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CSSFinder.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Jun 22 07:55:58 2022
ver 1.1.0
@author: wiesn
"""
import sys
import numpy as np
import math
#import scipy.io
from datetime import datetime
from os.path import exists
#####
#Matrix Functions:
#Outer product of two vectors
def Outer(p1,p2):
return(np.outer(np.array(p1),np.array(p2)).flatten())
#Normalization of a vector
def Normalize(p):
p2=np.dot(p,np.conj(p))
p2=math.sqrt(np.real(p2))
return(p/p2)
#Build a projection from a vector
def Project(p1):
return(np.outer(np.array(p1),np.conj(np.array(p1))))
#Scalar product of two matrices
def Product(t1,t2):
k=np.trace(np.matmul(t1,t2))
return(np.real(k))
#Generate a random vector with Haar measure
def Generate(d):
k1=np.random.normal(0,1,d)
k2=np.random.normal(0,1,d)
k3=k1+complex(0,1)*k2
return(k3)
#Identity Matrix
def IdMatrix(d):
p1=np.zeros((int(d),int(d)),dtype=complex)
for i1 in range(d):
p1[i1,i1]=1
return(p1)
# Kronecker Product
def Kronecker(p1,p2):
ddd1=len(p1)
ddd2=len(p2)
p3=np.reshape(np.swapaxes(np.tensordot(p1,p2,0),1,2),(ddd1*ddd2,ddd1*ddd2))
# p3=np.zeros((ddd1*ddd2,ddd1*ddd2),dtype=complex)
# for i1 in range(ddd1):
# for i2 in range(ddd2):
# for i3 in range(ddd1):
# for i4 in range(ddd2):
# p3[ddd2*i1+i2,ddd2*i3+i4]=p1[i1,i3]*p2[i2,i4]
return(p3)
#Expand an operator to n qubits
def Expand2FS(p1,n,j1):
return(Kronecker(Kronecker(IdMatrix(2**j1),p1),IdMatrix(2**(n-j1-1))))
#Expand an operator to n quDits
def ExpanddFS(p1,d,n,j1):
return(Kronecker(Kronecker(IdMatrix(int(d**j1)),p1),IdMatrix(int(d**(n-j1-1)))))
# sandwich an operator with a unitarry
def Rotate(rho2,U):
rho2a=np.matmul(rho2,np.conj(U).T)
rho2a=np.matmul(U,rho2a)
return rho2a
#MTX file read and write
#[1]: 'matrix' 'vector'
#[2]: 'array' 'coordinate'
#[3]: 'integer' 'real' 'complex' 'pattern'
#[4]: 'general' 'symmetric' 'skew-symmetric' 'hermitian
def getnum(file,vartype):
readnum=file.readline()
if vartype==0:
return(int(readnum))
elif vartype==1:
return(float(readnum))
elif vartype==2:
readnum=readnum.split()
kreadnum=list(map(float,readnum))
return(kreadnum[0]+complex(0,1)*kreadnum[1])
def get3num(file,vartype):
readnum=file.readline()
readnum=readnum.split
if vartype==0:
return([int(readnum[0]),int(readnum[1]),int(readnum[2])])
elif vartype==1:
return([int(readnum[0]),int(readnum[1]),float(readnum[2])])
elif vartype==2:
return([int(readnum[0]),int(readnum[1]),float(readnum[2])+complex(float(readnum[3]))])
def readmtx(filename):
with open(filename,"r") as file:
line=str(file.readline())
firstline=line.split()
if firstline[1]=='matrix':
shape=0
elif firstline[1]=='vector':
shape=1
if firstline[2]=='array':
descr=0
elif firstline[2]=='coordinate':
descr=1
if firstline[3]=='integer':
vartype=0
elif firstline[3]=='real':
vartype=1
elif firstline[3]=='complex':
vartype=2
if firstline[4]=='general':
symtype=0
elif firstline[4]=='symmetric':
symtype=1
elif firstline[4]=='skew-symmetric':
symtype=2
elif firstline[4]=='hermitian':
symtype=3
while line[0]=="%" or len(line)==1:
line=file.readline()
line=list(map(int,line.split()))
if shape==0 and descr==0:
rows=line[0]
cols=line[1]
if vartype==0:
wynik=np.zeros((rows,cols),dtype=int)
elif vartype==1:
wynik=np.zeros((rows,cols),dtype=float)
elif vartype==2:
wynik=np.zeros((rows,cols),dtype=complex)
if symtype==0:
for i1 in range(cols):
for i2 in range(rows):
wynik[i2][i1]=getnum(file,vartype)
elif symtype==1 and rows==cols:
for i1 in range(cols):
for i2 in range(i1,rows):
wynik[i2][i1]=getnum(file,vartype)
wynik[i1][i2]=wynik[i2][i1]
elif symtype==2 and rows==cols:
for i1 in range(0,cols):
for i2 in range(i1+1,rows):
wynik[i2][i1]=getnum(file,vartype)
wynik[i1][i2]=-wynik[i2][i1]
elif symtype==3 and rows==cols:
for i1 in range(0,cols):
for i2 in range(i1,rows):
wynik[i2][i1]=getnum(file,vartype)
wynik[i1][i2]=np.conj(wynik[i2][i1])
if shape==0 and descr==1:
rows=line[0]
cols=line[1]
nonzeros=line[3]
if vartype==0:
wynik=np.zeros((cols,rows),dtype=int)
elif vartype==1:
wynik=np.zeros((cols,rows),dtype=float)
elif vartype==2:
wynik=np.zeros((cols,rows),dtype=complex)
for i1 in range(nonzeros):
entry=get3num(file,vartype)
wynik[entry[1]][entry[0]]=entry[2]
if symtype==1 and rows==cols:
for i1 in range(rows):
for i2 in range(i1,cols):
if np.abs(wynik[i1][i2])!=0:
wynik[i2][i1]=wynik[i1][i2]
else:
wynik[i1][i2]=wynik[i2][i1]
elif symtype==2 and rows==cols:
for i1 in range(0,cols):
for i2 in range(i1+1,rows):
if np.abs(wynik[i1][i2])!=0:
wynik[i2][i1]=-wynik[i1][i2]
else:
wynik[i1][i2]=-wynik[i2][i1]
elif symtype==3 and rows==cols:
for i1 in range(0,cols):
for i2 in range(i1,rows):
if np.abs(wynik[i1][i2])!=0:
wynik[i2][i1]=np.conj(wynik[i1][i2])
else:
wynik[i1][i2]=np.conj(wynik[i2][i1])
file.close()
return(wynik)
def writemtx(filename,lista,vartype):
if vartype==1:
vartype1="real"
elif vartype==2:
vartype1="complex"
elif vartype==0:
vartype1="integer"
with open(filename,'w') as file:
file.write(" ".join(["%%MatrixMarket matrix array",vartype1,"general\n"]))
file.write("%Generated by CSSFinder\n")
file.write(str(len(lista)))
file.write(" ")
file.write(str(len(lista[0])))
file.write("\n")
for i1 in range(len(lista[0])):
for i2 in range(len(lista)):
if vartype==2:
file.write(str(np.real(lista[i2][i1])))
file.write(" ")
file.write(str(np.imag(lista[i2][i1])))
file.write("\n")
else:
file.write(str(lista[i2][i1]))
file.write("\n")
file.close()
#Random states:
#n qubit state
def Random2FS(n):
q1=Normalize(Generate(2))
if n>1:
for l1 in range(n-1):
q1=Outer(q1,Normalize(Generate(2)))
return(Project(q1))
#n quDit state
def RandomdFS(d,n):
q1=Normalize(Generate(d))
for l1 in range(n-1):
q1=Outer(q1,Normalize(Generate(d)))
return(Project(q1))
#biseparable state
def RandomBS(d1,d2):
return Project(Outer(Normalize(Generate(d1)),Normalize(Generate(d2))))
#biseparable state with three quDits
def Random3P(d1,swaps,i):
if i==0:
# aBC
return(RandomBS(d1,d1*d1))
if i==1:
#AbC
return(Rotate(RandomBS(d1,d1*d1),swaps[0]))
if i==2:
#ABc
return(RandomBS(d1*d1,d1))
#biseparable for 4 quDits
def Random4P(d1,swaps,i):
if i==0:
# aBCD
return(RandomBS(d1,d1*d1*d1))
if i==1:
#AbCD
return(Rotate(RandomBS(d1,d1*d1*d1),swaps[0]))
if i==2:
#ABcD
return(Rotate(RandomBS(d1*d1*d1,d1),swaps[3]))
if i==3:
#ABCd
return(RandomBS(d1*d1*d1,d1))
if i==4:
#abCD
return(RandomBS(d1*d1,d1*d1))
if i==5:
#aBcD
return(Rotate(RandomBS(d1*d1,d1*d1),swaps[2]))
if i==6:
#aBCd
return(Rotate(RandomBS(d1*d1,d1*d1),swaps[1]))
#Rendom Unitaries
#Biseparability
def RandomUBS(a,d1,d2):
if a==0:
rubsp1=(math.cos(0.01*math.pi)+complex(0,1)*math.sin(0.01*math.pi)-1)*Project(Normalize(Generate(d1)))+IdMatrix(d1)
return(Kronecker(rubsp1,IdMatrix(int(d2))))
if a==1:
rubsp1=(math.cos(0.01*math.pi)+complex(0,1)*math.sin(0.01*math.pi)-1)*Project(Normalize(Generate(d2)))+IdMatrix(d2)
return(Kronecker(IdMatrix(int(d1)),rubsp1))
# return(Kronecker(IdMatrix(d1),unitatry_group.rvs(d2)))
#n qubits
def RandomU2FS(n,j):
# p1=unitary_group.rvs(2)
p1=(math.cos(0.01*math.pi)+complex(0,1)*math.sin(0.01*math.pi)-1)*Random2FS(1)+IdMatrix(2)
return(Expand2FS(p1, n, j))
#n quDits
def RandomUdFS(d,n,j):
# p1=unitary_group.rvs(d)
p1=(math.cos(0.01*math.pi)+complex(0,1)*math.sin(0.01*math.pi)-1)*RandomdFS(d,1)+IdMatrix(d)
return(ExpanddFS(p1, d, n, j))
# Optimizers
#biseparability
def OptimizeBS(rho2,rho3,d1,d2):
pp1=Product(rho2,rho3)
for obsj1 in range(5*d1*d2):
U=RandomUBS(obsj1%2,d1,d2)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
return(rho2a)
#3-partite entanglement
def Optimized3P(rho2,swaps,rho3,d1,i1):
if i1==0:
pp1=Product(rho2,rho3)
for j1 in range(5*d1**6):
U=RandomUBS(j1%2,d1,d1*d1)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==1:
pp1=Product(rho2,rho3)
for j1 in range(5*d1**6):
U=Rotate(RandomUBS(j1%2,d1,d1*d1),swaps[0])
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==2:
pp1=Product(rho2,rho3)
for j1 in range(5*d1**6):
U=RandomUBS(j1%2,d1*d1,d1)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
return(rho2a)
#four partite entanglement
#swap12,swap13,swap23,swap34
def Optimized4P(rho2, rho3,swaps, d1,i1):
if i1==0:
# aBCD
pp1=Product(rho2,rho3)
for j1 in range(5*d1**8):
U=RandomUBS(j1%2,d1,d1**3)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==1:
#AbCD
pp1=Product(rho2,rho3)
for j1 in range(5*d1**8):
U=Rotate(RandomUBS(j1%2,d1,d1*d1*d1),swaps[0])
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==2:
#ABcD
pp1=Product(rho2,rho3)
for j1 in range(5*d1**8):
U=Rotate(RandomUBS(j1%2,d1**3,d1),swaps[3])
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==3:
#ABCd
pp1=Product(rho2,rho3)
for j1 in range(5*d1**8):
U=RandomUBS(j1%2,d1**3,d1)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==4:
#abCD
pp1=Product(rho2,rho3)
for j1 in range(5*d1**8):
U=RandomUBS(j1%2,d1*d1,d1*d1)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==5:
#aBcD
pp1=Product(rho2,rho3)
for j1 in range(5*d1**8):
U=Rotate(RandomUBS(j1%2,d1*d1,d1*d1),swaps[2])
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
if i1==6:
#aBCd
pp1=Product(rho2,rho3)
for j1 in range(5*d1**8):
U=Rotate(RandomUBS(j1%2,d1*d1,d1*d1),swaps[1])
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
return(rho2a)
#n qubits
def Optimize2FS(rho2,rho3,n):
pp1=Product(rho2,rho3)
for j1 in range(100*n):
U=RandomU2FS(n,j1%n)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
return(rho2a)
#n quDits
def OptimizedFS(rho2,rho3,ddd1,n):
pp1=Product(rho2,rho3)
for j1 in range(20*ddd1*ddd1*n):
U=RandomUdFS(ddd1,n,j1%n)
rho2a=Rotate(rho2,U)
if pp1>Product(rho2a,rho3):
U=U.conj().T
rho2a=Rotate(rho2,U)
while(Product(rho2a, rho3)>pp1):
rho2b=rho2a
pp1=Product(rho2b,rho3)
rho2a=Rotate(rho2a,U)
return(rho2a)
#SWAP GATES at dimension d
def swap123(d):
temp=np.zeros((d**3,d**3),dtype=complex)
for i1 in range(d):
for i2 in range(d):
for i3 in range(d):
temp[i1*d**2+i2*d+i3][i2*d**2+i1*d+i3]=1
return(temp)
# def swap133(d):
# temp=np.zeros((d**3,d**3),dtype=complex)
# for i1 in range(d):
# for i2 in range(d):
# for i3 in range(d):
# temp[i1*d**2+i2*d+i3][i3*d**2+i2*d+i1]=1
# return(temp)
# def swap233(d):
# temp=np.zeros((d**3,d**3),dtype=complex)
# for i1 in range(d):
# for i2 in range(d):
# for i3 in range(d):
# temp[i1*d**2+i2*d+i3][i1*d**2+i3*d+i2]=1
# return(temp)
def swap124(d):
temp=np.zeros((d**4,d**4),dtype=complex)
for i1 in range(d):
for i2 in range(d):
for i3 in range(d):
for i4 in range(d):
temp[i1*d**3+i2*d**2+i3*d+i4][i2*d**3+i1*d**2+i3*d+i4]=1
return(temp)
def swap134(d):
temp=np.zeros((d**4,d**4),dtype=complex)
for i1 in range(d):
for i2 in range(d):
for i3 in range(d):
for i4 in range(d):
temp[i1*d**3+i2*d**2+i3*d+i4][i3*d**3+i2*d**2+i1*d+i4]=1
return(temp)
# def swap144(d):
# temp=np.zeros((d**4,d**4),dtype=complex)
# for i1 in range(d):
# for i2 in range(d):
# for i3 in range(d):
# for i4 in range(d):
# temp[i1*d**3+i2*d**2+i3*d+i4][i4*d**3+i2*d**2+i3*d+i1]=1
# return(temp)
def swap234(d):
temp=np.zeros((d**4,d**4),dtype=complex)
for i1 in range(d):
for i2 in range(d):
for i3 in range(d):
for i4 in range(d):
temp[i1*d**3+i2*d**2+i3*d+i4][i1*d**3+i3*d**2+i2*d+i4]=1
return(temp)
# def swap244(d):
# temp=np.zeros((d**4,d**4),dtype=complex)
# for i1 in range(d):
# for i2 in range(d):
# for i3 in range(d):
# for i4 in range(d):
# temp[i1*d**3+i2*d**2+i3*d+i4][i1*d**3+i4*d**2+i3*d+i4]=1
# return(temp)
def swap344(d):
temp=np.zeros((d**4,d**4),dtype=complex)
for i1 in range(d):
for i2 in range(d):
for i3 in range(d):
for i4 in range(d):
temp[i1*d**3+i2*d**2+i3*d+i4][i1*d**3+i2*d**2+i4*d+i3]=1
return(temp)
#Initialize files
#read rho
def Initrho0(prefix):
# return(scipy.io.mmread("_".join([prefix,"in.mtx"])))
return(readmtx("_".join([prefix,"in.mtx"])))
#read or generate rho1
def Initrho1(prefix,rho,mode,d1,vis):
if exists("".join([prefix,"_out_",str(vis),".mtx"])):
# return(scipy.io.mmread("".join([prefix,"_out_",str(vis),".mtx"])))
return(readmtx("".join([prefix,"_out_",str(vis),".mtx"])))
elif exists("".join([prefix,"_out_",str(mode),"_",str(d1),"_",str(vis),".mtx"])):
return(readmtx("".join([prefix,"_out_",str(mode),"_",str(d1),"_",str(vis),".mtx"])))
else:
rhoa=np.zeros((len(rho),len(rho)),dtype=complex)
for j1 in range(len(rho)):
rhoa[j1][j1]=rho[j1][j1]
return(rhoa)
#Too slow convergence error
def tooslow(counter,prefix,vis):
with open("".join([prefix,"_abort_",str(mode),"_",str(d1),"_",str(vis),".mtx"]),'w') as file:
file.write("The program has done 10% of planned trails, but it found only ")
file.write(str(counter))
file.write(" corrections and it was terminated.\n")
file.write("Increase the number of trails or decrease the visibility.\n")
file.close()
def showtooslow():
if True:
print(" ███▄ █ ▓█████ ██▒ █▓▓█████ ██▀███ ▄████ ██▓ ██▒ █▓▓█████ █ ██ ██▓███ ")
if True:
print(" ██ ▀█ █ ▓█ ▀▓██░ █▒▓█ ▀ ▓██ ▒ ██▒ ██▒ ▀█▒▓██▒▓██░ █▒▓█ ▀ ██ ▓██▒▓██░ ██▒")
print("▓██ ▀█ ██▒▒███ ▓██ █▒░▒███ ▓██ ░▄█ ▒ ▒██░▄▄▄░▒██▒ ▓██ █▒░▒███ ▓██ ▒██░▓██░ ██▓▒")
print("▓██▒ ▐▌██▒▒▓█ ▄ ▒██ █░░▒▓█ ▄ ▒██▀▀█▄ ░▓█ ██▓░██░ ▒██ █░░▒▓█ ▄ ▓▓█ ░██░▒██▄█▓▒ ▒")
print("▒██░ ▓██░░▒████▒ ▒▀█░ ░▒████▒░██▓ ▒██▒ ░▒▓███▀▒░██░ ▒▀█░ ░▒████▒ ▒▒█████▓ ▒██▒ ░ ░")
if True:
print("░ ▒░ ▒ ▒ ░░ ▒░ ░ ░ ▐░ ░░ ▒░ ░░ ▒▓ ░▒▓░ ░▒ ▒ ░▓ ░ ▐░ ░░ ▒░ ░ ░▒▓▒ ▒ ▒ ▒▓▒░ ░ ░")
print("░ ░░ ░ ▒░ ░ ░ ░ ░ ░░ ░ ░ ░ ░▒ ░ ▒░ ░ ░ ▒ ░ ░ ░░ ░ ░ ░ ░░▒░ ░ ░ ░▒ ░")
print(" ░ ░ ░ ░ ░░ ░ ░░ ░ ░ ░ ░ ▒ ░ ░░ ░ ░░░ ░ ░ ░░")
print(" ░ ░ ░ ░ ░ ░ ░ ░ ░ ░ ░ ░ ░")
print(" ░ ░")
#Wrong dimension
def wrongdim(prefix,mode):
with open("".join([prefix,"_wrong_dim_.txt"]),'w') as file:
file.write("Dimension of the imput state not compatible with the declared mode")
file.close()
#Read symmetry transformations
def DefineSym(prefix):
symlist1=[]
symlist2=[]
symj1=0
symj2=0
if exists("_".join([prefix,"sym_0_0.mtx"])):
symflag=True
while exists("_".join([prefix,"sym",str(symj1),"0.mtx"])):
while exists("".join([prefix,"_sym_",str(symj1),"_",str(symj2),".mtx"])):
# symlist2.append(scipy.io.mmread("".join([prefix,"_sym_",str(symj1),"_",str(symj2),".mtx"])))
symlist2.append(readmtx("".join([prefix,"_sym_",str(symj1),"_",str(symj2),".mtx"])))
symj2=symj2+1
symj2=0
symlist1.append(symlist2)
symj1=symj1+1
return(symlist1)
#Apply symmetries to a state
def ApplySym(rho,symlist1):
asrho0=rho
for asj1 in range(len(symlist1)):
for asj2 in range(len(symlist1[asj1])):
asrho0=asrho0+Rotate(asrho0,symlist1[asj1][asj2])
asrho0=asrho0/np.trace(asrho0)
return(asrho0)
#Define projection
def DefineProj(projflag,prefix):
if exists("_".join([prefix,"proj",".mtx"])):
projflag=True
# return(scipy.io.mmread("_".join([prefix,"proj.mtx"])))
return(readmtx("_".join([prefix,"proj.mtx"])))
else:
return([[]])
#Gilbert algorithm
def Gilbert(mode,prefix,vis,rho,steps,corrs,d1,d2,verboseflag):
rho1=Initrho1(prefix, rho,mode,d1,vis)
symflag=False
symlist=DefineSym(prefix)
if len(symlist)>0:
symflag=True
print(len(symlist))
projflag=False
proj1=DefineProj(projflag, prefix)
# if symflag==True:
# rho1=ApplySym(rho1, symlist)
if projflag==True:
rho1=Rotate(rho1, proj1)
lastcorr=0
currentcorr=0
ll=[]
counter=0
flag=0
trail=0
if exists("".join([prefix,"_list_",str(vis),".mtx"])) and exists("".join([prefix,"_out_",str(vis),".mtx"])):
# ll2=scipy.io.mmread("".join([prefix,"_list_",str(vis),".mtx"]))
ll2=readmtx("".join([prefix,"_list_",str(vis),".mtx"]))
trail=int(ll2[len(ll2)-1][0])
counter=int(ll2[len(ll2)-1][1])
for i3 in range(len(ll2)):
ll.append([int(ll2[i3][0]),int(ll2[i3][1]),ll2[i3][2]])
if len(ll)==1:
currentcorr=ll[0][0]
elif len(ll)>1:
currentcorr=ll[len(ll)-1][0]
lastcorr=ll[len(ll)-2][0]
if exists("".join([prefix,"_list_",str(mode),"_",str(d1),"_",str(vis),".mtx"])) and exists("".join([prefix,"_out_",str(mode),"_",str(d1),"_",str(vis),".mtx"])):
# ll2=scipy.io.mmread("".join([prefix,"_list_",str(vis),".mtx"]))
ll2=readmtx("".join([prefix,"_list_",str(mode),"_",str(d1),"_",str(vis),".mtx"]))
trail=int(ll2[len(ll2)-1][0])
counter=int(ll2[len(ll2)-1][1])
for i3 in range(len(ll2)):
ll.append([int(ll2[i3][0]),int(ll2[i3][1]),ll2[i3][2]])
if len(ll)==1:
currentcorr=ll[0][0]
elif len(ll)>1:
currentcorr=ll[len(ll)-1][0]
lastcorr=ll[len(ll)-2][0]
if steps<0:
steps=trail-steps
steps=steps-steps%10
if corrs<0:
corrs=counter-corrs
corrs=corrs-corrs%50
now=datetime.now()
if verboseflag==True:
print(now.strftime("%d/%m/%Y %H:%M:%S")," Report: proceeding with",abs(steps)-trail," iterations and ",abs(corrs)-counter," corrections.")
realflag=True
for realcheck1 in range(len(rho)):
for realcheck2 in range(len(rho)):
if np.imag(rho[realcheck1][realcheck2])!=0:
realflag=False
break
if realflag==True and verboseflag==True :
print("\n")
print("Input state strictly real. Imaginary parts of the output state will be discarded")
aa1=Product(rho,rho)
aa4=2*Product(rho,rho1)
aa6=Product(rho1,rho1)
rho3=rho-rho1
dd1=Product(rho1,rho3)
if mode==3:
swaps=[swap123(d1)]
elif mode==4:
swaps=[swap124(d1),swap134(d1),swap234(d1),swap344(d1)]
# else:
# swaps=[]
if len(ll)==0 or ll[len(ll)-1][2]>0.000001:
carryonflag=True;
else:
carryonflag=False
while trail<=abs(steps) and counter<=abs(corrs) and (len(ll)==0 or ll[len(ll)-1][2]>0.0000001):
trail=trail+1
if currentcorr-lastcorr>(steps-trail):
if verboseflag==True:
print("Too few steps left. Quitting")
break
if divmod(10*trail/abs(steps),1)[1]==0:
if counter<50:
tooslow(counter,prefix,vis)
if verboseflag==True:
showtooslow()
break
now=datetime.now()
if verboseflag==True:
print(now.strftime("%d/%m/%Y %H:%M:%S")," Report: done",trail,"/",abs(steps))
# if mode==0:
# rho2=Random2FS(d1)
if mode==2:
rho2=RandomBS(d1,d2)
if mode==1:
rho2=RandomdFS(d1,d2)
if mode==3:
rho2=Random3P(d1,swaps,trail%3)
if mode==4:
rho2=Random4P(d1,swaps,trail%7)
if not(mode in range(1,5)):
if verboseflag==True:
print("Mode ",mode, "does not exist!")
DisplayHelp()
break
if Product(rho2,rho3)>dd1:
# if mode==0:
# rho2=Optimize2FS(rho2, rho3, d1)
if mode==2:
rho2=OptimizeBS(rho2, rho3, d1,d2)
if mode==1:
rho2=OptimizedFS(rho2, rho3, d1,d2)
if mode==3:
rho2=Optimized3P(rho2, swaps, rho3, d1,trail%3)
if mode==4:
rho2=Optimized4P(rho2, rho3,swaps,d1,trail%7)
if realflag==True:
rho2=np.real(rho2)
if symflag==True:
rho1=ApplySym(rho1, symlist)
if projflag==True:
rho1=Rotate(rho1, proj1)
rho1=rho1/np.trace(rho1)
aa3=Product(rho2,rho2)
aa2=2*Product(rho,rho2)
aa5=2*Product(rho1,rho2)
# bb1=aa1-aa2+aa3
bb2=-aa4+aa2+aa5-2*aa3
bb3=aa6-aa5+aa3
cc1=-bb2/(2*bb3)
# cc2=-bb2*bb2/(4*bb3)+bb1
if 0<=cc1 and cc1<=1:
rho1=cc1*rho1+(1-cc1)*rho2
if symflag==True and counter%50==0:
rho1=ApplySym(rho1, symlist)
counter=counter+1
if counter%2==0 and verboseflag==True:
marker=counter%50
print(marker,end=" ")
if marker==0:
print("")
# if marker in [2,4,6,8]:
# # print("\b",end="")
# # print("\b",end="")
# # print("",end="")
# print(marker,end=" ")
# elif marker==0:
# print("")
# # print("\b",end="")
# # print("\b",end="")
# else:
# # print("\b",end="")
# # print("\b",end="")
# print(marker,end=" ")
rho3=rho-rho1
aa4=2*Product(rho,rho1)
aa6=Product(rho1,rho1)
dd1=aa4/2-aa6
flag=1
if 0>cc1 or cc1>1:
flag=0
if counter % 50==0 and flag==1:
if verboseflag==True:
now=datetime.now()
print(now.strftime("%H:%M:%S: "),"Trails:",trail," Corrections:",counter,"D^2:",Product(rho3,rho3))
ll.append([trail,counter,Product(rho3, rho3)])
# scipy.io.mmwrite("".join([prefix,"_out_",str(vis),".mtx"]),rho1)
writemtx("".join([prefix,"_out_",str(mode),"_",str(d1),"_",str(vis),".mtx"]),rho1,2)
# scipy.io.mmwrite("".join([prefix,"_list_",str(vis),".mtx"]),ll)
writemtx("".join([prefix,"_list_",str(mode),"_",str(d1),"_",str(vis),".mtx"]),ll,1)
lastcorr=currentcorr
currentcorr=trail
return(ll)
def invert(c,a):
return(1/(c-a))
def mean(l):
return(sum(l)/len(l))
def R(l,a):
ll1=list(map(lambda x1: invert(x1,a),l))
return(mean(list(map(lambda x1,x2:x1*x2, ll1,list(range(len(l))))))-mean(ll1)*mean(list(range(len(l)))))/math.sqrt((mean(list(map(lambda x : x**2,ll1)))-mean(ll1)**2)*(mean(list(map(lambda x:x**2,list(range(len(l))))))-mean(list(range(len(l))))**2))
def listshift(l1,a1):
return(list(map(lambda x:x-a1,l1)))
def cov(l1,l2):
return(mean(list(map(lambda x1,x2:x1*x2,listshift(l1,mean(l1)),listshift(l2,mean(l2))))))
def trend(l1,l2):
l1a=list(map(lambda x: math.log(x), l1))
l2a=list(map(lambda x: math.log(x), l2))
return(cov(l1a,l2a)/cov(l1a,l1a))
def offset(l1,l2):
l1a=list(map(lambda x: math.log(x), l1))
l2a=list(map(lambda x: math.log(x), l2))
return(mean(l2a)-mean(l1a)*trend(l1,l2))
def findmaximum(ll):
list1=list(map(lambda x: x[2],ll))
list2=[]
for j1 in range(int(len(list1)/2),len(list1)):
list2.append(list1[j1])
aaa1=list2[len(list2)-1]-.000001
step1=aaa1/10000
while R(list2,aaa1-step1)>R(list2,aaa1) and aaa1>0:
aaa1=aaa1-step1
return(aaa1)
def makeshortreport(prefix, ll,mode,d1,vis):
ll10=list(map(lambda x: x[0],ll))
ll11=list(map(lambda x: x[1],ll))
kk=findmaximum(ll)
ll12=[]
for j1 in range(int(2*len(ll)/3),len(ll)):
ll12.append(ll[j1][2])
with open("".join([prefix,"_report_",str(mode),"_",str(d1),"_",str(vis),".txt"]),'w') as file:
file.write("Basing on decay, the squared HS distance is estimsated to be ")
file.write(str(kk))
file.write(" (R=")
file.write(str(R(ll12,kk)))
file.write(")\n")
file.write("The dependence between corrs and trail is approximately:\n")
file.write("corr=trail^")
file.write(str(trend(ll10,ll11)))
file.write("*")
file.write(str(math.exp(offset(ll10,ll11))))
file.write("\n-----------------\n")
file.close()
def makelongreport(prefix,mode,vis,swaps,d1,d2,ll,verboseflag):
# optw=OptimizeW(prefix, mode, vis, swaps, d1, d2,verboseflag)
# wdist0=WitnessDist(prefix, vis, optw,verboseflag)
# with open("".join([prefix,"_report_",str(vis),".txt"]),'a') as file:
# if wdist0==-2:
# file.write("The algorithm did not yield a valid entanglement witness.")
# else:
# file.write("The squared distance based on entanglement witness is ")
# file.write(str(wdist0))
# file.close()
rhoa=readmtx("".join([prefix,"_in.mtx"]))
# rhob=scipy.io.mmread("".join([prefix,"_out_",str(vis),".mtx"]))
rhob=readmtx("".join([prefix,"_out_",str(mode),"_",str(d1),"_",str(vis),".mtx"]))
rhoa=vis*rhoa+(1-vis)*IdMatrix(len(rhoa))/len(rhoa)
witness=rhoa-rhob
writemtx("".join([prefix,"_witness_",str(mode),"_",str(d1),"_",str(vis),".mtx"]),witness,2)
def OptimizeW(prefix, mode,vis, swaps,d1,d2,verboseflag):
l=-1
# rhoa=scipy.io.mmread("_".join([prefix,"in.mtx"]))
rhoa=readmtx("_".join([prefix,"in.mtx"]))
rhob=Initrho1(prefix, rhoa, vis)
witness=rhoa-rhob
# zasieg=1000*d1
if mode==2:
zasieg=1500
if mode==1:
zasieg=1500
if mode==3:
zasieg=1500
if mode==4:
zasieg=1500
if verboseflag==True:
print("Optimizing the potential witness operator. Number of trails:",zasieg)
for owi1 in range(zasieg):
# if mode==0:
# w1=Random2FS(d1)
# l.append(Optimize2FS(w1,witness, d1))
if owi1%100==0 and verboseflag:
print("trail:",owi1)
if mode==2:
w1=RandomBS(d1,d2)
rho2a=OptimizeBS(w1,witness, d1,d2)
l1=Product(rho2a,witness)
if l1>l:
l=l1
if mode==1:
w1=RandomdFS(d1,d2)
rho2a=OptimizedFS(w1,witness, d1,d2)
l1=Product(rho2a,witness)
if l1>l :
l=l1
if mode==3:
for owi2 in range(3):
w1=Random3P(d1,swaps[0],owi2)
rho2a=Optimize2FS(w1,witness, d1)
l1=Product(rho2a,witness)
if l1>l:
l=l1
if mode==4:
for owi2 in range(7):
w1=Random4P(d1,swaps[0],swaps[1],swaps[2],swaps[3],owi2)
rho2a=Optimize2FS(w1,witness, d1)
l1=Product(rho2a,witness)
if l1>l:
l=l1
return(l)
def WitnessDist(prefix,vis,sepmax,verboseflag):
# rhoa=scipy.io.mmread("".join([prefix,"_in.mtx"]))
rhoa=readmtx("".join([prefix,"_in.mtx"]))
# rhob=scipy.io.mmread("".join([prefix,"_out_",str(vis),".mtx"]))
rhob=readmtx("".join([prefix,"_out_",str(mode),"_",str(d1),"_",str(vis),".mtx"]))
rhoa=vis*rhoa+(1-vis)*IdMatrix(len(rhoa))/len(rhoa)
witness=rhoa-rhob
wdist=(Product(witness,rhoa)-sepmax)/math.sqrt(Product(witness,witness))
if wdist<0:
if verboseflag==True:
print("No entanglement witness found.")
else:
if verboseflag==True:
print("Witness-based estimated squared distance:", wdist**2," (VERIFY!!!)")
# scipy.io.mmwrite("".join([prefix,"_witness_",str(vis),".mtx"]),witness,"".join(["Estimated sqared distance:",str(wdist**2)]))
writemtx("".join([prefix,"_witness_",str(mode),"_",str(d1),"_",str(vis),".mtx"]),witness,2)
return(wdist**2)
def DetectDim0(mode, totaldim, verboseflag):
primes=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999]
ddflag=False
if mode==1:
for pr in primes:
if math.log(totaldim,pr)==int(math.log(totaldim,pr)):
if verboseflag==True:
print("Determined size: ",pr," number of subsystems:", int(math.log(totaldim,pr)))
return([pr,int(math.log(totaldim,pr))])
ddflag=True
break
elif mode==2:
if math.sqrt(totaldim)==int(math.sqrt(totaldim)):
pr=int(math.sqrt(totaldim))
if verboseflag==True:
print("Determined sizes of subsytems: ",pr, int(totaldim/pr))
return([int(math.sqrt(totaldim)),int(math.sqrt(totaldim))])
ddflag=True
else:
for pr in primes:
if totaldim%pr==0:
if verboseflag==True:
print("Determined sizes of subsytems: ",pr, int(totaldim/pr))
return([pr,int(totaldim/pr)])
ddflag=True
break
elif mode==3:
if totaldim**(1./3)==int(totaldim**(1./3)):
if verboseflag==True:
print("Determined size: ",int(totaldim**(1./3))," number of subsystems:", 3)
return([int(totaldim**(1./3)),3])
ddflag=True
elif mode==4:
if totaldim**(1./4)==int(totaldim**(1./4)):
if verboseflag==True:
print("Determined size: ",int(totaldim**(1./4))," number of subsystems:", 4)
return([int(totaldim**(1./4)),4])
ddflag=True
if ddflag==False:
return([0,0])
def DetectDim1(mode,totdim,d1,verboseflag):
ddflag=False
if mode==1:
if math.log(totdim,d1)==int(math.log(totdim,d1)):
ddflag==True
if verboseflag==True:
print("Determined size: ",d1," number of subsystems:", int(math.log(totdim,d1)))
return(int(math.log(totdim,d1)))
elif mode==2:
if totdim/d1==int(totdim/d1):
ddflag==True
if verboseflag==True: