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High-efficiency multiphoton boson sampling


Boson sampling is considered as a strong candidate to demonstrate ‘quantum computational supremacy’ over classical computers. However, previous proof-of-principle experiments suffered from small photon number and low sampling rates owing to the inefficiencies of the single-photon sources and multiport optical interferometers. Here, we develop two central components for high-performance boson sampling: robust multiphoton interferometers with 99% transmission rate and actively demultiplexed single-photon sources based on a quantum dot–micropillar with simultaneously high efficiency, purity and indistinguishability. We implement and validate three-, four- and five-photon boson sampling, and achieve sampling rates of 4.96 kHz, 151 Hz and 4 Hz, respectively, which are over 24,000 times faster than previous experiments. Our architecture can be scaled up for a larger number of photons and with higher sampling rates to compete with classical computers, and might provide experimental evidence against the extended Church–Turing thesis.

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Figure 1: Experimental set-up for multiphoton boson-sampling.
Figure 2: The single-photon source and interferometer for boson sampling.
Figure 3: Experimental results for the three-, four- and five-boson sampling.
Figure 4: Validating boson-sampling results.


  1. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    Article  ADS  Google Scholar 

  2. Pan, J.-W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012).

    Article  ADS  Google Scholar 

  3. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014).

    Article  ADS  Google Scholar 

  4. Monz, T. et al. Realization of a scalable Shor algorithm. Science 351, 1068–1070 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  5. Aaronson, S. & Arkhipov, A. The computational complexity of linear optics. In Proc. 43rd Annual ACM Symp. Theory of Computing 333–342 (ACM, 2011).

    Google Scholar 

  6. Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

    Article  ADS  Google Scholar 

  7. Rohde, P. R. & Ralph, T. C. Error tolerance of boson-sampling model for linear optical quantum computing. Phys. Rev. A 85, 022332 (2012).

    Article  ADS  Google Scholar 

  8. Wu, J.-J. et al. Computing permanents for boson sampling on Tianhe-2 supercomputer. Preprint at (2016).

  9. Broome, M. A. et al. Photonic boson sampling in a tunable circuit. Science 339, 794–798 (2013).

    Article  ADS  Google Scholar 

  10. Spring, J. B. et al. Boson sampling on a photonic chip. Science 339, 798–801 (2013).

    Article  ADS  Google Scholar 

  11. Tillmann, M. et al. Experimental boson sampling. Nat. Photon. 7, 540–544 (2013).

    Article  ADS  Google Scholar 

  12. Crespi, A. et al. Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nat. Photon. 7, 545–549 (2013).

    Article  ADS  Google Scholar 

  13. Carolan, J . et al. Universal linear optics. Science 349, 711–716 (2015).

    Article  MathSciNet  Google Scholar 

  14. Bentivegna, M . et al. Experimental scattershot boson sampling. Sci. Adv. 1, e1400255 (2015).

    Article  ADS  Google Scholar 

  15. Carolan, J. et al. On the experimental verification of quantum complexity in linear optics. Nat. Photon. 8, 621–626 (2014).

    Article  ADS  Google Scholar 

  16. Spagnolo, N. et al. Experimental validation of photonic boson sampling. Nat. Photon. 8, 615–620 (2014).

    Article  ADS  Google Scholar 

  17. Loredo, J. C. et al. Boson sampling with single photon Fock states from a bright solid-state source. Preprint at (2016).

  18. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    Article  ADS  Google Scholar 

  19. Pittman, T., Jacobs, B. & Franson, J. Single photons on pseudodemand from stored parametric down-conversion. Phys. Rev. A 66, 042303 (2002).

    Article  ADS  Google Scholar 

  20. Kaneda, F. et al. Time-multiplexed heralded single-photon source. Optica 2, 1010–1013 (2015).

    Article  ADS  Google Scholar 

  21. Lund, A. P. et al. Boson sampling from a Gaussian state. Phys. Rev. Lett. 113, 100502 (2014).

    Article  ADS  Google Scholar 

  22. Lounis, B. & Orrit, M. Single photon sources. Rep. Prog. Phys. 68, 1129–1179 (2005).

    Article  ADS  Google Scholar 

  23. Michler, P. et al. A quantum dot single-photon turnstile device. Science 290, 2282–2285 (2000).

    Article  ADS  Google Scholar 

  24. Santori, C., Fattal, D., Vučković, J., Solomon, G. S. & Yamamoto, Y. Indistinguishable photons from a single photon device. Nature 419, 594–597 (2002).

    Article  ADS  Google Scholar 

  25. Tillmann, M. et al. Generalized multiphoton quantum interference. Phys. Rev. X 5, 041015 (2015).

    Google Scholar 

  26. Shchesnovich, V. S. Partial indistinguishability theory of multiphoton experiments in multiport devices. Phys. Rev. A 91, 013844 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  27. Tichy, M. C. Sampling of partially distinguishable bosons and the relation to multidimensional permanent. Phys. Rev. A 91, 022316 (2015).

    Article  ADS  Google Scholar 

  28. He, Y.-M. et al. On-demand semiconductor single-photon source with near-unity indistinguishability. Nat. Nanotech. 8, 213–217 (2013).

    Article  ADS  Google Scholar 

  29. Ding, X. et al. On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett. 116, 020401 (2016).

    Article  ADS  Google Scholar 

  30. Somaschi, N. et al. Near-optimal single-photon sources in the solid state. Nat. Photon. 10, 340–345 (2016).

    Article  ADS  Google Scholar 

  31. Wang, H. et al. Near-transform-limited single photons from an efficient solid-state quantum emitter. Phys. Rev. Lett. 116, 213601 (2016).

    Article  ADS  Google Scholar 

  32. Patel, R. B. et al. Two-photon interference of the emission from electrically tunable remote quantum dots. Nat. Photon. 4, 632–635 (2010).

    Article  ADS  Google Scholar 

  33. Clements, W. R., Humphreys, P. C., Metcalf, B. J., Kolthammer, W. S. & Walmsley, I. A. An optimal design for universal quantum multiport interferometers. Preprint at (2016).

  34. Aaronson, S. & Arkhipov, A. Boson sampling is far from uniform. Quant. Inf. Comp. 14, 1383–1432 (2014).

    Google Scholar 

  35. Bentivegna, M. et al. Bayesian approach to boson sampling validation. Int. J. Quant. Inf. 12, 1560028 (2014).

    Article  MathSciNet  Google Scholar 

  36. Cover, T. M. & Thomas, J. A. Elements of Information Theory (John Wiley & Sons, 2006).

    MATH  Google Scholar 

  37. Lita, A. E., Miller, A. J. & Nam, S. W. Counting near-infrared single-photons with 95% efficiency. Opt. Express 16, 3032–3040 (2008).

    Article  ADS  Google Scholar 

  38. Zadeh, I. E. et al. Single-photon detectors combining near unity efficiency, ultra-high detection-rates, and ultra-high time resolution. Preprint at (2016).

  39. Unsleber, S. et al. Highly indistinguishable on-demand resonance fluorescence photons from a deterministic quantum dot micropillar device with 74% extraction efficiency. Opt. Express 24, 8539–8546 (2016).

    Article  ADS  Google Scholar 

  40. Muller, A. et al. Resonant fluorescence from a coherent driven semiconductor quantum dot in a cavity. Phys. Rev. Lett. 99, 187402 (2007).

    Article  ADS  Google Scholar 

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We thank S. Aaronson, B. Sanders and P. Rohde for helpful discussions. This work was supported by the National Natural Science Foundation of China, the Chinese Academy of Sciences, the National Fundamental Research Program and the State of Bavaria.

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Authors and Affiliations



C.-Y.L. and J.-W.P. conceived and designed the experiment, C.S., M.K. and S.H. grew and fabricated the quantum dot samples. H.W., Y.H., Y.-H.L., Z.-E.S., B.L., H.-L.H., X.D., M.-C.C., C.L., J.Q., J.-P.L., Y.-M.H., C.S., M.K., C.-Z.P., S.H. and C.-Y.L. performed the experiment, S.H., C.-Y. L. and J.-W.P. analysed the experimental data. C.-Y.L. and J.-W.P. wrote the paper.

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Correspondence to Chao-Yang Lu or Jian-Wei Pan.

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The authors declare no competing financial interests.

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Wang, H., He, Y., Li, YH. et al. High-efficiency multiphoton boson sampling. Nature Photon 11, 361–365 (2017).

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