express, qsimplify, and latexify updates (#57)

* latexify additions

* updated express and new doc

* qsimplify updates

* doctest fix

* rearranging maketerm defs and doctest change

* clean docs

* update changelop and doc

* minor fix

* update project.toml

CHANGELOG.md

@@ -1,5 +1,12 @@
 # News
 
+## v0.3.2 - 2024-06-28
+
+- Added documentation for `express`.
+- `qsimplify` can now traverse through subexpressions using Prewalk from SymbolicUtils.jl.
+- Updated `latexify` capabilities.
+- **(fix)** There was a bug for latexifying dagger objects.
+
 ## v0.3.1 - 2024-06-21
 
 - Macros for defining symbolic quantum objects.

Project.toml

@@ -1,7 +1,7 @@
 name = "QuantumSymbolics"
 uuid = "efa7fd63-0460-4890-beb7-be1bbdfbaeae"
 authors = ["QuantumSymbolics.jl contributors"]
-version = "0.3.1"
+version = "0.3.2"
 
 [deps]
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"

docs/src/express.md

@@ -0,0 +1,59 @@
+# Express functionality
+
+```@meta
+DocTestSetup = quote
+    using QuantumSymbolics, QuantumOptics, QuantumClifford
+end
+```
+
+A principle feature of `QuantumSymbolics` is to numerically represent symbolic quantum expressions in various formalisms using [`express`](@ref). In particular, one can translate symbolic logic to back-end toolboxes such as `QuantumOptics.jl` or `QuantumClifford.jl` for simulating quantum systems with great flexibiity.
+
+As a straightforward example, consider the spin-up state $|\uparrow\rangle = |0\rangle$, the eigenstate of the Pauli operator $Z$, which can be expressed in `QuantumSymbolics` as follows:
+
+```@example 1
+using QuantumSymbolics, QuantumClifford, QuantumOptics # hide
+ψ = Z1
+```
+Using [`express`](@ref), we can translate this symbolic object into its numerical state vector form in `QuantumOptics.jl`.
+
+```@example 1
+express(ψ)
+```
+
+By default, [`express`](@ref) converts a quantum object with `QuantumOpticRepr`. It should be noted that [`express`](@ref) automatically caches this particular conversion of `ψ`. Thus, after running the above example, the numerical representation of the spin-up state is stored in the metadata of `ψ`.
+
+```@example 1
+ψ.metadata
+```
+
+The caching feature of [`express`](@ref) prevents a specific representation for a symbolic quantum object from being computed more than once. This becomes handy for translations of more complex operations, which can become computationally expensive. We also have the ability to express $|Z_1\rangle$ in the Clifford formalism with `QuantumClifford.jl`:
+
+```@example 1
+express(ψ, CliffordRepr())
+```
+
+Here, we specified an instance of `CliffordRepr` in the second argument to convert `ψ` into a tableau of Pauli operators containing its stabilizer and destabilizer states. Now, both the state vector and Clifford representation of `ψ` have been cached:
+
+```@example 1
+ψ.metadata
+```
+
+More involved examples can be explored. For instance, say we want to apply the tensor product $X\otimes Y$ of the Pauli operators $X$ and $Y$ to the Bell state $|\Phi^{+}\rangle = \dfrac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right)$, and numerically express the result in the quantum optics formalism. This would be done as follows:
+
+```@example 2
+using QuantumSymbolics, QuantumClifford, QuantumOptics # hide
+bellstate = (Z1⊗Z1+Z2⊗Z2)/√2
+tp = σˣ⊗σʸ
+express(tp*bellstate)
+```
+
+## Examples of Edge Cases
+For Pauli operators, additional flexibility is given for translations to the Clifford formalism. Users have the option to convert a multi-qubit Pauli operator to an observable or operation with instances of `UseAsObservable` and `UseAsOperation`, respectively. Take the Pauli operator $Y$, for example, which in `QuantumSymbolics` is the constants `Y` or `σʸ`:
+
+```jldoctest
+julia> express(σʸ, CliffordRepr(), UseAsObservable())
++ Y
+
+julia> express(σʸ, CliffordRepr(), UseAsOperation())
+sY
+```

ext/QuantumCliffordExt/QuantumCliffordExt.jl

@@ -47,14 +47,15 @@ end
 express_nolookup(::XGate,            ::CliffordRepr, ::UseAsOperation) = QuantumClifford.sX
 express_nolookup(::YGate,            ::CliffordRepr, ::UseAsOperation) = QuantumClifford.sY
 express_nolookup(::ZGate,            ::CliffordRepr, ::UseAsOperation) = QuantumClifford.sZ
-express_nolookup(x::STensorOperator,r::CliffordRepr,u::UseAsOperation) = QCGateSequence([express(t,r,u) for t in x.terms])
+express_nolookup(x::STensorOperator,  r::CliffordRepr, u::UseAsOperation) = QCGateSequence([express(t,r,u) for t in x.terms])
 
 express_nolookup(op::QuantumClifford.PauliOperator, ::CliffordRepr, ::UseAsObservable) = op
 express_nolookup(op::STensorOperator, r::CliffordRepr, u::UseAsObservable) = QuantumClifford.tensor(express.(arguments(op),(r,),(u,))...)
 express_nolookup(::XGate, ::CliffordRepr, ::UseAsObservable) = QuantumClifford.P"X"
 express_nolookup(::YGate, ::CliffordRepr, ::UseAsObservable) = QuantumClifford.P"Y"
 express_nolookup(::ZGate, ::CliffordRepr, ::UseAsObservable) = QuantumClifford.P"Z"
 express_nolookup(op::SScaledOperator, r::CliffordRepr, u::UseAsObservable) = arguments(op)[1] * express(arguments(op)[2],r,u)
+express_nolookup(x::SMulOperator,     r::CliffordRepr, u::UseAsObservable) = (*)((express(t,r,u) for t in arguments(x))...)
 express_nolookup(op, ::CliffordRepr, ::UseAsObservable) = error("Can not convert $(op) into a `PauliOperator`, which is the only observable that can be computed for QuantumClifford objects. Consider defining `express_nolookup(op, ::CliffordRepr, ::UseAsObservable)::PauliOperator` for this object.")
 
 struct QCRandomSampler # TODO specify types

src/QSymbolicsBase/QSymbolicsBase.jl

@@ -1,9 +1,9 @@
 using Symbolics
 import Symbolics: simplify
 using SymbolicUtils
-import SymbolicUtils: Symbolic, _isone, flatten_term, isnotflat, Chain, Fixpoint
+import SymbolicUtils: Symbolic, _isone, flatten_term, isnotflat, Chain, Fixpoint, Prewalk
 using TermInterface
-import TermInterface: isexpr, head, iscall, children, operation, arguments, metadata
+import TermInterface: isexpr, head, iscall, children, operation, arguments, metadata, maketerm
 
 using LinearAlgebra
 import LinearAlgebra: eigvecs, ishermitian, inv
@@ -141,6 +141,7 @@ Base.:(-)(x::SymQObj) = (-1)*x
 Base.:(-)(x::SymQObj,y::SymQObj) = x + (-y)
 Base.hash(x::SymQObj, h::UInt) = isexpr(x) ? hash((head(x), arguments(x)), h) : 
 hash((typeof(x),symbollabel(x),basis(x)), h)
+maketerm(::Type{<:SymQObj}, f, a, t, m) = f(a...)
 
 function Base.isequal(x::X,y::Y) where {X<:SymQObj, Y<:SymQObj}
     if X==Y

src/QSymbolicsBase/basic_ops_homogeneous.jl

@@ -30,30 +30,36 @@ arguments(x::SScaled) = [x.coeff,x.obj]
 operation(x::SScaled) = *
 head(x::SScaled) = :*
 children(x::SScaled) = [:*,x.coeff,x.obj]
-Base.:(*)(c, x::Symbolic{T}) where {T<:QObj} = iszero(c) || iszero(x) ? SZero{T}() : SScaled{T}(c, x)
+function Base.:(*)(c, x::Symbolic{T}) where {T<:QObj} 
+    if iszero(c) || iszero(x)
+        SZero{T}()
+    else 
+        x isa SScaled ? SScaled{T}(c*x.coeff, x.obj) : SScaled{T}(c, x) 
+    end
+end
 Base.:(*)(x::Symbolic{T}, c) where {T<:QObj} = c*x
 Base.:(/)(x::Symbolic{T}, c) where {T<:QObj} = iszero(c) ? throw(DomainError(c,"cannot divide QSymbolics expressions by zero")) : (1/c)*x
 basis(x::SScaled) = basis(x.obj)
 
 const SScaledKet = SScaled{AbstractKet}
 function Base.show(io::IO, x::SScaledKet)
-    if x.coeff isa Number
+    if x.coeff isa Real
         print(io, "$(x.coeff)$(x.obj)")
     else
         print(io, "($(x.coeff))$(x.obj)")
     end
 end
 const SScaledOperator = SScaled{AbstractOperator}
 function Base.show(io::IO, x::SScaledOperator)
-    if x.coeff isa Number
+    if x.coeff isa Real
         print(io, "$(x.coeff)$(x.obj)")
     else
         print(io, "($(x.coeff))$(x.obj)")
     end
 end
 const SScaledBra = SScaled{AbstractBra}
 function Base.show(io::IO, x::SScaledBra)
-    if x.coeff isa Number
+    if x.coeff isa Real
         print(io, "$(x.coeff)$(x.obj)")
     else
         print(io, "($(x.coeff))$(x.obj)")
@@ -171,14 +177,14 @@ function ⊗(xs::Symbolic{T}...) where {T<:QObj}
 end
 basis(x::STensor) = tensor(basis.(x.terms)...)
 
+const STensorBra = STensor{AbstractBra}
+Base.show(io::IO, x::STensorBra) = print(io, join(map(string, arguments(x)),""))
 const STensorKet = STensor{AbstractKet}
 Base.show(io::IO, x::STensorKet) = print(io, join(map(string, arguments(x)),""))
 const STensorOperator = STensor{AbstractOperator}
 Base.show(io::IO, x::STensorOperator) = print(io, join(map(string, arguments(x)),"⊗"))
 const STensorSuperOperator = STensor{AbstractSuperOperator}
 Base.show(io::IO, x::STensorSuperOperator) = print(io, join(map(string, arguments(x)),"⊗"))
-const STensorBra = STensor{AbstractBra}
-Base.show(io::IO, x::STensorBra) = print(io, join(map(string, arguments(x)),""))
 
 """Symbolic commutator of two operators
 

src/QSymbolicsBase/express.jl

@@ -24,8 +24,15 @@ julia> express(X1, CliffordRepr())
 𝒮𝓉𝒶𝒷
 + X
 
+julia> express(QuantumSymbolics.X)
+Operator(dim=2x2)
+  basis: Spin(1/2)sparse([2, 1], [1, 2], ComplexF64[1.0 + 0.0im, 1.0 + 0.0im], 2, 2)
+
 julia> express(QuantumSymbolics.X, CliffordRepr(), UseAsOperation())
 sX
+
+julia> express(QuantumSymbolics.X, CliffordRepr(), UseAsObservable())
++ X
 ```
 """
 function express end

src/QSymbolicsBase/latexify.jl

@@ -20,32 +20,48 @@ function num_to_sub(n::Int)
         "0"=>"₀",
     )
 end
-
+@latexrecipe function f(x::SBra)
+    return Expr(:latexifymerge, "\\left\\langle ", symbollabel(x), "\\right|")
+end
 @latexrecipe function f(x::Union{SpecialKet,SKet})
     return Expr(:latexifymerge, "\\left|", symbollabel(x), "\\right\\rangle")
 end
-@latexrecipe function f(x::Union{SOperator,AbstractSingleQubitOp,AbstractTwoQubitOp,AbstractSingleBosonGate})
+@latexrecipe function f(x::Union{SOperator,SHermitianOperator,SUnitaryOperator,SHermitianUnitaryOperator,AbstractSingleQubitOp,AbstractTwoQubitOp,AbstractSingleBosonGate})
     return LaTeXString("\\hat $(symbollabel(x))")
 end
+@latexrecipe function f(x::SZero)
+    return LaTeXString("\\bm{O}")
+end
 @latexrecipe function f(x::SDagger)
-    if isexpr(x.ket)
-        return Expr(:latexifymerge, "\\left( ", x.ket, "\\right)^\\dagger")
+    if isexpr(x.obj)
+        return Expr(:latexifymerge, "\\left( ", latexify(x.obj), "\\right)^\\dagger")
     else
-        return Expr(:latexifymerge, "\\left\\langle ", symbollabel(x), "\\right|")
+        return Expr(:latexifymerge, latexify(x.obj), "\\^\\dagger")
     end
 end
-@latexrecipe function f(x::SScaled)
+@latexrecipe function f(x::Union{SScaled,SMulOperator,SOuterKetBra,SApplyKet,SApplyBra})
     cdot --> false
     return _toexpr(x)
 end
-
+@latexrecipe function f(x::SCommutator)
+    return Expr(:latexifymerge, "\\left\\lbrack", latexify(x.op1), ",", latexify(x.op2), "\\right\\rbrack")
+end
+@latexrecipe function f(x::SAnticommutator)
+    return Expr(:latexifymerge, "\\left\\{", latexify(x.op1), ",", latexify(x.op2), "\\right\\}")
+end
+@latexrecipe function f(x::SBraKet)
+    return Expr(:latexifymerge, "\\left\\langle ", symbollabel(x.bra), "\\mid ", symbollabel(x.ket), "\\right\\rangle")
+end
 @latexrecipe function f(x::MixedState)
     return LaTeXString("\\mathbb{M}")
 end
 
 @latexrecipe function f(x::IdentityOp)
     return LaTeXString("\\mathbb{I}")
 end
+@latexrecipe function f(x::SInvOperator)
+    return Expr(:latexifymerge, latexify(x.op), "\\^{-1}")
+end
 
 function _toexpr(x)
     if isexpr(x)

src/QSymbolicsBase/predefined.jl

@@ -236,7 +236,7 @@ end
 julia> @ket a; @op A;
 
 julia> dagger(2*im*A*a)
-0 - 2im|a⟩†A†
+(0 - 2im)|a⟩†A†
 
 julia> @op B;
 

src/QSymbolicsBase/rules.jl

@@ -121,19 +121,21 @@ If the keyword `rewriter` is not specified, then `qsimplify` will apply every de
 For performance or single-purpose motivations, the user has the option to define a specific rewriter for `qsimplify` to apply to the expression.
 
 ```jldoctest
+julia> qsimplify(σʸ*commutator(σˣ*σᶻ, σᶻ))
+(0 - 2im)Z
+
 julia> qsimplify(anticommutator(σˣ, σˣ), rewriter=qsimplify_anticommutator)
 2𝕀
 ```
 """
 function qsimplify(s; rewriter=nothing)
     if QuantumSymbolics.isexpr(s)
         if isnothing(rewriter)
-            Fixpoint(Chain(RULES_ALL))(s)
+            Fixpoint(Prewalk(Chain(RULES_ALL)))(s)
         else
-            Fixpoint(rewriter)(s)
+            Fixpoint(Prewalk(rewriter))(s)
         end
     else
         error("Object $(s) of type $(typeof(s)) is not an expression.")
     end
-end
-
+end

test/test_express_cliff.jl

@@ -15,3 +15,31 @@ withcache = @timed express(state2, CliffordRepr())
 @test withcache.bytes <= 200
 results = Set([express(state2, CliffordRepr()) for i in 1:20])
 @test length(results)==2
+
+CR = CliffordRepr()
+UseOp = UseAsOperation()
+UseObs = UseAsObservable()
+
+@testset "Clifford representations for basis states" begin
+    isequal(express(X1, CR), MixedDestabilizer(S"X"))
+    isequal(express(X2, CR), MixedDestabilizer(S"-X"))
+    isequal(express(Y1, CR), MixedDestabilizer(S"Y"))
+    isequal(express(Y2, CR), MixedDestabilizer(S"-Y"))
+    isequal(express(Z1, CR), MixedDestabilizer(S"Z"))
+    isequal(express(Z2, CR), MixedDestabilizer(S"-Z"))
+end
+
+@testset "Clifford representations as observables" begin
+    isequal(express(σˣ, CR, UseObs), P"X")
+    isequal(express(σʸ, CR, UseObs), P"Y")
+    isequal(express(σᶻ, CR, UseObs), P"Z")
+    isequal(express(im*σˣ, CR, UseObs), im*P"X")
+    isequal(express(σˣ⊗σʸ⊗σᶻ), P"X"⊗P"Y"⊗P"Z")
+    isequal(express(σˣ*σʸ*σᶻ), P"X"*P"Y"*P"Z")
+end
+
+@testset "Clifford representations as operations" begin
+    isequal(express(σˣ, CR, UseOp), sX)
+    isequal(express(σʸ, CR, UseOp), sY)
+    isequal(express(σᶻ, CR, UseOp), sZ)
+end