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 10850942524

Details

• 189 of 204 (92.65%) changed or added relevant lines in 9 files are covered.
• 2 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.02%) to 88.924%

---

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	92	98	93.88%
qiskit/circuit/library/generalized_gates/mcmt.py	55	62	88.71%

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	2	92.98%

Totals
Change from base Build 10838928352:	0.02%
Covered Lines:	73583
Relevant Lines:	82748

---

💛 - Coveralls

[ShellyGarion]

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