H.B. Keller Colloquium

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.