Changes in amino acid enantiomers and microbial performance in soils from a subtropical mountain oasis in Oman abandoned for different periods

An important feature of maintaining the agricultural stability in millennia-old mountain oases of northern Oman is the temporary abandonment of terraces. To analyse the effects of a fallow period on soil microbial performance, i.e. microbial activity and microbial biomass, samples of eight terrace soils abandoned for different periods were collected in situ, assigned to four fallow age classes and incubated for 30 days in the laboratory after rewetting. The younger fallow age classes of 1 and 5 years were based on the records of the farmers’ recollections, the two older fallow age classes of 10–20 and 25–60 years according to the increase in the D -to- L ratio of valine and leucine enantiomers. The increase in these two ratios was in agreement with that of the D -to- L ratio of lysine. The strongest relationship was observed between the increase in the D -to- L ratio of lysine and the decrease in soil microbial biomass C. However, the most stringent coherence between the increase in fallow age and soil properties was revealed by the decreases in cumulative respiration and net N mineralisation rates with decreasing availability of substrate to soil microorganisms. During the 30-day incubation following rewetting, relative changes in microbial activity (respiration and net N mineralisation) and microbial biomass (C and N)indices were similar in the eight terrace soils on a fallow age-class-specific level, indicating that the same basic processes occurred in all of the sandy terrace soils investigated.

Optimizing Robust Quantum Gates in Open Quantum Systems

We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum properties – due to unwanted interaction with the environment. This thesis addresses the problem of implementing entangling two-qubit quantum gates that are robust with respect to both decoherence and classical noise. It covers three aspects: the use of efficient numerical tools for the simulation and optimal control of open and closed quantum systems, the role of advanced optimization functionals in facilitating robustness, and the application of these techniques to two of the leading implementations of quantum computation, trapped atoms and superconducting circuits. After a review of the theoretical and numerical foundations, the central part of the thesis starts with the idea of using ensemble optimization to achieve robustness with respect to both classical fluctuations in the system parameters, and decoherence. For the example of a controlled phasegate implemented with trapped Rydberg atoms, this approach is demonstrated to yield a gate that is at least one order of magnitude more robust than the best known analytic scheme. Moreover this robustness is maintained even for gate durations significantly shorter than those obtained in the analytic scheme. Superconducting circuits are a particularly promising architecture for the implementation of a quantum computer. Their flexibility is demonstrated by performing optimizations for both diagonal and non-diagonal quantum gates. In order to achieve robustness with respect to decoherence, it is essential to implement quantum gates in the shortest possible amount of time. This may be facilitated by using an optimization functional that targets an arbitrary perfect entangler, based on a geometric theory of two-qubit gates. For the example of superconducting qubits, it is shown that this approach leads to significantly shorter gate durations, higher fidelities, and faster convergence than the optimization towards specific two-qubit gates. Performing optimization in Liouville space in order to properly take into account decoherence poses significant numerical challenges, as the dimension scales quadratically compared to Hilbert space. However, it can be shown that for a unitary target, the optimization only requires propagation of at most three states, instead of a full basis of Liouville space. Both for the example of trapped Rydberg atoms, and for superconducting qubits, the successful optimization of quantum gates is demonstrated, at a significantly reduced numerical cost than was previously thought possible. Together, the results of this thesis point towards a comprehensive framework for the optimization of robust quantum gates, paving the way for the future realization of quantum computers.