Related papers: Quantum approach to adaptive mutations. Didactic i…

These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.

We prove a general relation between adaptive and non-adaptive strategies in the quantum setting, i.e., between strategies where the adversary can or cannot adaptively base its action on some auxiliary quantum side information. Our relation…

Preface, introduction and contents to the book "Theory of Quantum Transport at Nanoscale", published in 2016 by Springer, the author version.

We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born--Oppenheimer approximations.

Lectures deliverd at the NATO Advanced Study Institute on QCD Perspectives on Hot and Dense Matter, Cargese, Aug. 6 - 18, 2001. Dedicated to the memory of Dominique Vautherin.

I provide a perspective on the development of quantum computing for data science, including a dive into state-of-the-art for both hardware and algorithms and the potential for quantum machine learning

This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…

Deeper insight leads to better practice. We show how the study of the foundations of quantum mechanics has led to new pictures of open systems and to a method of computation which is practical and can be used where others cannot. We…

This thesis (Habilitation \`a diriger des recherches) presents some of my research contributions since my Ph.D defense in 2008. I have had the chance to participate in the development of quantum programming languages since their early…

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical and efficient. These benefits are achieved while preserving the integrity and validity of the…

Introduction to papers on the modeling and analysis of network data

These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…

In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum…

Memoir on the Sigma invariants and their applications, version 2

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

This is a draft version of Part I of a three-part textbook on quantum field theory.

This paper explores the transformative potential of quantum computing in the realm of personalized learning. Traditional machine learning models and GPU-based approaches have long been utilized to tailor educational experiences to…

This paper is Comment on the paper: S.A.R. Horsley and M. Babiker, Phys. Rev. Lett. 95, 010405 (2005).

This is the final version of the lecture notes of the 23rd Internet Seminar on Evolutionary Equations, see also https://www.mat.tuhh.de/isem23/.

The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis.…