报告时间：2024年7月2日（周二）上午10:00 (10:00, July 2, 2024)

报告地点：物质科研楼A309会议室(Room A309 , Material Science Building)

报告题目：Geometric Analysis and Control of Quantum Systems; Methodology. Recent Results and Outlook

报告人：Professor Domenico D’Alessandro, Iowa State University, USA

报告人简介：

Domenico D’Alessandro received the Ph.D. degree in electrical engineering from the University of Padua, Padova, Italy, in 1997, and the Ph.D. degree in mechanical engineering from the University of California, Santa Barbara, CA, USA, in 1999. Since then he has been with the Department of Mathematics at Iowa State University, Ames, IA, USA, as an Assistant Professor (1999–2004), an Associate Professor (2004–2009), and then as a Professor (2009–Today). He is the author of the book Introduction to Quantum Control and Dynamics Chapman and Hall/CRC, 2008 with second edition published in 2022. His research interests are in the area of systems and control theory with emphasis on nonlinear and geometric methods, mathematical physics, Lie algebras and Lie groups, and applications to quantum and biological systems. Dr. D’Alessandro has been an Associate Editor for SIAM Journal on Control and Optimization, from 2012 to 2018 and in 2023–today. He is the recipient of the IEEE George Axelby Outstanding Paper Award for work on quantification and control of mixing in fluid flows, in 2000. He was also a recipient of the NSF CAREER Award, and the Iowa State Foundation Award for Early Achievement in Research.

报告摘要：

Geometric and Lie algebraic notions give a very powerful set of tools for the analysis and the optimal control of finite dimensional quantum systems. The starting point is recognizing that the set of possible evolutions for a quantum system is the Lie group associated to the Lie algebra generated by the available Hamiltonians. Once such a Lie algebra is calculated one can decompose the dynamics into invariant subspaces and analyze and control the system as a parallel of different subsystems. If each system is controllable, the quantum system is called subspace controllable. 

In this talk I will summarize the basic ideas of the geometric approach to the control of quantum systems. One central concept is the concept of a group of symmetries. The presence of symmetries allows to split the state space into invariant subspaces in the analysis of quantum systems and to reduce optimal control problems to a lower dimensional space where the explicit design is often more tractable. Recent results in this context will be summarized. These  concern networks of spin systems with symmetric all to all interaction and the optimal control of quantum Lambda systems with an occupancy cost. Future research directions in this area will also be discussed.