Qiskit / qiskit / 23049040177 / 1
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Make remove identity equiv multithreaded (#14719)

* Make remove identity equiv multithreaded

The RemoveIdentityEquiv transpiler pass analyzes each gate in the
circuit to check if it's equivalent to an identity operation to check
for removal. This checking was previously always performed serially but
there is no data dependency between the checks so they can be performed
in parallel using multithreading. While in practice the node removal
can end up dominating the runtime of the pass and must be performed
serially so this limits the potential speedup in cases with a lot of
nodes to remove. But in practice there aren't typically many gates that
get removed so there are real performance benefits available from doing
the analysis in parallel.

* Avoid an allocation for node indices in parallel path

* Use newer pass code after rebase

When this pass was updated to use main it ignored all the structural
changes in the file and was duplicating the logic of the pass which had
already been factored out into a standalone function. This commit
updates the new parallel pass to use this function and removes the
duplication. As a side-effect because the new function returns a
PyResult because of PauliEvolutionGate handling this PyResult needs to
be propogated out from the function now. This is at least until #15450
is implemented avoid the need to use python at all here.

* Add docs about threading to C API docs too

* Use a constant for PARALLEL_THRESHOLD

* Add release note

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Source Files on job 23049040177.1