Energy Is Not Enough: Leakage-Aware Ansatz Criterion for Variational Quantum Eigensolvers

In molecular variational quantum eigensolver (VQE) calculations for a fixed electron-number sector, the projected-sector energy alone does not certify that a prepared state is physically valid. We show that a state can have zero projected-sector error while almost all of its probability mass lies outside the target particle-number sector. We therefore evaluate ansatz families using three quantities: projected-sector error, leakage outside the physical sector and parameter count. Our noiseless experiments show that particle-preserving UCC-style families eliminate leakage induced by ansatze, but do not guarantee ground-state accuracy. In the parameter-budget comparison experiments, the one-shot ranking rules select identical generator sequences and yield identical errors. The adaptive hybrid procedure achieves lower mean projected-sector errors at selected budgets. Using established Kraus invariant-subspace criteria, we also express channel-induced leakage through a positive operator and discuss global and local depolarizing noise analytically. This gives a practical diagnostic framework for comparing ansatze beyond energy alone.