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Quantum-informed reduction algorithm for the maximum independent set problem

Martin J. A. Schuetz1,2,*,†, Romina Yalovetzky3,*,‡, Ruben S. Andrist1, Grant Salton1,2, Yue Sun3, Rudy Raymond3, Shouvanik Chakrabarti3, Atithi Acharya3, Ruslan Shaydulin3 et al.

Marco Pistoia3 and Helmut G. Katzgraber1

  • *These authors contributed equally to this work.
  • †Contact author: maschuet@amazon.com
  • ‡Contact author: romina.yalovetzky@jpmorgan.com
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Phys. Rev. Research 8, 033296 – Published 10 September, 2026

DOI: https://doi.org/10.1103/nh3b-1wv5

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.

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Phys. Rev. Research 8, 033296– Published 10 September, 2026
  • Received 2 May 2025
  • Revised 14 November 2025
  • Accepted 20 July 2026
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