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arXiv:2503.12551 · Physical Review Research

Quantum-informed reduction algorithm for the maximum independent set problem

Martin J. A. Schuetz, Romina Yalovetzky, Ruben S. Andrist, Grant Salton, Yue Sun, Rudy Raymond, Shouvanik Chakrabarti, Atithi Acharya, Ruslan Shaydulin, Marco Pistoia, Helmut G. Katzgraber

Published Jul 20, 2026• 0 citations
arXivHTMLPDF

Abstract

We propose and implement a quantum-informed reduction algorithm for the maximum independent set problem that integrates classical kernelization techniques with information extracted from quantum devices. Our larger framework consists of dedicated application, algorithm, and hardware layers, and easily generalizes to the maximum weight independent set problem. In this hybrid quantum-classical framework, which we call qReduMIS, the quantum computer is used as a coprocessor to inform classical reduction logic about frozen vertices that are likely (or unlikely) to be in large independent sets, thereby opening up the reduction space after removal of targeted subgraphs. We systematically assess the performance of qReduMIS based on experiments with up to 231 qubits run on Rydberg quantum hardware available through Amazon Braket. Our experiments show that qReduMIS can help address fundamental performance limitations faced by a broad set of (quantum) solvers including Rydberg quantum devices. We outline implementations of qReduMIS with alternative platforms, such as superconducting qubits or trapped ions, and we discuss potential future extensions.

DOI
10.1103/nh3b-1wv5

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We propose and implement a quantum-informed reduction algorithm for the maximum independent set problem that integrates classical kernelization techniques with information extracted from quantum devices. Our larger framework consists of dedicated application, algorithm, and hardware layers, and easily generalizes to the maximum weight independent set problem. In this hybrid quantum-classical framework, which we call qReduMIS, the quantum computer is used as a coprocessor to inform classical reduction logic about frozen vertices that are likely (or unlikely) to be in large independent sets, thereby opening up the reduction space after removal of targeted subgraphs. We systematically assess the performance of qReduMIS based on experiments with up to 231 qubits run on Rydberg quantum hardware available through Amazon Braket. Our experiments show that qReduMIS can help address fundamental performance limitations faced by a broad set of (quantum) solvers including Rydberg quantum devices. We outline implementations of qReduMIS with alternative platforms, such as superconducting qubits or trapped ions, and we discuss potential future extensions.
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We investigate the classical reducibility of random unit-disk graph (UDG) instances of the maximum independent set (MIS) and maximum weighted independent set (MWIS) problems, which can be natively realised in Rydberg atom quantum processors. Using state-of-the-art kernelisation techniques, we systematically probe how far classical preprocessing can simplify such native optimisation problems of varying size and connectivity. While many small or sparse instances can be fully reduced, dense graphs often retain finite irreducible kernels even after extensive reductions. Introducing vertex weights tends to increase reducibility, whereas extending the interaction range in the underlying UDG connectivity suppresses the reduction efficiency. By exploring where classical reductions cease to be effective, we aim to delineate the regime of problem instances that remain computationally demanding - those most relevant for testing and benchmarking near-term quantum optimisation hardware. We find that for the remaining finite kernels, quantum execution would require non-native embeddings with substantial resource overheads, suggesting that directly running native instances may be more practical than embedding a reduced kernel.
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Noisy Intermediate-Scale Quantum (NISQ) computers currently available have a few thousand qubits, and could potentially solve combinatorial optimization problems efficiently. However, the sizes of the problems that could be solved are limited by the number of qubits, their connectivity, high noise, and short coherence times. In this work, we propose hybrid quantum-classical algorithms based on the divide and conquer paradigm for solving larger Maximum Independent Set (MIS) and Maximum Weighted Independent Set (MWIS) problems on graphs than would otherwise be possible on NISQ devices. The machines include D-Wave Quantum Annealers and QuEra Quantum Computers with Neutral Atoms. Our algorithms are designed for separable graphs, which are classes of graphs with good vertex separators; these include planar graphs, finite element meshes with good aspect ratios, nearest neighbor graphs, and certain classes of geometrically defined graphs. The algorithms recursively employ vertex separators to create a collection of small subgraphs, from which NISQ computers obtain disjoint maximal independent sets, which are then augmented by independent vertices from the separators. We demonstrate competitive results compared to the classical Luby's algorithm, and KaMIS, a state-of-the-art classical MIS solver, on graphs with several thousand vertices. These divide and conquer-based algorithms are also well-suited for distributed quantum computer architectures.
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