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Fair sampling of ground-state configurations of binary optimization problems.

Zheng Zhu1, Andrew J Ochoa1, Helmut G Katzgraber1,2,3

  • 1Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.

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Summary
This summary is machine-generated.

This study introduces a new method for binary optimization problems, improving upon quantum annealing by sampling degenerate states equally. This approach enhances the accuracy of finding ground-state configurations for complex problems.

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Area of Science:

  • Computational Physics
  • Optimization Algorithms
  • Quantum Computing

Background:

  • Existing heuristics for binary optimization often yield correlated solutions for degenerate problems.
  • Transverse-field quantum annealing, used in commercial machines, can be exponentially biased when sampling solution spaces.
  • Degenerate problems, where multiple solutions have the same lowest energy, pose a significant challenge for current methods.

Purpose of the Study:

  • To develop a novel approach for sampling ground-state (or low-energy) configurations in binary optimization problems.
  • To address the limitations of existing heuristics, particularly their bias in sampling degenerate states.
  • To provide a method that samples degenerate states with nearly equal probability.

Main Methods:

  • A combination of parallel tempering Monte Carlo and isoenergetic cluster moves is employed.
  • The method is tested on two-dimensional Ising spin glasses.
  • The approach is also validated on spin glasses configured on the D-Wave Systems quantum annealer's chimera topology.

Main Results:

  • The proposed method effectively samples degenerate states with almost equal probability.
  • Demonstrated successful application to Ising spin glasses and D-Wave's chimera topology.
  • Introduced a heuristic for approximating the number of solutions in degenerate problems.

Conclusions:

  • The parallel tempering Monte Carlo with isoenergetic cluster moves offers a robust method for sampling low-energy states in binary optimization.
  • This technique overcomes the sampling bias issues inherent in some current heuristic approaches, including quantum annealing.
  • The developed heuristic provides a useful tool for characterizing the complexity of degenerate optimization problems.