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Normalize two_qubit_decomposition for odd CNOTs to preserve determinant 1 #6999

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Normalize two_qubit_decomposition for odd CNOTs to preserve determinant 1 #6999

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10 changes: 8 additions & 2 deletions pennylane/ops/op_math/decompositions/two_qubit_unitary.py
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Original file line number Diff line number Diff line change
Expand Up @@ -353,7 +353,10 @@ def _decomposition_1_cnot(U, wires):
C_ops = one_qubit_decomposition(C, wires[0])
D_ops = one_qubit_decomposition(D, wires[1])

return C_ops + D_ops + [qml.CNOT(wires=wires)] + A_ops + B_ops
# GlobalPhase added to preserve the determinant 1
# (as CNOT has determinant -1, see paragraph below
# Lemma II.1 in https://arxiv.org/abs/quant-ph/0308033)
return C_ops + D_ops + [qml.CNOT(wires=wires)] + A_ops + B_ops + [qml.GlobalPhase(np.pi / 4)]


def _decomposition_2_cnots(U, wires):
Expand Down Expand Up @@ -532,7 +535,10 @@ def _decomposition_3_cnots(U, wires):
D_ops = one_qubit_decomposition(D, wires[1])

# Return the full decomposition
return C_ops + D_ops + interior_decomp + A_ops + B_ops
# GlobalPhase added to preserve the determinant 1
# (as CNOT has determinant -1, see paragraph below
# Lemma II.1 in https://arxiv.org/abs/quant-ph/0308033)
return C_ops + D_ops + interior_decomp + A_ops + B_ops + [qml.GlobalPhase(np.pi / 4)]


def two_qubit_decomposition(U, wires):
Expand Down
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