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Efficient Ground-State Manifold Amplification for Rydberg Atom Arrays via Houdayer Cluster Updates

Andrew J. Ochoa, Martin J. A. Schuetz, Helmut G. Katzgraber · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28528 · cited by 0 works (OpenAlex) · open-access PDF

Japanese

We are discovering a hybrid quantum-classic approach to exploring ground-state multiples of maximum independent set problems, in which quantum hardware supplies the initial solutions and an entirely classic 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 problematic for applications that strongly depend on a wide 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 on our approach a test bed of 43 problem instances from Quera's Aquila's simple analogue device, achieving

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Quantum, Quantum annealing, Algorithm, Manifold (fluid mechanics), Set (abstract data type), Mathematics

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