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Modeling the Costas Array Problem in QUBO for Quantum Annealing

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Book cover Evolutionary Computation in Combinatorial Optimization (EvoCOP 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13222))

Abstract

We present experiments in solving constrained combinatorial optimization problems by means of Quantum Annealing. We describe how to model a hard combinatorial problem, the Costas Array Problem, in terms of QUBO (Quadratic Unconstrained Binary Optimization). QUBO is the input language of quantum computers based on quantum annealing such as the D-Wave systems and of the “quantum-inspired” special-purpose hardware such as Fujitsu’s Digital Annealing Unit or Hitachi’s CMOS Annealing Machine. We implemented the QUBO model for the Costas Array Problem on several hardware solvers based on quantum annealing (D-Wave Advantage, Fujitsu DA3 and Fixstars AE) and present some performance result for these implementations, along those of state-of-the-art metaheuristics solvers on classical hardware.

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Notes

  1. 1.

    Let us note that recently [3] proposed some “quantum-accelerated filtering algorithms” to encode the all-different constraint in the gate model of quantum computing, which is very different from what we consider here (QUBO and QA).

  2. 2.

    We used two versions derived from Barry O’Sullivan’s model by Hakan Kjellerstrand, available at http://www.hakank.org/minizinc: one written in MiniZinc with Gecode as back-end solver and one written in Python for the Google OR-Tools solver.

  3. 3.

    More precisely, the Chimera architecture of the D-Wave 2000X computer has only a 6-way qubit connectivity (meaning that each qubit is physically connected to at most 6 other qubits) and the Pegasus architecture of the D-Wave Advantage has a 15-way qubit connectivity.

  4. 4.

    There is a limit of 60 s per job when using Fixstars Amplify AE with developer accounts, we therefore took the same time limit for Fujitsu’s DAU.

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Authors and Affiliations

  1. JFLI, CNRS/Sorbonne University/University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Philippe Codognet

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  1. Philippe Codognet
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  1. Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Leslie Pérez Cáceres

  2. Université du Littoral Côte d’Opale, Calais, France

    Sébastien Verel

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Codognet, P. (2022). Modeling the Costas Array Problem in QUBO for Quantum Annealing. In: Pérez Cáceres, L., Verel, S. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2022. Lecture Notes in Computer Science, vol 13222. Springer, Cham. https://doi.org/10.1007/978-3-031-04148-8_10

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  • DOI: https://doi.org/10.1007/978-3-031-04148-8_10

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