Allow expectation values for density matrix, MPS, Clifford

[daxfohl]

Closes #3964.

More generically, this solves it for any SimulatesFinalState implementation whose TSimulationTrialResult type implements expectation_from_state.

[daxfohl]

@tonybruguier is there a quick way to add this to MPS as well? I see there is a state_vector field available on the trial result class. Could we add the same two lines there as I did here in state_vector_simulator and expect that to produce valid results?

[daxfohl]

@95-martin-orion is it possible to do the same for Clifford simulators?

[daxfohl]

@95-martin-orion oops, just saw you already had a fix. Up to you whether you'd rather use this one that generifies things or stick with the yagni approach.

[tonybruguier]

@tonybruguier is there a quick way to add this to MPS as well? I see there is a state_vector field available on the trial result class. Could we add the same two lines there as I did here in state_vector_simulator and expect that to produce valid results?

I am not sure what is required. Do you want the simulator to take a density matrix as initial state and return a density matrix at the output of the circuit? That could be involved to write.

Or do you want the simulator to just output a density matrix?

[daxfohl]

I am not sure what is required. Do you want the simulator to take a density matrix as initial state and return a density matrix at the output of the circuit? That could be involved to write.

I think I figured it out. Just needed to add a way to get an expectation value from MPSTrialResult, which turned out to be a one-liner. Took the tests from density matrix simulator tests (stolen from @95-martin-orion's PR), and changed them to use MPS, and they seem to pass.

[daxfohl]

Looks like Clifford also provides a function to generate a state vector from a trial result, so we can add an expectation value there too. Will add that before merging.

[daxfohl]

Clifford seems to be working now too.

[95-martin-orion]

Regardless of how this pans out, I think we need to document the Simulator hierarchy somewhere (maybe at the top of simulator.py?) once it's done. Multiple nested base classes make it tricky to track which one supports what behavior.

[95-martin-orion]

I suspect there is a more efficient way to extract expectiation values from an MPS state than converting it into its full state vector form.

[95-martin-orion]

Similar to the MPS simulator, there should be a way of calculating expectation values from the Clifford tableau without expanding it to the full state vector.

[95-martin-orion]

We should include a note that this is only a default implementation; depending on the simulator's behavior, there may be a more efficient simulation method that bypasses simulating the full state.

[95-martin-orion]

My concern here: the fact that expectation_from_state has no default implementation means that SimulatesFullState does not fully implement SimulatesExpectationValues, which means user-created subclasses will have a broken API.

We could update the class docstring to say that users must implement expectation_from_state in their result class, but that's kind of unwieldy for a class whose base purpose does not include calculating expectation values. This is part of why I mentioned needing a SimulatesEVsAndFullState type for this in #3979.

[daxfohl]

@95-martin-orion I agree. I think go ahead and merge your solution for density matrix. I'll look at how to improve this as time comes available.

[95-martin-orion]

Closing as superseded by #3979. There is still interest in deduplicating this behavior (#4209), but at this point it's likely easier to do so in a fresh PR. (Feel free to reopen if that's not the case.)