Expectation behavior of factory

[woodsp-ibm]

The expectation factory checks the operator and will return a valid expectation if the operator is all paulis or matrices. However for a mix the following happens raise ValueError('Expectations of Mixed Operators not yet supported.')

This test below was in test_qaoa - it has been updated/changed as part of qiskit-community/qiskit-aqua#1154 which ensures, when the expectation as supplied was None, and VQE should auto-select a valid expectation, that indeed this happens. specifically around re-use when backend and/or operator can be changed. Before the PR the very first expectation auto-selected by VQE ended up 'locked-in' since it simply checked an instance var where it stored it for None. This meant switching the backend or operator may fail to have the best, or even an expectation that simply worked with the new backend and/or operator.

        """ QAOA test """
        backend = BasicAer.get_backend('statevector_simulator')
        optimizer = COBYLA(maxiter=2)
        qubit_op, _ = max_cut.get_operator(W1)
        qubit_op = qubit_op.to_opflow().to_matrix_op()

        seed = 0
        aqua_globals.random_seed = seed
        qaoa = QAOA(qubit_op, optimizer, P1)
        quantum_instance = QuantumInstance(backend, seed_simulator=seed, seed_transpiler=seed)
        qaoa.run(quantum_instance)
        qaoa.operator = (X ^ qubit_op ^ Z)
        qaoa.run()

Here is sets a qubit_op the first time around as computed by qubit_op.to_opflow().to_matrix_op() which ends up with a MatrixOperator.Before qiskit-community/qiskit-aqua#1154 the next operator (a TensoredOp) passed (X ^ qubit_op ^ Z) would not cause an issue. However if it were passed in as the first one then the warning about Mixed Operators is raised. It seems that having the MatrixOperator 'locked-in' from the first operator it was able to at least not fail. The result was never checked and I do not know if things work as expected or not. Following qiskit-community/qiskit-aqua#1154 the change of the operator will cause it to autoselect an expectation via the factory and it will raise the error whether passed in first or second in the reuse test as above. (If MatrixExpectation instance is explicitly passed, meaning that there is no longer any auto-selection and VQE will used that until such time, if ever, its changed, then the TensoredOp is accepted).

Since there seems to be some difference in here in behavior around the factory which claims the expectation of mixed operators is not supported, and the fact that its accepted if a MatrixOperator is provided which seems to infer some under the covers conversion is happening I think this need investigating and improving in some way. Maybe the factory message should be more that the factory does not determine the most efficient way to convert mixed operators to determine the right expectation object. Thats a bit less blunt than expectation of mixed operators is not supported. Either way I think there is room for improvement here.

[woodsp-ibm]

Algorithms have been refactored over to use primitives and observable estimation (expectations) are now handled by these. As such I am closing this issue.