Lecture Notes on Quantum Algorithms for Scientific Computation

Understand

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.