April 09, 2013, ESB 2001

Lie Algebras and Lie Groups provide a comprehensive set of tools for the analysis and control of closed quantum systems in finite dimensions. The starting point in this context is the Lie algebra rank condition which is the result describing the set of reachable states for a given quantum system. Starting from this result I will survey some of the main techniques from this approach: The analysis of quantum dynamics based on Levi's Theorem for decompositions of Lie algebras; The technique to obtain general constructive control for finite dimensional quantum system; The conditions to test indirect controllability when a quantum system is controlled via the interaction with an auxiliary system.

Domenico D'Alessandro has a Ph.D. degree in Electrical Engineering from the Universita' di Padova, Italy, and a Ph.D. in Mechanical and Environmental Engineering from the University of California, Santa Barbara. Since August 1999, he has been with the Department of Mathematics at Iowa State University as an Assistant Professor (from 1999 until 2004), an Associate Professor (from 2004 until 2009) and as a Professor (from 2009 until today). On faculty development program he visited the Institute of Quantum Electronics at ETH, Zurich in 2004 and the Department of Mathematics of the University of Minnesota, Minneapolis, in 2010. He was the recipient in 2000 along with Mohammed Dahleh and Igor Mezic of the IEEE George Axelby Award for work on entropy based quantification and control of mixing. He received the NSF Career Award in 2003 and the Iowa State Foundation Award for Early Achievement in Research in 2004. Dr. D'Alessandro is the author of the book 'Introduction to Quantum Control and Dynamics' . He also authored papers in both quantum physics and control. He is an associate editor for SIAM Journal of Control and Optimization. His main research interest is in the area of control of quantum mechanical systems, nonlinear and geometric control theory, quantum information and mathematical physics.