U ≠ V

[agata-branczyk]

Is your feature request related to a problem? Please describe.
In the current implementation, it's not possible to treat the spin up and spin down subsystems differently.

Describe the solution you'd like
Breaking the U=V symmetry so that U ≠ V.

Additional context
This will be made possible after the new expectation values primitive is merged into qiskit terra.

[aeddins-ibm]

A small baby-step towards U != V could be taking the counts object returned from the backend (if that is available for now), and randomly assigning half the shots to one half of the subsystem and the other half to the other subsystem. This may be a little computationally heavy but should eliminate the spurious noise-correlation introduced by using the same shots for both subsystems, which I think is good to fix asap (assuming it’s still done that way in the latest code). It also would move the analysis code towards being ready for U != V. Later as you generalize the circuit-building part of the code for U!=V, you will have separate sets of circuits for the two subsystems, and will no longer need the random resampling of the counts object.

The spurious noise correlation between the subsystems can IIRC lead to a systematic bias in obtained expectation values (though I think it goes to zero for many shots), so it would be nice to fix this relatively soon.