From 57666fe4aa417fceee5bd3278be99b17f3bceeef Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Thu, 19 Dec 2024 19:48:26 +0000 Subject: [PATCH] build based on be8cb24 --- dev/.documenter-siteinfo.json | 2 +- dev/API/index.html | 78 +++++++++++++++++------------------ dev/QHO/index.html | 2 +- dev/bibliography/index.html | 2 +- dev/express/index.html | 2 +- dev/index.html | 4 +- dev/introduction/index.html | 2 +- dev/qubit_basis/index.html | 2 +- 8 files changed, 47 insertions(+), 47 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 57906f6..e85f8ca 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-21T22:24:52","documenter_version":"1.8.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-19T19:48:21","documenter_version":"1.8.0"}} \ No newline at end of file diff --git a/dev/API/index.html b/dev/API/index.html index ea5efa3..e6a2e11 100644 --- a/dev/API/index.html +++ b/dev/API/index.html @@ -4,33 +4,33 @@ padding-top: 0 !important; padding-bottom: 0 !important; } -

Autogenerated API list

QuantumSymbolics.CNOT — Constant

CNOT gate

source
QuantumSymbolics.CPHASE — Constant

CPHASE gate

source
QuantumSymbolics.Create — Constant

Creation operator, also available as the constant âꜛ, in an infinite dimension Fock basis. There is no unicode dagger superscript, so we use the uparrow

source
QuantumSymbolics.Destroy — Constant

Annihilation operator, also available as the constant â, in an infinite dimension Fock basis.

source
QuantumSymbolics.F₁ — Constant

Single photon basis state of n

source
QuantumSymbolics.H — Constant

Hadamard gate

source
QuantumSymbolics.I — Constant

Identity operator in qubit basis

source
QuantumSymbolics.N — Constant

Number operator, also available as the constant n̂, in an infinite dimension Fock basis.

source
QuantumSymbolics.Pm — Constant

Pauli "minus" operator, also available as the constant σ₋

source
QuantumSymbolics.Pp — Constant

Pauli "plus" operator, also available as the constant σ₊

source
QuantumSymbolics.X — Constant

Pauli X operator, also available as the constant σˣ

source
QuantumSymbolics.X1 — Constant

Basis state of σˣ

source
QuantumSymbolics.X2 — Constant

Basis state of σˣ

source
QuantumSymbolics.Y — Constant

Pauli Y operator, also available as the constant σʸ

source
QuantumSymbolics.Y1 — Constant

Basis state of σʸ

source
QuantumSymbolics.Y2 — Constant

Basis state of σʸ

source
QuantumSymbolics.Z — Constant

Pauli Z operator, also available as the constant σᶻ

source
QuantumSymbolics.Z1 — Constant

Basis state of σᶻ

source
QuantumSymbolics.Z2 — Constant

Basis state of σᶻ

source
QuantumSymbolics.vac — Constant

Vacuum basis state of n

source
QuantumSymbolics.AbstractRepresentation — Type

An abstract type for the supported representation of quantum objects.

source
QuantumSymbolics.CliffordRepr — Type

Representation using tableaux governed by QuantumClifford.jl

source
QuantumSymbolics.CoherentState — Type

Coherent state in defined Fock basis.

source
QuantumSymbolics.CreateOp — Type

Creation (raising) operator.

julia> f = FockState(2)
+
Autogenerated API list
QuantumSymbolics.Create — Constant
Creation operator, also available as the constant âꜛ, in an infinite dimension Fock basis. There is no unicode dagger superscript, so we use the uparrow
source
QuantumSymbolics.N — Constant
Number operator, also available as the constant n̂, in an infinite dimension Fock basis.
source
QuantumSymbolics.CreateOp — Type
Creation (raising) operator.
julia> f = FockState(2)
 |2⟩
 
 julia> create = CreateOp()
 a†
 
 julia> qsimplify(create*f, rewriter=qsimplify_fock)
-(sqrt(3))|3⟩
source
QuantumSymbolics.DestroyOp — Type
Annihilation (lowering or destroy) operator in defined Fock basis.
julia> f = FockState(2)
 |2⟩
 
 julia> destroy = DestroyOp()
 a
 
 julia> qsimplify(destroy*f, rewriter=qsimplify_fock)
-(sqrt(2))|1⟩
source
QuantumSymbolics.DisplaceOp — Type
Displacement operator in defined Fock basis.
julia> f = FockState(0)
 |0⟩
 
 julia> displace = DisplaceOp(im)
 D(im)
 
 julia> qsimplify(displace*f, rewriter=qsimplify_fock)
-|im⟩
source
QuantumSymbolics.IdentityOp — Type
The identity operator for a given basis
julia> IdentityOp(X1⊗X2)
 𝕀
 
 julia> express(IdentityOp(Z2))
 Operator(dim=2x2)
-  basis: Spin(1/2)sparse([1, 2], [1, 2], ComplexF64[1.0 + 0.0im, 1.0 + 0.0im], 2, 2)
source
QuantumSymbolics.KrausRepr — Type
Kraus representation of a quantum channel
julia> @op A₁; @op A₂; @op A₃;
+  basis: Spin(1/2)sparse([1, 2], [1, 2], ComplexF64[1.0 + 0.0im, 1.0 + 0.0im], 2, 2)
source
QuantumSymbolics.KrausRepr — Type
Kraus representation of a quantum channel
julia> @op A₁; @op A₂; @op A₃;
 
 julia> K = kraus(A₁, A₂, A₃)
 𝒦(A₁,A₂,A₃)
@@ -38,7 +38,7 @@
 julia> @op ρ;
 
 julia> K*ρ
-(A₁ρA₁†+A₂ρA₂†+A₃ρA₃†)
source
QuantumSymbolics.MixedState — Type
Completely depolarized state
julia> MixedState(X1⊗X2)
 𝕄
 
 julia> express(MixedState(X1⊗X2))
@@ -55,52 +55,52 @@
 
 𝒵ₗ━━
 + Z_
-+ _Z
source
QuantumSymbolics.NumberOp — Type
Number operator.
julia> f = FockState(2)
 |2⟩
 
 julia> num = NumberOp()
 n
 
 julia> qsimplify(num*f, rewriter=qsimplify_fock)
-2|2⟩
source
QuantumSymbolics.PauliNoiseCPTP — Type
Single-qubit Pauli noise CPTP map
julia> apply!(express(Z1), [1], express(PauliNoiseCPTP(1/4,1/4,1/4)))
 Operator(dim=2x2)
   basis: Spin(1/2)
  0.5+0.0im  0.0+0.0im
- 0.0+0.0im  0.5+0.0im
source
QuantumSymbolics.PhaseShiftOp — Type
Phase-shift operator in defined Fock basis.
julia> c = CoherentState(im)
 |im⟩
 
 julia> phase = PhaseShiftOp(pi)
 U(π)
 
 julia> qsimplify(phase*c, rewriter=qsimplify_fock)
-|1.2246467991473532e-16 - 1.0im⟩
source
QuantumSymbolics.SAdd — Type
Addition of quantum objects (kets, operators, or bras).
julia> @ket k₁; @ket k₂;
+|1.2246467991473532e-16 - 1.0im⟩
source
QuantumSymbolics.SAdd — Type
Addition of quantum objects (kets, operators, or bras).
julia> @ket k₁; @ket k₂;
 
 julia> k₁ + k₂
-(|k₁⟩+|k₂⟩)
source
QuantumSymbolics.SConjugate — Type
Complex conjugate of quantum objects (kets, bras, operators).
julia> @op A; @ket k;
 
 julia> conj(A)
 Aˣ
 
 julia> conj(k)
-|k⟩ˣ
source
QuantumSymbolics.SDagger — Type
Dagger, i.e., adjoint of quantum objects (kets, bras, operators).
julia> @ket a; @op A;
 
 julia> dagger(2*im*A*a)
 (0 - 2im)|a⟩†A†
@@ -116,22 +116,22 @@
 ℋ
 
 julia> dagger(U)
-U⁻¹
source
QuantumSymbolics.SPartialTrace — Type
Partial trace over system i of a composite quantum system
julia> @op 𝒪 SpinBasis(1//2)⊗SpinBasis(1//2);
 
 julia> op = ptrace(𝒪, 1)
 tr1(𝒪)
@@ -162,14 +162,14 @@
 ((0 + ⟨b||k⟩)B+(tr(A))|k⟩⟨b|)
 
 julia> ptrace(mixed_state, 2)
-((0 + ⟨b||k⟩)A+(tr(B))|k⟩⟨b|)
source
QuantumSymbolics.SProjector — Type
Projector for a given ket.
julia> projector(X1⊗X2)
 𝐏[|X₁⟩|X₂⟩]
 
 julia> express(projector(X2))
 Operator(dim=2x2)
   basis: Spin(1/2)
   0.5+0.0im  -0.5-0.0im
- -0.5+0.0im   0.5+0.0im
source
QuantumSymbolics.SScaled — Type
Scaling of a quantum object (ket, operator, or bra) by a number.
julia> @ket k
 |k⟩
 
 julia> 2*k
@@ -179,10 +179,10 @@
 A
 
 julia> 2*A
-2A
source
QuantumSymbolics.STrace — Type
Trace of an operator
julia> @op A; @op B;
 
 julia> tr(A)
 tr(A)
@@ -193,7 +193,7 @@
 julia> @bra b; @ket k;
 
 julia> tr(k*b)
-⟨b||k⟩
source
QuantumSymbolics.STranspose — Type
Transpose of quantum objects (kets, bras, operators).
julia> @op A; @op B; @ket k;
 
 julia> transpose(A)
 Aᵀ
@@ -202,17 +202,17 @@
 (Aᵀ+Bᵀ)
 
 julia> transpose(k)
-|k⟩ᵀ
source
QuantumSymbolics.SVec — Type
Vectorization of a symbolic operator.
julia> @op A; @op B;
 
 julia> vec(A)
 |A⟩⟩
 
 julia> vec(A+B)
-(|A⟩⟩+|B⟩⟩)
source
QuantumSymbolics.SqueezeOp — Type
Squeezing operator in defined Fock basis.
julia> S = SqueezeOp(pi)
 S(π)
 
 julia> qsimplify(S*vac, rewriter=qsimplify_fock)
-|0,π⟩
source
QuantumSymbolics.StabilizerState — Type
State defined by a stabilizer tableau
For full functionality you also need to import the QuantumClifford library.
julia> using QuantumClifford, QuantumOptics # needed for the internal representation of the stabilizer tableaux and the conversion to a ket
+|0,π⟩
source
QuantumSymbolics.StabilizerState — Type
State defined by a stabilizer tableau
For full functionality you also need to import the QuantumClifford library.
julia> using QuantumClifford, QuantumOptics # needed for the internal representation of the stabilizer tableaux and the conversion to a ket
 
 julia> StabilizerState(S"XX ZZ")
 𝒮₂
@@ -221,12 +221,12 @@
 Ket(dim=2)
   basis: Spin(1/2)
   0.7071067811865475 + 0.0im
- -0.7071067811865475 + 0.0im
source
Base.conj — Method
conj(x::Symbolic{AbstractKet})
+ -0.7071067811865475 + 0.0im
source
Base.conj — Method
conj(x::Symbolic{AbstractKet})
 conj(x::Symbolic{AbstractBra})
 conj(x::Symbolic{AbstractOperator})
-conj(x::Symbolic{AbstractSuperOperator})
Symbolic transpose operation. See also SConjugate.
source
Base.transpose — Method
transpose(x::Symbolic{AbstractKet})
+conj(x::Symbolic{AbstractSuperOperator})
Symbolic transpose operation. See also SConjugate.
source
Base.transpose — Method
transpose(x::Symbolic{AbstractKet})
 transpose(x::Symbolic{AbstractBra})
-transpose(x::Symbolic{AbstractOperator})
Symbolic transpose operation. See also STranspose.
source
Base.vec — Method
vec(x::Symbolic{AbstractOperator})
Symbolic vector representation of an operator. See also SVec.
source
QuantumSymbolics.express — Function
express(s, repr::AbstractRepresentation=QuantumOpticsRepr()[, use::AbstractUse])
The main interface for expressing quantum objects in various representations.
julia> express(X1)
+transpose(x::Symbolic{AbstractOperator})
Symbolic transpose operation. See also STranspose.
source
Base.vec — Method
vec(x::Symbolic{AbstractOperator})
Symbolic vector representation of an operator. See also SVec.
source
QuantumSymbolics.express — Function
express(s, repr::AbstractRepresentation=QuantumOpticsRepr()[, use::AbstractUse])
The main interface for expressing quantum objects in various representations.
julia> express(X1)
 Ket(dim=2)
   basis: Spin(1/2)
  0.7071067811865475 + 0.0im
@@ -246,7 +246,7 @@
 sX
 
 julia> express(QuantumSymbolics.X, CliffordRepr(), UseAsObservable())
-+ X
source
QuantumSymbolics.qexpand — Method
qexpand(s)
Manually expand a symbolic expression of quantum objects. 
julia> @op A; @op B; @op C;
 
 julia> qexpand(commutator(A, B))
 (-1BA+AB)
@@ -257,20 +257,20 @@
 julia> @ket k₁; @ket k₂;
 
 julia> qexpand(A*(k₁+k₂))
-(A|k₁⟩+A|k₂⟩)
source
QuantumSymbolics.qsimplify — Method
qsimplify(s; rewriter=nothing)
Manually simplify a symbolic expression of quantum objects. 
If the keyword rewriter is not specified, then qsimplify will apply every defined rule to the expression.  For performance or single-purpose motivations, the user has the option to define a specific rewriter for qsimplify to apply to the expression. The defined rewriters for simplification are the following objects:     - qsimplify_pauli     - qsimplify_commutator     - qsimplify_anticommutator
julia> qsimplify(σʸ*commutator(σˣ*σᶻ, σᶻ))
+(A|k₁⟩+A|k₂⟩)
source
QuantumSymbolics.qsimplify — Method
qsimplify(s; rewriter=nothing)
Manually simplify a symbolic expression of quantum objects. 
If the keyword rewriter is not specified, then qsimplify will apply every defined rule to the expression.  For performance or single-purpose motivations, the user has the option to define a specific rewriter for qsimplify to apply to the expression. The defined rewriters for simplification are the following objects:     - qsimplify_pauli     - qsimplify_commutator     - qsimplify_anticommutator
julia> qsimplify(σʸ*commutator(σˣ*σᶻ, σᶻ))
 (0 - 2im)Z
 
 julia> qsimplify(anticommutator(σˣ, σˣ), rewriter=qsimplify_anticommutator)
-2𝕀
source
QuantumSymbolics.@bra — Macro
@bra(name, basis=SpinBasis(1//2))
Define a symbolic bra of type SBra. By default, the defined basis is the spin-1/2 basis.
julia> @bra b₁
+2𝕀
source
QuantumSymbolics.@bra — Macro
@bra(name, basis=SpinBasis(1//2))
Define a symbolic bra of type SBra. By default, the defined basis is the spin-1/2 basis.
julia> @bra b₁
 ⟨b₁|
 
 julia> @bra b₂ FockBasis(2)
-⟨b₂|
source
QuantumSymbolics.@ket — Macro
@ket(name, basis=SpinBasis(1//2))
Define a symbolic ket of type SKet. By default, the defined basis is the spin-1/2 basis.
julia> @ket k₁
+⟨b₂|
source
QuantumSymbolics.@ket — Macro
@ket(name, basis=SpinBasis(1//2))
Define a symbolic ket of type SKet. By default, the defined basis is the spin-1/2 basis.
julia> @ket k₁
 |k₁⟩
 
 julia> @ket k₂ FockBasis(2)
-|k₂⟩
source
QuantumSymbolics.@op — Macro
@op(name, basis=SpinBasis(1//2))
Define a symbolic ket of type SOperator. By default, the defined basis is the spin-1/2 basis.
julia> @op A
+|k₂⟩
source
QuantumSymbolics.@op — Macro
@op(name, basis=SpinBasis(1//2))
Define a symbolic ket of type SOperator. By default, the defined basis is the spin-1/2 basis.
julia> @op A
 A
 
 julia> @op B FockBasis(2)
-B
source
+Bsource diff --git a/dev/QHO/index.html b/dev/QHO/index.html index 22c28d4..608c4c2 100644 --- a/dev/QHO/index.html +++ b/dev/QHO/index.html @@ -75,4 +75,4 @@ 1.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 1.41421+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 1.73205+0.0im 0.0+0.0im 0.0+0.0im - 0.0+0.0im 0.0+0.0im 0.0+0.0im 2.0+0.0im 0.0+0.0im + 0.0+0.0im 0.0+0.0im 0.0+0.0im 2.0+0.0im 0.0+0.0im diff --git a/dev/bibliography/index.html b/dev/bibliography/index.html index 04b474e..9bb4ee4 100644 --- a/dev/bibliography/index.html +++ b/dev/bibliography/index.html @@ -1,2 +1,2 @@ -Bibliography · QuantumSymbolics.jl
GitHub
+Bibliography · QuantumSymbolics.jl
GitHub
diff --git a/dev/express/index.html b/dev/express/index.html index 5815235..53c2ead 100644 --- a/dev/express/index.html +++ b/dev/express/index.html @@ -36,4 +36,4 @@ 0.0+0.0im 1.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 2.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 3.0+0.0im 0.0+0.0im - 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 4.0+0.0im + 0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 4.0+0.0im diff --git a/dev/index.html b/dev/index.html index ee6a5ef..e69ce63 100644 --- a/dev/index.html +++ b/dev/index.html @@ -65,7 +65,7 @@

Impure states, represented as sum of density matrices

-
(MixedState(X1)+SProjector(Z1)) / 2

\[0.5 \mathrm{projector}\left( \left|Z_1\right\rangle \right) + \mathbb{M}\]

+
(MixedState(X1)+SProjector(Z1)) / 2

\[0.5 \mathbb{M} + \mathrm{projector}\left( \left|Z_1\right\rangle \right)\]

express((MixedState(X1)+SProjector(Z1)) / 2)
Operator(dim=2x2)
   basis: Spin(1/2)
  0.75+0.0im   0.0+0.0im
@@ -79,4 +79,4 @@
 + Z
-
Stabilizer state expressions

The state written as $\frac{|Z₁⟩⊗|Z₁⟩+|Z₂⟩⊗|Z₂⟩}{√2}$ is a well known stabilizer state, namely a Bell state. However, automatically expressing it as a stabilizer is a prohibitively expensive computational operation in general. We do not perform that computation automatically. If you want to ensure that states you define can be automatically converted to tableaux for Clifford simulations, avoid using summation of kets. On the other hand, in all of our Clifford Monte-Carlo simulations, ⊗ is fully supported, as well as projector, MixedState, StabilizerState, and summation of density matrices.

+
Stabilizer state expressions

The state written as $\frac{|Z₁⟩⊗|Z₁⟩+|Z₂⟩⊗|Z₂⟩}{√2}$ is a well known stabilizer state, namely a Bell state. However, automatically expressing it as a stabilizer is a prohibitively expensive computational operation in general. We do not perform that computation automatically. If you want to ensure that states you define can be automatically converted to tableaux for Clifford simulations, avoid using summation of kets. On the other hand, in all of our Clifford Monte-Carlo simulations, ⊗ is fully supported, as well as projector, MixedState, StabilizerState, and summation of density matrices.

diff --git a/dev/introduction/index.html b/dev/introduction/index.html index fc474af..12c7e7c 100644 --- a/dev/introduction/index.html +++ b/dev/introduction/index.html @@ -132,4 +132,4 @@ 𝒟ℯ𝓈𝓉𝒶𝒷 + Z 𝒮𝓉𝒶𝒷 -+ X

For more details on using express, refer to the express functionality page.

++ X

For more details on using express, refer to the express functionality page.

diff --git a/dev/qubit_basis/index.html b/dev/qubit_basis/index.html index d5f3fd0..7b956ee 100644 --- a/dev/qubit_basis/index.html +++ b/dev/qubit_basis/index.html @@ -102,4 +102,4 @@ Ket(dim=2) basis: Spin(1/2) 0.7071067811865475 + 0.0im - 0.0 - 0.7071067811865475im + 0.0 - 0.7071067811865475im