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Solving perfect matchings by frequency-grouped multi-photon events using a silicon chip

Author

Listed:
  • Pingyu Zhu

    (National University of Defense Technology)

  • Qilin Zheng

    (National University of Defense Technology)

  • Kun Wang

    (National University of Defense Technology)

  • Miaomiao Yu

    (National University of Defense Technology)

  • Gongyu Xia

    (National University of Defense Technology)

  • Jiacheng Liu

    (National University of Defense Technology)

  • Yong Liu

    (National University of Defense Technology)

  • Zhihong Zhu

    (National University of Defense Technology)

  • Ping Xu

    (National University of Defense Technology
    Hefei National Laboratory)

Abstract

Computing the number of perfect matchings of a graph is a famous #P-complete problem. In this work, taking the advantages of the frequency dimension of photon, we propose and implement a photonic perfect matching solver, by combining two key techniques, frequency grouping and multi-photon counting. Based on a broadband photon-pair source from a silicon quantum chip and a wavelength-selective switch, we configure graphs up to sixteen vertices and estimate the perfect matchings of subgraphs up to six vertices. The experimental fidelities are more than 90% for all the graphs. Moreover, we demonstrate that the developed photonic system can enhance classical stochastic algorithms for solving nondeterministic-polynomial-time(NP) problems, such as the Boolean satisfiability problem and the densest subgraph. Our work contributes a promising method for solving the perfect matchings problem, which is simple in experiment setup and convenient to transform or scale up the object graph by regulating the frequency-correlated photon pairs.

Suggested Citation

  • Pingyu Zhu & Qilin Zheng & Kun Wang & Miaomiao Yu & Gongyu Xia & Jiacheng Liu & Yong Liu & Zhihong Zhu & Ping Xu, 2025. "Solving perfect matchings by frequency-grouped multi-photon events using a silicon chip," Nature Communications, Nature, vol. 16(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-58711-8
    DOI: 10.1038/s41467-025-58711-8
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