Expectation value API for simulators

[95-martin-orion]

Is your feature request related to a use case or problem? Please describe.

Currently, finding expectation values from a simulator in Cirq requires implementing the SimulatesFinalState interface and using the resulting state vector to get the expectation values. If simulators provide a more efficient way of producing expectation values, we should prefer that instead.

Describe the solution you'd like

In addition to SimulatesFinalState, SimulatesAmplitudes, etc., Cirq should offer a SimulatesExpectationValues interface for simulators that generate expectation values.

What is the urgency from your perspective for this issue? Is it blocking important work?

P2 - we should do it in the next couple of quarters. The current workaround is to continue using SimulatesFinalState, but as noted above this may be inefficient.

[balopat]

Discussed on Cirq Cynq: this is a good idea, needed and PauliSums are the way to go.

[95-martin-orion]

Further discussion on the qsim weekly sync identified that this is a proper prerequisite for trajectory-based Monte Carlo simulations; using SimulatesFinalState and processing each result in turn would reduce performance to the point of being infeasible.

[95-martin-orion]

Moving forward with the format discussed in the RFC: https://tinyurl.com/cirq-expectation-value-api