Building an iterative heuristic solver for a quantum annealer

Abstract

A quantum annealer heuristically minimizes quadratic unconstrained binary optimization (QUBO) problems, but is limited by the physical hardware in the size and density of the problems it can handle. We have developed a meta-heuristic solver that utilizes D-Wave Systems’ quantum annealer (or any other QUBO problem optimizer) to solve larger or denser problems, by iteratively solving subproblems, while keeping the rest of the variables fixed. We present our algorithm, several variants, and the results for the optimization of standard QUBO problem instances from OR-Library of sizes 500 and 2500 as well as the Palubeckis instances of sizes 3000–7000. For practical use of the solver, we show the dependence of the time to best solution on the desired gap to the best known solution. In addition, we study the dependence of the gap and the time to best solution on the size of the problems solved by the underlying optimizer. Our results were obtained by simulation, using a tabu 1-opt solver, due to the huge number of runs required and limited quantum annealer time availability.

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Notes

  1. 1.

    The problem that the machine actually solves is known as an Ising model in the physics community, and can easily be transformed into the form \(x^T Q x\), which is more common in the scientific computing community.

  2. 2.

    The chip is current as of April 2016.

  3. 3.

    A one-flip gain is the change in the objective function’s value given a flip of a single bit. We refer to the collection of all possible single flips and their corresponding change in the objection function’s value as the “one-flip gains”.

  4. 4.

    We chose 0.02 s based on 1000 anneals each taking 20  \({\upmu }\)s (which is the current minimum anneal time). This is the actual time for computation, and does not include extra time for programming the chip, thermalization, etc. Since future run times are not known, this number is only meant as a rough estimate, to give an idea of the actual time the computation could take.

  5. 5.

    The source code of the generator and the input files to create these problems can be found at http://www.proin.ktu.lt/~gintaras/ubqop_its.html. This page was last retrieved on July 21, 2015.

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Acknowledgments

The authors would like to thank Marko Bucyk for editing a draft of this paper and Robyn Foerster, Phil Goddard, and Pooya Ronagh for their useful comments. This work was supported by 1QB Information Technologies (1QBit) and Mitacs.

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Correspondence to Gili Rosenberg.

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EH declares no conflict of interest. GR, BW, and MV were academic interns at 1QBit when the work was done, and GR and BW are still at 1QBit. 1QBit is focused on solving real-world problems using quantum computers. D-Wave Systems is a minority investor in 1QBit.

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Rosenberg, G., Vazifeh, M., Woods, B. et al. Building an iterative heuristic solver for a quantum annealer. Comput Optim Appl 65, 845–869 (2016). https://doi.org/10.1007/s10589-016-9844-y

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Keywords

  • Quantum annealing
  • Quadratic unconstrained binary optimization
  • Combinatoric optimization
  • k-opt
  • Local search
  • Iterative heuristic solver