Lecture Notes on Quantum Algorithms for Scientific Computation

TL;DR

This paper provides graduate-level lecture notes on quantum algorithms tailored for scientific computation, emphasizing matrix operations, quantum phase estimation, and their applications in solving complex scientific problems.

Contribution

It introduces quantum algorithms like QPE, block encoding, and quantum signal processing, focusing on their application to scientific computation tasks.

Findings

Explains quantum algorithms for eigenvalue problems

Demonstrates quantum methods for linear systems

Shows potential of quantum algorithms in scientific computing

Abstract

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.