Qiskit / qiskit / 8282173373

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Oxidize TwoQubitWeylDecomposition (#11946)

* Oxidize TwoQubitWeylDecomposition

This commit is part 1 of migrating the default 2q unitary synthesis to leverage
parallel rust described in #8774, the eventual goal is to be able to
run unitary synthesis in parallel for all the unitary matrices in a
circuit in a single call from the `UnitarySynthesis` pass. This commit
lays the initial groundwork for doing this by starting with the largest
piece of the default 2q unitary synthesis code, the
TwoQubitWeylDecomposition class. It migrates the entire class
to be a pyclass in rust. There is still a Python subclass for it that
handles the actual QuantumCircuit generation and also the string
representations which are dependent on circuit generation. The goal of
this is to keep the same basic algorithm in place but re-implement
as-is in Rust as a common starting point for eventual improvements to
the underlying algorithm as well as parallelizing the synthesis of
multiple 2q unitary matrices.

* Fix typo in closest_partial_swap()

This commit fixes a typo the formula in the function.
This is the same fix from #11953.

Co-authored-by: Shelly Garion <46566946+ShellyGarion@users.noreply.github.com>

* Run black and lint

* Fix potential imaginary component sign flip in determinant

* Run cargo fmt

* Simplify using numpy eigh example comment

* Add missing checks to decompose_two_qubit_product_gate()

* Use rng first trial from Python implementation

To aid in debugging and rule out rng differences causing different
results this commit switches the first iteration of the randomized loop
to have hard coded values that are identical to what the rng in numpy
was returning. It is very unlikely that this will have any impact
because the specific random numbers used shouldn't matter, this is
mostly to just rule it out as a possibility in debugging the remaining
test failures.

* Fix whitespace in error message

* Fix assert check

* Fix missing multiplier on specialized... (continued)

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