Should analytical decompositions return an empty list when decomposing identity operation?

[tanujkhattar]

We have many analytical decompositions in https://github.com/quantumlib/Cirq/tree/master/cirq-core/cirq/transformers/analytical_decompositions which are used to decompose a given unitary matrix / operation into a specific target gateset (eg: cz/fsim/sqrt_iswap etc.). The behavior of these decompositions when trying to decompose an identity operation currently differs across implementations -- some return an empty list while some return only single qubit ops and others return a longer decomposition. Eg:

>>> import cirq
>>> import numpy as np
>>> eye = np.eye(4)
>>> q0, q1 = cirq.LineQubit.range(2)
>>> cirq.two_qubit_matrix_to_sqrt_iswap_operations(q0, q1, eye)
[]
>>> cirq.two_qubit_matrix_to_operations(q0, q1, eye, allow_partial_czs=False, clean_operations=False)
[cirq.S(cirq.LineQubit(0)), (cirq.Z**1.5).on(cirq.LineQubit(0))]

There are also other inconsistencies in the API's of these analytical decompositions. For example:

1. Calling a list of cleanup operations on the decomposed operation list:

• two_qubit_matrix_to_operations has a default clean_operations=True flag in the constructor which calls a long list of cleanup operations on the list of final decomposed operations.
• two_qubit_matrix_to_ion_operations does not have a configurable cleanup_operations=True flag and always calls the same list of cleanup operations on the final decomposed operations
• two_qubit_matrix_to_sqrt_iswap_operations has no flag and does not call the cleanup operations on the final decomposed operations.

2. API of the analytical decompositions:

• two_qubit_matrix_to_* versions expect a q0, q1, mat
• decompose_two_qubit_interaction_into_four_fsim_gates expects as Union['cirq.Operation', 'cirq.Gate', np.ndarray, Any] and a qubits: Sequence['cirq.Qid'] = None instead of q0, q1 etc.
• decompose_cphase_into_two_fsim expects CZPowGate and FSimGates (not operations or matrices)

[tanujkhattar]

• We should return cirq.I or [] .
• Let's fix the API and make things more consistent.