}$ and the so-called flag qubit labeling the good/bad subspaces. \n", + "Given this implementation for the Grover iterator $\\mathcal{Q}$ it is straightforward to implement a QAA routine ```qaa(...)``` which repeatedly applies the iterator $\\mathcal{Q}$ for a given number of iterations. \n", + "\n", + "The full code (imported into this notebook in the [imports and setup](#IMPORTS-and-SETUP) section) is available in the module ```utils_qaa.py```. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```python\n", + "@circuit.subroutine(register=True)\n", + "def grover_iterator(A,flag_qubit,qubits=None,use_explicit_unitary=False):\n", + " \"\"\"\n", + " Function to implement the Grover iterator Q=A R_0 A* R_B. \n", + "\n", + " Args:\n", + " A: Circuit defining the unitary A\n", + " flag_qubit: Specifies which of the qubits A acts on labels the good/bad subspace.\n", + " Must be an element of qubits (if passed) or A.qubits.\n", + " qubits: list of qubits on which to apply the gates (including the flag_qubit).\n", + " If qubits is different from A.qubits, A is applied to qubits instead.\n", + " use_explicit_unitary: Flag to specify that we should implement R_0 using using a custom\n", + " gate defined by the unitary diag(-1,1,...,1). Default is False.\n", + " \"\"\"\n", + " # If no qubits are passed, apply the gates to the targets of A\n", + " if qubits is None:\n", + " qubits = A.qubits\n", + " else:\n", + " # If qubits are passed, make sure it's the right number to remap from A.\n", + " if len(qubits)!=len(A.qubits):\n", + " raise ValueError('Number of desired target qubits differs from number of targets in A'.format(flag_qubit=repr(flag_qubit)))\n", + " \n", + " # Verify that flag_qubit is one of the qubits on which A acts, or one of the user defined qubits\n", + " if flag_qubit not in qubits:\n", + " raise ValueError('flag_qubit {flag_qubit} is not in targets of A'.format(flag_qubit=repr(flag_qubit)))\n", + " \n", + " # Instantiate the circuit\n", + " circ = Circuit()\n", + " \n", + " # Apply -R_B to the flag qubit\n", + " circ.minus_R_B(flag_qubit)\n", + " \n", + " # Apply A^\\dagger. Use target mapping if different qubits are specified\n", + " circ.add_circuit(A.adjoint(),target=qubits)\n", + " \n", + " # Apply -R_0\n", + " circ.minus_R_zero(qubits,use_explicit_unitary)\n", + " \n", + " # Apply A, mapping targets if desired.\n", + " circ.add_circuit(A,target=qubits)\n", + " \n", + " return circ\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```python\n", + "@circuit.subroutine(register=True)\n", + "def qaa(A,flag_qubit,num_iterations,qubits=None,use_explicit_unitary=False):\n", + " \"\"\"\n", + " Function to implement the Quantum Amplitude Amplification Q^m, where Q=A R_0 A* R_B, m=num_iterations. \n", + "\n", + " Args:\n", + " A: Circuit defining the unitary A\n", + " flag_qubit: Specifies which of the qubits A acts on labels the good/bad subspace.\n", + " Must be an element of qubits (if passed) or A.qubits.\n", + " num_iterations: number of applications of the Grover iterator Q.\n", + " qubits: list of qubits on which to apply the gates (including the flag_qubit).\n", + " If qubits is different from A.qubits, A is applied to qubits instead.\n", + " use_explicit_unitary: Flag to specify that we should implement R_0 using using a custom\n", + " gate defined by the unitary diag(-1,1,...,1). Default is False.\n", + " \"\"\"\n", + " # Instantiate the circuit\n", + " circ = Circuit()\n", + " \n", + " # Apply the Grover iterator num_iterations times:\n", + " for _ in range(num_iterations):\n", + " circ.grover_iterator(A,flag_qubit,qubits,use_explicit_unitary)\n", + " \n", + " return circ\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## NUMERICAL EXAMPLE" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This section shows how to use QAA to amplify the amplitude of $|11\\rangle$ of a two-qubit state, thereby increasing the entanglement between the two qubits. Consider a single qubit in the state \n", + "\n", + "$$|\\psi\\rangle=\\sqrt{1-\\delta^2}|0\\rangle + \\delta |1\\rangle,$$\n", + "\n", + "where $\\delta$ is small. This state can be prepared using a small rotation around the $y$ direction:\n", + "\n", + "$$R_y(\\epsilon)|0\\rangle=|\\psi\\rangle,$$\n", + "\n", + "where $\\epsilon$ is chosen to give a coefficient of $\\delta=\\sin(\\epsilon/2) \\approx \\epsilon/2$ to $|1\\rangle$.\n", + "\n", + "Suppose $|1\\rangle$ is the \"good\" state and $|0\\rangle$ is the \"bad\" state. \n", + "We can use a single ancilla qubit to mark whether our register qubit is in the \"good\" or \"bad\" state, which can be accomplished by applying a single $\\mathrm{CNOT}$ gate to our ancilla qubit and $|\\psi\\rangle$. \n", + "Thus,\n", + "\n", + "$$\n", + "\\mathcal{A}|0\\rangle|0\\rangle = \\mathrm{CNOT}\\circ R_y(\\epsilon)|0\\rangle|0\\rangle = \\mathrm{CNOT}|\\psi\\rangle|0\\rangle = \\sqrt{1-\\delta^2}|00\\rangle + \\delta |11\\rangle.\n", + "$$\n", + "\n", + "Our goal is to amplify the coefficient of the \"good\" state. Using the previous algorithm, this amplification corresponds to applying Quantum Amplitude Amplification with an input unitary $\\mathcal{A}=\\mathrm{CNOT}\\circ R_y(\\epsilon)$. We then test whether the flag qubit is in the $|1\\rangle$ state, which we can achieve by checking the amplitude of the $|11\\rangle$ state.\n", + "\n", + "Let us check the effectiveness of the algorithm by plotting the probability of measuring $|11\\rangle$ as a function of the number of repetitions $m$, which corresponds to the number of queries of the oracle, in the classical problem. According to the description given previously, we should see a distribution that looks like $O(\\sin^2(m))$. Note that the probability `ResultType` we will use requires a non-zero value for `shots` when running on an on-demand simulator." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Set up the state A|00>\n", + "flag_qubit = 1\n", + "epsilon = 0.05\n", + "A_circ = Circuit().ry(0, epsilon).cnot(0,1)\n", + "\n", + "# Add marginal probability for flag qubit as result Type \n", + "A_circ.probability(target=[flag_qubit])\n", + "\n", + "# Let's find the probability of measuring |11> for different values of m, the number of applications of QAA:\n", + "probabilities = []\n", + "stepsize = 2\n", + "iterations = range(1, 40, stepsize)\n", + "for m in iterations:\n", + " \n", + " # Get circuit object\n", + " circ = Circuit()\n", + " # Apply QAA using A defined by A_circ\n", + " circ.qaa(A_circ, flag_qubit, m, use_explicit_unitary=True)\n", + " \n", + " # Classically simulate the circuit\n", + " # Give the correct device.run call depending on whether the device is local or on-demand\n", + " if isinstance(device, LocalSimulator):\n", + " task = device.run(circ, shots=0)\n", + " else:\n", + " task = device.run(circ, shots=1000)\n", + " \n", + " # Get result\n", + " result = task.result()\n", + " # Append the probability of measuring |11> for this value of m.\n", + " probabilities.append(result.values[0][1])\n", + "\n", + "# Get analytical result for comparison\n", + "probs_theo = [np.sin((2*mm+1)*epsilon/2)**2 for mm in iterations]\n", + " \n", + "# Plot the results\n", + "plt.figure(figsize=(7,5))\n", + "plt.plot(iterations, probabilities, 'o');\n", + "plt.plot(iterations, probs_theo);\n", + "plt.xlabel('Number of Iterations');\n", + "plt.ylabel('Probability of measuring flag qubit in |1>');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, we see that the repeated application of the Grover iterator $\\mathcal{Q}$ does increase the amplitude associated with the state $|11\\rangle$. \n", + "The probability of measuring the bitstring 11 follows the expected analytical result, given by $(P_{11} = \\sin^{2}[(2m+1)\\epsilon/2])$, and shown as the solid orange line.\n", + "Moreover, we have verified that the optimal number of iterations is approximately given by $\\lfloor \\frac{\\pi}{4\\theta}\\rfloor= \\lfloor \\frac{\\pi}{2\\epsilon}\\rfloor \\approx 31$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "## APPENDIX" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Version: 0.6.0\r\n" + ] + } + ], + "source": [ + "# Check SDK version\n", + "# alternative: braket.__version__\n", + "!pip show amazon-braket-sdk | grep Version" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## APPENDIX: ALTERNATIVE RUN WITH AMPLITUDE RESULT TYPE" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Rather than just examining the marginal probability to find the flag qubit in state $|1\\rangle$ as done before, we can also investigate the behavior of the amplitude associated with the state $|11\\rangle$.\n", + "This amplitude is initially given by $\\delta=\\sin(\\epsilon/2)\\approx \\epsilon/2$ for small $\\epsilon$. We can check explicitly that this amplitude increases using repeated applications of the Grover iterator, and recover the plot using the absolute value squared of the amplitudes. \n", + "\n", + "Using amplitudes also presents a learning opportunity:\n", + "If we use $N-1$ ancilla qubits to implement the reflection $\\mathcal{R}_{0}$ (by fixing ```use_explicit_unitary = False```), then measurement outcomes are bitstrings of size $N+N-1=2N-1$ (as we measure the original qubits on which the circuit acts, as well as the ancilla qubits).\n", + "\n", + "Since the ancilla qubits are initialized in $|0, 0, ...\\rangle$ and are uncomputed back to their initial state in the last step of the algorithm, we can find the amplitude of a given bitstring on the register qubits by padding that target bitstring (for example, $11$ in our example) with the right number ($N-1$) of zeros. \n", + "\n", + "Using a classical simulator backend, we can attach the corresponding amplitude as a `ResultType` to the circuit, as shown in the following code. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Amplitude <11|Initial State>:\n", + " {'11': (0.024997395914712332+0j)} \n", + "\n", + "Maximum amplified amplitude <110|Final State> after approximately 31 Grover iterations:\n", + " {'11': (0.9997837641893592+0j)}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Set up the state A|00>\n", + "flag_qubit = 1\n", + "epsilon = 0.05\n", + "A_circ = Circuit().ry(0, epsilon).cnot(0,1)\n", + "\n", + "# set switch to either use explicit unitary diag(-1, 1, ...) [True] or use ancillas [False]\n", + "use_explicit_unitary = True\n", + "\n", + "# Let's find the probability of measuring |11> for different values of m, the number of applications of QAA:\n", + "probabilities = []\n", + "stepsize = 2\n", + "iterations = range(1, 40, stepsize)\n", + "for m in iterations:\n", + " \n", + " # Get circuit object\n", + " circ = Circuit()\n", + " # Apply QAA using A defined by A_circ\n", + " circ.qaa(A_circ, flag_qubit, m, use_explicit_unitary=use_explicit_unitary)\n", + " \n", + " if use_explicit_unitary:\n", + " target_string = '11'\n", + " circ.amplitude(state=[target_string])\n", + " else:\n", + " number_ancillas = A_circ.qubit_count - 1\n", + " target_string = '11'+'0'*number_ancillas\n", + " circ.amplitude(state=[target_string])\n", + " \n", + " # Classically simulate the circuit\n", + " # Execute the correct device.run call depending on whether the device is local or on-demand\n", + " if isinstance(device, LocalSimulator):\n", + " task = device.run(circ, shots=0)\n", + " else:\n", + " task = device.run(circ, shots=0)\n", + " \n", + " # Get result\n", + " result = task.result() \n", + " # Append the probability of measuring |11> for this value of m.\n", + " probabilities.append(np.linalg.norm(result.values[0][target_string])**2)\n", + "\n", + "# Get analytical result for comparison\n", + "probs_theo = [np.sin((2*mm+1)*epsilon/2)**2 for mm in iterations]\n", + " \n", + "# Plot the results\n", + "plt.figure(figsize=(7,5))\n", + "plt.plot(iterations, probabilities);\n", + "plt.plot(iterations, probs_theo, 'o');\n", + "plt.xlabel('Number of Iterations');\n", + "plt.ylabel('Probability of measuring 11');\n", + "\n", + "# Let's compare the amplitude of |11> in the initial state versus the state with maximum probability:\n", + "# Print the initial amplitude of |11>\n", + "\n", + "# Add a Result Type to output the amplitude of |11> for A\n", + "A_initial = A_circ.copy()\n", + "A_initial.amplitude(state=['11'])\n", + "\n", + "if isinstance(device, LocalSimulator):\n", + " initial_result = device.run(A_initial, shots=0).result()\n", + "else:\n", + " initial_result = device.run(A_initial, shots=0).result()\n", + "print(\"Amplitude <11|Initial State>:\\n\", initial_result.values[0],\"\\n\")\n", + "\n", + "# Find the number of iterations required to achieve the maximum probability:\n", + "max_prob = max(probabilities)\n", + "max_iter = iterations[probabilities.index(max_prob)]\n", + "\n", + "# Generate that state:\n", + "circ = Circuit()\n", + "circ.qaa(A_circ, flag_qubit, max_iter, use_explicit_unitary=use_explicit_unitary)\n", + "circ.amplitude(state=[target_string])\n", + "\n", + "# Run the simulator\n", + "if isinstance(device, LocalSimulator):\n", + " task = device.run(circ, shots=0)\n", + " result = task.result()\n", + "else:\n", + " task = device.run(circ, shots=0)\n", + " result = task.result()\n", + "\n", + "# Print the final amplitude of |11>:\n", + "info = \"Maximum amplified amplitude <110|Final State> after approximately\"\n", + "print(info+\" {} Grover iterations:\\n {}\".format(max_iter, result.values[0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "## References\n", + "\n", + "[1] Wikipedia: [Amplitude Amplification](https://en.wikipedia.org/wiki/Amplitude_amplification).\n", + "\n", + "[2] G. Brassard, P. Høyer, \"An exact quantum polynomial-time algorithm for Simon's problem\", Proceedings of Fifth Israeli Symposium on Theory of Computing and Systems. IEEE Computer Society Press: 12–23, [arXiv:quant-ph/9704027](https://arxiv.org/abs/quant-ph/9704027) (1997). \n", + "\n", + "[3] G. Brassard, P. Høyer, M. Mosca, A. Tapp, \"Quantum Amplitude Amplification and Estimation\", [arXiv:quant-ph/0005055](https://arxiv.org/pdf/quant-ph/0005055.pdf) (2000).\n", + "\n", + "[4] Y. Suzuki, S. Uno, R. Raymond, T. Tanaka, T. Onodera, N. Yamamoto, \"Amplitude Estimation without Phase Estimation\", [arXiv:1904.10246](https://arxiv.org/pdf/1904.10246.pdf) (2019). " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "conda_braket", + "language": "python", + "name": "conda_braket" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/modules/1_Continue_Exploring/C_qtm_algorithms/canonical_algorithms/Quantum_Amplitude_Amplification/R0.png b/modules/1_Continue_Exploring/C_qtm_algorithms/canonical_algorithms/Quantum_Amplitude_Amplification/R0.png new file mode 100644 index 0000000000000000000000000000000000000000..ba436798c0043268a4363e06264862fe58679c12 GIT binary patch literal 40357 zcmdSBbySt>*DeeQN{FBmDiV^?CEX$|As`)!bb}xvDWW0@3Q|&ngh)w9r-F1hNGKpB zAl-20vk>hUW7a4Q(5~@|i|M zbLK!po4tdECK!o^Mrt2Za!VL~z_FLrz7LJ90?ufr!1YI7$idqH+~7Z(>c7j8B?M>BR#0RaJa 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This is achieved by applying XZX to the ancilla qubit. + + Args: + qubit: the ancilla qubit on which we apply XZX. + """ + # instantiate circuit object + circ = Circuit() + + # Apply sequence XZX to given qubit + circ.x(qubit).z(qubit).x(qubit) + + return circ + + +# Helper function to apply rotation -R0 +@circuit.subroutine(register=True) +def minus_R_zero(qubits, use_explicit_unitary=False): + """ + Function to implement transformation: |0,0,...0> -> -|0,0,...0>, all others unchanged. + + Args: + qubits: list of qubits on which to apply the gates + use_explicit_unitary (default False): Flag to specify that we could instead implement + the desired gate using a custom gate defined by the unitary diag(-1,1,...,1). + """ + + circ = Circuit() + + # If the use_explicit_matrix flag is True, we just apply the unitary defined by |0,0,...0> -> -|0,0,...0> + if use_explicit_unitary: + # Create the matrix diag(-1,1,1,...,1) + unitary = np.eye(2 ** len(qubits)) + unitary[0][0] = -1 + # Add a gate defined by this matrix + circ.unitary(matrix=unitary, targets=qubits) + + # Otherwise implement the unitary using ancilla qubits: + else: + # Flip all qubits. We now need to check if all qubits are |1>, rather than |0>. + circ.x(qubits) + + # If we have only 1 qubit, we only need to apply XZX to that qubit to pick up a minus sign on |0> + if len(qubits) < 2: + circ.z(qubits) + + # For more qubits, we use Toffoli (or CCNOT) gates to check that all the qubits are in |1> (since we applied X) + else: + + # Dynamically add ancilla qubits, starting on the next unused qubit in the circuit + # TODO: if this subroutine is being applied to a subset of qubits in a circuit, these ancilla + # registers might already be used. We could pass in circ as an argument and add ancillas outside of + # circ.targets + ancilla_start = max(qubits) + 1 + + # Check that the first two register qubits are both 1's using a CCNOT on a new ancilla qubit. + circ.ccnot(qubits[0], qubits[1], ancilla_start) + + # Now add a CCNOT from each of the next register qubits, comparing with the ancilla we just added. + # Target on a new ancilla. If len(qubits) is 2, this does not execute. + for ii, qubit in enumerate(qubits[2:]): + circ.ccnot(qubit, ancilla_start + ii, ancilla_start + ii + 1) + + # Apply a Z gate to the last ancilla qubit to pick up a minus sign if all of the register qubits are |1> + ancilla_end = ancilla_start + len(qubits[2:]) + circ.z(ancilla_end) + + # Now uncompute to disentangle the ancilla qubits by applying CCNOTs in the reverse order to above. + for jj, qubit in enumerate(reversed(qubits[2:])): + circ.ccnot(qubit, ancilla_end - jj - 1, ancilla_end - jj) + + # Finally undo the last CCNOT on the first two register qubits. + circ.ccnot(qubits[0], qubits[1], ancilla_start) + + # Flip all qubits back + circ.x(qubits) + + return circ + + +@circuit.subroutine(register=True) +def grover_iterator(A, flag_qubit, qubits=None, use_explicit_unitary=False): + """ + Function to implement the Grover iterator Q=A R_0 A* R_B. + + Args: + A: Circuit defining the unitary A + flag_qubit: Specifies which of the qubits A acts on labels the good/bad subspace. + Must be an element of qubits (if passed) or A.qubits. + qubits: list of qubits on which to apply the gates (including the flag_qubit). + If qubits is different from A.qubits, A is applied to qubits instead. + use_explicit_unitary: Flag to specify that we should implement R_0 using using a custom + gate defined by the unitary diag(-1,1,...,1). Default is False. + """ + # If no qubits are passed, apply the gates to the targets of A + if qubits is None: + qubits = A.qubits + else: + # If qubits are passed, make sure it's the right number to remap from A. + if len(qubits) != len(A.qubits): + raise ValueError( + "Number of desired target qubits differs from number of targets in A".format( + flag_qubit=repr(flag_qubit) + ) + ) + + # Verify that flag_qubit is one of the qubits on which A acts, or one of the user defined qubits + if flag_qubit not in qubits: + raise ValueError( + "flag_qubit {flag_qubit} is not in targets of A".format(flag_qubit=repr(flag_qubit)) + ) + + # Instantiate the circuit + circ = Circuit() + + # Apply -R_B to the flag qubit + circ.minus_R_B(flag_qubit) + + # Apply A^\dagger. Use target mapping if different qubits are specified + circ.add_circuit(A.adjoint(), target=qubits) + + # Apply -R_0 + circ.minus_R_zero(qubits, use_explicit_unitary) + + # Apply A, mapping targets if desired. + circ.add_circuit(A, target=qubits) + + return circ + + +@circuit.subroutine(register=True) +def qaa(A, flag_qubit, num_iterations, qubits=None, use_explicit_unitary=False): + """ + Function to implement the Quantum Amplitude Amplification Q^m, where Q=A R_0 A* R_B, m=num_iterations. + + Args: + A: Circuit defining the unitary A + flag_qubit: Specifies which of the qubits A acts on labels the good/bad subspace. + Must be an element of qubits (if passed) or A.qubits. + num_iterations: number of applications of the Grover iterator Q. + qubits: list of qubits on which to apply the gates (including the flag_qubit). + If qubits is different from A.qubits, A is applied to qubits instead. + use_explicit_unitary: Flag to specify that we should implement R_0 using using a custom + gate defined by the unitary diag(-1,1,...,1). Default is False. + """ + # Instantiate the circuit + circ = Circuit() + + # Apply the Grover iterator num_iterations times: + for _ in range(num_iterations): + circ.grover_iterator(A, flag_qubit, qubits, use_explicit_unitary) + + return circ diff --git a/modules/1_Continue_Exploring/C_qtm_algorithms/canonical_algorithms/Quantum_Amplitude_Amplification/vectors.png b/modules/1_Continue_Exploring/C_qtm_algorithms/canonical_algorithms/Quantum_Amplitude_Amplification/vectors.png new file mode 100644 index 0000000000000000000000000000000000000000..14128039f45701b80c92fb6e1ea0079a0ae003e0 GIT binary patch literal 192825 zcmeFZ`9IX}+dhsc<%LQSva}$35wa^G#Mt+xED1BVv5sYEAqi#8t}J64(_rj_7AE_? zGstf2jD7h&CtmmWbAKQA`|}Tc?_WF~sd>(Io!5CD=W!h8^(<6NQ-$^d%LOtrGFsIq zk9Ek%&U%xPQFKtB1%6XZ9w1Fd#!067_@SOR`Qqp~Z$15^W7o37t;oV00V9QPxA+FM zw9)+HW`shlwQ#=Cr7ZQ34qxFe-xch(g(A;IilF;X9_=5bt=RG;^dzWqH^yxHv!}L< zR7{WbV{J6swv$&RK?2mAfn*f_@yA0h7YnV}xF0wFZ~ut;9T`16`G0;0HRnYe3QF%+ 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zHAC*9#QmS<%iRC|U%C6PV)x?W)p6_w-0y^duJGvSymXYUQ966o`RcX%lICZf^1foJ z=ql!Y+CF+(eJs1f=^3irK%)Z%%f14S06Vy9R+@eBpVQY<-#!5*t;GLPtTi6#|29TV z^Amhkc>7Iv+~WG4$*c+oR3GRuGHjVy=v@7J@}uUn@0ef67)9NCTYr7!B>kuB*H1iq z)AyWW=BsIjdyl?NULyaEQO0~pdG-|E5{n#WW`+!7@oJ$HS08yQ99Wvjr@*k_tjaOh z)20?-X0NB_a$c4JX1wbUA`ZzHbb?~V3^cm&O@Q42I8p)3>58`M7bXJR_zbyP`<4fP zcKWmD909*+rh;6);qltfFCCVK zf3@2$Q?^OP3\n", + " Note: This section and the next verbatim box section uses the Rigetti Aspen-M-3 device. When you run this notebook, make sure the device is currently available. You can find QPU availability windows on the Devices page in the Amazon Braket Console\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Verbatim Compilation with OpenQASM\n", + "\n", + "In [a previous example notebook](https://github.com/aws/amazon-braket-examples/blob/main/examples/braket_features/Verbatim_Compilation.ipynb), we talked about verbatim compilation on Braket to gain more precise control on Rigetti devices. With OpenQASM3.0, we can use the `box` syntax together with the `verbatim` pragma to perform verbatim compilation. Here is an example:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "program_with_verbatim_box = \"\"\"\n", + "OPENQASM 3;\n", + "\n", + "bit[2] ro;\n", + "#pragma braket verbatim\n", + "box{\n", + " rx(3.141592653589793) $0;\n", + " rx(3.141592653589793) $0;\n", + " cz $0, $1;\n", + "}\n", + "ro[0] = measure $0;\n", + "ro[1] = measure $1;\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To program with verbatim boxes, we need to make sure that\n", + "- we are using native gates supported by Rigetti devices. Native gates can be found using the following script:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The native gates for the Aspen-M-3 device are:\n", + "rx\n", + "rz\n", + "cz\n", + "cphaseshift\n", + "xy\n" + ] + } + ], + "source": [ + "print(\"The native gates for the\", aspen_m.name, \"device are:\")\n", + "for gate in aspen_m.properties.paradigm.nativeGateSet:\n", + " print(gate)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- we use the physical qubit notation.\n", + "- qubit operands are indeed connected on the physical device. Recall that the device qubit connectivity can be found using the following commands:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'0': ['1', '7'], '1': ['0', '16', '2'], '10': ['11', '113', '17'], '100': ['101', '107'], '101': ['100', '102', '116'], '102': ['101', '103', '115'], '103': ['102', '104'], '104': ['103', '105', '7'], '105': ['104', '106'], '106': ['105', '107'], '107': ['100', '106'], '11': ['10', '12', '26'], '110': ['111', '117'], '111': ['110', '112', '126'], '112': ['111', '113', '125'], '113': ['10', '112', '114'], '114': ['113', '115', '17'], '115': ['102', '114', '116'], '116': ['101', '115', '117'], '117': ['110', '116'], '12': ['11', '13', '25'], '120': ['121', '127'], '121': ['120', '122', '136'], '122': ['121', '123', '135'], '123': ['122', '124', '20'], '124': ['123', '125', '27'], '125': ['112', '124', '126'], '126': ['111', '125', '127'], '127': ['120', '126'], '13': ['12', '14'], '130': ['131', '137'], '131': ['130', '132', '146'], '132': ['131', '133', '145'], '133': ['132', '134', '30'], '134': ['133', '135', '37'], '135': ['122', '134', '136'], '136': ['121', '135', '137'], '137': ['130', '136'], '14': ['13', '15'], '140': ['141', '147'], '141': ['140', '142'], '142': ['141', '143'], '143': ['142', '144', '40'], '144': ['143', '145', '47'], '145': ['132', '144', '146'], '146': ['131', '145', '147'], '147': ['140', '146'], '15': ['14', '16', '2'], '16': ['1', '15', '17'], '17': ['10', '16', '114'], '2': ['1', '15', '3'], '20': ['123', '21', '27'], '21': ['20', '22', '36'], '22': ['21', '23', '35'], '23': ['22', '24'], '24': ['23', '25'], '25': ['12', '24', '26'], '26': ['11', '25', '27'], '27': ['20', '26', '124'], '3': ['2', '4'], '30': ['133', '31', '37'], '31': ['30', '32', '46'], '32': ['31', '33', '45'], '33': ['32', '34'], '34': ['33', '35'], '35': ['22', '34', '36'], '36': ['21', '35', '37'], '37': ['30', '36', '134'], '4': ['3', '5'], '40': ['143', '41', '47'], '41': ['40', '42'], '42': ['41', '43'], '43': ['42', '44'], '44': ['43', '45'], '45': ['32', '44', '46'], '46': ['31', '45', '47'], '47': ['40', '46', '144'], '5': ['4', '6'], '6': ['5', '7'], '7': ['0', '6', '104']}\n" + ] + }, + { + "data": { + "image/png": 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