exp-val: fix handling of identity in meas basis

[aeddins-ibm]

Currently, if a user passes in a measurement basis containing an identity (I) -- which is admittedly a weird thing to do -- that basis may pass a compatibility check with a given observable term, but not really be valid for evaluating that observable term. For example, the basis IZ cannot be used to evaluate the observable term ZZ, but is qubit-wise commuting.

I think the check happens here (?):

qiskit-addon-utils/qiskit_addon_utils/exp_vals/expectation_values.py

Lines 357 to 359 in 6247521

	commutes = (
	np.dot(observable_element.z, basis.x) + np.dot(observable_element.x, basis.z)
	) % 2 == 0

I'm thinking we should modify how we check compatibility to something like this, instead of checking qubit-wise commutativity:

mask = term.z|term.x
compatible = np.all(term[mask] == basis[mask])

It would also be a little more accurate to change language in code/docstrings/errors about "commuting" to "compatible." (Observable XX is commuting with basis ZZ but is not compatible. Observable ZZ is qubit-wise commuting with basis IZ but is not compatible.)

(Alternatively, we could just raise an error when validating measurement bases if they are not all full-weight. But maybe there's some abstract case where it's convenient to work with measurement bases that have identity characters, indicating basically a dummy bit.)

[caleb-johnson]

Thanks, @aeddins-ibm. good catch.

error when validating measurement bases if they are not all full-weight: Wouldn't requiring full-weight bases be too restrictive and a bit arbitrary? The trivial example is just wanting to measure a single low-weight observable ... of course then the measurement basis would not be full weight. If we did measure all qubits associated only with I terms, would we be introducing unnecessary noise into the computation, or is readout noise mostly/entirely isolated to the qubit being read out?

[aeddins-ibm]

Sorry I should clarify "full weight" above.

I do NOT mean that when measuring a weight-two observable, the measurement basis should be 128 bits (e.g.) to match the qubit number of the device.

Only that when measuring a weight-two observable (i.e. when the BitArray has two bits), the measurement basis is two non-identity Pauli characters. So ZZ is "full weight," but not IZ.