In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we first discuss how to compute the permanent efficiently on a parallel computer, followed by algorithms which provide an exponential speed-up for sparse matrices and linear run times for matrices of limited bandwidth. The parallel algorithm has been implemented in a freely available software package, also available in an efficient serial version. As part of the timing runs for this package we set a new world record for the matrix order on which a permanent has been computed. Next we perform a simulation study of several conjectures regarding the distribution of the permanent for random matrices. Here we focus on permanent anti-concentration conjecture, which has been used to find the classical computational complexity of Boson sampling. We find a good agreement with the basic versions of these conjectures and based on our data we propose refined versions of some of them. For small systems we also find noticable deviations from a propose strengthening of a bound for the number of photons in a Boson sampling system.
Weak Permanent Anti-Concentration for Random Gaussian Matrices in Boson Sampling
University of Glasgow（格拉斯哥大学）；City University of Hong Kong（香港城市大学）；Southern University of Science and Technology（南方科技大学）；National University of Singapore（新加坡国立大学）；International Quantum Academy（国际量子学院）
High performance Boson Sampling simulation via data-flow engines
Eötvös Loránd University（罗兰大学）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院哥白尼天文学中心）；ACC Cyfronet, University of Science and Technology, Cracow（克拉科夫科学技术大学 ACC Cyfronet）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；Wigner Research Centre for Physics of the Hungarian Academy of Sciences（匈牙利科学院维格纳物理研究中心）；Maxeler Technologies, a Groq company（Maxeler Technologies（Groq旗下公司））；Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）；NASK National Research Institute（NASK国家研究所）
Bipartite Gaussian Boson Sampling for Hamiltonian Cycles in Directed Graphs
College of Computer Science and Technology, National University of Defense Technology（国防科技大学计算机学院）；College of Advanced Interdisciplinary Studies, National University of Defense Technology（国防科技大学前沿交叉学院）
线性光学量子计算的一个基本问题是理解物理系统中量子霸权的起源。发现多模线性光学跃迁振幅是通过跃迁算子矩阵的积和来计算的，这是经典模拟中的一个难题（玻色子采样问题）。我们可以通过考虑直接决定计算跃迁振幅的运行时间的量子测度来理解这个问题。本文提出了一种量子度量--“Fock态并发和”$C_S$，它是对“广义Fock态并发”（一种类似于纠缠和相干的广义并发的度量）所有成员的求和.通过引入广义算法计算的Fock状态玻色子采样与任意数量的光子每模式的跃迁振幅，我们表明，所有已知的算法的最小经典运行时间直接依赖于$C_S$。因此，我们可以说，\emph{the Fock state concurrence sum $C_S$ behaves as a collective measure that controls the computational complexity of Fock state BS}。我们期望我们对Fock态并发在积算中的作用的观察将为解释线性光学的量子计算能力提供一个统一的观点。
