Recent progress in quantum control landscapes

We will overview some directions in modern theory of quantum control—control of atomic and molecular scale systems obeying quantum dynamics. High interest to this topic is motivated by numerous existing and prospective applications ranging from quantum information and computing to laser control of chemical reactions and laser-assisted accelerators. We will start from the mathematical description of the dynamics of closed and open quantum systems, formulate various objectives, and outline recent progress in the analysis of local extrema (traps) in quantum control landscapes.