Environment as a resource for controlling quantum systems

In this talk, we consider environment as a resource for controlling quantum systems. We will discuss a speed-up of generating mixed states for an open qubit using coherent control and time-dependent incoherent control found with GPM approach, as well as using gradient search for this problem. We will present rigorous results about convergence of the speed gradient method to optimal solution for a dissipative quantum oscillator driven by coherent and incoherent controls, and discuss conditions on the parameters of the method which guarantee that the obtained controls are physical. In addition, we will discuss recent results on Hessian structure of quantum control landscape for single qubit gate generation.