inv implementation for TwoQubitOperator (#315)

Co-authored-by: Fe-r-oz <ferozahmad7cf@gmail.com>
Co-authored-by: Stefan Krastanov <stefan@krastanov.org>

CHANGELOG.md

@@ -5,6 +5,10 @@
 
 # News
 
+## v0.9.9 - 2024-08-05
+
+- `inv` is implemented for all Clifford operator types (symbolic, dense, sparse).
+
 ## v0.9.8 - 2024-08-03
 
 - New group-theoretical tools:

Project.toml

@@ -1,7 +1,7 @@
 name = "QuantumClifford"
 uuid = "0525e862-1e90-11e9-3e4d-1b39d7109de1"
 authors = ["Stefan Krastanov <stefan@krastanov.org> and QuantumSavory community members"]
-version = "0.9.8"
+version = "0.9.9"
 
 [deps]
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"

src/QuantumClifford.jl

@@ -50,7 +50,7 @@ export
     sHadamard, sPhase, sInvPhase, SingleQubitOperator, sId1, sX, sY, sZ,
     sCNOT, sCPHASE, sSWAP,
     sXCX, sXCY, sXCZ, sYCX, sYCY, sYCZ, sZCX, sZCY, sZCZ,
-    sZCrY,
+    sZCrY, sInvZCrY,
     # Misc Ops
     SparseGate,
     sMX, sMY, sMZ, PauliMeasurement, Reset, sMRX, sMRY, sMRZ,

src/misc_ops.jl

@@ -32,6 +32,10 @@ function apply!(state::AbstractStabilizer, g::SparseGate; kwargs...)
     apply!(state, g.cliff, g.indices; kwargs...)
 end
 
+function LinearAlgebra.inv(g::SparseGate; phases=true)
+  return SparseGate(inv(g.cliff;phases=phases), g.indices)
+end
+
 """Reset the specified qubits to the given state.
 
 Be careful, this operation implies first tracing out the qubits, which can lead to mixed states

src/noise.jl

@@ -34,17 +34,14 @@ struct PauliNoise{T} <: AbstractNoise
     py::T
     pz::T
 end
+
 function PauliNoise(px::Real, py::Real, pz::Real)
     px, py, pz = float.((px, py, pz))
     px, py, pz = promote(px, py, pz)
     T = typeof(px)
     return PauliNoise{T}(px, py, pz)
 end
 
-"""A convenient constructor for various types of Pauli noise models.
-Returns more specific types when necessary."""
-function PauliNoise end
-
 """Constructs an unbiased Pauli noise model with total probability of error `p`."""
 function PauliNoise(p)
     UnbiasedUncorrelatedNoise(p)

src/pauli_operator.jl

@@ -122,7 +122,13 @@ Base.hash(p::PauliOperator, h::UInt) = hash(p.phase,hash(p.nqubits,hash(p.xz, h)
 
 Base.copy(p::PauliOperator) = PauliOperator(copy(p.phase),p.nqubits,copy(p.xz))
 
-function Base.deleteat!(p::PauliOperator, subset) 
+function LinearAlgebra.inv(p::PauliOperator)
+  ph = p.phase[]
+  phin = xor((ph << 1) & ~(UInt8(1) << 2), ph)
+  return PauliOperator(phin, p.nqubits, copy(p.xz))
+end
+
+function Base.deleteat!(p::PauliOperator, subset)
     p =p[setdiff(1:length(p), subset)]
     return p
 end

src/symbolic_cliffords.jl

@@ -301,6 +301,7 @@ end
 @qubitop2 YCZ    (x1⊻x2   , x2⊻z1    , x2       , z2⊻x1⊻z1, ~iszero( (x2 & (x1 ⊻ z1) & (z2 ⊻ x1)) ))
 
 @qubitop2 ZCrY  (x1, x1⊻z1⊻x2⊻z2, x1⊻x2, x1⊻z2, ~iszero((x1 & ~z1 & x2) | (x1 & ~z1 & ~z2) | (x1 & x2 & ~z2)))
+@qubitop2 InvZCrY (x1, x1⊻z1⊻x2⊻z2, x1⊻x2, x1⊻z2, ~iszero((x1 & z1 & ~x2 & ~z2) | (x1 & ~z1 & ~x2 & z2) | (x1 & z1 & ~x2 & z2) | (x1 & z1 & x2 & z2)))
 
 #=
 To get the boolean formulas for the phase, it is easiest to first write down the truth table for the phase:
@@ -346,6 +347,21 @@ function Base.show(io::IO, op::AbstractTwoQubitOperator)
     end
 end
 
+LinearAlgebra.inv(op::sSWAP) = sSWAP(op.q1, op.q2)
+LinearAlgebra.inv(op::sCNOT) = sCNOT(op.q1, op.q2)
+LinearAlgebra.inv(op::sCPHASE) = sCPHASE(op.q1, op.q2)
+LinearAlgebra.inv(op::sZCX) = sZCX(op.q1, op.q2)
+LinearAlgebra.inv(op::sZCY) = sZCY(op.q1, op.q2)
+LinearAlgebra.inv(op::sZCZ) = sZCZ(op.q1, op.q2)
+LinearAlgebra.inv(op::sXCX) = sXCX(op.q1, op.q2)
+LinearAlgebra.inv(op::sXCY) = sXCY(op.q1, op.q2)
+LinearAlgebra.inv(op::sXCZ) = sXCZ(op.q1, op.q2)
+LinearAlgebra.inv(op::sYCX) = sYCX(op.q1, op.q2)
+LinearAlgebra.inv(op::sYCY) = sYCY(op.q1, op.q2)
+LinearAlgebra.inv(op::sYCZ) = sYCZ(op.q1, op.q2)
+LinearAlgebra.inv(op::sZCrY) = sInvZCrY(op.q1, op.q2)
+LinearAlgebra.inv(op::sInvZCrY) = sZCrY(op.q1, op.q2)
+
 ##############################
 # Functions that perform direct application of common operators without needing an operator instance
 ##############################

test/test_noisycircuits.jl

@@ -5,8 +5,16 @@
     test_sizes = [1,2,10,63,64,65,127,128,129] # Including sizes that would test off-by-one errors in the bit encoding.
 
     using QuantumClifford.Experimental.NoisyCircuits
+
     import AbstractAlgebra
 
+    @testset "SparseGate" begin
+        g = SparseGate(random_clifford(2), randperm(10)[1:2])
+        gi = inv(g)
+        c = random_stabilizer(10)
+        @assert apply!(apply!(copy(c), g), gi) == c
+    end
+
     @testset "Noisy Gates" begin
         g1 = SparseGate(tId1, [1])
         g2 = SparseGate(tCNOT, [2,3])
@@ -25,6 +33,7 @@
         resp = petrajectories(copy(state), [ng1,ng2,ng3,ng4,ng5])
         @test all(values(resp).==0)
     end
+
     @testset "Monte Carlo Purification examples" begin
         g1 = SparseGate(tCNOT, [1,3])
         g2 = SparseGate(tCNOT, [2,4])
@@ -49,8 +58,6 @@
         @test nonoise[true_success_stat] == 10
     end
 
-
-
     @testset "Perturbative expansion Purification examples" begin
         @testset "Comparison to MC" begin
             compare(a,b, symbol) = abs(a[symbol]/500-b[symbol]) / (a[symbol]/500+b[symbol]+1e-5) < 0.3
@@ -79,6 +86,7 @@
             @test compare(mc,pe,false_success_stat)
             @test compare(mc,pe,true_success_stat)
         end
+
         @testset "Symbolic" begin
             R, (e,) = AbstractAlgebra.polynomial_ring(AbstractAlgebra.RealField, ["e"])
             unity = R(1);
@@ -97,6 +105,7 @@
             @test pe_symbolic[true_success_stat]       == 27.0*e^4 + -54.0*e^3 + 36.0*e^2 + -10.0*e + 1.0
         end
     end
+
     @testset "Measurements" begin
         @testset "BellMeasurements" begin
             stateX = S"X"
@@ -138,6 +147,7 @@
             @test random2_pe[failure_stat]+random2_pe[false_success_stat] == 1
             @test random2_pe[true_success_stat] == 0
         end
+
         @testset "PauliMeasurements" begin
             ghzState = S"XXX
             ZZI
@@ -174,6 +184,7 @@
             @test random2_pe[false_success_stat] == 1
             @test random2_pe[true_success_stat] == 0
         end
+
         @testset "Sparse Measurements" begin
             ghzState = S"XXX
             ZZI
@@ -212,6 +223,7 @@
             @test random2_pe[false_success_stat] == 1
             @test random2_pe[true_success_stat] == 0
         end
+
         @testset "Conforming to the project! interface" begin
             state = Register(MixedDestabilizer(S"ZZ"), zeros(Bool, 1))
             meas = PauliMeasurement(P"ZI", 1)
@@ -222,6 +234,7 @@
             ZI"
         end
     end
+
     @testset "Classical Bits" begin
         @testset "DecisionGate" begin
             X_error = CliffordOperator([P"X", P"-Z"])
@@ -256,6 +269,7 @@
             canonicalize!(quantumstate(r))
             @test stabilizerview(r) == expectedFinalState
         end
+
         @testset "ConditionalGate" begin
             id_op = CliffordOperator([P"X", P"Z"])
             X_error = CliffordOperator([P"X", P"-Z"])

test/test_paulis.jl

@@ -38,6 +38,11 @@
         @test prodphase(P"XX",P"YY") == 0x2
         @test prodphase(P"ZZZ",P"XXX") == prodphase(S"III ZZZ",P"XXX",2) == prodphase(P"ZZZ",S"III XXX",2) == prodphase(S"III ZZZ",S"III XXX",2,2) == 0x3
     end
+
+    for Pop in [P"X", P"iX", P"-iXYZ", random_pauli(100; nophase=false, realphase=false)]
+        @test Pop * inv(Pop) == zero(Pop)
+    end
+
     @testset "Commutation implies real phase" begin
         for i in 1:10
             for n in test_sizes

test/test_symcliff.jl

@@ -77,4 +77,17 @@
             @test CliffordOperator(inv(SingleQubitOperator(random_op)), i) == inv(CliffordOperator(random_op, i))
         end
     end
+
+    @testset "TwoQubitOperator inv methods" begin
+        for gate_type in subtypes(QuantumClifford.AbstractTwoQubitOperator)
+            n₁ = rand(2: 10)
+            n₂ = rand(1:(n₁ - 1))
+            @test CliffordOperator(inv(gate_type(n₁, n₂)), n₁) == inv(CliffordOperator(gate_type(n₁, n₂), n₁))
+            @test CliffordOperator(inv(gate_type(n₂, n₁)), n₁) == inv(CliffordOperator(gate_type(n₂, n₁), n₁))
+            @test CliffordOperator(inv(sZCX(n₁, n₂)), n₁) == inv(CliffordOperator(sCNOT(n₁, n₂), n₁))
+            @test CliffordOperator(inv(sXCZ(n₁, n₂)), n₁) == inv(CliffordOperator(sCNOT(n₂, n₁), n₁))
+            @test CliffordOperator(inv(sZCrY(n₁, n₂)), n₁) == inv(CliffordOperator(sZCrY(n₁, n₂), n₁))
+            @test CliffordOperator(inv(sInvZCrY(n₁, n₂)), n₁) == inv(CliffordOperator(sInvZCrY(n₁, n₂), n₁))
+        end
+    end
 end