`MCMTGate` & plugins

[Cryoris]

Summary

Make the MCMT circuits a gate with pluggable synthesis method, plus port the V-chain synthesis to Rust. This is part of #13046.

Details and comments

Even though the focus of this PR is the restructuring into a block that the compiler can reason about, there's also a nice speedup due to the port to Rust:

New runtime / Old runtime = 0.63 (geo mean)

``` -- n = 50 ntarg = 1 main: 5.604e-04 +- 1.514e-04 this: 3.490e-04 +- 1.771e-04 fraction: 0.64 -- n = 50 targ = 5 main: 5.612e-04 +- 1.180e-04 this: 3.051e-04 +- 1.267e-04 fraction: 0.54 -- n = 50 targ = 25 main: 7.027e-04 +- 1.188e-04 this: 3.727e-04 +- 1.225e-04 fraction: 0.53 -- n = 200 targ = 1 main: 2.074e-03 +- 2.704e-04 this: 1.631e-03 +- 2.565e-03 fraction: 0.78 -- n = 200 targ = 20 main: 2.693e-03 +- 2.488e-03 this: 1.646e-03 +- 2.433e-03 fraction: 0.62 -- n = 200 targ = 100 main: 2.616e-03 +- 2.670e-04 this: 1.880e-03 +- 2.594e-03 fraction: 0.71 -- n = 1000 targ = 1 main: 1.087e-02 +- 4.227e-03 this: 6.820e-03 +- 5.478e-03 fraction: 0.62 -- n = 1000 targ = 100 main: 1.251e-02 +- 6.234e-03 this: 7.843e-03 +- 6.380e-03 fraction: 0.62 -- n = 1000 targ = 500 main: 1.415e-02 +- 5.152e-03 this: 9.360e-03 +- 6.755e-03 fraction: 0.66 ```

[qiskit-bot]

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

• @Cryoris
• @Qiskit/terra-core
• @ajavadia
• @kevinhartman
• @mtreinish

[coveralls]

Pull Request Test Coverage Report for Build 11176416050

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.

• For more information on this, see Tracking coverage changes with pull request builds.
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• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 193 of 209 (92.34%) changed or added relevant lines in 9 files are covered.
• 14 unchanged lines in 2 files lost coverage.
• Overall coverage increased (+0.02%) to 88.893%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/transpiler/passes/synthesis/hls_plugins.py	25	27	92.59%
crates/accelerate/src/synthesis/multi_controlled/mcmt.rs	94	101	93.07%
qiskit/circuit/library/generalized_gates/mcmt.py	57	64	89.06%
<!--	Total:	193	209	92.34%	-->

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/parse.rs	6	97.61%
crates/qasm2/src/lex.rs	8	91.48%
<!--	Total:	14		-->

Totals
Change from base Build 11161049152:	0.02%
Covered Lines:	74476
Relevant Lines:	83782

---

💛 - Coveralls

[ShellyGarion]

thanks @Cryoris for opening this PR! It also handles issue #12863. What do you think about issue https://github.com/Qiskit/qiskit/issues/10698 ? I think it should be a small addition, but could also be handled in a follow-up PR.

[alexanderivrii]

Lol, the tests have failed due to cargo clippy warnings. And I caught one of them in the review. :)

[alexanderivrii]

Thank you very much! As per your question, could you please add a table for documenting MCMT synthesis plugins (in hls_plugins.py, the output should be in https://docs.quantum.ibm.com/api/qiskit/transpiler_synthesis_plugins) and the new synthesis function (the output should be in https://docs.quantum.ibm.com/api/qiskit/synthesis). Also this deserves a release note, listing new functionality and deprecations.

[mtreinish]

This has a merge conflict now that https://github.com/Qiskit/qiskit/commit/642debf8b2433aa2d814341b96fdc6803b53cbc0 has merged. The interface for CircuitData::from_packed_operations has changed to include a result and its usage here will need to be updated.

[Cryoris]

Done in 60a82a3 👍🏻