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.

Land use change from rainforests to oil palm plantations and food gardens in Papua New Guinea: Effects on soil properties and S fractions

Changes in soil sulfur (S) fractions were assessed in oil palm and food garden land use systems developed on forest vegetation in humid tropical areas of Popondetta in northern Province. The study tested a hypothesis that S in food gardens are limiting nutrient factor and are significantly lower than in plantations and forests. Subsistence food gardens are under long-term slash and burn practice of cropping and such practice is expected to accelerate loss of biomass S from the ecosystem. From each land use, surface soil (0–15 cm) samples were characterised and further pseudocomplete fractionated for S. Conversion of forest to oil palm production decreased (p<0.001) soil pH and electrical conductivity values. The reserve S fraction in soil increased significantly (p<0.05) due to oil palm production ( 28 %) and food gardening activity (∼ 54 %). However, plant available SO42--S was below 15 mg kg^(−1) in the food garden soils and foliar samples of sweet potato crop indicating deficiency of plant available S. Soil organic carbon content (OC) was positively and significantly correlated to total S content (r=0.533; p<0.001) among the land use systems. Thus, crop management practices that affect OC status of the soils would potentially affect the S availability in soils. The possible changes in the chemical nature of mineralisable organic S compounds leading to enhanced mineralisation and leaching losses could be the reasons for the deficiency of S in the food garden soils. The results of this study conclude that long-term subsistence food gardening activity enriched top soils with reserve S or total S content at the expense of soluble S fraction. The subsistence cropping practices such as biomass burning in food gardens and reduced fallow periods are apparently threatening food security of oil palm households. Improved soil OC management strategies such as avoiding burning of fallow vegetation, improved fallows, mulching with fallow biomass, use of manures and S containing fertilisers must be promoted to sustain food security in smallholder oil palm system.