[WIP] Pauli evolve in rust

[ShellyGarion]

Summary

Pauli evolution by a Clifford in rust.
This is needed for #14657.

Details and comments

• This currently implements pauli.evolve(clifford, frame="s"). For pauli.evolve(clifford, frame="h") we should calculate clifford.adjoint().
• The rust code should be written more efficiently.
• performance benchmarks should be added (n = 50, 100, 200...)

[coveralls]

Pull Request Test Coverage Report for Build 18906329844

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

• 292 of 292 (100.0%) changed or added relevant lines in 1 file are covered.
• 1964 unchanged lines in 56 files lost coverage.
• Overall coverage decreased (-0.007%) to 88.215%

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Files with Coverage Reduction	New Missed Lines	%
crates/cext/build.rs	1	96.77%
crates/circuit/src/classical/expr/binary.rs	1	98.68%
crates/circuit/src/classical/expr/index.rs	1	98.15%
crates/circuit/src/classical/expr/value.rs	1	97.87%
crates/circuit/src/converters.rs	2	97.33%
crates/circuit/src/lib.rs	2	94.57%
qiskit/transpiler/passes/optimization/consolidate_blocks.py	2	96.92%
crates/circuit/src/classical/expr/stretch.rs	3	93.65%
crates/qasm2/src/lex.rs	3	92.03%
crates/quantum_info/src/pauli_lindblad_map/phased_qubit_sparse_pauli.rs	3	94.82%

Totals
Change from base Build 18229727033:	-0.007%
Covered Lines:	93959
Relevant Lines:	106511

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💛 - Coveralls

[jakelishman]

Shelly: since this says it's needed for an issue which is already solved (the Litinski transform), is this PR something we're still doing?

[ShellyGarion]

Shelly: since this says it's needed for an issue which is already solved (the Litinski transform), is this PR something we're still doing?

There are other use-cases of porting the Pauli and Clifford methods to rust, such as some of the add-ons.
Let's keep this PR open for now.

[jakelishman]

Ok, then heads up: I'll ask about prioritisation and timelines for it within the Qiskit 2.3 milestone at the meeting.

[ShellyGarion]

I think that this PR is now superseded by #15974.
we should consider how to properly externalize the evolve method which is a Clifford class method there (get_inverse_pauli)