IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v626y2023ics0378437123006441.html
   My bibliography  Save this article

Quantum alternating operator ansatz for solving the minimum exact cover problem

Author

Listed:
  • Wang, Sha-Sha
  • Liu, Hai-Ling
  • Song, Yan-Qi
  • Gao, Fei
  • Qin, Su-Juan
  • Wen, Qiao-Yan

Abstract

The Quantum Alternating Operator Ansatz (QAOA+) is an extension of the Quantum Approximate Optimization Algorithm (QAOA), where the search space is smaller in solving constrained combinatorial optimization problems. However, QAOA+ requires a trivial feasible solution as the initial state, so it cannot be applied directly for problems that are difficult to find a trivial feasible solution. For simplicity, we call them as Non-Trivial-Feasible-Solution Problems (NTFSP). In this paper, we take the Minimum Exact Cover (MEC) problem as an example, studying how to apply QAOA+ to NTFSP. As we know, Exact Cover (EC) is the feasible space of MEC problem, which has no trivial solutions. To overcome the above problem, the EC problem is divided into two steps to solve. First, disjoint sets are obtained, which is equivalent to solving independent sets. Second, on this basis, the sets covering all elements (i.e., EC) are solved. In other words, we transform MEC into a multi-objective constrained optimization problem, where feasible space consists of independent sets that are easy to find. Finally, we also verify the feasibility of the algorithm from numerical experiments. Furthermore, we compare QAOA+ with QAOA, and the results demonstrated that QAOA+ has a higher probability of finding a solution with the same rounds of both algorithms. Our method provides a feasible way for applying QAOA+ to NTFSP, and is expected to expand its application significantly.

Suggested Citation

  • Wang, Sha-Sha & Liu, Hai-Ling & Song, Yan-Qi & Gao, Fei & Qin, Su-Juan & Wen, Qiao-Yan, 2023. "Quantum alternating operator ansatz for solving the minimum exact cover problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
  • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006441
    DOI: 10.1016/j.physa.2023.129089
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123006441
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2023.129089?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Timothy L. Jacobs & Laurie A. Garrow & Manoj Lohatepanont & Frank S. Koppelman & Gregory M. Coldren & Hadi Purnomo, 2012. "Airline Planning and Schedule Development," International Series in Operations Research & Management Science, in: Cynthia Barnhart & Barry Smith (ed.), Quantitative Problem Solving Methods in the Airline Industry, edition 127, chapter 0, pages 35-99, Springer.
    2. Guo, Mingchao & Liu, Hailing & Li, Yongmei & Li, Wenmin & Gao, Fei & Qin, Sujuan & Wen, Qiaoyan, 2022. "Quantum algorithms for anomaly detection using amplitude estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    3. Liu, Hai-Ling & Yu, Chao-Hua & Wan, Lin-Chun & Qin, Su-Juan & Gao, Fei & Wen, Qiaoyan, 2022. "Quantum mean centering for block-encoding-based quantum algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ning, Tong & Yang, Youlong & Du, Zhenye, 2023. "Quantum kernel logistic regression based Newton method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    2. Yu, Kai & Lin, Song & Guo, Gong-De, 2023. "Quantum dimensionality reduction by linear discriminant analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    3. Lurkin, Virginie & Garrow, Laurie A. & Higgins, Matthew J. & Newman, Jeffrey P. & Schyns, Michael, 2017. "Accounting for price endogeneity in airline itinerary choice models: An application to Continental U.S. markets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 100(C), pages 228-246.
    4. Liang, Zhe & Feng, Yuan & Zhang, Xiaoning & Wu, Tao & Chaovalitwongse, Wanpracha Art, 2015. "Robust weekly aircraft maintenance routing problem and the extension to the tail assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 238-259.
    5. Kenan, Nabil & Diabat, Ali & Jebali, Aida, 2018. "Codeshare agreements in the integrated aircraft routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 272-295.
    6. Keji Wei & Vikrant Vaze, 2020. "Airline Timetable Development and Fleet Assignment Incorporating Passenger Choice," Transportation Science, INFORMS, vol. 54(1), pages 139-163, January.
    7. Nenem, Sukru & Graham, Anne & Dennis, Nigel, 2020. "Airline schedule and network competitiveness: A consumer-centric approach for business travel," Annals of Tourism Research, Elsevier, vol. 80(C).
    8. Stefano Coniglio & Mathias Sirvent & Martin Weibelzahl, 2021. "Airport capacity extension, fleet investment, and optimal aircraft scheduling in a multilevel market model: quantifying the costs of imperfect markets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 367-408, June.
    9. Bet, Germán, 2021. "Product specification under a threat of entry: Evidence from Airlines’ departure times," International Journal of Industrial Organization, Elsevier, vol. 75(C).
    10. Chen, Xin & Xuan, Chao & Qiu, Rui, 2021. "Understanding spatial spillover effects of airports on economic development: New evidence from China’s hub airports," Transportation Research Part A: Policy and Practice, Elsevier, vol. 143(C), pages 48-60.
    11. Grosche, Tobias & Klophaus, Richard & Seredyński, Adam, 2020. "Market concentration in German air transport before and after the Air Berlin bankruptcy," Transport Policy, Elsevier, vol. 94(C), pages 78-88.
    12. Li, Jing & Gao, Fei & Lin, Song & Guo, Mingchao & Li, Yongmei & Liu, Hailing & Qin, Sujuan & Wen, QiaoYan, 2023. "Quantum k-fold cross-validation for nearest neighbor classification algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006441. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.