Address #22

CHANGELOG.md

@@ -1,5 +1,9 @@
 # News
 
+## v0.3.3 - dev
+
+- Add single qubit simplification rules.
+
 ## v0.3.2 - 2024-07-02
 
 - Added documentation for `express`.

Project.toml

@@ -1,7 +1,7 @@
 name = "QuantumSymbolics"
 uuid = "efa7fd63-0460-4890-beb7-be1bbdfbaeae"
 authors = ["QuantumSymbolics.jl contributors"]
-version = "0.3.2"
+version = "0.3.3-dev"
 
 [deps]
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"

docs/src/index.md

@@ -202,4 +202,4 @@ express(MixedState(X1)/2+SProjector(Z1)/2, CliffordRepr())
 
 !!! warning "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 sumation of kets. On the other hand, in all of our Clifford Monte-Carlo simulations, `⊗` is fully supported, as well as [`SProjector`](@ref), [`MixedState`](@ref), [`StabilizerState`](@ref), and sumation of density matrices.
+    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 [`SProjector`](@ref), [`MixedState`](@ref), [`StabilizerState`](@ref), and summation of density matrices.

src/QSymbolicsBase/rules.jl

@@ -11,6 +11,7 @@ function hasscalings(xs)
     end
 end
 _isa(T) = x->isa(x,T)
+_isequal(obj) = x->(x==obj)
 _vecisa(T) = x->all(_isa(T), x)
 
 ##
@@ -30,7 +31,38 @@ RULES_PAULI = [
     @rule(~o1::_isa(XGate)*~o2::_isa(ZGate) => -im*Y),
     @rule(~o1::_isa(HGate)*~o2::_isa(XGate)*~o3::_isa(HGate) => Z),
     @rule(~o1::_isa(HGate)*~o2::_isa(YGate)*~o3::_isa(HGate) => -Y),
-    @rule(~o1::_isa(HGate)*~o2::_isa(ZGate)*~o3::_isa(HGate) => X)
+    @rule(~o1::_isa(HGate)*~o2::_isa(ZGate)*~o3::_isa(HGate) => X),
+
+    @rule(~o::_isa(XGate)*~k::_isequal(X1) => X1),
+    @rule(~o::_isa(YGate)*~k::_isequal(X1) => -im*X2),
+    @rule(~o::_isa(ZGate)*~k::_isequal(X1) => X2),
+
+    @rule(~o::_isa(XGate)*~k::_isequal(X2) => -X2),
+    @rule(~o::_isa(YGate)*~k::_isequal(X2) => im*X1),
+    @rule(~o::_isa(ZGate)*~k::_isequal(X2) => X1),
+
+    @rule(~o::_isa(XGate)*~k::_isequal(Y1) => im*Y2),
+    @rule(~o::_isa(YGate)*~k::_isequal(Y1) => Y1),
+    @rule(~o::_isa(ZGate)*~k::_isequal(Y1) => Y2),
+
+    @rule(~o::_isa(XGate)*~k::_isequal(Y2) => -im*Y1),
+    @rule(~o::_isa(YGate)*~k::_isequal(Y2) => -Y2),
+    @rule(~o::_isa(ZGate)*~k::_isequal(Y2) => Y1),
+
+    @rule(~o::_isa(XGate)*~k::_isequal(Z1) => Z2),
+    @rule(~o::_isa(YGate)*~k::_isequal(Z1) => im*Z2),
+    @rule(~o::_isa(ZGate)*~k::_isequal(Z1) => Z1),
+
+    @rule(~o::_isa(XGate)*~k::_isequal(Z2) => Z1),
+    @rule(~o::_isa(YGate)*~k::_isequal(Z2) => -im*Z1),
+    @rule(~o::_isa(ZGate)*~k::_isequal(Z2) => -Z2),
+
+    @rule(~o::_isa(HGate)*~k::_isequal(X1) => Z1),
+    @rule(~o::_isa(HGate)*~k::_isequal(X2) => Z2),
+    @rule(~o::_isa(HGate)*~k::_isequal(Y1) => (X1+im*X2)/sqrt(2)),
+    @rule(~o::_isa(HGate)*~k::_isequal(Y2) => (X1-im*X2)/sqrt(2)),
+    @rule(~o::_isa(HGate)*~k::_isequal(Z1) => X1),
+    @rule(~o::_isa(HGate)*~k::_isequal(Z2) => X2)
 ]
 
 # Commutator identities

test/runtests.jl

@@ -36,6 +36,7 @@ println("Starting tests with $(Threads.nthreads()) threads out of `Sys.CPU_THREA
 @doset "dagger"
 @doset "zero_obj"
 @doset "expand"
+@doset "pauli"
 
 VERSION >= v"1.9" && @doset "doctests"
 get(ENV,"JET_TEST","")=="true" && @doset "jet"

test/test_expand.jl

@@ -6,6 +6,10 @@ using Test
 
 @op A; @op B; @op C; @op D;
 
+@testset "expand errors" begin
+    @test_throws ErrorException qexpand(X)
+end
+
 @testset "expand rules" begin
     @test isequal(qexpand(commutator(A, B)), A*B - B*A)
     @test isequal(qexpand(anticommutator(A, B)), A*B + B*A)

test/test_pauli.jl

@@ -0,0 +1,50 @@
+using QuantumSymbolics
+using Test
+
+@testset "simplify errors" begin
+    @test_throws ErrorException qsimplify(X)
+end
+
+@testset "MulOperator tests" begin
+    @test isequal(qsimplify(X*X,rewriter=qsimplify_pauli), I)
+    @test isequal(qsimplify(Y*Y,rewriter=qsimplify_pauli), I)
+    @test isequal(qsimplify(Z*Z,rewriter=qsimplify_pauli), I)
+    @test isequal(qsimplify(X*Y,rewriter=qsimplify_pauli), im*Z)
+    @test isequal(qsimplify(Y*Z,rewriter=qsimplify_pauli), im*X)
+    @test isequal(qsimplify(Z*X,rewriter=qsimplify_pauli), im*Y)
+    @test isequal(qsimplify(Y*X,rewriter=qsimplify_pauli), -im*Z)
+    @test isequal(qsimplify(Z*Y,rewriter=qsimplify_pauli), -im*X)
+    @test isequal(qsimplify(X*Z,rewriter=qsimplify_pauli), -im*Y)
+    @test isequal(qsimplify(H*X*H,rewriter=qsimplify_pauli), Z)
+    @test isequal(qsimplify(H*Y*H,rewriter=qsimplify_pauli), -Y)
+    @test isequal(qsimplify(H*Z*H,rewriter=qsimplify_pauli), X)
+end
+
+@testset "ApplyKet tests" begin
+   @test isequal(qsimplify(X*X1,rewriter=qsimplify_pauli), X1)
+   @test isequal(qsimplify(Y*X1,rewriter=qsimplify_pauli), -im*X2)
+   @test isequal(qsimplify(Z*X1,rewriter=qsimplify_pauli), X2)
+
+   @test isequal(qsimplify(X*X2,rewriter=qsimplify_pauli), -X2)
+   @test isequal(qsimplify(Y*X2,rewriter=qsimplify_pauli), im*X1)
+   @test isequal(qsimplify(Z*X2,rewriter=qsimplify_pauli), X1)
+
+   @test isequal(qsimplify(X*Y1,rewriter=qsimplify_pauli), im*Y2)
+   @test isequal(qsimplify(Y*Y1,rewriter=qsimplify_pauli), Y1)
+   @test isequal(qsimplify(Z*Y1,rewriter=qsimplify_pauli), Y2)
+
+   @test isequal(qsimplify(X*Z1,rewriter=qsimplify_pauli), Z2)
+   @test isequal(qsimplify(Y*Z1,rewriter=qsimplify_pauli), im*Z2)
+   @test isequal(qsimplify(Z*Z1,rewriter=qsimplify_pauli), Z1)
+
+   @test isequal(qsimplify(X*Z2,rewriter=qsimplify_pauli), Z1)
+   @test isequal(qsimplify(Y*Z2,rewriter=qsimplify_pauli), -im*Z1)
+   @test isequal(qsimplify(Z*Z2,rewriter=qsimplify_pauli), -Z2)
+
+   @test isequal(qsimplify(H*X1,rewriter=qsimplify_pauli), Z1)
+   @test isequal(qsimplify(H*X2,rewriter=qsimplify_pauli), Z2)
+   @test isequal(qsimplify(H*Y1,rewriter=qsimplify_pauli), (X1+im*X2)/sqrt(2))
+   @test isequal(qsimplify(H*Y2,rewriter=qsimplify_pauli), (X1-im*X2)/sqrt(2))
+   @test isequal(qsimplify(H*Z1,rewriter=qsimplify_pauli), X1)
+   @test isequal(qsimplify(H*Z2,rewriter=qsimplify_pauli), X2)
+end