Efficient Ground-State Manifold Amplification for Rydberg Atom Arrays via Houdayer Cluster Updates
Abstract
We demonstrate a hybrid quantum-classical approach for exploring ground-state manifolds of maximum independent set problems, in which quantum hardware supplies the initial solutions and an entirely classical post-processing algorithm expands them, increasing the solution diversity of quantum hardware measurements by up to several orders of magnitude. Quantum optimization devices, while capable of generating high-quality solutions, can suffer from fundamental sampling limitations. This is particularly problematic for applications that strongly depend on a large variety of uncorrelated optimal solutions. We apply the Houdayer cluster update algorithm to systematically expand quantum-generated solution sets through classical post-processing. We validate our approach on a test bed of 43 problem instances from QuEra's Aquila analog annealing device, achieving diversity amplification factors, defined as the increase in the number of distinct solutions at a given set size, of up to 11923x with a median of 24.3x across different problem scales and hardness parameters. Because exact ground-state degeneracies are known for these instances, the recovered fraction of the manifold can be measured rather than bounded: post-processing recovers a median of 21% of the ground-state manifold, and provably all of it for six instances. We also demonstrate that, in some cases, the classical post-processing can discover independent sets larger than those found by the quantum hardware, thus improving on solution quality and not just diversity. While the method is non-ergodic and cannot guarantee complete manifold coverage, it consistently discovers a larger number of high-quality, and in some cases strictly better, configurations than quantum sampling alone. This work demonstrates how simple classical post-processing can enhance the utility of quantum optimization results.
Related
BibTeX
@misc{ochoa2026efficient,
title = {{Efficient Ground-State Manifold Amplification for Rydberg Atom Arrays via Houdayer Cluster Updates}},
author = {Andrew J. Ochoa and Martin J. A. Schuetz and Helmut G. Katzgraber},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28528},
eprint = {2610.28528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28528},
}
RIS
TY - UNPB
TI - Efficient Ground-State Manifold Amplification for Rydberg Atom Arrays via Houdayer Cluster Updates
AU - Andrew J. Ochoa
AU - Martin J. A. Schuetz
AU - Helmut G. Katzgraber
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.28528
UR - https://arxiv.org/abs/2610.28528
AB - We demonstrate a hybrid quantum-classical approach for exploring ground-state manifolds of maximum independent set problems, in which quantum hardware supplies the initial solutions and an entirely classical post-processing algorithm expands them, increasing the solution diversity of quantum hardware measurements by up to several orders of magnitude. Quantum optimization devices, while capable of generating high-quality solutions, can suffer from fundamental sampling limitations. This is particularly problematic for applications that strongly depend on a large variety of uncorrelated optimal solutions. We apply the Houdayer cluster update algorithm to systematically expand quantum-generated solution sets through classical post-processing. We validate our approach on a test bed of 43 problem instances from QuEra's Aquila analog annealing device, achieving diversity amplification factors, defined as the increase in the number of distinct solutions at a given set size, of up to 11923x with a median of 24.3x across different problem scales and hardness parameters. Because exact ground-state degeneracies are known for these instances, the recovered fraction of the manifold can be measured rather than bounded: post-processing recovers a median of 21% of the ground-state manifold, and provably all of it for six instances. We also demonstrate that, in some cases, the classical post-processing can discover independent sets larger than those found by the quantum hardware, thus improving on solution quality and not just diversity. While the method is non-ergodic and cannot guarantee complete manifold coverage, it consistently discovers a larger number of high-quality, and in some cases strictly better, configurations than quantum sampling alone. This work demonstrates how simple classical post-processing can enhance the utility of quantum optimization results.
ER -