发表机构
International Iberian Nanotechnology Laboratory (INL); Albert-Ludwigs-Universität Freiburg; EUCOR Centre for Quantum Science and Quantum Computing; Laboratoire d’Informatique de Paris 6, CNRS, Sorbonne Université; Quandela; DIENS, École Normale Supérieure, PSL University, CNRS, INRIA; Department of Engineering, University of Minho; Department of Physics, Korea Advanced Institute of Science and Technology（伊比利亚纳米技术实验室; 弗赖堡大学; EUCOR量子科学与量子计算中心; 巴黎第六大学计算机实验室; Quandela; 法国高等师范学院; 米尼奥大学工程学院; 韩国科学技术院物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出高效经典算法，在加性误差内近似估计玻色子采样线性统计量，统一了分子振动谱模拟与探测器分箱粗粒化方法，并可用于评估基于玻色子采样的单向函数。
AI 中文摘要
玻色子采样是展示量子计算优势的重要候选方案，但大规模玻色子采样器能否找到有用的计算应用仍不清楚。挑战在于，要使用玻色子采样器估计（例如）物理可观测量，必须对输出分布进行粗粒化处理，这是因为输出空间规模呈指数级增长，且玻色子采样分布具有反集中特性。在本工作中，我们分析了一类基于输出光子占据数的线性函数的玻色子采样分布粗粒化方法的复杂性，我们称之为线性统计量。我们提出了一种高效的经典算法，用于在加性误差内近似估计不同输入态（如福克态和压缩态）下玻色子采样器的线性统计量。这使我们能够在同一框架内统一近期关于模拟分子振动电子谱的高效量子启发经典算法，以及基于探测器分箱的粗粒化分布的高效经典近似结果。此外，我们展示了如何利用我们的算法经典地评估一种基于玻色子采样的单向函数提案，而其他密码学应用的提案则超出了我们经典模拟技术的范围。我们留下非线性统计量的经典可模拟性问题作为开放问题，并将其与计算具有一层相互作用的线性光学电路跃迁振幅的问题联系起来。
英文摘要
Boson Sampling is a prominent candidate for the demonstration of quantum computational advantage but it remains unclear whether a large-scale boson sampler can find useful computational applications. The challenge is that to use a boson sampler to estimate, for example, a physical observable, it is necessary to coarse grain the outcome distribution, owing to the exponential size of the outcome space and the anti-concentration properties of the Boson Sampling distribution. In this work, we analyse the complexity of a specific type of coarse-graining of Boson Sampling distributions based on linear functions of the output photon occupation numbers, which we refer to as linear statistics. We present an efficient classical algorithm for approximating linear statistics of boson samplers within additive error for different kinds of input states, such as Fock states and squeezed states. This allows us to unify in the same framework recent results on efficient quantum-inspired classical algorithms for simulating molecular vibronic spectra, or efficient classical approximations of coarse-grained distributions based on detector binning. Additionally, we show how our algorithm can be used to classically evaluate a proposed one-way function based on Boson Sampling, while other proposals for cryptographic applications escape our classical simulation techniques. We leave open the question of classical simulability of non-linear statistics and connect it to the problem of computing transition amplitudes of linear-optical circuits with one layer of interactions.
Comments10 pages, 3 figures, 8 pages of appendix
