马尔可夫链蒙特卡罗光子损失玻色采样模拟

Simulation of Markov Chain Monte Carlo Boson Sampling Based on Photon Losses

光子在制备、传播和探测的过程中产生的损失极大地限制了玻色采样的量子计算优越性。为研究光学网络中光子损失对玻色采样结果的影响,基于Clements模型,通过马尔可夫链蒙特卡罗(MCMC)方法实现了4光子8模式的玻色采样模拟,并通过贝叶斯检验方法,对模拟获取的玻色采样结果和光子源处产生光子损失的玻色采样进行了区分。模拟结果表明,基于引入光子损失的光学网络,利用MCMC方法获取的采样结果均能有效通过贝叶斯检验。当MCMC采样样本之间的跳跃样本数增大,通过检验所需的样本数均逐渐减少并趋于稳定。而随着光学网络规模的增大,MCMC方法需要更大的跳跃样本数以达到快速通过贝叶斯检验的需求。通过MCMC方法成功模拟了光学网络中发生光子损失的玻色采样过程,为考虑误差的玻色采样研究提供了参考。

The losses during the preparation,propagation,and detection of photons greatly limit the quantum computing advantages of Boson sampling.Boson sampling simulations with four photons and eight modes are realized based on the Clements model using the Markov chain Monte Carlo(MCMC)method to study the influence of photon losses on Boson sampling results in optical networks,and the simulation results are validated and distinguished from the Boson sampling with photon losses at the photon source using the Bayesian test method.The simulation results show that by introducing photon losses based on the optical network,the sampling results obtained using the MCMC method can effectively satisfy the Bayesian test.The number of samples required to satisfy the Bayesian test decreases gradually and tends to be stable when the interval of samples increases.Conversely,as the scale of the optical network increases,the MCMC method requires a larger interval of samples to quickly satisfy the Bayesian test.In this study,Boson sampling with photon losses in optical networks is successfully simulated using MCMC method,giving a clue for Boson sampling researches while considering the errors.