Universität Stuttgart

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Subject: search.filters.subject.530Publication Type: search.filters.UBSTyp.BuchStart date: 2020

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    Quantum algorithms and quantum machine learning for differential equations
    (2023) Schillo, Niclas
    The fast and accurate solution of differential equations is a highly researched topic. Classical methods are able to solve very large systems, however, this can require highperformance computers and very long computational times. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of differential equations have received a lot of attention. Particularly interesting are algorithms that are relevant in the current Noisy-Intermediate-Scale-Quantum (NISQ) era, characterized by small and error-prone systems. In this context, promising candidates are variational quantum algorithms which are hybrid quantumclassical algorithms where only a part of the algorithm is executed on the quantum computer. Thus, they typically require fewer qubits and qubit gates and can tolerate the errors stemming from an imperfect quantum computer. One important example of variational quantum algorithms is the so-called quantum circuit learning (QCL) algorithm, which can be used to approximate functions. Here, an ansatz function is formed with a data encoding layer, subsequently transformed by a shallow parameterized circuit and finally the measurement of an expectation value defines the function value. In this thesis, this method is investigated in great detail, developing new and improved circuit designs and comparing their usefulness in approximating different functions. The method is also tested on a real quantum computer, which has not been reported in literature yet. For this purpose, the algorithm is executed on the superconducting quantum computer IBM Quantum System One in Ehningen to investigate its applicability in the NISQ era. The concept of QCL can be combined with the parameter shift rule to determine derivatives. This enables the solution of nonlinear differential equations. This procedure is subjected to thorough testing across a multitude of differential equations while being compared to other quantum algorithms for solving differential equations. The strengths of this algorithm are shown but also the weaknesses are analyzed. Going beyond the current state of research, the method is extended to solve coupled differential equations with a single circuit, significantly reducing the computational effort. Lastly, a differential equation is successfully solved on the quantum computer IBM Quantum System One in Ehningen.
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    Formen und Kräfte : ein mathematisch-physikalischer Gang zur Kunst auf dem Campus Vaihingen
    (Stuttgart : Fakultät 8 - Mathematik und Physik, Universität Stuttgart, 2022) Stroppel, Markus; Scheffler, Marc; Engstler, Katja Stefanie; Engstler, Katja Stefanie (Konzept und Gestaltung)
    Der Rundgang erläutert und interpretiert einzelne Objekte und künstlerische Elemente der Lernstraße auf dem Campus Vaihingen aus mathematischer und physikalischer Sicht für die interessierte Allgemeinheit, aber auch für Schüler­innen und Schüler und für Studierende.
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    SOFIA - Mission infrarotes Universum
    (Stuttgart : Universität Stuttgart, Institut für Raumfahrtsysteme, 2025) Krabbe, Alfred; Mehlert, Dörte; Wolf, Jürgen
    Warum haben die NASA und das DLR - die amerikanische und deutsche Raumfahrtagentur - eine fliegende Sternwarte betrieben? Mit welchen Tricks haben Ingenieure und Ingenieurinnen das Teleskop des Stratosphären Observatoriums Für Infrarot Astronomie (SOFIA) stabilisiert? Was ist am infraroten Universum so interessant? Wozu hatte die Universität Stuttgart eine Außenstelle in Kalifornien? Welche Rolle spielte die deutsche Wiedervereinigung während der Entwicklungsphase? Diese und viele weitere Fragen rund um die fliegende Sternwarte SOFIA beantwortet dieses von Insidern geschriebene Buch in Bildern und Texten. Lassen Sie sich auf einen Forschungsflug an Bord des einzigartigen Observatoriums mitnehmen, gewinnen Sie einen Überblick über die wissenschaftlichen Erkenntnisse des Observatoriums und fragen Sie: Wie könnte das nächste Stratosphären-Observatorium für Infrarot-Astronomie aussehen? In diesem Buch finden Sie alles, was Sie schon immer über SOFIA wissen wollten.