Seminar on Quantum Information Theory

• Mathematical Analysis, Linear Algebra and Probability Theory.
• No prior knowledge on Quantum Physics is assumed.

Target audience:

• Originally intended for master students from the Master Program in Mathematical Physics or Advanced Quantum Physics.
• But also open to any student from any other master or bachelor program in the Mathematics Department, or related to Mathematics.

Schedule:

We will block all the sessions of the seminar into two weeks, from December 5 to December 16, 2022. The specific time slots for each talk will be decided jointly with the students. All talks will be streamed by zoom.

List of topics:

Below I present a list of the different topics that will be addressed in this seminar, as well as a brief overview on each of them and the order in which they will take place. Some of these topics are still subject to change depending on the specific interest and/or background of the attendees. Note that the speaker written for each of the topics is preliminary and it could be changed until three weeks before the beginning of the seminar.

PDF with list of topics here.

Session 1: Introduction to quantum information theory

We will provide a short introduction to quantum mechanics, as well as review some topics such as qubits, elementary gates, classical and quantum circuits, etc.

Speaker: Angela Capel

Session 2: First protocols in quantum computing

In this session, we will discuss some of the first protocols that appeared in Quantum Information Theory. In particular, we will review the no-cloning theorem, quantum teleportation and superdense coding.

Speaker: Katharina Leibfarth

Session 3: An introduction to tensor networks

The speaker will present an overview on tensor networks and how they can be used in the context of quantum information theory. Additionally, he will discuss how they can be related to the classical partition function.

Speaker: Diwakar Naidu

Session 4: Shor's factoring algorithm

Here, the famous Shor’s factoring algorithm will be presented, describing the algorithm itself as well as some of the techniques required to understand its proof (including Fourier transform and phase estimation).

Speaker: Tobias Schnieders

Session 5: Models for computation and quantum complexity theory

In this session, we will present an overview on some basic notions concerning quantum computing and quantum complexity theory. These notions include Turing machines, quantum circuits and some complexity classes.

Speaker: Shrish Roy

Session 6: Entanglement and non-locality

Here, we will discuss the notion of non-locality in quantum theory, as well as its applications in communication and information theory, as well as cryptography.

It is also possible that we choose a different paper to discuss, also in the line of non-locality.

Speaker: Can Atacan

Session 7: MIP*=RE

This is one of the most important breakthroughs in the development of Quantum Information Theory. In this paper, it was proven that the two complexity classes mentioned in the name are equal. This has important implications in other fields of Mathematics, as it is equivalent to proving in the negative both the Connes' Embedding Problem as well as the Tsirelson's Problem.

Speaker: Simon Höfer

Session 8: Undecidability of the spectral gap

In this session, we discuss the following result: Given the Hamiltonian of a quantum many-body system, the question whether it is gapped or gapless, is an undecidable problem. Specifically, we will show some families of quantum spin systems on a two-dimensional lattice with certain conditions for which the spectral gap problem is undecidable.

Speaker: Carla Rubiliani

Session 9: Fault tolerance. State of the art

We will discuss how encoded quantum information can be processed without serious propagation of errors, and how it may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware.

Speaker: Janik Ettwein

Session 10: Topological quantum computation

Here, we will briefly review the basics of topological quantum computation, i.e. quantum computing with anyons. For that, we will introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information.

Speaker: Marius Wesle

Session 11: Quantum cryptography

In this session, we will provide an introduction to Quantum Cryptography, i.e. the design cryptographic systems that explicitly rely on quantum effects.

Speaker: Sebastian Krüger

Session 12: Quantum machine learning

Here, we will discuss how quantum computing changes and helps machine learning. In this setting, the learner will be a quantum computer, and the data may be classical or quantum.

Speaker: Jasper Toussaint