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Mean field approximation for solving QUBO problems

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  • Máté Tibor Veszeli
  • Gábor Vattay

Abstract

The Quadratic Unconstrained Binary Optimization (QUBO) problem is NP-hard. Some exact methods like the Branch-and-Bound algorithm are suitable for small problems. Some approximations like stochastic simulated annealing for discrete variables or mean-field annealing for continuous variables exist for larger ones, and quantum computers based on the quantum adiabatic annealing principle have also been developed. Here we show that the mean-field approximation of the quantum adiabatic annealing leads to equations similar to those of thermal mean-field annealing. However, a new type of sigmoid function replaces the thermal one. The new mean-field quantum adiabatic annealing can replicate the best-known cut values on some of the popular benchmark Maximum Cut problems.

Suggested Citation

  • Máté Tibor Veszeli & Gábor Vattay, 2022. "Mean field approximation for solving QUBO problems," PLOS ONE, Public Library of Science, vol. 17(8), pages 1-12, August.
    • Handle: RePEc:plo:pone00:0273709
    DOI: 10.1371/journal.pone.0273709
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    References listed on IDEAS

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    1. Fuda Ma & Jin-Kao Hao, 2017. "A multiple search operator heuristic for the max-k-cut problem," Annals of Operations Research, Springer, vol. 248(1), pages 365-403, January.
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