Research On Bayesian Validation Approaches To Boson Sampling

Quantum supremacy is a milestone in quantum computation research,representing the surpass of quantum computing setup over the fastest classical computers in some specific questions,it's an important area in quantum computing research.While boson sampling model is a promising candidate to demonstrate quantum supremacy,the corresponding mathematical problem is daunting task for classical computers,however the physical implementations only requires the identical photons?linear optical network and passive detectors,so it's much feasible to achieve.Boson sampling validation is crucial the implementation in related research.However the valid verification for the experimental setups remains a challenge.The deterministic validation approach which validate the output results completely is an exponential problem,and it's unfeasible to extend to he large scale experiments.However current approach is partial validation based on the limited samples from physical setups,which aims to exclude some common mistakes.However the current ideal-experiment-based partial validation method does not consider the impact of noise,for example,the photons can not be perfectly identical.This paper combines with practical physical circumstances,improving the current validation approach by commonly-used Bayesian validation approach in physical experiments to overcome the noise in experiments.Besides the validation number complexity becomes a key point when experiment scale extends and the validation complexity grows exponentially.The main contributions of this research is as follows:(1)Slope-based Bayesian validation based on imperfect photons boson sampling.This study proposes a slope-based approach which is an extended Bayesian validation to detect the imperfectly identical photons boson sampling.The experiments show that the proposed approach can describe the impact of photon indistinguishability,validating boson sampling against the classical particles distribution and uniform distribution correctly.(2)Validation number complexity based on ideal boson sampling.Connecting the cross entropy benchmark with Bayesian validation approach,then displaying the variational tendency of Bayesian validation numbers in theory or simulations with numerical simulations.The expected Bayesian validation number tends to decrease as boson sampling scales up.This result provides theoretical support for the boson sampling physical experiments.(3)Numerical simulations on boson sampling Bayesian validation approach.This paper demonstrate Markov chain monte carlo method to simulate the boson sampling output samples under the circumstance that the scale of current physical boson sampling is relatively small,the Bayesian validations are simulated both in ideal and imperfectly identical photon boson sampling.