Host: 刘锦鹏

Abstract: Quantum computation technology has drawn significant attention in recent years, particularly due to its promise in accelerating the solution of sophisticated computational tasks, such as optimization and machine learning. Among the extensive literature in the field, an emerging paradigm involves designing novel quantum optimization algorithms via dynamical systems. In this talk, we introduce Quantum Hamiltonian Descent (QHD), a quantum optimization algorithm inspired by the interplay between accelerated gradient descent and Hamiltonian mechanics. Similar to its classical counterpart, a global convergence result for convex optimization is obtained through Lyapunov analysis. Notably, for nonconvex problems, QHD exhibits drastically different behavior due to quantum interference. The quantum advantage of QHD is investigated through both theoretical and numerical means. We will also discuss the natural generalization of QHD using higher-order information, which leads to a new class of quantum algorithms with faster convergence and potentially better global performance.

Bio: Jiaqi Leng is a Simons Quantum Postdoctoral Fellow at Simons Institute for the Theory of Computing at UC Berkeley, hosted by Umesh Vazirani and Lin Lin. Jiaqi got his Ph.D. from the University of Maryland in 2024, advised by Xiaodi Wu. His research focuses on quantum algorithms for continuous optimization and scientific computing. Specifically, he advocates Hamiltonian-oriented quantum algorithm design, a new paradigm in quantum computation that emphasizes both provable quantum speedups and realistic hardware implementability.