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This research introduces a hybrid quantum-classical framework that uses classical Houdayer cluster updates to significantly expand the solution diversity generated by QuEra's analog annealing device. By addressing fundamental sampling limitations in quantum optimization, the method recovers up to 21% of the ground-state manifold and occasionally identifies higher-quality configurations than quantum hardware alone. This approach effectively mitigates sampling bottlenecks in Rydberg atom arrays, offering a practical pathway to enhance the utility of current quantum optimization devices for complex combinatorial problems.
Efficient Ground-State Manifold Amplification for Rydberg Atom Arrays via Houdayer Cluster Updates
arXiv:2610.28528v1 Announce Type: new 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.
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.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas); Optimization and Control (math.OC)
arXiv:2610.28528 [quant-ph]
(or arXiv:2610.28528v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.28528 arXiv-issued DOI via DataCite (pending registration)
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