Certification of Boson Sampling Devices with Coarse-Grained Measurements

A boson sampling device could efficiently sample from the output probability distribution of noninteracting bosons undergoing many-body interference. This problem is not only classically intractable, but its solution is also believed to be classically unverifiable. Hence, a major difficulty in experiment is to ensure a boson sampling device performs correctly. We present an experimental friendly scheme to extract useful and robust information from the quantum boson samplers based on coarse-grained measurements. The procedure can be applied to certify the equivalence of boson sampling devices while ruling out alternative fraudulent devices. We perform numerical simulations to demonstrate the feasibility of the method and consider the effects of realistic noise. Our approach is expected to be generally applicable to other many-body certification tasks beyond the boson sampling problem.

[1]  Andreas Buchleitner,et al.  Counting statistics of many-particle quantum walks , 2010, 1009.5241.

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

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

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

[5]  Nicolò Spagnolo,et al.  Experimental scattershot boson sampling , 2015, Science Advances.

[6]  Scott Aaronson,et al.  Bosonsampling is far from uniform , 2013, Quantum Inf. Comput..

[7]  J. Eisert,et al.  Reliable quantum certification of photonic state preparations , 2014, Nature Communications.

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

[9]  D Porras,et al.  Bose-Einstein condensation and strong-correlation behavior of phonons in ion traps. , 2004, Physical review letters.

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

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

[12]  V. Shchesnovich,et al.  Partial indistinguishability theory for multiphoton experiments in multiport devices , 2014, 1410.1506.

[13]  Shi-Liang Zhu,et al.  Trapped ion quantum computation with transverse phonon modes. , 2006, Physical review letters.

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

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

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

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

[18]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

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

[20]  Valery Shchesnovich,et al.  Sufficient condition for the mode mismatch of single photons for scalability of the boson-sampling computer , 2013, 1311.6796.

[21]  Barry C. Sanders,et al.  Generalized Multiphoton Quantum Interference , 2014, 1403.3433.

[22]  L. Duan,et al.  Scalable implementation of boson sampling with trapped ions. , 2013, Physical review letters.

[23]  Scott Aaronson,et al.  The Computational Complexity of Linear Optics , 2013, Theory Comput..

[24]  Jens Eisert,et al.  Boson-Sampling in the light of sample complexity , 2013, ArXiv.

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

[26]  S. Scheel,et al.  Permanents in linear optical networks , 2004, quant-ph/0406127.

[27]  Yasunobu Nakamura,et al.  Quantum computers , 2010, Nature.

[28]  Malte C. Tichy,et al.  Interference of identical particles from entanglement to boson-sampling , 2013, 1312.4266.