[WIP] Move utility functions _inverse_pattern and _get_ordered_swap to Rust

[jpacold]

Summary

This PR starts addressing #12225. I moved the implementations of two functions from qiskit/synthesis/permutation/permutation_utils.py to Rust.

Details and comments

• Created permutation.rs

  • I added some checks to ensure that inputs are actually permutations. Otherwise, _get_ordered_swap uses the same logic as it did in Python.
  • Performance is better than Python, but sensitive to input type (more notes below)

• Added a module qiskit._accelerate.permutation and a submodule qiskit._accelerate.permutation.permutation_utils (following the structure of the existing Python modules). The wrapped functions are in the permutation_utils submodule.

• Replaced the function bodies in permutation_utils.py with calls to the Rust functions.

• Added tests.

Performance

As expected, this implementation of _get_ordered_swap is faster than the Python version. However, the input type is expected to be an array of int64 and there is a performance cost for converting from any other type. On my machine:

Input type	Speedup over Python
Numpy array (int64)	~15x
Numpy array (int32, uint32, or uint64)	~4x
Python list	~7x

For now, I don't think this matters much, because the bottleneck in synth_permutation_basic is constructing the circuit, but it is something that might need to be optimized later on.

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All committers have signed the CLA.

[coveralls]

Pull Request Test Coverage Report for Build 9109062685

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

• 84 of 84 (100.0%) changed or added relevant lines in 4 files are covered.
• 7 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.03%) to 89.629%

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Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	7	92.62%

Totals
Change from base Build 9100255975:	0.03%
Covered Lines:	62371
Relevant Lines:	69588

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💛 - Coveralls

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