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  • Open Access

Quantum Computational Advantage of Noisy Boson Sampling with Partially Distinguishable Photons

Byeongseon Go1, Changhun Oh2,*, and Hyunseok Jeong1,†

  • *Contact author: changhun0218@gmail.com
  • †Contact author: h.jeong37@gmail.com
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PRX Quantum 6, 030362 – Published 25 September, 2025

DOI: https://doi.org/10.1103/rflv-gc66

Abstract

Boson sampling stands out as a promising approach toward experimental demonstration of quantum computational advantage. However, the presence of physical noise in near-term experiments hinders the realization of quantum computational advantage with boson sampling. Since physical noise in near-term boson-sampling devices is inevitable, precise characterization of the boundary of noise rates where the classical intractability of boson sampling is maintained is crucial for quantum computational advantage using near-term devices. In this work, we identify the level of partial-distinguishability noise that upholds the classical intractability of boson sampling. We find that boson sampling with on average O(logN) distinguishable photons out of N input photons maintains the equivalent complexity to the ideal boson-sampling case. By providing strong complexity-theoretical evidence for the classical intractability of noisy boson sampling, we expect that our findings will ultimately facilitate the demonstration of quantum computational advantage with noisy boson-sampling experiments in the near future.

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Popular Summary

Boson sampling is one of the most promising candidates for experimental demonstration of quantum computational advantage because of its experimental feasibility and strong evidence of computational complexity. However, the presence of physical noise in current experimental setups, such as photon loss and partial distinguishability, hinders the demonstration of quantum computational advantage, which allows efficient classical simulation as the noise rate increases. Since physical noise in near-term boson-sampling devices is unavoidable, precise characterization of the boundary of noise rates where the classical intractability of boson sampling is maintained is crucial for quantum computational advantage using near-term devices.

In this work, we identify the level of partial-distinguishability noise that upholds the classical intractability of boson sampling. We find that boson sampling with, on average, a logarithmic number of distinguishable photons over the input photons maintains the equivalent complexity to the ideal boson-sampling case. The key idea is to show the average-case hardness of noisy boson sampling by establishing complexity-theoretical reduction from the current average-case hardness result of ideal boson sampling, which is polytime reducible for at most a logarithmic number of photons that become distinguishable on average. This indicates that such noisy boson sampling still upholds the classical intractability of ideal boson sampling.

We believe that our results can help in understanding the regimes of classical intractability for noisy boson sampling and can serve as a benchmark for the level of physical noise to achieve quantum computational advantage with near-term boson-sampling experiments.

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PRX Quantum 6, 030362– Published 25 September, 2025
  • Received 22 February 2025
  • Revised 8 July 2025
  • Accepted 15 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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