Adds a fake session to primitives

What should we add?

The base classes, reference implementations, and backend implementations of primitives do not take a session while qiskit-ibm-runtime version of primitives takes session to reduce latency. Here is a sample code of runtime estimator with session.

        with Session(service=service, backend="ibmq_qasm_simulator") as session:
            estimator = Estimator(session=session)
            theta1 = [0, 1, 1, 2, 3, 5]
            # calculate [ <psi1(theta1)|H1|psi1(theta1)> ]
            psi1_H1 = estimator.run(circuits=[psi1], observables=[H1], parameter_values=[theta1])
            print(psi1_H1.result())

If users implement algorithms with the base class or reference impl of primitives, the code cannot take advantage of session when they replace the primitives with the runtime version. If users implement algorithms with runtime primitives, they need to adjust the code to test their implementation using the reference impl. So, it would be useful to introduce a fake session and extend the base classes of primitives to take the fake session as an argument.

[jakelishman]

the rest of the primitive usage is (should be) fully consistent and through the defined API.

I should be clearer on this point: I mean that all the running of circuits on primitives is a defined part of the API, and so this code should look the same no matter what Estimator is used, but the actual constructor of an Estimator isn’t part of the interface, so it’s totally normal for it to look a bit different between implementations.

If there is meant to be a single defined construction method, then this needs formalising into an API that everyone can implement. For the Backend path, such a factory class is (approximately) Provider, as an example. I personally don’t see a need for a unified construction interface here (I think they generally don’t reduce any complexity, they just move it to the construction of a different object), but I’m not the best person to design the UX of these interfaces.

[t-imamichi]

Thank you for your comment, Jake. I ask @adekusar-drl to describe the details of this request.