A quantum computer offers both the potential to solve certain problems more efficiently than any classical computer and to contribute to questions across practically the entire spectrum of physical research, as well as beyond, through quantum simulations. One of the most advanced approaches to realizing a quantum computer to date is based on ultracold ions trapped in a Paul trap. The main challenge here, as with all other physical implementation methods, lies in the development of a complete system that can be scaled into a quantum computer capable of solving problems of practical relevance. This dissertation contributes to the efforts to develop technologies for the realization of a scalable ion-based quantum computer. An optical method for the precise determination of the position of trapped ions based on fluorescence light is presented, which allows localization in all three spatial dimensions with an accuracy well below the wavelength of the ion fluorescence. This method enables the development of a novel approach to minimizing undesired micromotion of trapped ions. The approach is based on the analysis of ion trajectories generated by deliberate manipulation of the trapping potential of an ion trap and is particularly suitable for use with extended, planar trap chips, as it is independent of the propagation direction of the laser light used. Furthermore, a method is developed to use a trapped ion as a highly sensitive force sensor, capable of detecting forces in the yoctonewton range. This method is also based on optical position determination and requires only knowledge of the trapping potential in addition. It is highly compatible with miniaturized and highly integrated ion traps, making it suitable for applications in precision metrology. The use of magnetic field gradients enables the manipulation of individual qubits and the realization of multi-qubit gates solely through radiofrequency signals. Due to their high integrability, this represents a potential key technology for scaling ion-based quantum computers. Thiswork extends the functionality of a microstructured ion trap with integrated solenoid structures to include a dynamically controllable magnetic field gradient. The generated gradients can be static or oscillating and can be varied on timescales in the microsecond range. Oscillating magnetic field gradients enable the acceleration of multiqubit gates as well as the creation of customized, temporary coupling patterns between qubits. The newly created degree of freedom provided by dynamic gradient control is used to demonstrate optimized qubit addressing in the frequency domain.

The term sustainability is omnipresent in everyday language. This gives the impression that the interpretation of what is or could be sustainable not only varies slightly, but also diverges across a broader spectrum. “Sustainability” is instrumentalized by the most diverse interest groups for their respective purposes: Sustainable consumption, sustainable growth, sustainable stock market returns - do they really exist? This mixture of interpretations and knowledge leads to a completely inconsistent and barely comprehensible concept of sustainability, which has also become established in common parlance. This paper uses various examples to show that the school sector also suffers from this little reflected approach. Even a clear definition of the concept of sustainability is all too often a desideratum in schools, which inevitably leads to intellectual difficulties that naturally prevent adequate competencies for action. The curriculum analysis of the concept of sustainability shows that the topic is of little importance in the teaching context. “Sustainability” is not defined by way of example, but instead appears in different contexts and connotations. When examining teaching materials for schools, this ambiguity is clearly recognizable: sustainability is predominantly used to describe processes in the sense of “lasting”. If sustainability is to be used as a criterion in other cases, there is usually no definition given. As shown in this doctoral thesis, it can also be demonstrated on the basis of students' views and behaviors that they are hardly focused on the classic idea of sustainability - namely the regenerative capacity of resources. The dissertation takes these findings as its starting point and sets itself the main goal of placing the discussion on sustainability in schools on a solid scientific basis. This is based on the classic sustainability discourse, which, however, requires a conceptual expansion. This expansion proposed by the author is aimed at aspects of sustainability that are frequently mentioned in today's social discussion on the one hand and can be derived from the idea of classical sustainability on the other. There are five aspects of sustainability, whose interaction is being explained, form the basis of a model of a “sustainability traffic light” proposed by the author. This “sustainability traffic light” makes it possible to deal with the complex of sustainability in a targeted manner, for example a discussion of different issues in the classroom guided by criteria. The primary aim is not to assign the “label” of sustainability, but to compare and weigh up different civilizational behaviors. In addition, tasks are provided for lessons to illustrate sustainability in practice. This enables conceptually clean and fact-based intellectual discussions on the topic of sustainability in the classroom.

Deep Neural Networks (DNNs) have proven to be successful in various computer vision applications such that vision models even infer in safety-critical situations. Therefore, the models need to be robust to disturbances such as image noise or blur. While seminal benchmarks exist to evaluate model robustness to diverse image corruptions, blur is often approximated in an overly simplistic way to model e.g. defocus, while ignoring the different blur kernel shapes that result from optical systems. This thesis proposes several test methods and datasets of optical blur corruptions, referred to as OpticsBench and LensCorruptions. OpticsBench examines primary aberrations such as coma, defocus, and astigmatism, i.e. aberrations that can be represented by varying a single parameter of Zernike polynomials and are easy to interpret. The OpticsBench method ensures comparability of the optical blur corruptions to in-size or in-accuracy matched references to investigate relative distribution shifts. To go beyond the principled but synthetic setting of primary aberrations, LensCorruptions samples linear combinations in the vector space spanned by Zernike polynomials, corresponding to real lenses. The evaluation on differently blurred ImageNet-1k images shows that the results for models confronted to the OpticsBench blur and to a disk-shaped reference blur, vary up to 5 % and the class-wise accuracy varies up to 30 % for optical image corruptions against a disk-shaped reference. We therefore conclude that the colour-dependent kernel shape must be taken into account when testing the model robustness as the accuracy cannot be explained sufficiently with the reference blur accuracy. To this end, we provide a large test dataset of optical blur distribution shifts, using the complementary LensCorruptions method, which simplifies future robustness research. The evaluation shows that some models favour certain blur types when confronted with a large number of lens blurs. Since increased image blur is generally detrimental to performance, we also show that the performance loss caused by optical aberrations can be significantly compensated for using the OpticsAugment data augmentation method and demonstrate superior performance compared to a strong baseline on both the proposed optical blur test datasets and 2D and 3D corruptions. Finally, since lens blur generally depends on the image location, a space-variant image blur corruption and corresponding test dataset are discussed on the Berkeley Deep Drive automotive dataset for several object detection models. To analyse how this spatial variance may affect the local performance of object detection models, the local evaluation method SRIA is proposed. In summary, the thesis provides several concepts and methods to test for optical blur corruptions and to improve the model robustness. The combination of these efficient evaluation methods and improvements in model robustness increases the safety of future computer vision systems.

Quantum computers promise to solve computational problems more efficiently than classical computers ever could. Trapped 171Yb+ ions in a linear Paul trap exposed to a magnetic field gradient have already been used to demonstrate quantum computing. The qubits are encoded in hyperfine states of the electronic ground state of 171Yb+ ions. The susceptibility of the qubit levels to magnetic fields by a linear Zeeman effect generates the coupling of the qubits and allows for individual addressing in frequency space. In a register of qubits stored in a linear Paul trap, the coupling generated by the magnetic field gradient is an inherent all-to-all coupling. Implementing a given quantum circuit on a register of qubits requires tuning the coupling strength. Here tuning the coupling with up to four qubits is demonstrated using a pulsed dynamical decoupling sequence, which protects the qubits from dephasing while the coupling can be chosen. Direct implementation of quantum gates with three or more qubits is necessary to exploit the full capabilities of a trapped-ion quantum computer. An example is the Toffoli gate implemented here. A driving field, applied to the target qubit, is used to perform a conditional rotation based on the control qubits state, while a dynamical decoupling sequence protects the coherence of the qubits. The Toffoli gate is then applied in a half-adder and is used to generate a three-qubit Greenberger Horne Zeilinger state. Half-adders, which are used as elementary units in classical computer science, form the basis of classical arithmetic units. In a quantum computer, they can be realized using the Toffoli gate and a CNOT gate. Perceptrons are a part of neural networks, a fundamental building block in modern computer science. Here a Perceptron gate is demonstrated on a register of three qubits where two qubits serve as control qubits and one as a perceptron. The characteristic tunable sigmoid excitation of the perceptron is shown using an adiabatic driving field interleaved with a dynamical decoupling sequence to prolong coherence times and tune the interaction strength between the qubits. The perceptron is then applied in a two-layer neural network to implement an XNOR operation. In addition to its use as a qubit, the dependence of the qubit resonance on the magnetic field allows an ion qubit to be used as a quantum sensor for magnetic fields and thus, using a magnetic field gradient, to measure forces in the 10^(-23) N range.