Universität Stuttgart
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Item Open Access Über die Lösung der Navier-Stokes-Gleichungen mit Hilfe der Moore-Penrose-Inversen des Laplace-Operators im Vektorraum der Polynomkoeffizienten(2024) Große-Wöhrmann, Bärbel; Resch, Michael (Prof. Dr.-Ing.)Die bekannten numerischen Standard-Verfahren zur Lösung partieller Differentialgleichungen basieren auf einer räumlichen Diskretisierung des Berechnungsgebiets. Ihre Performance und Skalierbarkeit auf modernen massiv-parallelen Höchstleistungsrechnern ist von der Verfügbarkeit effizienter numerischer Verfahren zur Lösung linearer Gleichungssysteme abhängig. Angesichts grundlegender Herausforderungen erscheint die Entwicklung neuer Lösungsansätze sinnvoll. Ich stelle in dieser Arbeit einen Polynomansatz zur Lösung partieller Differentialgleichungen vor, der nicht auf einer räumlichen Diskretisierung beruht und mit Hilfe der Moore-Penrose-Inversen des Laplace-Operators die Entkopplung der Navier-Stokes-Gleichungen ermöglicht. Dabei ist der Grad der Polynome nicht grundsätzlich beschränkt, so dass eine hohe räumliche Auflösung erreicht werden kann.Item Open Access Rigorous compilation for near-term quantum computers(2024) Brandhofer, Sebastian; Polian, Ilia (Prof.)Quantum computing promises an exponential speedup for computational problems in material sciences, cryptography and drug design that are infeasible to resolve by traditional classical systems. As quantum computing technology matures, larger and more complex quantum states can be prepared on a quantum computer, enabling the resolution of larger problem instances, e.g. breaking larger cryptographic keys or modelling larger molecules accurately for the exploration of novel drugs. Near-term quantum computers, however, are characterized by large error rates, a relatively low number of qubits and a low connectivity between qubits. These characteristics impose strict requirements on the structure of quantum computations that must be incorporated by compilation methods targeting near-term quantum computers in order to ensure compatibility and yield highly accurate results. Rigorous compilation methods have been explored for addressing these requirements as they exactly explore the solution space and thus yield a quantum computation that is optimal with respect to the incorporated requirements. However, previous rigorous compilation methods demonstrate limited applicability and typically focus on one aspect of the imposed requirements, i.e. reducing the duration or the number of swap gates in a quantum computation. In this work, opportunities for improving near-term quantum computations through compilation are explored first. These compilation opportunities are included in rigorous compilation methods to investigate each aspect of the imposed requirements, i.e. the number of qubits, connectivity of qubits, duration and incurred errors. The developed rigorous compilation methods are then evaluated with respect to their ability to enable quantum computations that are otherwise not accessible with near-term quantum technology. Experimental results demonstrate the ability of the developed rigorous compilation methods to extend the computational reach of near-term quantum computers by generating quantum computations with a reduced requirement on the number and connectivity of qubits as well as reducing the duration and incurred errors of performed quantum computations. Furthermore, the developed rigorous compilation methods extend their applicability to quantum circuit partitioning, qubit reuse and the translation between quantum computations generated for distinct quantum technologies. Specifically, a developed rigorous compilation method exploiting the structure of a quantum computation to reuse qubits at runtime yielded a reduction in the required number of qubits of up to 5x and result error by up to 33%. The developed quantum circuit partitioning method optimally distributes a quantum computation to distinct separate partitions, reducing the required number of qubits by 40% and the cost of partitioning by 41% on average. Furthermore, a rigorous compilation method was developed for quantum computers based on neutral atoms that combines swap gate insertions and topology changes to reduce the impact of limited qubit connectivity on the quantum computation duration by up to 58% and on the result fidelity by up to 29%. Finally, the developed quantum circuit adaptation method enables to translate between distinct quantum technologies while considering heterogeneous computational primitives with distinct characteristics to reduce the idle time of qubits by up to 87% and the result fidelity by up to 40%.Item Open Access Gold nanoparticle-mediated DNA origami nanoarchitectures(2024) Peil, Andreas; Na Liu, Laura (Prof. Dr.)Since its origin in the 1980s, DNA (deoxyribonucleic acid) nanotechnology has established itself as a captivating nanofabrication technique with ever increasing impact that combines aspects from physics, chemistry, and biology to construct artificial nanosystems by means of molecular self assembly. Within the field of DNA nanotechnology, the DNA origami technique represents one of the most versatile fabrication tools to craft functional two-dimensional (2D) and three-dimensional (3D) nanostructures from the bottom up. These structures offer precisely tailored geometries along with programmable functions, featuring positional addressability with sub-5 nm resolution and exceptional spatiotemporal accuracy. This thesis discusses strategies to employ the DNA origami technique to assemble intricate hybrid nanosystems with synergistically integrated gold nanoparticles (AuNPs). The AuNPs take over different roles; they grant (i) structural and (ii) functional features and enable the (iii) optical monitoring of the systems. This approach allows the fabrication of nanostructures piece by piece to explore their structural and functional properties at the nanoscale in detail. The first publication covers different strategies for the hierarchical assembly of topological DNA origami structures using a AuNP-templated self-assembly approach. The assembly of [2], [3], and [4]catenanes with interconnecting AuNPs is elucidated. The AuNPs can be controllably released to disconnect the individual rings, leaving only the mechanical bond of the catenane chain. In the second publication, a dynamic AuNP-DNA origami gear system is presented that is designed to emulate a planetary gearset with precise spatiotemporal control over its rotation dynamics. The AuNPs serve three crucial tasks. They (i) structurally link the origami ring modules, (ii) mediate the rotation and (iii) enable the real time optical tracking of the rotation via fluorescence spectroscopy. The system enables tightly orchestrated and programmable bidirectional rotations. In the third publication, reconfigurable chiral metastructures comprising multiple plasmonic particles that are accurately positioned in a helical manner around a DNA origami template are discussed. The implementation of a DNA ‘swingarm strategy’ enables the simultaneous and efficient relocation of multiple closely spaced AuNPs over large distances to precisely tune the chiroptical response of the system. The presented publications illustrate the beneficial synergies between DNA origami systems and rationally integrated AuNPs with the aim to advance and expand the application spectrum of these hybrid nanosystems within their scientific disciplines.Item Open Access Resilience of quantum optimization algorithms(2024) Ji, Yanjun; Polian, Ilia (Prof. Dr.)Quantum optimization algorithms (QOAs) show promise in surpassing classical methods for solving complex problems. However, their practical application is limited by the sensitivity of quantum systems to noise. This study addresses this challenge by investigating the resilience of QOAs and developing strategies to enhance their performance and robustness on noisy quantum computers. We begin by establishing an evaluation framework to assess the performance of QOAs under various conditions, including simulated noise-free and error-modeled environments, as well as real noisy hardware, providing a foundation for guiding the development of enhancement strategies. We then propose innovative techniques to improve the performance of algorithms on near-term quantum devices characterized by limited qubit connectivity and noisy operations. Our study introduces an effective compilation process that maximizes the utilization of classical and quantum resources. To overcome the restricted connectivity of hardware, we develop an algorithm-oriented qubit mapping approach that bridges the gap between heuristic and exact methods, providing scalable and optimal solutions. Additionally, we demonstrate, for the first time, selective optimization of quantum circuits on real hardware by optimizing only gates implemented with low-quality native gates, providing significant insights for large-scale quantum computing. We also investigate error mitigation strategies and their dependence on hardware features and algorithm implementation details, emphasizing the synergistic effects of error mitigation and circuit design. While error mitigation can suppress the effects of noise, hardware quality and circuit design are ultimately more critical for achieving high performance. Building upon these insights, we explore the cooptimization of algorithm design and hardware implementation to achieve optimal performance and resilience. By optimizing gate sequences and parameters at the algorithmic level and minimizing error-prone two-qubit gates during compilation, we demonstrate significant improvements in QOA performance. Finally, we explore the practical application of QOAs in real-world problems, emphasizing the importance of optimizing parameters in problem instances to identify optimal solutions. With extensive experiments conducted on real devices, this dissertation makes a substantial contribution to the field of quantum optimization, providing both theoretical foundations and practical strategies for addressing the challenges posed by near-term quantum hardware. Our findings pave the way for the realization of practical quantum computing applications and unlock the full potential of QOAs.