Qiskit / qiskit-fermions / 40712548054

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Refactor `QDrift` (#406)

* fix(transpiler): compare array-valued synthesis settings in MergeEvolutions

`MergeEvolutions` decides whether two neighbouring `Evolution` gates
decompose the same way by comparing `vars()` of their synthesis methods
as whole dicts. A method that holds an array, such as sampling weights,
makes that comparison raise `ValueError` ("truth value of an array is
ambiguous") instead of answering, because `dict.__eq__` calls `==` on
the values and an array has no single truth value.

Compare the settings entry by entry and use `np.array_equal` for arrays.
Gates whose arrays differ are now left unmerged, as they must be, since
merging them would pick one way of decomposing for both. Equal arrays in
distinct objects describe the same method and merge.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

* refactor(circuit): make qDRIFT a fermion-to-fermion synthesis method

qDRIFT was the one Trotterization that lived outside the synthesis
framework, as a pass of its own, whereas upstream Qiskit treats it as a
product formula on an equal footing with Lie and Suzuki. Move the
sampling into `FermionicQDrift`, registered as `Evolution.QDrift,` so it
is chosen like any other method through `F2FSynthesis`.

The method is stateless: it derives the distribution from the gate it is
given and holds only num_terms, weights and rng. That is why the guard
against reusing a weights array on several gates became a per-gate
length check; a stateless method cannot count the gates it saw.

`filter_trivial` stays in `QDriftTrotterization`, now slimmed down to
what a method cannot do: tracking occupation across the whole circuit to
reject draws that cannot move a particle. It takes the method as its
argument and draws through the same sampler, so both paths share one
implementation of the protocol. Using the pass is what enables the
filtering, so the flag is gone.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

* feat(transpiler): m... (continued)

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