  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.
