Qiskit / qiskit-fermions / 36869250772

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feat: support `measure` instructions on `FermionicCircuit` (#368)

* fix: preserve classical bits through the transpilation stages

Three optimization passes rebuilt their output DAG by calling
`apply_operation_back` with `qargs` only. `DAGCircuit` defaults `cargs` to an
empty tuple and does not complain when it is omitted, so any copied-through
instruction carrying classical bits silently lost them: a one-clbit measurement
became a zero-clbit one, and the circuit was corrupted rather than rejected.

`MergeSlaterDeterminantPreparation` is the one that matters most, because it
runs in the default Jordan-Wigner preset. The resulting failure surfaces far
from its cause -- a bare `StopIteration` from inside a simulator iterating the
(now empty) `clbits` of a measurement -- so this had to be fixed before any
measurement instruction could be trusted through the pipeline.

Separately, `F2QSynthesis` builds its output DAG from scratch (deliberately, to
keep the wire graph consistent) and copied only the classical *registers*. A
clbit outside any register was therefore dropped, and emitting an operation onto
it failed with an opaque `KeyError` naming an anonymous bit. The clbits are now
copied in the input's own order before the registers are re-added, which also
pins the clbit indices -- those indices are what the positions of a sampled
bitstring mean.

None of this was reachable through the public API before, since nothing could
put a classical instruction on a `FermionicCircuit`; it is fixed first so the
measurement support built on top starts from a working base.

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

* refactor: introduce FermionicInstruction as the base fermionic op

`FermionicGate` extends `qiskit.circuit.Gate`, whose `__init__` fixes the
classical-bit count at zero. That makes it structurally impossible for a
measurement to be a `FermionicGate`, so the two places that decide whether an
operation belongs on a fermionic circuit -- `Fermi... (continued)

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