Oxidize `NLocal` & family

[Cryoris]

Summary

Part of #13046: create the n_local function and port the internals to Rust. This will include other parts of the NLocal family, such as TwoLocal, EfficientSU2, RealAmplitudes etc. EvolvedOperatorAnsatz is potentially a bit more involved and might be done in a follow-up.

Details and comments

The new code is particularly fast when dealing with gates we already have in Rust and that don't need any special re-parameterization. In this case:

the new code is ~22x faster for 100 qubits, full entanglement and 10 reps

num qubits: 10, speedup: 9.075
main: 0.005 +- 0.004
this: 0.001 +- 0.000

num qubits: 50, speedup: 18.138
main: 0.063 +- 0.014
this: 0.003 +- 0.003

num qubits: 100, speedup: 22.011
main: 0.251 +- 0.034
this: 0.011 +- 0.007

num qubits: 200, speedup: 26.829
main: 0.957 +- 0.034
this: 0.036 +- 0.010

But if custom gates or special parameterizations are used (e.g. RXGate(x + 3 * y)) we need to go back to Python space to correctly handle the parameter logic. This slows down the code and in this case:

the new code is ~3.5x faster for 100 qubits, linear entanglement (full took too long) and 10 reps

num qubits: 10, speedup: 4.594
main: 0.027 +- 0.006
this: 0.006 +- 0.000

num qubits: 50, speedup: 3.947
main: 0.162 +- 0.006
this: 0.041 +- 0.011

num qubits: 100, speedup: 3.666
main: 0.366 +- 0.031
this: 0.100 +- 0.019

To do

• [x] Improve docstrings
• [x] Make the entanglement handling rust-side a bit better to understand instead of a 4-times nested vec
• [ ] ~~Use n_local in NLocal (i.e. fast path for Python code)~~ This might not be possible since NLocal works with QuantumCircuits as blocks, but n_local needs gates. Functionally it'd be the same but the circuits are nested differently, which is not backward compatible. We could add a fast-path in case the inputs are not circuits but gates.
• [x] Add the family members, like efficient_su2 etc.

[coveralls]

Pull Request Test Coverage Report for Build 11723083102

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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• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 530 of 530 (100.0%) changed or added relevant lines in 14 files are covered.
• 843 unchanged lines in 32 files lost coverage.
• Overall coverage increased (+0.1%) to 88.87%

---

Files with Coverage Reduction	New Missed Lines	%
qiskit/transpiler/target.py	1	96.13%
qiskit/circuit/parameter.py	1	98.36%
qiskit/synthesis/unitary/qsd.py	1	97.58%
qiskit/compiler/transpiler.py	1	93.14%
qiskit/circuit/library/arithmetic/adders/draper_qft_adder.py	1	96.97%
qiskit/circuit/library/generalized_gates/gms.py	2	94.44%
qiskit/circuit/library/generalized_gates/rv.py	2	84.62%
qiskit/transpiler/passes/optimization/consolidate_blocks.py	2	96.15%
crates/qasm2/src/lex.rs	3	92.48%
qiskit/transpiler/preset_passmanagers/generate_preset_pass_manager.py	3	97.83%
<!--	Total:	843

Totals
Change from base Build 11683622570:	0.1%
Covered Lines:	78307
Relevant Lines:	88114

---

💛 - Coveralls

[qiskit-bot]

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

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

[Cryoris]

069f45c added tests for the flagged lines in Coveralls (for the new functions, not for the existing classes), so I think we should have the 100% on that 🙂