Lecture Notes on Quantum Algorithms for Scientific Computation

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.

Cited by in corpus (10)

• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• FABLE: Fast Approximate Quantum Circuits for Block-Encodings
• Towards Quantum Computational Mechanics
• Stable factorization for phase factors of quantum signal processing
• Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
• Solving the Hele-Shaw flow using the Harrow-Hassidim-Lloyd algorithm on superconducting devices: A study of efficiency and challenges
• The cost of solving linear differential equations on a quantum computer: fast-forwarding to explicit resource counts
• Dictionary-based Block Encoding of Sparse Matrices with Low Subnormalization and Circuit Depth
• Ladder Operator Block-Encoding
• Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme