Port TwoQubitControlledUDecomposer to rust

[ShellyGarion]

Summary

close #12907

Details and comments

depends on #13168

Performance improvement:
Synthesizing 100 random 4x4 unitary matrices into each of the basis gates [RXX, RYY, RZZ, RZX, CRZ, CPhase] takes:
in Python: 20.57 sec
in Rust: 8.85

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core
• @levbishop

[coveralls]

Pull Request Test Coverage Report for Build 11812175968

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

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Details

• 352 of 380 (92.63%) changed or added relevant lines in 2 files are covered.
• 1761 unchanged lines in 86 files lost coverage.
• Overall coverage increased (+0.2%) to 88.929%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
crates/accelerate/src/two_qubit_decompose.rs	345	373	92.49%

Files with Coverage Reduction	New Missed Lines	%
crates/accelerate/src/unitary_synthesis.rs	1	92.2%
qiskit/circuit/library/boolean_logic/inner_product.py	1	96.0%
crates/qasm2/src/expr.rs	1	94.02%
qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py	1	94.54%
qiskit/circuit/store.py	1	97.06%
qiskit/circuit/library/iqp.py	1	96.15%
crates/qasm2/src/lex.rs	1	92.73%
qiskit/circuit/library/boolean_logic/quantum_or.py	1	98.08%
qiskit/circuit/library/arithmetic/adders/draper_qft_adder.py	1	96.97%
qiskit/circuit/parameter.py	1	98.36%

Totals
Change from base Build 11582517625:	0.2%
Covered Lines:	79333
Relevant Lines:	89209

---

💛 - Coveralls

[mtreinish]

Overall the code looks good, I left a few inline comments on how to simplify or optimize things a bit. The biggest concern I have right now though is the backwards incompatibility of the API. This PR restricts the gate objects that TwoQubitControlledUDecomposer class can work with to just standard gates defined in Qiskit. This wasn't a limitation before the rust rewrite and would be considered a breaking api change. However, I'm not sure the class is considered public, it's never been externally documented from what I can tell. I'm curious of your thoughts on this though because I'm not sure what you're thinking about making this class public or not.

[mtreinish]

Do you think we should treat this class as public at all? The python space definition wasn't limited to standard gates, it would support any python space Gate object including a custom defined gate. This will error in the case of a custom PyGate though.

[ShellyGarion]

Currently, rxx_equivalent_gate could be only a StandardGate since in the code we need to invert it, and there is currently no inverse function for other types, see these lines:

                let circ_c = self.to_rxx_gate(gamma)?;
                ...
                for gate in circ_c.gates.into_iter().rev() {
                    let (inv_gate_name, inv_gate_params, inv_gate_qubits) = invert_2q_gate(gate);

[ShellyGarion]

As for making this class public, I think that it may be useful. Should we do it now or only after it's added to the UnitarySynthesis transpiler pass #13320?

[mtreinish]

I'd say lets do it later as the PR is large and intricate enough that we should review the change making it public on its own.

[ShellyGarion]

Overall the code looks good, I left a few inline comments on how to simplify or optimize things a bit. The biggest concern I have right now though is the backwards incompatibility of the API. This PR restricts the gate objects that TwoQubitControlledUDecomposer class can work with to just standard gates defined in Qiskit. This wasn't a limitation before the rust rewrite and would be considered a breaking api change. However, I'm not sure the class is considered public, it's never been externally documented from what I can tell. I'm curious of your thoughts on this though because I'm not sure what you're thinking about making this class public or not.

I would appreciate @levbishop opinion regarding this question as he wrote the original Python code.
I agree that as far as I know this class has never been published as part of Qiskit API. We can make it public if we think it will be useful. perhaps after adding it to the UnitarySynthesis transpiler pass #13320.
In addition, in the tests we test only standard gates:

qiskit/test/python/synthesis/test_synthesis.py

Line 1429 in fbfe738

for gate in [RXXGate, RYYGate, RZZGate, RZXGate, CPhaseGate, CRZGate]:

So I wonder if this class was ever meant to be used with basic gates that are not standard gates.
Anyway, since the Pulse library is being deprecated in #13164, the users will not be able to calibrate their own basic gates with Qiskit and hence this code will be useful only for standard gates.

[mtreinish]

This LGTM now. I have one small suggestion on the test code but once that's fixed I think we're good to merge.