Quantum Algorithms for General Nonlinear Dynamics Based on the Carleman Embedding

Quantum Scientific Computation and Quantum Artificial Intelligence

Organizer：

Jin-Peng Liu 刘锦鹏 (YMSC)

Speaker：

Jingyao Wang

Ph.D. Student, Tsinghua University

Time：

Wed., 10:30-11:30 am, Nov 5, 2025

Venue：

Ningzhai 宁斋 104

Online:

腾讯会议/Voov: 963-193-309

Title:

Quantum Algorithms for General Nonlinear Dynamics Based on the Carleman Embedding

Abstract:

This talk overviews a recent framework that substantially broadens rigorous guarantees for Carleman linearization when simulating nonlinear ODEs on quantum computers. The authors pose three central questions—(i) when the truncated Carleman embedding converges, (ii) when efficient quantum algorithms follow, and (iii) whether exponential quantum advantage extends to genuinely nonlinear problems—and give positive answers in large regimes beyond purely dissipative dynamics. The work corrects prior analyses and broaden them with a list of Lyapunov-based mathematical tools mainly used in control theory before, and have found a much wider space of convergence for Carleman embedding than previous work. Some other recent work on Carleman may also be included in the talk.