Recent advances in quantum control

Quantum control is nowadays an important area of modern mathematical physics which attracts much interest due to rich mathematical problems and many existing and prospective applications ranging from quantum information and computing to laser control of chemical reaction. General quantum control problems can be formulated as maximization of certain objective functionals of the control field. In this talk we will outline some recent major results in quantum control including proof of complete controllability of open quantum systems, relation of quantum control of open systems to optimization on complex Stiefel manifolds, and the analysis of traps, i.e. local but not global optima, in quantum control landscapes (which is the graph of the objective functional) including recently discovered first proof of the absence of traps for qubits and nowel unexpected results on the existence of trapping behavour for multilevel quantum systems.