H.B. Keller Colloquium
Lin Lin is a Professor in the Department of Mathematics at UC Berkeley, and a Senior Faculty Scientist in the Mathematics Group at Lawrence Berkeley National Laboratory. His research focuses on solving quantum many-body problems by developing both classical and quantum algorithms. He has received the Sloan Research Fellowship (2015), the National Science Foundation CAREER award (2017), the Department of Energy Early Career award (2017), the (inaugural) SIAM Computational Science and Engineering (CSE) early career award (2017), the Presidential Early Career Awards for Scientists and Engineers (PECASE) (2019), the ACM Gordon Bell Prize (Team, 2020), and the Simons Investigator in Mathematics award (2021).
Quantum computers promise transformative advances in scientific computing. Which challenges in this field stand to benefit most from quantum computation? We will begin by outlining some general criteria for achieving quantum advantages, and discuss how traditional scientific computing tasks may fit into this emerging computational paradigm. One particularly promising application is estimating the smallest eigenvalue of a Hermitian matrix, also known as the ground state energy estimation problem in quantum physics. We will present recent advancements in quantum algorithms for ground state energy estimation, as well as methods for estimating multiple eigenvalues simultaneously. With such developments, these tasks become particularly well-suited for early fault-tolerant quantum computers. A key ingredient for achieving this is the efficient processing of noisy signals on classical computers. We will also discuss how recent theoretical developments in this area contribute to advances in understanding classical signal processing techniques.