What can quantum optics say about complexity theory?
暂无分享,去创建一个
Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPP^{NP} complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output.
[1] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[2] Larry J. Stockmeyer,et al. The complexity of approximate counting , 1983, STOC.
[3] L. Mandel,et al. Optical Coherence and Quantum Optics , 1995 .
[4] Zach DeVito,et al. Opt , 2017 .