Mathematical Foundations of Quantum Information

Lecturer: Prof. Dr. Moritz Weber, Nicolas Faroß

Contents

Quantum information is a rapidly growing field of research. To some extent, it includes the „Software of Quantum Computing“, which is, quite fascinating, already in practical use nowadays, for instance in the form of quantum inspired algorithms (run on a classical computer, but in its nature truly different from classical algorithms - and sometimes superior). Although quantum information has some of its roots in quantum physics, it is a truly interdisciplinary field at the intersection of physics, mathematics and computer science - with the advantage that it can be approached from various perspectives.

In our lecture, we will focus on the mathematical foundation of the theory. In particular, we do NOT require any prior knowledge on physics: This lecture is designed for (Bachelor’s or Master’s) students in Mathematics or Computer Science - but students from Physics or other fields are also very welcome, of course! We expect participants to be familiar with the material covered in the lectures „Math for Computer Scientists 1-3“ or similarly „Analysis 1-2“ + „Linear Algebra 1“.

We will introduce (mathematically) in detail the concepts of Hilbert spaces and their operators, tensor products, unitary matrices, entropy, quantum channels, qubits and entanglement amongst others, before giving a brief introduction to quantum algorithms and other concepts in quantum information. The lecture will be held in English. There will be exercise sessions and you need to obtain at least 50% of the points in order to be admitted to the written oral at the end of the lecture.

You will obtain 9 ECTS for this lecture.