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Rust Shannon Decomposition (#14797)

* [WIP] Port QSD to rust

This commit implements the quantum shannon decomposition algorithm in
rust based on the current Python qs_decomposition function implementation.
This function doesn't support the arbitrary 1q and 2q decomposer
arguments so the Python version of the function is retained and used
while those arguments are supported.

Fixes #12213

* Added ZXZ decomposition; working on random unitaries for 4 qubits but failing on 5

* Fix merge conflicts

This commit fixes merge conflicts as the original qsd implementation in
the first commit is about one month old and the APIs it used on main
have changed slightly in the intervening time.

* Fix failures for 2-qubit matrices by using closest unitary

* Code cleanup

* Changes according to PR review

* A2 optimization fixes

* Fix for axes handling in `extract_multiplex_blocks`

* Linting

* add condition number calculation (not actually needed for QSD but may be generally useful)

* add verification checks for linear algebra methods

* replace svd by try_svd

* update atol

* remove verify

* add closest_unitary

* remove closest_unitary

* update atol as a function of the number of qubits

* add move verification methods. add closest_unitary in demultiplex.

* update tol in tests to 1e-6

* minor fix

* update EPS in internal verification

* update EPS in internal verification

* update EPS in internal verification

* update tolerance in tests

* try to make linux-arm tests pass

* replace nalgebra SVD by faer SVD.
Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* update SVD to faer, updating bounds, formatting

* update bounds in tests

* update bounds, formatting

* update bounds in tests

* debug_assert in verification functions

* ignore clippy errors in stack!

* replace zero by 0 in stack

* fix lint errors

* Changes according to PR review

* Switch to default faer-nalgebra conversions, Partially return closest_unitary

* Return all closest_unita... (continued)

697 of 785 new or added lines in 8 files covered. (88.79%)

172 existing lines in 4 files now uncovered.

92741 of 105108 relevant lines covered (88.23%)

534622.06 hits per line

Relevant lines Covered
105108 RELEVANT LINES 92741 COVERED LINES
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17643780183 gh-readonly-queue/main/pr-14797-d595578b62e10f47b6f2515a9cdd687b898ac9e4 Rust Shannon Decomposition (#14797) * [WIP] Port QSD to rust This commit implements the quantum shannon decomposition algorithm in rust based on the current Python qs_decomposition function implementation. This function doesn't support the arbit... push web-flow github
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