论文标题
关于科学计算的量子算法的讲义
Lecture Notes on Quantum Algorithms for Scientific Computation
论文作者
论文摘要
这是一套在2021年秋季学期的数学系，加州大学伯克利分校数学系的应用数学课程中使用的一组讲义的注释，称为“科学计算量子算法”。这些讲座说明仅着重于量子算法与科学计算相关的量子算法，尤其是Matrix Compution。本讲录的主要目的是引入量子相估计（QPE）和``QPE''方法，例如块编码，量子信号处理和量子奇异值转换，并证明其在求解特征值问题，线性系统方程式系统和差分方程方面的应用。预期的受众是有兴趣使用易于故障量子计算机来解决具有挑战性的科学计算问题的广泛计算科学与工程（CSE）社区。
This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture notes focus only on quantum algorithms closely related to scientific computation, and in particular, matrix computation. The main purpose of the lecture notes is to introduce quantum phase estimation (QPE) and ``post-QPE'' methods such as block encoding, quantum signal processing, and quantum singular value transformation, and to demonstrate their applications in solving eigenvalue problems, linear systems of equations, and differential equations. The intended audience is the broad computational science and engineering (CSE) community interested in using fault-tolerant quantum computers to solve challenging scientific computing problems.
