Energy Is Not Enough: Leakage-Aware Ansatz Criterion for Variational Quantum Eigensolvers
Abstract
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.
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BibTeX
@misc{chen2026energy,
title = {{Energy Is Not Enough: Leakage-Aware Ansatz Criterion for Variational Quantum Eigensolvers}},
author = {Yuan-Chieh Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13521},
eprint = {2609.13521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13521},
}
RIS
TY - UNPB
TI - Energy Is Not Enough: Leakage-Aware Ansatz Criterion for Variational Quantum Eigensolvers
AU - Yuan-Chieh Chen
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13521
UR - https://arxiv.org/abs/2609.13521
AB - 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.
ER -