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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
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    References listed on IDEAS

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    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).
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