Qiskit / qiskit-fermions / 40293829302

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feat(transpiler): merge adjacent Evolution gates of the same operator (#396)

Two evolutions under the same operator compose exactly,
exp(-i t2 H) exp(-i t1 H) = exp(-i (t1 + t2) H), so neighbouring gates
that share an operator can always be fused. Palindromic product formulas
produce such neighbours at every seam: between repetitions, and between
the sub-sweeps of the higher-order Suzuki recursion.

Fusing inside FermionicSuzukiTrotter only sees the seams of a single
synthesis. The same neighbours also arise across gate boundaries (repeated
circuits, consecutive UCC/UCJ layers, qDRIFT samples), so add a general
MergeEvolutions pass in the style of MergeOrbitalRotations. Unlike orbital
rotations, a run of Evolution gates does not compose unconditionally, so
the pass splits each run into stretches of equivalent operators and merges
only gates that agree on wires, operator type, atomicity and synthesis. The
atomic and synthesis checks keep a merge from turning a terminal factor into
a splittable one, or changing how a gate decomposes.

Keep the in-synthesis fusion as well, behind a `merge_adjacent` flag that
defaults to on: it is O(n), needs no operator comparison, and also applies
to a bare `decompose()` without the transpiler. This changes the default
gate sequence for reps > 1 and order >= 4 (the guide's reps=4 count drops
from 20 to 17), hence the upgrade note; `merge_adjacent=False` restores it.

Co-authored-by: Claude Sonnet 5.5 <noreply@anthropic.com>

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