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Distinguishing noisy boson sampling from classical simulations

Profile image of valery shchesnovichvalery shchesnovich

2021, Quantum

https://doi.org/10.22331/Q-2021-03-29-423
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Abstract

Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise. Recently found classical algorithms can efficiently approximate, to any small error, the output of boson sampling with finite-amplitude noise. In this work it is shown analytically and confirmed by numerical simulations that one can efficiently distinguish the output distribution of such a noisy boson sampling from the approximations accounting for low-order quantum multiboson interferences, what includes the mentioned classical algorithms. The number of samples required to tell apart the quantum and classical output distributions is strongly affected by the previously unexplored parameter: density of bosons, i.e., the ratio of total number of interfering bosons to number of input ports of interferometer. Such critical dependence is strikingly remi...

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References (82)

  1. R. Feynman. Simulating Physics with Com- puters. Int. J. Theoret. Phys. 21, 467-488 (1982).
  2. P. W. Shor. Algorithms for quantum com- putation: discrete logarithms and factoring. Proceedings of the 35th Annual Symposium Foundations of Computer Science (IEEE, New York, 1994), p. 124-134.
  3. J. Preskill. Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018).
  4. S. Aaronson and A. Arkhipov, The compu- tational complexity of linear optics. Theory of Computing 9, 143 (2013).
  5. M. J. Bremner, A. Montanaro, and D. J. Shepherd. Achieving quantum supremacy with sparse and noisy commuting quantum computations. Quantum 1, 8 (2017).
  6. J. Bermejo-Vega, D. Hangleiter, M. Schwarz, R. Raussendorf, and J. Eisert. Architectures for Quantum Simulation Showing a Quantum Speedup. Phys. Rev. X 8, 021010 (2018).
  7. S. O. Boixo, S. V. Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Brem- ner, J. M. Martinis, and H. Neven. Char- acterizing quantum supremacy in near-term devices. Nature Physics, 14, 595-600 (2018).
  8. X. Gao, S.-T. Wang, and L.-M. Duan. Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model. Phys. Rev. Lett. 118, 040502 (2017).
  9. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505- 510 (2019).
  10. G. Kalai. The Quantum Computer Puzzle. Notices of the AMS, 63, 508-516 (2016).
  11. A. Arkhipov and G. Kuperberg. The bosonic birthday paradox. Geometry & Topology Monographs 18, 1-7 (2012).
  12. E. R. Caianiello. On quantum field the- ory -I: explicit solution of Dyson's equa- tion in electrodynamics without use of Feyn- man graphs. Nuovo Cimento, 10, 1634- 1652 (1953); Combinatorics and Renormal- ization in Quantum Field Theory, Frontiers in Physics, Lecture Note Series (W. A. Ben- jamin, Reading, MA, 1973).
  13. S. Scheel. Permanents in linear optical net- works. arXiv:quant-ph/0406127.
  14. L. G. Valiant. The complexity of computing the permanent. Theoretical Comput. Sci., 8, 189-201 (1979).
  15. M. Jerrum, A. Sinclair, and E. Vigoda. A polynomial-time approximation algorithm for the permanent of a matrix with nonnega- tive entries. Journal of the ACM 51, 671-697 (2004).
  16. S. Aaronson. A linear-optical proof that the permanent is #P-hard. Proc. Roy. Soc. Lon- don A, 467, 3393-3405 (2011).
  17. H. Ryser, Combinatorial Mathematics (Cams Mathematical Monographs, No. 14; published by The Mathematical Association of America, distributed by John Wiley and Sons, 1963).
  18. M. A. Broome, A. Fedrizzi, S. Rahimi- Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White. Photonic Boson Sampling in a Tunable Circuit. Science 339, 794-798 (2013).
  19. J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley. Boson Sampling on a Photonic Chip. Sci- ence, 339, 798-801 (2013).
  20. M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther. Exper- imental boson sampling. Nature Photonics, 7, 540-544 (2013).
  21. A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvão, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino. Integrated multimode interfer- ometers with arbitrary designs for photonic boson sampling. Nature Photonics, 7, 545- 549 (2013).
  22. J. Carolan, J. D. A. Meinecke, P. J. Shad- bolt, N. J. Russell, N. Ismail, K. Wörhoff, T. Rudolph, M. G. Thompson, J. L. O'Brien, J. C. F. Matthews, and A. Laing. On the experimental verification of quantum com- plexity in linear optics. Nature Photonics, 8, 621-626 (2014).
  23. A. P. Lund, A. Laing, S. Rahimi-Keshari, T. Rudolph, J. L. O'Brien, and T. C. Ralph. Boson Sampling from a Gaussian State. Phys. Rev. Lett. 113, 100502 (2014).
  24. M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino. Experimental scattershot bo- son sampling. Science Advances 1, e1400255 (2015).
  25. H.-S. Zhong, L.-C. Peng, Y. Li, Y. Hu, W. Li, J. Qin, D. Wu, W. Zhang, H. Li, L. Zhang, Z. Wang et al. Experimental Gaus- sian Boson sampling. Science Bulletin, 64, 511-515 (2019).
  26. K. R. Motes, A. Gilchrist, J. P. Dowling, and P. P. Rohde. Scalable Boson Sampling with Time-Bin Encoding Using a Loop-Based Ar- chitecture. Phys. Rev. Lett. 113, 120501 (2014).
  27. Y. He, X. Ding, Z. E. Su, H. L. Huang, J. Qin, C. Wang, S. Unsleber, C. Chen, H. Wang, Y. M. He, et al. Time-Bin-Encoded Boson Sampling with a Single-Photon De- vice. Phys. Rev. Lett. 118, 190501 (2017).
  28. J. C. Loredo, M. A. Broome, P. Hilaire, O. Gazzano, I. Sagnes, A. Lemaitre, M. P. Almeida, P. Senellart, and A. G. White. Boson Sampling with Single-Photon Fock States from a Bright Solid-State Source. Phys. Rev. Lett. 118, 130503 (2017).
  29. H. Wang, Y. He, Y.-H. Li, Z.-E. Su, B. Li, H.-L. Huang, X. Ding, M.-C. Chen, C. Liu, J. Qin et al. High-efficiency multiphoton bo- son sampling. Nature Photonics 11, 361-365 (2017).
  30. H. Wang, W. Li, X. Jiang, Y. M. He, Y. H. Li, X. Ding, M. C. Chen, J. Qin, C. Z. Peng, C. Schneider et al. Toward Scalable Boson Sampling with Photon Loss. Phys. Rev. Lett. 120, 230502 (2018).
  31. H.-S. Zhong, Y. Li, W. Li, L.-C. Peng, Z.-E. Su, Y. Hu, Y.-M. He, X. Ding, W. Zhang, H. Li et al. 12-Photon Entanglement and Scal- able Scattershot Boson Sampling with Opti- mal Entangled-Photon Pairs from Paramet- ric Down-Conversion. Phys. Rev. Lett. 121, 250505 (2018).
  32. H. Wang, J. Qin, X. Ding, M.-C. Chen, S. Chen, X. You, Y.-M. He, X. Jiang, L. You, Z. Wang, C. Schneider, J. J. Renema, S. Höfling, C.-Y. Lu, and J.-W. Pan. Boson Sampling with 20 Input Photons and a 60- Mode Interferometer in a 10 14 -Dimensional Hilbert Space. Phys. Rev. Lett. 123, 250503 (2019).
  33. C. Shen, Z. Zhang, and L.-M. Duan. Scal- able Implementation of Boson Sampling with Trapped Ions. Phys. Rev. Lett. 112, 050504 (2014).
  34. B. Peropadre, G. G. Guerreschi, J. Huh, and A. Aspuru-Guzik. Proposal for Mi- crowave Boson Sampling. Phys. Rev. Lett. 117, 140505 (2016).
  35. S. Goldstein, S. Korenblit, Y. Bendor, H. You, M. R. Geller, and N. Katz. Decoher- ence and interferometric sensitivity of boson sampling in superconducting resonator net- works. Phys. Rev. B 95, 020502(R) (2017).
  36. A. Deshpande, B. Fefferman, M. C. Tran, M. Foss-Feig and A. V. Gorshkov. Dynami- cal Phase Transitions in Sampling Complex- ity. Phys. Rev. Lett. 121, 030501 (2018).
  37. B. Peropadre, J. Huk and C. Sabín. Dynam- ical Casimir Effect for Gaussian Boson Sam- pling. Scientific Reports 8, 3751 (2018).
  38. A. Neville, C. Sparrow, R. Clifford, E. John- ston, P. M. Birchall, A. Montanaro, and A. Laing. Classical boson sampling algo- rithms with superior performance to near- term experiments. Nature Physics 13, 1153- 1157 (2017).
  39. P. Clifford, and R. Clifford. The Classical Complexity of Boson Sampling. Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms pp. 146-55.
  40. G. Kalai and G. Kindler. Gaussian Noise Sensitivity and BosonSampling. arXiv:1409.3093 [quant-ph].
  41. A. Leverrier and R. García-Patrón. Anal- ysis of circuit imperfections in BosonSam- pling. Quant. Inf. & Computation 15, 489- 512 (2015).
  42. V. S. Shchesnovich. Sufficient condition for the mode mismatch of single photons for scalability of the boson-sampling computer. Phys. Rev. A 89, 022333 (2014).
  43. A. Arkhipov. BosonSampling is robust against small errors in the network matrix. Phys. Rev. A 92, 062326 (2015).
  44. S. Aaronson and D. J. Brod. BosonSampling with lost photons. Phys. Rev. A 93, 012335 (2016).
  45. L. Latmiral, N. Spagnolo and F. Sciarrino. Towards quantum supremacy with lossy scattershot boson sampling. New J. Phys. 18, 113008 (2016).
  46. P. P. Rohde and T. C. Ralph. Error toler- ance of the boson-sampling model for linear optics quantum computing. Phys. Rev. A 85, 022332 (2012).
  47. S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves. Sufficient Conditions for Efficient Classical Simulation of Quantum Optics. Phys. Rev. X 6, 021039 (2016).
  48. J. J. Renema, A. Menssen, W. R. Clements, G. Triginer, W. S. Kolthammer, and I. A. Walmsley. Efficient Classical Algorithm for Boson Sampling with Partially Distin- guishable Photons. Phys. Rev. Lett. 120, 220502 (2018).
  49. M. Oszmaniec and D. J. Brod. Classical sim- ulation of photonic linear optics with lost particles. New J. Phys. 20, 092002 (2018).
  50. R. García-Patrón, J. J. Renema, and V. S. Shchesnovich. Simulating boson sam- pling in lossy architectures. Quantum 3, 169 (2019).
  51. D. J. Brod and M. Oszmaniec. Classical sim- ulation of linear optics subject to nonuni- form losses. Quantum 4, 267 (2020).
  52. J. J. Renema, V. S. Shchesnovich, and R. García-Patrón. Classical simulability of noisy boson sampling. arXiv:1809.01953 [quant-ph].
  53. V. S. Shchesnovich. Noise in boson sampling and the threshold of efficient classical simu- latability. Phys. Rev. A 100, 012340 (2019).
  54. S. Aaronson and A. Arkhipov. Bosonsam- pling is far from uniform. Quant. Inform. & Computation 14, 1383 (2014).
  55. C. Gogolin, M. Kliesch, L. Aolita, and J. Eisert. Boson-Sampling in the light of sam- ple complexity. arXiv:1306.3995 [quant-ph].
  56. V. S. Shchesnovich. Universality of Gener- alized Bunching and Efficient Assessment of Boson Sampling. Phys. Rev. Lett. 116, 123601 (2016).
  57. M. Walschaers, J. Kuipers, J.-D. Urbina, K. Mayer, M. C. Tichy, K. Richter, and A. Buchleitner. Statistical benchmark for BosonSampling. New J. Phys. 18, 032001 (2016).
  58. T. Giordani, F. Flamini, M. Pompili, N. Vig- gianiello, N. Spagnolo, A. Crespi, R. Osel- lame, N. Wiebe, M. Walschaers, A. Buch- leitner, and F. Sciarrino. Experimental sta- tistical signature of many-body quantum interference. Nature Photonics 12, 173-178 (2018).
  59. S. T. Wang and L.-M. Duan. Certification of Boson Sampling Devices with Coarse- Grained Measurements. arXiv:1601.02627 [quant-ph].
  60. I. Agresti, N. Viggianiello, F. Flamini, N. Spagnolo, A. Crespi, R. Osellame, N. Wiebe, and F. Sciarrino. Pattern Recognition Tech- niques for Boson Sampling Validation. Phys. Rev. X 9, 011013 (2019).
  61. V. S. Shchesnovich. On the classical com- plexity of sampling from quantum interfer- ence of indistinguishable bosons. Int. J. of Quantum Inform. 18, 2050044 (2020).
  62. A. I. Barvinok. Two Algorithmic Results for the Traveling Salesman Problem. Math. of Oper. Research, 21 65-84 (1996); see theo- rem (3.3).
  63. V. S. Shchesnovich. Asymptotic evaluation of bosonic probability amplitudes in linear unitary networks in the case of large num- ber of bosons. Int. J. Quantum Inform. 11, 1350045 (2013); see appendix D.
  64. A. E. Moylett, R. García-Patrón, J. J. Ren- ema, and P. S. Turner. Classically simulat- ing near-term partially-distinguishable and lossy boson sampling. Quantum Sci. Tech- nol. 5, 015001 (2020).
  65. A. L. Migdall, D. Branning, and S. Castel- letto. Tailoring single-photon and multi- photon probabilities of a single-photon on- demand source. Phys. Rev. A 66, 053805. (2002).
  66. S. M. Barnett, C. R. Gilson, B. Huttner, and N. Imoto. Field Commutation Relations in Optical Cavities. Phys. Rev. Lett. 77, 1739 (1996).
  67. C. K. Hong, Z. Y. Ou, and L. Mandel. Mea- surement of subpicosecond time intervals be- tween two photons by interference. Phys. Rev. Lett. 59, 2044 (1987).
  68. V. S. Shchesnovich. Partial indistinguisha- bility theory for multiphoton experiments in multiport devices. Phys. Rev. A 91, 013844 (2015).
  69. R. P. Stanley, Enumerative Combinatorics, 2nd ed., Vol. 1 (Cambridge University Press, 2011).
  70. V. S. Shchesnovich and M. E. O. Bezerra. Collective phases of identical particles inter- fering on linear multiports. Phys. Rev. A 98, 033805 (2018).
  71. V. S. Shchesnovich and M. E. O. Bezerra. Distinguishability theory for time-resolved photodetection and boson sampling. Phys. Rev. A 101, 053853 (2020).
  72. Z. Puchala and J. A. Miszczak. Symbolic in- tegration with respect to the Haar measure on the unitary groups. Bull. Polish Acad. Sci.: Techn. Sci. 65, 21-27 (2017).
  73. V. S. Shchesnovich. Asymptotic Gaussian law for noninteracting indistinguishable par- ticles in random networks. Scientific Reports 7, 31 (2017).
  74. S. Rahimi-Keshari, A. P. Lund, and T. C. Ralph. What Can Quantum Optics Say about Computational Complexity Theory? Phys. Rev. Lett. 114, 060501 (2015).
  75. L. Chakhmakhchyan, N. J. Cerf, and R. García-Patrón. Quantum-inspired algo- rithm for estimating the permanent of posi- tive semidefinite matrices. Phys. Rev. A 96, 022329 (2017).
  76. A. Agresti and B. A. Coull. Approximate is Better than "Exact" for Interval Estima- tion of Binomial Proportions. The American Statistician 52, 119-126 (1998).
  77. N. N. Bogolyubov and N. N. Bogolyubov (Jr.), Introduction to Quantum Statistical Mechanics (Nauka, Moscow (1984)).
  78. M. N. J. R. Ensher, M. R. Math- ews, C. E. Wieman and E. A. Cornell. Ob- servation of Bose-Einstein Condensation in a Dilute Atomic Vapor. Science 269, 198-201 (1995).
  79. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle. Bose-Einstein Condensa- tion in a Gas of Sodium Atoms. Phys. Rev. Lett. 75, 3969 (1995).
  80. L. P. Pitaevskii. Vortex lines in an imperfect Bose gas. Soviet Phys. JETP 13, 451-454 (1961).
  81. E. P. Gross. Structure of a quantized vortex in boson systems. Il Nuovo Cimento 20, 454- 477 (1961).
  82. L. Takács. On the Method of Inclusion and Exclusion. J. of Amer. Stat. Assoc. 62, 102- 113 (1967).

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valery shchesnovich

2019

Inevitable noise is the main problem in demonstration of computational advantage of quantum devices, such as boson sampling, over digital computers. Can a noisy realization of boson sampling be efficiently and faithfully simulated classically? It is shown how one can distinguish the output distribution of noisy N-boson sampling from that of classical approximations with mixtures of quantum interferences of up to K≪√(N) bosons, with a number of samples that depends solely on K, noise amplitude and density of bosons ρ = N/M, where M is network size. The surprising result is that noisy boson sampling in a regime of finite density of bosons ρ< 1, i.e., on a small network M = N/ρ, retains scalable quantum advantage to arbitrary large number of bosons despite the presence of finite noise.

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