Universität Innsbruck

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    Problem-Driven Compilation of Quantum Optimization Algorithms for Graph Coloring

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    Quantum computing holds the potential to efficiently solve certain problems believed to be intractable for classical computers. Realizing this potential, however, requires substantial physical resources, including large qubit counts, sufficient connectivity, and long coherence times. As current quantum devices are still far from this regime, the efficient compilation of quantum algorithms into hardware-compatible instructions remains a central challenge in quantum computing, especially for near-term applications. A representative example of such applications is combinatorial optimization, where exponentially large search spaces motivate quantum algorithms that leverage interference to approximate solutions more efficiently than classical heuristics, even at modest system sizes. Two prominent paradigms in this context are quantum annealing and the Quantum Approximate Optimization Algorithm (QAOA): Quantum annealing realizes optimization via continuous-time quantum dynamics implemented on analog hardware, while QAOA is a variational, gate-based approach that builds parameterized quantum circuits from problem-specific Hamiltonians. Both paradigms require compilation strategies tailored to the constraints of their respective hardware architectures. Most existing compilation strategies are problem-agnostic and therefore broadly applicable, yet often suboptimal for specific tasks. This thesis uses the graph coloring problem as a case study to investigate a problem-driven approach to quantum compilation, where structural features of the problem class are exploited to design tailored compilation schemes that offer improved efficiency and scalability for the targeted application. To address hardware connectivity constraints, the presented approaches adopt the parity framework, which encodes long-range interactions into single-qubit terms. This thesis develops two novel problem-driven compilation methods for the graph coloring problem, the Bandwidth-Optimized LHZ layout and the 2D-Twine circuit. The former leverages bandwidth minimization to optimize parity encodings for analog quantum annealers, while the latter constructs QAOA unitaries for gate-based optimization using parallelized Parity Twine circuits. Both approaches are benchmarked against general-purpose methods and demonstrate substantial improvements in qubit usage or circuit complexity. These results illustrate the advantages of incorporating problem structure into the compilation process and provide a proof-of-concept for the effectiveness of problem-driven compilation strategies.Masterarbeit Universität Innsbruck 202

    Numerical Simulation of Cosmic-ray transport in cylindrical coordinates

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    In this thesis we present a newly developed solver for the numerical solution of the cos- mic ray transport equation in cylindrical coordinates. This solver was implemented in the PICARD code. The numerical scheme presented here uses a multiple-semicoarsening multigrid scheme, which allows the solver to accurately solve problems with large anisotropies in the cou- pling coefficients. In order to solve the cosmic ray transport equation using an it- erative matrix solver we discretized the problem in cylindrical coordinates using the finite difference method. The newly developed solver was validated using the method of manufactured solutions and compared to a preexisting cylindrical solver. We further tested the solver in PICARD and compared the results to a cartesian multigrid solver. These tests showed, that the new cylindrical solver gives correct results and has advan- tages compared to the already implemented cylindrical solver. Among these is, that the multiple-semicoarsening multigrid solver can solve problems with anisotropic diffusion coefficients, whereas the preexisting cylindrical solver fails to give correct results for these configurations.Masterarbeit Universität Innsbruck 202

    Barrier reverse convertibles and information : an experiment on the influence of information on risk assessment

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    This thesis examines the impact of information on risk assessment and investment decision-making by private, non-professional investors in the context of multi-asset Barrier Reverse Convertibles (BRCs). BRCs are a type of equity-linked structured product, and previous literature has identified systematic risk misperception regarding investment in BRCs. This misperception can be attributed to a cognitive bias, which is either explained by the conjunction fallacy or the dieter's paradox. The objective of this thesis is to ascertain whether the dissemination of information has the potential to mitigate the misperceptions private investors have regarding BRCs and whether the provision of different types of information exerts a substantial influence on their risk assessment and investment decision-making processes. In order to ascertain the influence of information, an online survey was conducted with 116 participants. The aim was to gain insights into the effect of five information levels. The participants provided their assessment of the risk and indicated their level of willingness to invest in a specific multi-asset BRC, which was outlined in the factsheet provided at the outset. The results indicate that the provision of information to private and unprofessional investors is associated with an increase in their risk perception. Furthermore, as more information becomes available, we expect to see a decrease in the number of participants willing to invest in the multi-asset BRC. The findings of this study provide a valuable addition to the existing literature on financial decision-making by underscoring the pivotal role that information plays in mitigating behavioural biases. Furthermore, this thesis offers implications for policy makers based on the results and theoretical framework that suggest that displaying additional information for investors significantly changes their risk perception and therefore their decision to invest in multi-asset BRCs.Tobias RunggDiplomarbeit Universität Innsbruck 202

    Measurement and analysis of lateral sway of ropeway cabins depending on wind conditions

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    Annabel Galliani, BScMasterarbeit Universität Innsbruck 202

    Effekte einer kurzfristigen Vorakklimatisation auf physiologische submaximale Belastungsparameter in Hypoxie

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    Masterarbeit Universität Innsbruck 202

    Die Reichsritterschaft Vils : Entstehung, herrschaftlich-urbane Strukturen & Verflechtung einer edelfreien Herrschaft zu König und Reich

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    Diese Masterarbeit untersucht die Entwicklung der Herrschaft Vils zur Reichsritterschaft im Kontext des Heiligen Römischen Reiches. Dabei liegt der Fokus auf der Frage, ob die Herrschaft Vils die Kriterien für Reichsunmittelbarkeit erfüllte und welche Verflechtungen zwischen der Reichsritterschaft, dem Reichsoberhaupt und zentralen Institutionen bestanden. Ergänzend werden die städtischen Strukturen von Vils analysiert, um seine Funktion als mittelalterliche Stadt und Teil der Reichsritterschaft zu bewerten. Trotz des Stadtrechts von 1327 blieb Vils stark von der Herrschaft der Hohenegger geprägt und vereinte städtische und dörfliche Elemente. Der Untersuchungszeitraum reicht von der Mitte des 13. Jahrhunderts, mit dem Niedergang der Staufer, bis zum Tod Kaiser Maximilians I. Die Ergebnisse zeigen, dass Vils ein Paradebeispiel für die Dynamik zwischen lokaler Herrschaft und Reichspolitik darstellt.This master's thesis examines the development of the lordship of Vils into an Imperial Knighthood within the context of the Holy Roman Empire. The focus lies on whether Vils met the criteria for imperial immediacy and the connections between the Imperial Knighthood, the Emperor, and central institutions of the Empire. Additionally, the urban structures of Vils are analyzed to assess its role as a medieval town and part of the Imperial Knighthood. Despite being granted town rights in 1327, Vils remained heavily influenced by the rule of the Hohenegger family, blending urban and rural elements. The study spans from the mid-13th century, during the decline of the Hohenstaufen dynasty, to the death of Emperor Maximilian I. in 1519. The findings demonstrate that Vils serves as an exemplary case of the dynamics between local lordship and imperial politics.Masterarbeit Universität Innsbruck 202

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