Abstract
Boson sampling is strongly believed to be intractable for classical computers but solvable with photons in linear optics, which raises widespread concern as a rapid way to demonstrate the quantum supremacy. However, due to its solution is mathematically unverifiable, how to certify the experimental results becomes a major difficulty in the boson sampling experiment. Here, we develop a statistical analysis scheme to experimentally certify the collision-free boson sampling. Numerical simulations are performed to show the feasibility and practicability of our scheme, and the effects of realistic experimental conditions are also considered, demonstrating that our proposed scheme is experimentally friendly. Moreover, our broad approach is expected to be generally applied to investigate multi-particle coherent dynamics beyond the boson sampling.
Highlights
Quantum computers offer the promise of efficiently solving certain problems, such as factorization[1], that are intractable for classical computers
A novel statistical approach towards the certification of boson sampling experiments has been proposed by Walschaers et al.[37], which provides an efficient and reliable strategy for distinguishing different particle types, such as bosons, distinguishable particles, fermions, or simulated bosons, by analyzing the two mode correlation function of the output state
To show the practicability and reliability of our scheme, numerical simulations are performed to demonstrate our scheme could still work with limited samples, and our scheme could tolerate a moderate amount of experimental noise while strong noise will be identified and excluded
Summary
He-Liang Huang[1,2,3], Han-Sen Zhong[2,3], Tan Li1,2, Feng-Guang Li1,2, Xiang-Qun Fu1,2, Shuo Zhang[1,2], Xiang Wang1,2 & Wan-Su Bao[1,2]. A novel statistical approach towards the certification of boson sampling experiments has been proposed by Walschaers et al.[37], which provides an efficient and reliable strategy for distinguishing different particle types, such as bosons, distinguishable particles, fermions, or simulated bosons, by analyzing the two mode correlation function of the output state. Suppose we consider sufficiently many choices for output modes i, j ∈ {1, ..., m}, i < j, and compute the corresponding two mode correlation function Cij. a set of data C = {Cij|i, j ∈ {1, ..., m} and i < j} could be obtained, on which we can do some further statistical analysis to construct a proper discriminator, which could clearly reveal the different characteristics of collision-free boson sampling and other types of sampling and could be used to certify the genuine collision-free boson sampling. Compared to[37], two more typical types of sampling (uniform sampling and thermal state sampling) are added as a comparison to show the universality of our scheme
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