Geometry of random landscapes for control of a qubit

Control of quantum systems is a rapidly growing area of mathematical physics. A fundamental problem in this area is to study the geometry of the control landscapes, that is, graphs of the objective functionals. A typical situation is the presence of noise in the control that leads to the need of investigation of the geometry of random control landscapes. In this report we will present our recent results for geometry of random landscapes for control of a qubit which is a basic element of quantum information theory and quantum computing.