Add explicit `controlled-U` bloqs for single qubit unitaries `U` and annotate them with costs / decompositions

[tanujkhattar]

Some bloqs which need this are

• Rotations - Rx, Ry, Rz
• Hadamard - CH

etc.

[mpharrigan]

CHadamard is implemented. I've annotated it with 2 rotations and 4 cliffords with the following description:

This is based on the decomposition provided by cirq.decompose_multi_controlled_rotation which uses three cirq.MatrixGate's to do a controlled version of any single-qubit gate. The first MatrixGate happens to be a clifford, Hadamard operation in this case. The other two are considered 'rotations'.

[tanujkhattar]

We should update the annotation with 2 T gates + 9 cliffords instead of 2 rotations as per my comment in https://github.com/quantumlib/Qualtran/issues/233

Here is a quirk link that shows the decomposition

Specifically, this part:

[mpharrigan]

CHadamard and CZPowGate exist.

CRx, CRy, CRz, CXPowGate, CYPowGate are needed.

I've encountered CS and CT in the library; we need those as well.

---

For Rx(theta) and friends; we do angle simplification in the QECGatesCost resource counting. We look for angles that are actually clifford or the T gate. The existing hacky logic (that links to this issue) treats any Controlled(Rotation) as one rotation

[mpharrigan]

Circuits for CT https://quantumcomputing.stackexchange.com/a/13135

[mpharrigan]

A user points out that the QECGatesCost doesn't accurately track clifford count for controlled rotations.