Estimator with approximation=True gives poor approximation #1986
Description
Informations
- Qiskit Aer version: 0.13.0
- Python version: 3.10.12
- Operating system: Arch Linux
What is the current behavior?
I initialize a noise model from a fake backend. I run the estimator with a simple circuit and observable. The ideal expectation value is 1.0. approximation=True gives 0.981. approximation=False gives 0.916.
Steps to reproduce the problem
from qiskit import QuantumCircuit
from qiskit.providers.fake_provider import FakeGuadalupeV2
from qiskit.quantum_info import SparsePauliOp
from qiskit_aer.primitives import Estimator
from qiskit_aer.noise import NoiseModel
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
observable = SparsePauliOp("ZZ")
fake_backend = FakeGuadalupeV2()
noise_model = NoiseModel.from_backend(fake_backend)
print("approximation=True")
estimator = Estimator(backend_options=dict(noise_model=noise_model), approximation=True)
job = estimator.run(qc, [observable])
result = job.result()
exp_value = result.values[0]
print(exp_value)
print()
print("approximation=False")
estimator = Estimator(backend_options=dict(noise_model=noise_model), approximation=False)
job = estimator.run(qc, [observable], shots=100000)
result = job.result()
exp_value = result.values[0]
print(exp_value)approximation=True
[/tmp/ipykernel_93816/3992086219.py:18](https://file+.vscode-resource.vscode-cdn.net/tmp/ipykernel_93816/3992086219.py:18): DeprecationWarning: ``qiskit_aer.primitives.estimator.Estimator.__init__()``'s argument ``approximation`` is deprecated as of qiskit-aer 0.13. It will be removed no earlier than 3 months after the release date. approximation=True will be default in the future.
estimator = Estimator(backend_options=dict(noise_model=noise_model), approximation=True)
0.9817418982111457
approximation=False
[/tmp/ipykernel_93816/3992086219.py:26](https://file+.vscode-resource.vscode-cdn.net/tmp/ipykernel_93816/3992086219.py:26): DeprecationWarning: ``qiskit_aer.primitives.estimator.Estimator.__init__()``'s argument ``approximation`` is deprecated as of qiskit-aer 0.13. It will be removed no earlier than 3 months after the release date. approximation=True will be default in the future.
estimator = Estimator(backend_options=dict(noise_model=noise_model), approximation=False)
[/tmp/ipykernel_93816/3992086219.py:26](https://file+.vscode-resource.vscode-cdn.net/tmp/ipykernel_93816/3992086219.py:26): DeprecationWarning: Option approximation=False is deprecated as of qiskit-aer 0.13. It will be removed no earlier than 3 months after the release date. Instead, use BackendEstmator from qiskit.primitives.
estimator = Estimator(backend_options=dict(noise_model=noise_model), approximation=False)
0.91606
What is the expected behavior?
Should be a better approximation.