Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Strategies towards evaluation beyond scientific impact

Various research fields, like organic agricultural research, are dedicated to solving real-world problems and contributing to sustainable development. Therefore, systems research and the application of interdisciplinary and transdisciplinary approaches are increasingly endorsed. However, research performance depends not only on self-conception, but also on framework conditions of the scientific system, which are not always of benefit to such research fields. Recently, science and its framework conditions have been under increasing scrutiny as regards their ability to serve societal benefit. This provides opportunities for (organic) agricultural research to engage in the development of a research system that will serve its needs. This article focuses on possible strategies for facilitating a balanced research evaluation that recognises scientific quality as well as societal relevance and applicability. These strategies are (a) to strengthen the general support for evaluation beyond scientific impact, and (b) to provide accessible data for such evaluations. Synergies of interest are found between open access movements and research communities focusing on global challenges and sustainability. As both are committed to increasing the societal benefit of science, they may support evaluation criteria such as knowledge production and dissemination tailored to societal needs, and the use of open access. Additional synergies exist between all those who scrutinise current research evaluation systems for their ability to serve scientific quality, which is also a precondition for societal benefit. Here, digital communication technologies provide opportunities to increase effectiveness, transparency, fairness and plurality in the dissemination of scientific results, quality assurance and reputation. Furthermore, funders may support transdisciplinary approaches and open access and improve data availability for evaluation beyond scientific impact. If they begin to use current research information systems that include societal impact data while reducing the requirements for narrative reports, documentation burdens on researchers may be relieved, with the funders themselves acting as data providers for researchers, institutions and tailored dissemination beyond academia.