Abstract

Quantum-classical hybrid dynamics is crucial for accurately simulating complex systems where both quantum and classical behaviors need to be considered. However, coupling between classical and quantum degrees of freedom and the exponential growth of the Hilbert space present significant challenges. Current machine learning approaches for predicting such dynamics, while promising, remain unknown in their error bounds, sample complexity, and generalizability. In this work, we establish a generic theoretical framework for analyzing quantum-classical adiabatic dynamics with learning algorithms. Based on quantum information theory, we develop a provably efficient adiabatic learning (PEAL) algorithm with logarithmic system size sampling complexity and favorable time scaling properties. We benchmark PEAL on the Holstein model, and demonstrate its accuracy in predicting single-path dynamics and ensemble dynamics observables as well as transfer learning over a family of Hamiltonians. Our framework and algorithm open up new avenues for reliable and efficient learning of quantum-classical dynamics.

Bio

刘锦鹏，清华大学数学科学中心助理教授，2022-2024年在麻省理工和伯克利任博士后，2022年博士毕业于马里兰大学，2017年本科毕业于北航-中科院华罗庚班。研究方向为量子科学计算与量子科学智能，发表PNAS、Nat.Commun. 、PRL、CMP、JCP、Quantum等期刊和NeurIPS、QIP、TQC等会议，受到Quanta、SIAM News、MATH+等科技媒体报道，担任量子信息权威期刊Quantum（JCR Q1，IF 6.4）的编委（中国高校仅3人）。