Some Methods of Construction of Controls for Quantum Systems

Recently, various control problems for quantum systems, such as individual atoms, molecules, electron states at quantum points, etc. have been actively researched. In this paper, we briefly discuss methods of construction of controls for quantum system by means of gradient algorithms, genetic algorithms, and the speed gradient. The violation of the asymptotic stabilizability condition for the problem of generation of unitary operations is proved by the speed gradient method in two-level quantum systems.