Master Thesis MSTR-2022-02

BibliographyPonomarenko, Wladimir: Solving Differential Equations using Quantum Computing: A Survey.
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Master Thesis No. 2 (2022).
61 pages, german.

In the recent past quantum computers gained more and more popularity. Due to the new technology quantum computers allow us to solve problems we were not able to solve or not able to finish in a feasible amount of time on classical machines. Due to the quantum technology significant speedups can be achieved which opens up a lot of potential uses and calculation possibilities that were not available before. One of the frequently used tasks, which can not be efficiently solved on classic computers for most cases, are differential equations. Recently developed algorithms promise exponential speedup when utilizing a quantum computer for at least a part of the computation utilizing it’s properties to gain an advantage over the pure classical computation. As most research on that matter happened mainly in the past few years, determining the current research state might help future research on that topic and show deficits of the current approaches as well as the lack of algorithms for certain application fields. In this thesis I will present a survey on the state of the art regarding differential equation algorithms and solvers utilizing quantum computers. The goal is to determine whether solutions for such equations exits, whether they are practically applicable as of now and what advantages they bring towards classical approaches. I am able to find several quantum algorithms for differential equations that utilize quantum computing of which some have been tested and confirmed to achieve and essential speedup. But I am also able to determine the lack of executable code and evaluation in several publications, due to the purely theoretical and general approach of the authors. Additionally I will observe the need of further research and especially algorithms and their implementations that are able to function on currently available NISQ devices. Furthermore the survey will show that some differential equation types, like the partial differential equations, have received way more attention as others (f.e. stochastic differential equations). After that I will discuss the survey results and determine potential error sources of the study. The survey design and execution will be critically reviewed regarding potential validity problems and downsides. I will also implement and test one of the algorithms obtained by the survey results as a proof-ofconcept. The algorithm will be run on simulators as well as real quantum machines. I will also present a small tool to help with systematic literature research that I wrote myself. The tool will be briefly explained and tested comparing its results to the actual ones of this survey.

Department(s)University of Stuttgart, Institute of Architecture of Application Systems
Superviser(s)Leymann, Prof. Frank; Weder, Benjamin
Entry dateApril 28, 2022
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