Speaker: 安冬，北京大学-北京国际数学研究中心

Inviter: 邵长鹏

Title: Quantum eigenvalue transformation from and beyond Hamiltonian simulation

Language: Chinese

Time & Venue: 2024.01.14 15:00-16:00 数学院南楼420

Abstract: Quantum computers are expected to simulate unitary dynamics (i.e., Hamiltonian simulation) much faster than classical computers. However, most scientific computing applications involve non-unitary eigenvalue transformations. In this talk, we will discuss quantum algorithms for implementing those non-unitary eigenvalue transformations. We will start with a recently proposed quantum algorithm for solving general linear differential equations. The idea of the algorithm is to reduce general differential equations to a linear combination of Hamiltonian simulation (LCHS) problems. For the first time, this approach allows quantum algorithms to solve linear differential equations with near-optimal dependence on all parameters. Additionally, we will discuss how to apply the idea of LCHS to design quantum algorithms for various other non-unitary eigenvalue transformation operators. [arXiv:2303.01029, 2312.03916, 2411.04010]