Estimator on SparsePauliOp(["XY", "XX"], ...) and SparsePauliOp([Pauli("XYZ"), Pauli("XX")], ...) have different result

[rht]

Informations

• Qiskit Aer version: 0.12.2
• Python version: 3.11
• Operating system: Linux

What is the current behavior?

"XX" and Pauli("XX") as an argument on SparsePauliOp has different results for qiskit_aer.primitives, while qiskit.primitives results are correct.

Steps to reproduce the problem

from qiskit import QuantumCircuit
from qiskit.primitives import Estimator as e1
from qiskit_aer.primitives import Estimator as e2
from qiskit.quantum_info import Pauli, SparsePauliOp


qc = QuantumCircuit(3)
qc.h(0)
qc.rx(0.2, 0)
qc.h(1)
qc.ry(0.6, 1)
qc.h(2)
qc.rz(0.7, 2)
pauli_sum1 = SparsePauliOp(["XYZ", "XXX"], coeffs=[0.5, 0.2j])
pauli_sum2 = SparsePauliOp([Pauli("XYZ"), Pauli("XXX")], coeffs=[0.5, 0.2j])

estimator1 = e1()
estimator2 = e2(run_options={"approximation": True, "shots": None})
print("qiskit.primitives")
print(estimator1.run(qc, pauli_sum1).result().values)
print(estimator1.run(qc, pauli_sum2).result().values)
print()
print("qiskit_aer.primitives")
print(estimator2.run(qc, pauli_sum1).result().values)
print(estimator2.run(qc, pauli_sum2).result().values)

Output:

qiskit.primitives
[0.+0.1262503j]
[0.+0.1262503j]

qiskit_aer.primitives
[-0.00195312+0.13476562j]
[0.03710938+0.13125j]

What is the expected behavior?

They should all be the same number, but qiskit_aer.primitives output are inconsistent.

[ikkoham]

The fluctuation is due to sampling errors in the measurement. In other words, it is not approximation=True.

approximation is not run_option, so

estimator2 = e2(approximation=True)

is correct. However, this does not support non-Hermitian operator. Actually, whether Estimator supports non-Hermitian operator is implementation-dependent.

[rht]

I specified both in the run_options as recommended in the migration guide: https://github.com/Qiskit/qiskit/blob/ff4dc0becb84af7b38ea3b7590fc285796b7566b/docs/migration_guides/opflow_migration.rst?plain=1#L1265.

Actually, whether Estimator supports non-Hermitian operator is implementation-dependent.

I replaced the 0.2j with 0.2, and the result still doesn't match with qiskit.primitives

Upon retrying several times, I did get different number each time. So it seems that it is not doing exact computation according to

qiskit-aer/qiskit_aer/primitives/estimator.py

Lines 45 to 46 in 73f0847

	The number of shots. If None and approximation is True, it calculates the exact
	expectation values. Otherwise, it calculates expectation values with sampling.

.

[rht]

I confirmed that estimator2 = e2(approximation=True, run_options={"shots": None}) does indeed give the correct answer, as long as the observables are Hermitian.

[ikkoham]

Oh... It's a typo. Thank you for finding.

[rht]

Closed via Qiskit/qiskit#10966.