subexperiments associated with the identity Pauli observable should not be passed to Sampler

[caleb-johnson]

We do not need to run circuits associated with the Identity observable, as the measurement readout is trivial.

Now, the cutting workflow in the tutorials will fail ungracefully when the subexperiments associated with the I observable are passed to the Sampler, as they do not contain any end-of-circuit measurements. Passing these circuits results in:

ValueError: The 0-th circuit does not have any classical bit. Sampler requires classical bits, plus measurements on the desired qubits.

How do we handle this? Do we only return subexperiments which need actual measurement? If we do that, we'd need to extrapolate the trivial I measurements back into the final answer somehow.

[garrison]

The way a user can hack around it without requiring any changes to CKT is to add a Pauli Z observable somewhere in the subsystem that is currently throwing an error with all identities.

But even better would be not to run these experiments at all. I've had this in mind as one of the special cases at #262, but it looks like I failed to ever explicitly mention this there. I did mention it at #378 (comment), and I think the follow up at #387 is relevant to fixing this.

I will also think if there's something we can do that doesn't involve breaking interfaces, which #387 would, technically. We could always write a helper function that elides calling the Sampler if there are no measurements, but then we're back to where we started: hiding the Sampler from the user. Alternatively, perhaps the sampler could be modified to have a flag that elides execution (rather than errors) if there are no measurements, but it would take time to get that integrated into all the Sampler implementations.

[garrison]

The way a user can hack around it without requiring any changes to CKT is to add a Pauli Z observable somewhere in the subsystem that is currently throwing an error with all identities.

Actually, automating this hack is probably the best way for us to "quick fix" this, too. We can modify generate_cutting_experiments to always have at least one measurement in each circuit, and this can be done in 0.4.1, without breaking anything.

The "better" fix is going to be to skip the circuit evaluation altogether, which will probably involve tweaking an interface and is related to the issues I linked above.