From Projected Subspaces to Full-Space Implementations: Representation-Equivalence Audits for Open-Shell ADAPT-VQE
A variational state optimized in a symmetry-projected space need not be the state prepared by exponentiating the corresponding unprojected parent generators. For an orthogonal target-space projector $P$, $Q=I-P$, and an anti-Hermitian generator $A$, exact equivalence for all amplitudes requires target-space invariance,...