Qiskit / qiskit-fermions / 30005363214

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Adds the `PrepareSlaterDeterminant` gate (#200)

* feat(circuit): add PrepareSlaterDeterminant gate

This gate is the composition of an InitializeModes reference occupation
followed by an OrbitalRotation. Bundling the two lets a later synthesis
plugin exploit the known occupation to use the rectangular
givens_decomposition_slater for a reduced-gate-count decomposition,
rather than the full square decomposition an OrbitalRotation alone needs.

Under simulation the gate is validate-then-rotate (mirroring the post-#198
InitializeModes/UCJ convention): its definition walks an InitializeModes
validator then the OrbitalRotation. That construction guarantees the
correctness contract the upcoming merge optimization pass depends on --
fusing an InitializeModes and an OrbitalRotation into a single
PrepareSlaterDeterminant leaves the simulated state exactly unchanged.

Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>

* feat(transpiler): add reduced Slater determinant synthesis plugin

GivensDecompositionSlaterDeterminantSynthesis lowers a
PrepareSlaterDeterminant using the rectangular givens_decomposition_slater:
it realizes only the m occupied orbitals of the rotation (the occupied
columns of the rotation unitary), emitting at most m(n-m) XXPlusYYGates and
no phase gates -- versus the n(n-1)/2 brick-wall plus n phases the full
OrbitalRotation synthesis needs. The reduced decomposition drops the
occupied-space and global phases, so the determinant is prepared up to a
global phase (physically irrelevant for state preparation).

Registered as the PrepareSlaterDeterminant.GivensDecompositionSlater
entry-point and documented in the builtin synthesis plugin table. Tests
check the reduced gate count and verify the prepared state matches the
trusted InitializeModes + square-OrbitalRotation synthesis up to a global
phase (which also confirms the reference-seeding indexing).

Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>

* feat(transpiler): lower Prepa... (continued)

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