Computational hardness of spin-glass problems with tile-planted solutions

Dilina Perera, Firas Hamze, Jack Raymond, Martin Weigel, Helmut G. Katzgraber

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)
    9 Downloads (Pure)


    We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into edge-disjoint subgraphs, and planting frustrated, elementary subproblems that share a common local ground state, which guarantees that the ground state of the entire problem is known a priori. Using population annealing Monte Carlo, we compare the typical hardness of problem classes over a large region of the multi-dimensional tuning parameter space. Our results show that the problems have a wide range of tunable hardness. Moreover, we observe multiple transitions in the hardness phase space, which we further corroborate using simulated annealing and simulated quantum annealing. By investigating thermodynamic properties of these planted systems, we demonstrate that the harder samples undergo magnetic ordering transitions which are also ultimately responsible for the observed hardness transitions on changing the sample composition.
    Original languageEnglish
    Article number023316
    JournalPhysical Review E
    Issue number2
    Publication statusPublished - 28 Feb 2020

    Bibliographical note

    12 pages, 14 figures, 1 table, loads of love


    • cond-mat.dis-nn
    • quant-ph

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Statistical and Nonlinear Physics
    • Statistics and Probability


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