From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems

Firas Hamze, Darryl C. Jacob, Andrew J. Ochoa, Dilina Perera, Wenlong Wang, and Helmut G. Katzgraber
Phys. Rev. E 97, 043303 – Published 13 April 2018

Abstract

We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {1,+1}, are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint-satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.

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  • Received 24 November 2017
  • Revised 11 February 2018

DOI:https://doi.org/10.1103/PhysRevE.97.043303

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsGeneral Physics

Authors & Affiliations

Firas Hamze1, Darryl C. Jacob2, Andrew J. Ochoa2, Dilina Perera2, Wenlong Wang2, and Helmut G. Katzgraber2,3,4

  • 1D-Wave Systems, Inc., 3033 Beta Avenue, Burnaby, British Columbia, Canada V5G 4M9
  • 2Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
  • 31QB Information Technologies, Vancouver, British Columbia, Canada V6B 4W4
  • 4Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

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Issue

Vol. 97, Iss. 4 — April 2018

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