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Statevector._expectation_value_pauli returns incorrect result in certain cases #13029

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#13345
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Statevector._expectation_value_pauli returns incorrect result in certain cases#13029
#13345
@yjh-bill

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@yjh-bill
yjh-bill
opened on Aug 23, 2024

The calculation for the expectation value of the identity operator seems incorrect when the statevector is not normalized to 1.

I think the reason is that one should use the norm squared rather than the norm in the following lines.

qiskit/qiskit/quantum_info/states/statevector.py

Lines 478 to 479 in 1be2c5a

if x_mask + z_mask == 0:
return pauli_phase * np.linalg.norm(self.data)

The whole function is attached below to provide context.

qiskit/qiskit/quantum_info/states/statevector.py

Lines 458 to 491 in 1be2c5a

def _expectation_value_pauli(self, pauli, qargs=None):
"""Compute the expectation value of a Pauli.
Args:
pauli (Pauli): a Pauli operator to evaluate expval of.
qargs (None or list): subsystems to apply operator on.
Returns:
complex: the expectation value.
"""
n_pauli = len(pauli)
if qargs is None:
qubits = np.arange(n_pauli)
else:
qubits = np.array(qargs)
x_mask = np.dot(1 << qubits, pauli.x)
z_mask = np.dot(1 << qubits, pauli.z)
pauli_phase = (-1j) ** pauli.phase if pauli.phase else 1
if x_mask + z_mask == 0:
return pauli_phase * np.linalg.norm(self.data)
if x_mask == 0:
return pauli_phase * expval_pauli_no_x(self.data, self.num_qubits, z_mask)
x_max = qubits[pauli.x][-1]
y_phase = (-1j) ** pauli._count_y()
y_phase = y_phase[0]
return pauli_phase * expval_pauli_with_x(
self.data, self.num_qubits, z_mask, x_mask, y_phase, x_max
)

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