Qiskit / qiskit-fermions / 34605419033

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Add `apply` to the `FermionicTrotterization` pass (#346)

* fix(transpiler): use global mode indices in RelabelModes

`find_permutation` read each `Evolution`'s operator directly to gather the
excitations it feeds to `build_excitation_span_minimization_model`. Those mode
indices are local to the gate: a `FermionicEvolutionSynthesis` narrows every
factor it emits onto that factor's support, leaving the factor's position in the
register encoded in the node's `qargs` alone. The model is defined over the
register's modes, so the two disagree for any circuit whose evolutions have been
decomposed.

The effect was not a permutation that merely came out worse. Every narrowed
two-mode factor was gathered as the excitation (0, 1) no matter which modes it
actually coupled, so a long-range coupling -- the excitation a span-minimizing
model most wants to see -- disappeared from the model entirely, and the pass
silently optimized a Hamiltonian that was not the circuit's. Nothing raised,
because local indices are perfectly valid indices.

Translate through `qargs` before gathering, reusing qdrift's `_global_modes`.
This mirrors what the fermion-to-qubit stage already does with the same operators
(`MapperFnEvolutionSynthesis` lifts the local operator onto its global mode
indices before mapping), so both consumers now agree on what a factor's modes
mean.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

* feat(transpiler): apply the synthesis in FermionicTrotterization

The pass only tagged each `Evolution` with a synthesis method and left the
expansion to a separate `Decompose("Evolution")`. The stated reason was to keep
whole operators available to later passes, `RelabelModes` above all, but that
premise does not hold: `RelabelModes.run` rewires by permuting `qargs` and never
touches an operator, and its automatic model now translates through `qargs`
before gathering excitations, so it reads a decomposed circuit as faithfully as
an undecomposed one. Deferring ... (continued)

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