IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i8p1294-d792958.html
   My bibliography  Save this article

Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems

Author

Listed:
  • Evangelos Stogiannos

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece
    These authors contributed equally to this work.)

  • Christos Papalitsas

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece
    These authors contributed equally to this work.)

  • Theodore Andronikos

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece
    These authors contributed equally to this work.)

Abstract

This paper studies the Hamiltonian cycle problem (HCP) and the traveling salesman problem (TSP) on D-Wave quantum systems. Motivated by the fact that most libraries present their benchmark instances in terms of adjacency matrices, we develop a novel matrix formulation for the HCP and TSP Hamiltonians, which enables the seamless and automatic integration of benchmark instances in quantum platforms. We also present a thorough mathematical analysis of the precise number of constraints required to express the HCP and TSP Hamiltonians. This analysis explains quantitatively why, almost always, running incomplete graph instances requires more qubits than complete instances. It turns out that QUBO models for incomplete graphs require more quadratic constraints than complete graphs, a fact that has been corroborated by a series of experiments. Moreover, we introduce a technique for the min-max normalization for the coefficients of the TSP Hamiltonian to address the problem of invalid solutions produced by the quantum annealer, a trend often observed. Our extensive experimental tests have demonstrated that the D-Wave Advantage_system4.1 is more efficient than the Advantage_system1.1, both in terms of qubit utilization and the quality of solutions. Finally, we experimentally establish that the D-Wave hybrid solvers always provide valid solutions, without violating the given constraints, even for arbitrarily big problems up to 120 nodes.

Suggested Citation

  • Evangelos Stogiannos & Christos Papalitsas & Theodore Andronikos, 2022. "Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems," Mathematics, MDPI, vol. 10(8), pages 1-24, April.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1294-:d:792958
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/8/1294/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/8/1294/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1294-:d:792958. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.