AerPauliExpectation.compute_variance returns zero variance

[ikkoham]

What is the expected enhancement?

AerPauliExpectation.compute_variance returns zero variance as the comment said.
https://qiskit.org/documentation/stubs/qiskit.aqua.operators.expectations.AerPauliExpectation.compute_variance.html

However, AerPauliExpectation has a finite (=non-zero) variance in general. In SnapshotExpectationValue used here, an optional argument of variance is True. It seems that this returns variance computed in Aer.

[Cryoris]

Which variance do you mean exactly?

As far as I know, the variance argument in the SnapshotExpectationValue does not return an estimator for the sampling noise but only if you add a noise model to the backend. I.e. it cannot be used as a replacement of PauliExpectation.

[ikkoham]

Yeah, SnapshotExpectationValue returns an expectation value <psi | H psi>. This is not an estimator.

The variance here is
<psi | H^2 psi> - <psi |H psi>^2.

[woodsp-ibm]

Is this still valid, and if so should it be moved to Terra repo given that opflow has been moved and is being maintained there now? Or should this be closed?

[yaelbh]

It's an Aer thing. As commented above, the variance should be equal to 0, since this is not an estimator. But it is perhaps about to change, @chriseclectic should know more.

[ikkoham]

This will be resolved by usingSaveExpVal in AerPauliExpectation.
Qiskit/qiskit-aer#1101

Closable in Aqua.

Move to Terra and we need to update opflow.AerPauliExpectation after SaveExpVal.

[manoelmarques]

If this issue replaces SnapshotExpectationValue with SaveExpectationValue in AerPauliExpectation, then it will also fix #6504

[ikkoham]

Close once. Please reopen if you want.