谁能与量子计算机竞争？基于张量网络的量子启发式计算技术讲义
Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques
AI总结：
本讲义系统介绍张量网络核心算法（MPS/MPO），强调其作为超大矩阵线性代数工具，涵盖DMRG、TCI等算法，并展示在量子计算模拟、量子退火和偏微分方程求解中的应用。
摘要：
这是一套关于张量网络的讲义，重点强调涉及矩阵乘积态（MPS）和矩阵乘积算符（MPO）的核心算法。与其他介绍相比，本讲义特别注重将张量网络与量子多体问题的方面分离：MPO/MPS算法被呈现为处理极大（指数级）矩阵和向量上的线性代数的一种方式，而不考虑任何特定应用。讲义包括寻找MPO特征向量的著名算法（著名的DMRG）、解决线性问题的算法，以及最近的学习算法，该算法允许将已知函数映射到MPS中（张量交叉插值，即TCI算法）。讲义最后讨论了如何使用“量子化”表示来表示函数并用张量网络进行微积分。它们包括重要MPO的详细解析构造，例如用于微分、不定积分、卷积和量子傅里叶变换的MPO。详细讨论了三个具体应用：量子计算机的模拟（精确或压缩）、量子退火器的模拟，以及在“量子化”表示中求解偏微分方程（例如泊松方程、扩散方程或Gross-Pitaevskii方程）的技术。本讲义设计为对一年级博士生可读，并包含所有陈述的详细证明。
英文摘要：
This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are presented as a way to deal with linear algebra on extremely (exponentially) large matrices and vectors, regardless of any particular application. The lectures include well-known algorithms to find eigenvectors of MPOs (the celebrated DMRG), solve linear problems, and recent learning algorithms that allow one to map a known function into an MPS (the Tensor Cross Interpolation, or TCI, algorithm). The lectures end with a discussion of how to represent functions and perform calculus with tensor networks using the "quantics" representation. They include the detailed analytical construction of important MPOs such as those for differentiation, indefinite integration, convolution, and the quantum Fourier transform. Three concrete applications are discussed in detail: the simulation of a quantum computer (either exactly or with compression), the simulation of a quantum annealer, and techniques to solve partial differential equations (e.g. Poisson, diffusion, or Gross-Pitaevskii) within the "quantics" representation. The lectures have been designed to be accessible to a first-year PhD student and include detailed proofs of all statements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
