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Efficient solution of the number partitioning problem on a quantum annealer: a hybrid quantum-classical decomposition approach

Author

Listed:
  • Zongji Li

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Tobias Seidel

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Dominik Leib

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Michael Bortz

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Raoul Heese

    (Fraunhofer Institute for Industrial Mathematics ITWM)

Abstract

Current quantum computers can only solve optimization problems of a very limited size. For larger problems, decomposition methods are required in which the original problem is broken down into several smaller sub-problems. These are then solved on the quantum computer and their solutions are recombined into a final solution for the original problem. Often, these decomposition methods do not take the specific problem structure into account. In this paper, we present a tailored method using a divide-and-conquer strategy to solve the 2-way Number partitioning problem (NPP) with a large number of variables. The idea is to perform a specialized decomposition into smaller NPPs, which are solved on a quantum computer, and then recombine the results into another small auxiliary NPP. Solving this auxiliary problem yields an approximate solution of the original larger problem. We experimentally verify that our method allows to solve NPPs with over a thousand variables using the D-Wave Advantage quantum annealer (Advantage_system6.4).

Suggested Citation

  • Zongji Li & Tobias Seidel & Dominik Leib & Michael Bortz & Raoul Heese, 2025. "Efficient solution of the number partitioning problem on a quantum annealer: a hybrid quantum-classical decomposition approach," Journal of Heuristics, Springer, vol. 31(2), pages 1-20, June.
    • Handle: RePEc:spr:joheur:v:31:y:2025:i:2:d:10.1007_s10732-025-09556-3
    DOI: 10.1007/s10732-025-09556-3
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    References listed on IDEAS

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    1. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    2. S. Boettcher & S. Mertens, 2008. "Analysis of the Karmarkar-Karp differencing algorithm," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(1), pages 131-140, September.
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