Control of Open Quantum Systems: Examples & Methods for Non-Markovian Dynamics

Usually open quantum systems are considered to be under the influence of noise and therefore faulty. On the other hand, a controlled system is regarded as something stable and predictable. It is often neglected, that the two aspects are very closely related. A perfectly isolated quantum system will not be subject to environmental influences, but this makes it also impossible to interact with it in any manner. Controlling and measuring such a system is impossible and therefore of no technical relevance. Every system used in any technological device therefore must be in contact with its environment. The question, which is the starting point of this thesis is whether it is possible to not only control a system despite of its contact to some environment, but whether there are cases, where this interaction can be necessary, or at least helpful for certain control tasks. The first part of the thesis focuses on such a task, namely the purification of a qubit. Here the environment is essential, in order to serve as an entropy sink. The simplicity of the chosen model allowed us to derive the necessary time for the purification process analytically for arbitrary controls and interactions. This is helpful for architectures, where implementations of various configurations is possible. The second half of the thesis covers more methodogical work. In the example of the qubit reset, we see that the necessary time to perform the task is determined by the coupling between the system and environment. In order to perform such tasks fast, we have to develop a framework, which allows to analyse systems beyond the usual weakcoupling limit. There exists so far no general method for the propagation of such systems, which also allows for thermalisation. The surrogate Hamiltonian method is a promising candidate to capture dynamics beyond the weak-coupling limit and its extension, the stochastic surrogate Hamiltonian, allows for thermalisation. We expand the stochastic surrogate Hamiltonian by introducing a new method of performing stochastic swaps. This method is then tested on a simple example model.