implement squeezing (#83)

* implement squeezing * change `SqueezedCoherentState` to `SqueezedState` * update changelog and project.toml
QuantumSavory · Sep 17, 2024 · c41ff6b · c41ff6b · apkille · Sep 17, 2024
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diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # News
 
+## v0.4.4 - 2024-09-16
+
+- Implement squeezing with `SqueezeOp` and `SqueezedState`.
+
 ## v0.4.3 - 2024-08-13
 
 - **(fix)** Fix for incorrect basis for `express(_,::QuantumOpticsRepr)` for certain operators.

diff --git a/Project.toml b/Project.toml
@@ -1,7 +1,7 @@
 name = "QuantumSymbolics"
 uuid = "efa7fd63-0460-4890-beb7-be1bbdfbaeae"
 authors = ["QuantumSymbolics.jl contributors"]
-version = "0.4.3"
+version = "0.4.4"
 
 [deps]
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"

diff --git a/docs/src/QHO.md b/docs/src/QHO.md
@@ -10,7 +10,7 @@ In this section, we describe symbolic representations of bosonic systems in Quan
 
 ## States
 
-A Fock state is a state with well defined number of excitation quanta of a single quantum harmonic oscillator (an eigenstate of the number operator). In the following example, we create a `FockState` with 3 quanta in an infinite-dimension Fock space:
+A Fock state is a state with well defined number of excitation quanta of a single quantum harmonic oscillator (an eigenstate of the number operator). In the following example, we create a [`FockState`](@ref) with 3 quanta in an infinite-dimension Fock space:
 
 ```jldoctest
 julia> f = FockState(3)
@@ -22,7 +22,7 @@ Both vacuum (ground) and single-photon states are defined as constants in both u
 - `vac = F₀ = F0` $=|0\rangle$ in the number state representation,
 - `F₁ = F1` $=|1\rangle$ in the number state representation.
 
-To create quantum analogues of a classical harmonic oscillator, or monochromatic electromagnetic waves, we can define a coherent (a.k.a. semi-classical) state $|\alpha\rangle$, where $\alpha$ is a complex amplitude, with `CoherentState(α::Number)`:
+To create quantum analogues of a classical harmonic oscillator, or monochromatic electromagnetic waves, we can define a coherent (a.k.a. semi-classical) state $|\alpha\rangle$, where $\alpha$ is a complex amplitude, with [`CoherentState`](@ref):
 
 ```jldoctest
 julia> c = CoherentState(im)
@@ -31,9 +31,15 @@ julia> c = CoherentState(im)
 !!! note "Naming convention for quantum harmonic oscillator bases"
     The defined basis for arbitrary symbolic bosonic states is a `FockBasis` object, due to a shared naming interface for Quantum physics packages. For instance, the command `basis(CoherentState(im))` will output `Fock(cutoff=Inf)`. This may lead to confusion, as not all bosonic states are Fock states. However, this is simply a naming convention for the basis, and symbolic and numerical results are not affected by it.
 
+Summarized below are supported bosonic states.
+
+- Fock state: `FockState(idx::Int)`,
+- Coherent state: `CoherentState(alpha::Number)`,
+- Squeezed vacuum state: `SqueezedState(z::Number)`.
+
 ## Operators
 
-Operations on bosonic states are supported, and can be simplified with `qsimplify` and its rewriter `qsimplify_fock`. For instance, we can apply the raising (creation) $\hat{a}^{\dagger}$ and lowering (annihilation or destroy) $\hat{a}$ operators on a Fock state as follows:
+Operations on bosonic states are supported, and can be simplified with [`qsimplify`](@ref) and its rewriter `qsimplify_fock`. For instance, we can apply the raising (creation) $\hat{a}^{\dagger}$ and lowering (annihilation or destroy) $\hat{a}$ operators on a Fock state as follows:
 
 ```jldoctest
 julia> f = FockState(3);
@@ -68,8 +74,10 @@ Constants are defined for number and ladder operators in unicode and ASCII:
 - `Create = âꜛ` $=\hat{a}^{\dagger}$,
 - `Destroy = â` $=\hat{a}$.
 
-Phase-shift $U(\theta)$ and displacement $D(\alpha)$ operators, defined respectively as 
+Phase-shift $U(\theta)$ and displacement $D(\alpha)$ operators, defined respectively as
+
 $$U(\theta) = \exp\left(-i\theta\hat{n}\right) \quad \text{and} \quad D(\alpha) = \exp\left(\alpha\hat{a}^{\dagger} - \alpha\hat{a}\right),$$ 
+
 can be defined with usual simplification rules. Consider the following example:
 
 ```jldoctest
@@ -85,19 +93,20 @@ U(π)
 julia> qsimplify(phase*c, rewriter=qsimplify_fock)
 |1.2246467991473532e-16 - 1.0im⟩
 ```
-Here, we generated a coherent state $|i\rangle$ from the vacuum state $|0\rangle$ by applying the displacement operator defined by `DisplaceOp`. Then, we shifted its phase by $\pi$ with the phase shift operator (which is called with `PhaseShiftOp`) to get the result $|-i\rangle$.
+Here, we generated a coherent state $|i\rangle$ from the vacuum state $|0\rangle$ by applying the displacement operator defined by [`DisplaceOp`](@ref). Then, we shifted its phase by $\pi$ with the phase shift operator (which is called with [`PhaseShiftOp`](@ref)) to get the result $|-i\rangle$.
 
 Summarized below are supported bosonic operators.
 
 - Number operator: `NumberOp()`,
 - Creation operator: `CreateOp()`,
 - Annihilation operator: `DestroyOp()`,
 - Phase-shift operator: `PhaseShiftOp(phase::Number)`,
-- Displacement operator: `DisplaceOp(alpha::Number)`.
+- Displacement operator: `DisplaceOp(alpha::Number)`,
+- Squeezing operator: `SqueezeOp(z::Number)`.
 
 ## Numerical Conversions to QuantumOptics.jl
 
-Bosonic systems can be translated to the ket representation with `express`. For instance:
+Bosonic systems can be translated to the ket representation with [`express`](@ref). For instance:
 
 ```jldoctest
 julia> f = FockState(1);
@@ -132,7 +141,7 @@ Ket(dim=3)
 ```
 
 !!! warning "Cutoff specifications for numerical representations of quantum harmonic oscillators"
-    Symbolic bosonic states and operators are naturally represented in an infinite dimension basis. For numerical conversions of such quantum objects, a finite cutoff of the highest allowed state must be defined. By default, the basis dimension of numerical conversions is set to 3 (so the number representation cutoff is 2), as demonstrated above. To define a different cutoff, one must customize the `QuantumOpticsRepr` instance, e.g. provide `QuantumOpticsRepr(cutoff=n::Int)` to `express`.
+    Symbolic bosonic states and operators are naturally represented in an infinite dimension basis. For numerical conversions of such quantum objects, a finite cutoff of the highest allowed state must be defined. By default, the basis dimension of numerical conversions is set to 3 (so the number representation cutoff is 2), as demonstrated above. To define a different cutoff, one must customize the `QuantumOpticsRepr` instance, e.g. provide `QuantumOpticsRepr(cutoff=n::Int)` to [`express`](@ref).
 
 If we wish to specify a different numerical cutoff, say 4, to the previous examples, then we rewrite them as follows:
 

diff --git a/ext/QuantumOpticsExt/QuantumOpticsExt.jl b/ext/QuantumOpticsExt/QuantumOpticsExt.jl
@@ -84,10 +84,12 @@ function finite_basis(s,r)
 end
 express_nolookup(s::FockState, r::QuantumOpticsRepr) = fockstate(finite_basis(s,r),s.idx)
 express_nolookup(s::CoherentState, r::QuantumOpticsRepr) = coherentstate(finite_basis(s,r),s.alpha)
+express_nolookup(s::SqueezedState, r::QuantumOpticsRepr) = (b = finite_basis(s,r); squeeze(b, s.z)*fockstate(b, 0))
 express_nolookup(o::NumberOp, r::QuantumOpticsRepr) = number(finite_basis(o,r))
 express_nolookup(o::CreateOp, r::QuantumOpticsRepr) = create(finite_basis(o,r))
 express_nolookup(o::DestroyOp, r::QuantumOpticsRepr) = destroy(finite_basis(o,r))
 express_nolookup(o::DisplaceOp, r::QuantumOpticsRepr) = displace(finite_basis(o,r), o.alpha)
+express_nolookup(o::SqueezeOp, r::QuantumOpticsRepr) = squeeze(finite_basis(o,r), o.z)
 express_nolookup(x::MixedState, r::QuantumOpticsRepr) = identityoperator(finite_basis(x,r))/length(finite_basis(x,r)) # TODO there is probably a more efficient way to represent it
 express_nolookup(x::IdentityOp, r::QuantumOpticsRepr) = identityoperator(finite_basis(x,r))
 

diff --git a/src/QSymbolicsBase/QSymbolicsBase.jl b/src/QSymbolicsBase/QSymbolicsBase.jl
@@ -41,8 +41,8 @@ export SymQObj,QObj,
        MixedState,IdentityOp,
        SApplyKet,SApplyBra,SMulOperator,SSuperOpApply,SCommutator,SAnticommutator,SBraKet,SOuterKetBra,
        HGate,XGate,YGate,ZGate,CPHASEGate,CNOTGate,
-       XBasisState,YBasisState,ZBasisState,FockState,CoherentState,
-       NumberOp,CreateOp,DestroyOp,PhaseShiftOp,DisplaceOp,
+       XBasisState,YBasisState,ZBasisState,FockState,CoherentState,SqueezedState,
+       NumberOp,CreateOp,DestroyOp,PhaseShiftOp,DisplaceOp,SqueezeOp,
        XCXGate,XCYGate,XCZGate,YCXGate,YCYGate,YCZGate,ZCXGate,ZCYGate,ZCZGate,
        qsimplify,qsimplify_pauli,qsimplify_commutator,qsimplify_anticommutator,qsimplify_fock,
        qexpand,

diff --git a/src/QSymbolicsBase/predefined_fock.jl b/src/QSymbolicsBase/predefined_fock.jl
@@ -18,6 +18,14 @@ end
 CoherentState(alpha::Number) = CoherentState(alpha, inf_fock_basis)
 symbollabel(x::CoherentState) = "$(x.alpha)"
 
+"""Squeezed vacuum state in defined Fock basis."""
+@withmetadata struct SqueezedState <: SpecialKet
+    z::Number
+    basis::FockBasis
+end
+SqueezedState(z::Number) = SqueezedState(z, inf_fock_basis)
+symbollabel(x::SqueezedState) = "0,$(x.z)"
+
 const inf_fock_basis = FockBasis(Inf,0.)
 """Vacuum basis state of n"""
 const vac = const F₀ = const F0 = FockState(0)
@@ -136,4 +144,21 @@ const N = const n̂ = NumberOp()
 There is no unicode dagger superscript, so we use the uparrow"""
 const Create = const âꜛ = CreateOp()
 """Annihilation operator, also available as the constant `â`, in an infinite dimension Fock basis."""
-const Destroy = const â = DestroyOp()
+const Destroy = const â = DestroyOp()
+
+"""Squeezing operator in defined Fock basis.
+
+```jldoctest
+julia> S = SqueezeOp(pi)
+S(π)
+
+julia> qsimplify(S*vac, rewriter=qsimplify_fock)
+|0,π⟩
+```
+"""
+@withmetadata struct SqueezeOp <: AbstractSingleBosonOp
+    z::Number
+    basis::FockBasis
+end
+SqueezeOp(z::Number) = SqueezeOp(z, inf_fock_basis)
+symbollabel(x::SqueezeOp) = "S($(x.z))"
diff --git a/src/QSymbolicsBase/rules.jl b/src/QSymbolicsBase/rules.jl
@@ -105,7 +105,8 @@ RULES_FOCK = [
     @rule(~o1::_isa(PhaseShiftOp) * ~o2::_isa(DestroyOp) * dagger(~o1) => ~o2*exp(im*((~o1).phase))),
     @rule(dagger(~o1::_isa(DisplaceOp)) * ~o2::_isa(DestroyOp) * ~o1 => (~o2) + (~o1).alpha*IdentityOp((~o2).basis)),
     @rule(dagger(~o1::_isa(DisplaceOp)) * ~o2::_isa(CreateOp) * ~o1 => (~o2) + conj((~o1).alpha)*IdentityOp((~o2).basis)),
-    @rule(~o::_isa(DisplaceOp) * ~k::((x->(isa(x,FockState) && x.idx == 0))) => CoherentState((~o).alpha))
+    @rule(~o::_isa(DisplaceOp) * ~k::((x->(isa(x,FockState) && x.idx == 0))) => CoherentState((~o).alpha)),
+    @rule(~o::_isa(SqueezeOp) * ~k::_isequal(vac) => SqueezedState((~o).z, (~o).basis))
 ]
 
 RULES_SIMPLIFY = [RULES_PAULI; RULES_COMMUTATOR; RULES_ANTICOMMUTATOR; RULES_FOCK]

diff --git a/test/test_express_opt.jl b/test/test_express_opt.jl
@@ -43,4 +43,8 @@
     @test express(Create*F1) ≈ express(Create)*express(F1)
     @test express(Destroy*F1) ≈ express(Destroy)*express(F1)
     @test express(displace*cstate) ≈ express(displace)*express(cstate)
+
+    squeezed = SqueezedState(pi/4)
+    squeezeop = SqueezeOp(pi/4)
+    @test express(squeezed) ≈ express(squeezeop)*express(vac)
 end
diff --git a/test/test_fock.jl b/test/test_fock.jl
@@ -6,6 +6,8 @@
     phase1 = PhaseShiftOp(0)
     phase2 = PhaseShiftOp(pi)
     displace = DisplaceOp(im)
+    squeezeop = SqueezeOp(pi)
+    sstate = SqueezedState(pi)
 
     @testset "ladder and number operators" begin
         @test isequal(qsimplify(Destroy*vac, rewriter=qsimplify_fock), SZeroKet())
@@ -23,4 +25,8 @@
         @test isequal(qsimplify(dagger(displace)*Create*displace, rewriter=qsimplify_fock), Create - im*IdentityOp(inf_fock_basis))
         @test isequal(qsimplify(displace*vac, rewriter=qsimplify_fock), cstate)
     end
+
+    @testset "Squeeze operators" begin
+        @test isequal(qsimplify(squeezeop*vac, rewriter=qsimplify_fock), sstate)
+    end
 end