Make sure all cirq gates decompose to XPow/YPow/ZPow/CZPow + Measurement

[tanujkhattar]

As part of https://tinyurl.com/cirq-organize-decompose-rfc, we want to make sure that all cirq gates decompose to the XPow/YPow/ZPow/CZPow + Measuremet gateset.

This issue is to track all the gates where we need to explicitly add a _decompose_ method to make sure all decompositions end on the above target gateset.
We should also discuss what happens for gates where trivial decomposition is not present?

1. MatrixGates : Should we add an analytical decomposition to the _decompose_ method of matrix gates?
2. Same question as above for ControlledGates.

P1 - I need this no later than the next release (end of quarter)

Part of #3242

[vtomole]

Should we add an analytical decomposition to the decompose method of matrix gates

How would this work? Is it possible to decompose any arbitrary MatrixGate into a target gateset?

[tanujkhattar]

@vtomole Yes. We have utilities in Cirq to decompose any arbitrary 2q Matrix Gate into the CZ gateset (see See https://github.com/quantumlib/Cirq/blob/master/cirq-core/cirq/transformers/analytical_decompositions/two_qubit_to_cz.py) and there's an open issue #4022 to add compilation of any arbitrary unitary to 1/2q gates

[daxfohl]

I also think we should have MeasurementGate with invert_mask decompose into a series of pre- and post-measurement Xs that represent the invert mask (and the subsequent uninversion), so that "measurement" can be a uniquely defined thing.