Quantum algorithms for eigenvalue problems

**Abstract:** The problem of finding the smallest eigenvalue of a Hermitian matrix (also called the ground state energy) has wide applications in quantum physics. In this talk, I will first briefly introduce the mathematical setup of quantum algorithms, and discuss how to use textbook quantum algorithms to tackle this problem. I will then introduce a new quantum algorithm that can significantly and provably reduce the circuit depth for solving this problem (the reduction can be around two orders of magnitude). This algorithm reduces the requirement on the maximal coherent time for the quantum computer, and can therefore be suitable for early fault-tolerant quantum devices. No prior knowledge on quantum algorithms is necessary for understanding most parts of the talk.

(Joint work with Zhiyan Ding)

**Bio:** Lin Lin received his B.S. degree in Computational Mathematics from Peking University in 2007, and Ph.D. degree in Applied and Computational Mathematics from Princeton University in 2011, advised by Professor Weinan E and Professor Roberto Car. His research focuses on the development of efficient and accurate numerical methods for electronic structure calculations, with broad applications in quantum chemistry, quantum physics and materials science. His recent interests also include quantum algorithms for scientific computation, and neural network methods for quantum many-body problems. He is currently an associate professor in the Department of Mathematics at UC Berkeley, a faculty scientist at Berkeley Lab’s Mathematics Group within the Applied Mathematics and Computational Research Division, and a mathematician within Berkeley Lab's Center for Advanced Mathematics for Energy Research Applications (CAMERA). 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).