Resolution of the Frobenius Problem with an Adiabatic Quantum Computer

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


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.


Quantum computation Adiabatic quantum computation Numerical semigroups Frobenius problem 


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Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

Authors and Affiliations

  1. 1.Departamento de ÁlgebraUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Álgebra – IMUSUniversidad de SevillaSevillaSpain

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