Statevector._expectation_value_pauli returns incorrect result in certain cases

[yjh-bill]

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
	)

[jakelishman]

Please can you show a reproducing code block following the bug report template, and the output you expected?

[yjh-bill]

Sure. Here it is

from qiskit.quantum_info import Statevector, SparsePauliOp, Pauli

state_normed = Statevector.from_label("0")
state_not_normed = 2 * state_normed

identity_op = SparsePauliOp.from_list([("I", 1)])

# using the public interface (expectation_value)
print(state_not_normed.expectation_value(identity_op))

# using _expectation_value_pauli (the backend)
print(state_not_normed._expectation_value_pauli(Pauli('I')))

Environment

Python 3.11.6
qiskit 0.45.3

Judging from the source code on github, the issue should be platform-independent and exists across different versions.

What is the expected result

The two print statement should give 4+0j and 4.0 respectively.

What is the actual result

The two print statement gave 2+0j and 2.0 respectively.

[Cryoris]

Nice catch, that seems to be unique only to the Pauli-I operator. Would you like to open a PR to fix the issue? 🙂

[yjh-bill]

Sure, I have created one PR.