Introduction to Quantum Control and Dynamics (Advances in Applied Mathematics)

The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory.

To advantage students, instructors and practitioners, and since the field is highly interdisciplinary, this book presents an introduction with all the basic notions in the same place. The field has seen a large development in parallel with the neighboring fields of quantum information, computation and communication. The author has maintained an introductory level to encourage course use.

After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics.

Changes to the New Edition:

• New Chapter 4: Uncontrollable Systems and Dynamical Decomposition
• New section on quantum control landscapes
• A brief discussion of the experiments that earned the 2012 Nobel Prize in Physics
• Corrections and revised concepts are made to improve accuracy

Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematics, physics and engineering work.

Domenico D’Alessandro received a Ph.D. degree in Electrical Engineering from the University of Padua (Italy) and a Ph.D. in Mechanical Engineering from the University of California, Santa Barbara. He is Professor of Mathematics at Iowa State University. He has held visiting positions at Tsinghua University in Beijing and USTC in Hefei (both in China), the Institute of Mathematics and Applications in Minneapolis, and ETH Zurich. He received the IEEE George Axelby Outstanding Paper Award for work on quantification and control of mixing in fluid flows. He received the NSF CAREER Award and the Iowa State Foundation Award for Early Achievement in Research. His research interests are in the areas 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.