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Mathematical methods for controlling quantum systems—individual atoms, molecules, etc.—represent important tools for quantum technologies. The development of such methods is of both high fundamental interest and significant demand due to various existing and promising applications of quantum technologies, such as construction of quantum computing devices (e.g., for high fidelity fast generation of qubit states and quantum gates), control of atomic and molecular dynamics, laser chemistry, nuclear magnetic resonance, etc. Methods for controlling quantum systems are being developed or applied at many of the world's leading research centers and large corporations. This course examines the fundamentals of the mathematical apparatus of quantum system control methods. The first semester examines methods for controlling closed quantum systems, i.e., systems isolated from the environment. The second semester is primarily devoted to methods for controlling open quantum systems. We discuss typical classes of optimal control problems, controllability conditions, analytical results about local properties of objective functionals for quantum gate generation and transition probability maximization problems, properties of quantum control landscapes, including questions about the existence of traps, the Pontryagin maximum principle, time optimal control, Lyapunov-based design, and quantum feedback control. We also examine control of open quantum systems with coherent and/or incoherent controls, control problems in terms of Kraus maps, and related optimization on complex Stiefel manifolds. Numerical optimization methods, such as GRAPE method and genetic algorithms, are also discussed.
Spring Semester Schedule of 2025/2026:
Time: Wednesday 13:10 – 14:35
First lecture: February 4
 RSS: Forthcoming seminars
 Lecturers
Volkov Boris Olegovich
Pechen Alexander Nikolaevich
Organizations
Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
