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Quantum-Accelerated Global Constraint Filtering

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Book cover Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

Abstract

Motivated by recent advances in quantum algorithms and gate-model quantum computation, we introduce quantum-accelerated filtering algorithms for global constraints in constraint programming. We adapt recent work in quantum algorithms for graph problems and identify quantum subroutines that accelerate the main domain consistency algorithms for the alldifferent constraint and the global cardinality constraint (gcc). The subroutines are based on quantum algorithms for finding maximum matchings and strongly connected components in graphs, and provide speedups over the best classical algorithms. We detail both complete and bounded-probability frameworks for quantum-accelerated global constraint filtering algorithms within backtracking search.

As Eleanor Rieffel is a U.S. Government employee, the U.S. Government asserts no copyright in the U.S. related to her contributions of authorship to a non-segregable joint work.

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Notes

  1. 1.

    We note that the instance size at which the asymptotic scaling becomes relevant is so large that, in practice, matrix multiplication takes cubic time.

  2. 2.

    For an algorithm intended to find an item with a certain property, we say that the algorithm has perfect completeness if it always finds such an item, if one exists, and the algorithm has perfect soundness if it never returns an item without the property.

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Acknowledgements

K.B., J.M., and S.H. were supported by NASA Academic Mission Services (NAMS), contract number NNA16BD14C. K.B. was also supported by the NASA Advanced Exploration Systems (AES) program. B.O. was supported by a NASA Space Technology Research Fellowship. We thank the anonymous reviewers and Prof. J. Christopher Beck whose valuable feedback helped improve the final version of the manuscript.

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Authors and Affiliations

  1. Quantum AI Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA, 94035, USA

    Kyle E. C. Booth, Bryan O’Gorman, Jeffrey Marshall, Stuart Hadfield & Eleanor Rieffel

  2. USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA, 94043, USA

    Kyle E. C. Booth, Jeffrey Marshall & Stuart Hadfield

  3. University of California, Berkeley, CA, 94720, USA

    Bryan O’Gorman

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  1. Kyle E. C. Booth
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  5. Eleanor Rieffel
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Correspondence to Kyle E. C. Booth .

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  1. Insight Centre for Data Analytics, School for Computer Science and Information Technology, University College Cork, Cork, Ireland

    Helmut Simonis

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Booth, K.E.C., O’Gorman, B., Marshall, J., Hadfield, S., Rieffel, E. (2020). Quantum-Accelerated Global Constraint Filtering. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-58475-7_5

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