Qiskit / qiskit-fermions / 33877189194

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feat(transpiler): add a FermionicTrotterization pass (#316)

An `Evolution` gate carries the synthesis method it is decomposed with, which
means choosing one per gate -- and threading that choice through everything that
constructs an `Evolution`, including `UCC` and `UCJ`, which build their own
internally. This pass applies one method to every `Evolution` in a circuit, so the
choice can be made once for a whole pipeline.

The pass selects a synthesis method rather than expanding the evolution there and
then. That keeps each `Evolution` a single node for the passes that follow, which
matters for `RelabelModes`: it reads the operator of every `Evolution` to build its
mode-relabeling model, and expanding first would hand it one fragment per factor
instead of a whole operator.

`QDriftTrotterization` makes the opposite choice, and the asymmetry is deliberate:
its sampling is random and one-shot, so deferring it would draw a different sample
each time the definition was rebuilt. A deterministic product formula is a pure
function of the gate, so deferring costs nothing.

The optional `filter` predicate exists because not every operator wants the same
formula. A `UCJ`'s diagonal-Coulomb evolutions have all-commuting groups, so any
order synthesizes them exactly and a higher one only adds depth.

Note that the pass substitutes a *new* gate rather than assigning to `node.op`.
Qiskit copies gates with a shallow `__dict__` copy, so a gate instance can be
shared between circuits, and mutating it in place would retroactively change the
synthesis of every other circuit holding the same object.

Refs #298

Co-authored-by: Claude Opus 5 <noreply@anthropic.com>

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