Aranya Bhattacharya (Krakow)

Angela Capel Cuevas (Cambridge)

Michael Wolf (Munich)

Ramona Wolf (Siegen)

The autumn school will take place in lecture hall O1 of the O-building at Paderborn University. See here for a site map of the university. Registration, coffee and lunch breaks will take place in (and in front of) the seminar room O1.224, directly next to the upper entrance of O1.

In case you want to particiapte short notice, please write an e-mail to Benjamin Hinrichs.

Aranya Bhattacharya: Introduction to Krylov complexity and its many facets

The goal of these lectures is to make the broader audience of this school aware of the exciting developments in the field of complexity in Physics, which connects various branches of Physics like quantum information, condensed matter, and high-energy physics. The main topic I will be discussing is the concept of Krylov complexity. In the 1st lecture, I will introduce the basic notion of complexity and how it is theoretically understood. Then, I will shift to one specific proposal of complexity that has attracted much attention lately, namely the Krylov complexity. In the first and second lectures, I will describe the idea of Krylov complexity in detail before shifting to the application side of it. In the second half of the 2nd lecture and the whole of 3rd lecture, I will focus on a bunch of applications of Krylov complexity in different kinds of systems, e.g., quantum circuits, measurement-induced systems, PT-symmetric systems, scattering amplitudes, and holography to elucidate how it finds applications in various fields of research and ties them nicely with each other.

Angela Capel Cuevas: Thermalization of open quantum systems

Designing quantum computers to tackle problems beyond classical capabilities is a major scientific challenge, hindered by external noise that causes decoherence and shortens the effective quantum behavior of these systems. Understanding quantum dissipative evolutions, modeled by local Lindbladians, is key to controlling this noise and enhancing the coherence of quantum memories. Recent advancements in dissipative state engineering, which leverage these evolutions to stabilize quantum states against noise, have shown promise in experimental results. Additionally, rapid decoherence can aid in preparing relevant phases of matter and estimating algorithm runtimes. In these lectures, we will investigate thermalization in open quantum systems governed by Lindbladians, focusing on the speed of convergence to thermal equilibrium. We will derive conditions for rapid mixing and briefly review how to utilize these findings to develop efficient algorithms to prepare Gibbs states.

Michael Wolf: Algebraic / transcendental / undecidable - Quantum information through an unorthodox lens

We will begin by reviewing the fundamental concepts of quantum information theory, including states, measurements, channels, and their dilations. Notably, in finite-dimensional Hilbert spaces, these all form semi-algebraic sets. This property extends to derived concepts such as entanglement and various constructs in finite-shot information theory and non-asymptotic many-body theory. However, the conventional limits of information theory and quantum many-body theory may transcend the semi-algebraic realm, venturing into transcendental or even undecidable territories. In this lecture series, we will explore such examples, examine available tools, and discuss their applications, implications, and open problems.

Ramona Wolf: Quantum Key Distribution

Quantum Key Distribution (QKD) offers the promise of provable security, grounded solely in the fundamental laws of physics, even against the most powerful adversaries. While the theoretical potential of QKD is compelling, translating this concept into practical implementation involves navigating a complex landscape of technical challenges. In this lecture, I will explain the basic principles and protocols in QKD, discuss the general structure of its security proof, and address common challenges encountered in practice. Additionally, I will discuss some open questions and ongoing research in this area.