Noiseless estimator not working with non-Hermitian fermionic operators

[erikkjellgren]

Informations

• Qiskit Aer version: 0.14.0.1
• Python version: 3.12.2
• Operating system: Ubuntu 22.04.4 LTS

What is the current behavior?

Throws the following error:

ValueError: Input operator is not Hermitian.

Steps to reproduce the problem

from qiskit import QuantumCircuit
from qiskit.quantum_info.operators import SparsePauliOp
from qiskit_aer.primitives import Estimator

qc = QuantumCircuit(2)
op = SparsePauliOp(["XY", "XX"], coeffs=[0.5, 0.2j])

estimator1 = Estimator(run_options={"shots": 1000})
estimator2 = Estimator(approximation=True, run_options={"shots": None})
print("Estimator with shot noise")
print(estimator1.run(qc, op).result().values)
print(estimator1.run(qc, op).result().values)
print()
print("Estimator without shot noise")
print(estimator2.run(qc, op).result().values)
print(estimator2.run(qc, op).result().values)

What is the expected behavior?

The expected behavior is to give the noiseless result instead of throwing an error.

Suggested solutions

I looked into the source code of qiskit_aer and found the following code (in qiskit_aer.primitives.estimator beginning on line 454):

                      if shots is None:
                          circuit.save_expectation_value(observable, self._layouts[i])
                      else:
                          for term_ind, pauli in enumerate(observable.paulis):
                              circuit.save_expectation_value(
                                  pauli, self._layouts[i], label=str(term_ind)
                              )

It looks like when shot=None and approximation=True, it saves the expectation value differently than when there is shot-noise.