Quantum Computing and HPC Techniques for Solving Microrheology and Dimensionality Reduction Problems

Abstract

The purpose of this thesis is twofold. First, and as a main objective, it is intended to solve a series of formally defined problems, previously mentioned. As will be seen in the thesis, some of these solutions may well be extrapolated to other fields of application. However, in this thesis we present them in the context in which we have encountered and solved them. The second purpose of this thesis is to contribute to the development of quantum computing in a practical way. The applicability of this computing paradigm has an important bottleneck caused by the scarcity of resources of current quantum computers and the high computational demands of quantum simulators. In this thesis we study in detail the ways to reduce this problem, and we propose solutions in the form of circuits that will extend the use of quantum computing to larger problems. The document is divided into four chapters. Since both paradigms (quantum and classical computing) are used for the same purpose of solving certain problems, the structure is focused on differentiating those problems, so that all efforts towards the same result are presented synergistically, not as competing alternatives. The first chapter presents the objectives of the thesis and the context in which it is developed. The technologies used throughout the thesis are presented in depth (but without repeating the content presented in the scientific articles that make up the thesis), so that the reader can have a global perspective of its contents. It also explains our contributions in the design of quantum circuits, which have made it possible for us to successfully apply this computing paradigm to our problems. And finally, the problems addressed by the thesis and in which we have applied all the knowledge previously explained are presented. The second chapter presents the articles that make up this thesis. There are a total of 10 articles, 9 of them already published in recognized high impact journals, and one of them is currently under review. Since it would be chaotic to present the articles individually or in chronological order based on their date of publication, the chapter is divided into sections, each of which deals with one of the problems addressed in the thesis. In this way, all the solutions we have applied in the same field can be found in the same section. Solutions that, as a rule, are fully complementary. The third chapter makes an extensive listing of all the scientific contributions made as part of the thesis. A thesis by compendium requires a minimum number of articles published in journals with a high scientific index. However, our publications are not limited to these articles, but include a large number of contributions to congresses, conferences, journals without impact index, reviews for journals, and teaching papers. The last chapter presents the conclusions we have drawn from the work done in the thesis. The development of the objectives of this work and the key computational and application aspects are discussed. We also highlight some limitations of the solutions provided and define the future work we intend to undertake. We conclude this preface by summarizing the structure of this document: The first chapter summarizes the work carried out in the thesis. The second chapter shows the publications that make up this thesis. The third chapter lists the scientific contributions not included in the second chapter. Finally, the fourth chapter presents the conclusions