Qiskit / qiskit-fermions / 40322929403

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fix: visit DAG nodes in circuit order in passes that rebuild the circuit (#401) (#402)

`F2QSynthesis` walked the input DAG with `op_nodes()`, which returns the
nodes in storage order, not in the order of their dependencies. The two
agree for a circuit built by appending, but not after a pass has
replaced a node by a sub-circuit (`substitute_node_with_dag`): the
replacement is stored after everything already there, so the factors of
two successive replacements end up interleaved. The output is then a
well-formed circuit for a different unitary, since the gates of
neighbouring replacements share qubits and do not commute. Nothing
fails; the result is just wrong.

`RelabelModes` and `QDriftTrotterization` rebuild their output node by
node in the same way and had the same problem. For qDRIFT the occupation
tracking behind `filter_trivial` additionally depends on seeing
`InitializeModes` and `OrbitalRotation` gates in the order they act. All
three now iterate with `topological_op_nodes()`.

The passes that only substitute nodes in place
(`FermionicTrotterization`) are safe with either order, and the
iteration that merely gathers excitations for the `RelabelModes`
permutation model is order-insensitive, so both are left alone.

The regression tests trotterize evolutions in fermionic space, so each
is replaced by several gates. For the synthesis they compare the lowered
circuit with the ordered product of the exact group evolutions (off by
about 0.26 without the change, 1e-16 with it); for `RelabelModes` and
`QDriftTrotterization` they check that the circuit order survives the
pass. They do not involve any of the orbital-rotation machinery that
surfaced this: any pass that substitutes nodes could hit it.


(cherry picked from commit 196301357)

Co-authored-by: Max Rossmannek <21973473+mrossinek@users.noreply.github.com>
Co-authored-by: Claude Sonnet 5.5 <noreply@anthropic.com>

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