Bayesian approach to Boson sampling validation

The Boson sampling problem consists in sampling from the output probability distribution of a bosonic Fock state, after it evolves through a linear interferometer. There is strong evidence that Boson sampling is computationally hard for classical computers, while it can be solved naturally by bosons. This has led it to draw increasing attention as a possible way to provide experimental evidence for the quantum computational supremacy. Nevertheless, the very complexity of the problem makes it hard to exclude the hypothesis that the experimental data are sampled from a different probability distribution. By exploiting integrated quantum photonics, we have carried out a set of three-photon Boson sampling experiments and analyzed the results using a Bayesian approach, showing that it represents a valid alternative to currently used methods. We adopt this approach to provide evidence that the experimental data correspond to genuine three-photon interference, validating the results against fully and partially-distinguishable photon hypotheses.

[1]  A. Politi,et al.  Quantum Walks of Correlated Photons , 2010, Science.

[2]  E. Mazur,et al.  Femtosecond laser micromachining in transparent materials , 2008 .

[3]  A. Politi,et al.  Silica-on-Silicon Waveguide Quantum Circuits , 2008, Science.

[4]  Moochan B. Kim,et al.  Inefficiency of classically simulating linear optical quantum computing with Fock-state inputs , 2013, 1304.4206.

[5]  David C. Burnham,et al.  Observation of Simultaneity in Parametric Production of Optical Photon Pairs , 1970 .

[6]  A. Crespi,et al.  Integrated multimode interferometers with arbitrary designs for photonic boson sampling , 2013, Nature Photonics.

[7]  A. Politi,et al.  Shor’s Quantum Factoring Algorithm on a Photonic Chip , 2009, Science.

[8]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[9]  R. Feynman.  Simulating physics with computers , 1999 .

[10]  Andrew G. White,et al.  Photonic Boson Sampling in a Tunable Circuit , 2012, Science.

[11]  Peter C Humphreys,et al.  Multiphoton quantum interference in a multiport integrated photonic device , 2012, Nature Communications.

[12]  Scott Aaronson,et al.  Quantum Computing since Democritus , 2013 .

[13]  Philip Walther,et al.  Experimental boson sampling , 2012, Nature Photonics.

[14]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[15]  Shih,et al.  New high-intensity source of polarization-entangled photon pairs. , 1995, Physical review letters.

[16]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[17]  Timothy C. Ralph,et al.  Error tolerance of the boson-sampling model for linear optics quantum computing , 2011, 1111.2426.

[18]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[19]  Stefano Taccheo,et al.  Femtosecond writing of active optical waveguides with astigmatically shaped beams , 2003 .

[20]  Peter P Rohde,et al.  Scalable boson sampling with time-bin encoding using a loop-based architecture. , 2014, Physical review letters.

[21]  Nicolò Spagnolo,et al.  Experimental validation of photonic boson sampling , 2014, Nature Photonics.

[22]  Andreas Buchleitner,et al.  Stringent and efficient assessment of boson-sampling devices. , 2013, Physical review letters.

[23]  Jonathan P. Dowling,et al.  Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit for boson sampling , 2013, 1307.8238.

[24]  J. O'Brien,et al.  On the experimental verification of quantum complexity in linear optics , 2013, Nature Photonics.

[25]  Nicolò Spagnolo,et al.  General rules for bosonic bunching in multimode interferometers. , 2013, Physical review letters.

[26]  B. J. Metcalf,et al.  Boson Sampling on a Photonic Chip , 2012, Science.

[27]  G. Vallone,et al.  Two-particle bosonic-fermionic quantum walk via integrated photonics. , 2011, Physical review letters.