In the first semester of this two-semester course, the basics of the mathematical apparatus for solving problems of control of closed quantum systems are considered. An overview of the typical classes of optimal control problems with Mayer type objective functionals and with coherent control in the Hamiltonian is given. The main theorems about the controllability of quantum systems are presented. The properties of the control landscapes for closed quantum systems are discussed, including theorems about the absence of traps in the kinematic landscape for N-level quantum systems and the absence of traps in the dynamic landscape for two-level quantum systems, including the tasks of creating target states and generating quantum gates. An existence of higher traps for quantum systems with dimension more than two is discussed. Some numerical optimization methods are described. Various key concepts are presented such as the Pontryagin maximum principle, the quantum control landscape, expansions of the objective functionals to the first/second order, gradient and Hessian of the objective functionals, singular controls, traps in control tasks, etc.

Fall Semester Schedule of 2024/2025:

Time: Monday 13:10 – 14:35

First lecture: September 9

Lecturers
Pechen Alexander Nikolaevich
Volkov Boris Olegovich
Morzhin Oleg Vasilevich

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