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Quantum bridge analytics I: a tutorial on formulating and using QUBO models

Author

Listed:
  • Fred Glover

    (Entanglement, Inc.)

  • Gary Kochenberger

    (Entanglement, Inc.)

  • Rick Hennig

    (Entanglement, Inc.)

  • Yu Du

    (University of Colorado at Denver)

Abstract

Quantum Bridge Analytics relates generally to methods and systems for hybrid classical-quantum computing, and more particularly is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the first of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications, with an emphasis on supplementing models with numerical illustrations. In Part 1 (the present paper) we focus on the Quadratic Unconstrained Binary Optimization model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. This document extends an original version published in 4OR to include a section on advanced models related to quantum optimization and a section reporting comparative computational results on challenging combinatorial applications.

Suggested Citation

  • Fred Glover & Gary Kochenberger & Rick Hennig & Yu Du, 2022. "Quantum bridge analytics I: a tutorial on formulating and using QUBO models," Annals of Operations Research, Springer, vol. 314(1), pages 141-183, July.
    • Handle: RePEc:spr:annopr:v:314:y:2022:i:1:d:10.1007_s10479-022-04634-2
    DOI: 10.1007/s10479-022-04634-2
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    References listed on IDEAS

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    1. Daniel O’Malley & Velimir V Vesselinov & Boian S Alexandrov & Ludmil B Alexandrov, 2018. "Nonnegative/Binary matrix factorization with a D-Wave quantum annealer," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-12, December.
    2. Gary Kochenberger & Fred Glover & Bahram Alidaee & Haibo Wang, 2005. "Clustering of Microarray data via Clique Partitioning," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 77-92, August.
    3. Elad Schneidman & Michael J. Berry & Ronen Segev & William Bialek, 2006. "Weak pairwise correlations imply strongly correlated network states in a neural population," Nature, Nature, vol. 440(7087), pages 1007-1012, April.
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    6. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
    7. Frank Phillipson & Harshil Singh Bhatia, 2020. "Portfolio Optimisation Using the D-Wave Quantum Annealer," Papers 2012.01121, arXiv.org.
    8. Gary Kochenberger & Fred Glover & Bahram Alidaee & Cesar Rego, 2005. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem," Annals of Operations Research, Springer, vol. 139(1), pages 229-241, October.
    9. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    10. Iain Dunning & Swati Gupta & John Silberholz, 2018. "What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 608-624, August.
    11. Fred Glover & Gary Kochenberger & Yu Du, 2019. "Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models," 4OR, Springer, vol. 17(4), pages 335-371, December.
    12. Alidaee, Bahram & Kochenberger, Gary & Lewis, Karen & Lewis, Mark & Wang, Haibo, 2008. "A new approach for modeling and solving set packing problems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 504-512, April.
    13. Gary Kochenberger & Fred Glover & Bahram Alidaee & Karen Lewis, 2005. "Using the unconstrained quadratic program to model and solve Max 2-SAT problems," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 89-100.
    14. Davide Venturelli & Alexei Kondratyev, 2018. "Reverse Quantum Annealing Approach to Portfolio Optimization Problems," Papers 1810.08584, arXiv.org, revised Oct 2018.
    15. Glover, Fred & Alidaee, Bahram & Rego, Cesar & Kochenberger, Gary, 2002. "One-pass heuristics for large-scale unconstrained binary quadratic problems," European Journal of Operational Research, Elsevier, vol. 137(2), pages 272-287, March.
    16. Wang, Yang & Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2012. "Path relinking for unconstrained binary quadratic programming," European Journal of Operational Research, Elsevier, vol. 223(3), pages 595-604.
    17. Glover, Fred & Lewis, Mark & Kochenberger, Gary, 2018. "Logical and inequality implications for reducing the size and difficulty of quadratic unconstrained binary optimization problems," European Journal of Operational Research, Elsevier, vol. 265(3), pages 829-842.
    18. Jeffrey Cohen & Alex Khan & Clark Alexander, 2020. "Portfolio Optimization of 60 Stocks Using Classical and Quantum Algorithms," Papers 2008.08669, arXiv.org.
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    Cited by:

    1. Xunzhao Yin & Yu Qian & Alptekin Vardar & Marcel Günther & Franz Müller & Nellie Laleni & Zijian Zhao & Zhouhang Jiang & Zhiguo Shi & Yiyu Shi & Xiao Gong & Cheng Zhuo & Thomas Kämpfe & Kai Ni, 2024. "Ferroelectric compute-in-memory annealer for combinatorial optimization problems," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    2. Fred Glover & Gary Kochenberger & Moses Ma & Yu Du, 2022. "Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange," Annals of Operations Research, Springer, vol. 314(1), pages 185-212, July.

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