Abstract
Excitation-energy accuracy is currently the dominant validation criterion for excited-state quantum algorithms. We show that this practice can conceal severe failures in physically relevant observables. Using quantum equation-of-motion (qEOM) as a representative case study, we demonstrate that excitation-energy accuracy and observable accuracy can become effectively decoupled. While both qEOM and Quantum Subspace Expansion (QSE) yield highly accurate excitation energies, their predictions for dipole moments differ dramatically, establishing observable fidelity as an independent benchmark dimension that cannot be inferred from energy agreement alone. To investigate the origin of this discrepancy, we introduce anti-Hermitized qEOM (AqEOM), an a posteriori anti-Hermitian transformation applied to the qEOM-derived state-transfer operator before direct property evaluation. Across multiple systems, AqEOM substantially improves dipole moments, state-overlap diagnostics, and reduced density matrix-based observables while leaving the underlying excitation-energy description essentially unchanged. These results demonstrate that excitation-energy accuracy does not guarantee observable accuracy and that energy-only validation can overlook significant failures in physically relevant properties. AqEOM provides a concrete mechanistic demonstration of this principle, highlighting observable fidelity as an independent benchmark dimension for excited-state quantum algorithms.