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Resolution of the Frobenius Problem with an Adiabatic Quantum Computer

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Intelligent Computing

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 283))

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Abstract

The (Diophantine) Frobenius problem is a well-known NP-hard problem (also called the stamp problem or the chicken nugget problem) whose origins lie in the realm of combinatorial number theory. In this paper we present an algorithm which solves it, via a translation into a QUBO problem of the so-called Apéry set of a numerical semigroup. This algorithm was specifically designed to run in an adiabatic quantum computer (a D-Wave 2X machine), and the performance problems for this precise setting are also discussed.

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Author information

Authors and Affiliations

  1. Departamento de Álgebra, Universidad de Sevilla, 41012, Sevilla, Spain

    J. Ossorio-Castillo

  2. Departamento de Álgebra – IMUS, Universidad de Sevilla, 41012, Sevilla, Spain

    José M. Tornero

Authors
  1. J. Ossorio-Castillo
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  2. José M. Tornero
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Corresponding author

Correspondence to J. Ossorio-Castillo .

Editor information

Editors and Affiliations

  1. Faculty of Science and Engineering, Saga University, Saga, Japan

    Kohei Arai

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Ossorio-Castillo, J., Tornero, J.M. (2022). Resolution of the Frobenius Problem with an Adiabatic Quantum Computer. In: Arai, K. (eds) Intelligent Computing. Lecture Notes in Networks and Systems, vol 283. Springer, Cham. https://doi.org/10.1007/978-3-030-80119-9_16

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