add a test for the T1 noise

test/test_quantumoptics.jl

@@ -2,6 +2,54 @@
 
 using BPGates, QuantumClifford, QuantumOptics
 
+using BPGates: T1NoiseOp
 
+using LinearAlgebra: diag
+
+# define some BP objects
+λ = 0.2
+N = 100000
+s = BellState(1)
+opBP = T1NoiseOp(1, λ)
+
+# compute using BP the density matrix after T1 noise
+ρBP = sum([dm(Ket(Stabilizer(apply!(s,op)))) for i in 1:N])/N
+
+# define some QO objects
+b = SpinBasis(1//2)
+l0 = spinup(b)
+l1 = spindown(b)
+l00 = l0⊗l0
+l01 = l0⊗l1
+l10 = l1⊗l0
+l11 = l1⊗l1
+bell00 = (l00+l11)/sqrt(2)
+bell01 = (l01+l10)/sqrt(2)
+bell10 = (l00-l11)/sqrt(2)
+bell11 = (l01-l10)/sqrt(2)
+#|`00`|`+XX +ZZ`|`∣00⟩+∣11⟩`|`∣++⟩+∣--⟩`|`∣i₊i₋⟩+∣i₋i₊⟩`|
+#|`01`|`+XX -ZZ`|`∣01⟩+∣10⟩`|`∣++⟩-∣--⟩`|`∣i₊i₊⟩-∣i₋i₋⟩`|
+#|`10`|`-XX +ZZ`|`∣00⟩-∣11⟩`|`∣+-⟩+∣-+⟩`|`∣i₊i₊⟩+∣i₋i₋⟩`|
+#|`11`|`-XX -ZZ`|`∣01⟩-∣10⟩`|`∣+-⟩-∣-+⟩`|`∣i₊i₋⟩-∣i₋i₊⟩`|
+
+# compute using QO the density matrix after T1 noise
+krausOp1 = projector(l0) + √(1-λ) * projector(l1)
+krausOp2 = √(λ) * projector(l0, l1')
+id = identityoperator(b)
+k1 = krausOp1⊗id
+k2 = krausOp2⊗id
+k3 = id⊗krausOp1
+k4 = id⊗krausOp2
+ρ0 = dm(bell00)
+ρ1  = k1*ρ0*k1' + k2*ρ0*k2'
+ρQO = k3*ρ1*k3' + k4*ρ1*k4'
+
+# switch to the Bell basis
+to_bell_basis = projector(l00,bell00')+projector(l01,bell01')+projector(l10,bell10')+projector(l11,bell11')
+
+ρbBP = to_bell_basis*ρBP*to_bell_basis'
+ρbQO = to_bell_basis*ρQO*to_bell_basis'
+
+@test_broken isapprox(diag(ρbBP.data), diag(ρbQO.data), atol=10/sqrt(N))
 
 end