Some topics in quantum control

Quantum control, that is control of individual quantum systems, attracts now high attention both due to fundamental interest and various existing and prospective applications in quantum technologies. In practical applications, controlled systems typically interact with the external environment, so that they are open quantum systems. We will discuss incoherent control of open quantum systems which uses spectral density of the environment as a tool to manipulate the system's dynamics, including a recent analysis of controllability and finding of unreachable sets of states for a qubit interacting with the environment. The controllability of controlled system is the first main question which should be answered. The next question is how difficult or easy to find optimal controls. This question is related to the analysis of quantum control landscapes. We will discuss various results on the analysis of quantum control landscapes, including a recent finding of trap-free behavior for single qubit phase-shift gate generation. In the context of gradient optimization for quantum technologies, we will discuss a convenient parametrization of quantum channels by points of the complex Stiefel manifold. Another topic is the control by measurements, including by back-action of non-selective measurements and feedback control, with possible applications to energy transfer in quantum photosynthesis.