On-site format: The lecture will be held on-site and in flesh and blood.
Place: 1.1.16 FB-Raum (Arnimallee 14)
Date and time:
Monday 8:15-10:00 Wednesday 8:15-10:00
Tutorials: We offer four tutorials, by Alexander Townsend-Teague, Antonio Mele, Janek Denzler, Ansgar Burchards. Hand in the homework in the tray in front of room 1.3.14. The deadline for the submission of the exercises is agreed upon with the tutor of each tutorial. You can also mark the questions you would like to have corrected and marked in detail.
This course provides an overview of an exciting emerging field of research, that of quantum information theory. The field is concerned with the observation that single quantum systems used as elementary carriers of information allows for entirely new modes of quantum information processing and communication, quite radically different from their classical counterparts. Quantum key distribution suggests to communicate in a fashion, secure from any eavesdropping by illegitimate users. Quantum simulators can outperform classical supercomputers in simulation tasks. The anticipated - but now rapidly developing - devices of quantum computers can solve not all, but some delicate computational problems that are intractable on classical supercomputers. This course will give a comprehensive overview over these developments. At the heart of the course will be method development, setting the foundations in the field, building upon basic quantum theory. We will also make the point that quantum information is not only about information processing, but a mindset that can be used to tackle problems in other fields, most importantly in consensed matter research, with which quantum information is much intertwined for good reasons.
Content:
1. Introduction 1.1 Some introductory words 1.2 Quantum information: A new kind of information?
13. Quantum error correction 13.1 Peres Code 13.2 Shor code 13.3 Elements of a theory of quantum error correction 13.4 Stabilizer codes and the toric code
Literature: See the script.
Seminar: Recent advances in tensor networks: from condensed matter physics to machine learning (20123011)
Lecturer: Jens Eisert
Date and time: Mondays 14:15-16:00
Room: 1.3.48 Seminarraum T3 (Arnimallee 14)
Tutors: Alexander Nietner will be the head tutor, but we will take turns and have several experts involved in this, to make this a collective and fun effort
Jan Naumann
Philipp Schmoll
Andreas Bauer
Steven Thomson and others
Topic of the research seminar:
To understand the intricated behavior of quantum systems of many constituents is one of the main aims of modern physics. This is because they exhibit a wide range of interesting and exotic phenomena with no parallel in classical physics, including phase transitions at zero temperature, superconductivity, or topological effects. Yet, the very same complexity that is responsible for the rich physics is at the same time a road block in their study. The dimension of Hilbert space, so the configuration space of quantum mechanics, scales exponentially with the system size, rendering naive methods often inapplicable.
This research seminar introduces to notions of tensor networks that are designed to capture natural properties of interacting quantum many-body systems and beyond. We will look at area laws for entanglement entropies, matrix product states, projected entangled pair states, notions of parent Hamiltonians and of topologically ordered systems. We will turn to numerical techniques to tackle interacting quantum many-body systems in and out of equilibrium. But also look at fresh applications in machine learning, where similar ideas increasingly move into the focus of attention.
During the first day, October 17, an overview will be given by Jens Eisert.
Then we will distribute topics to students so that every participant can give a talk on an exciting topic in its own right:
00 17.10.2022 Introduction 24.10.2022 No session 01 31.10.2022 Area law and entanglement entropies (Philipp Schmoll) 02 07.11.2022 Matrix product states, canonical and parent Hamiltonians (Shozab Qasim) 03 14.11.2022 Time dependent tensor network methods (Alex Nietner) 04 21.11.2022 Density matrix renormalization group (Jan Naumann) 05 28.11.2022 Time dependent variational principle (Frederik Wilde) 06 05.12.2022 Projected entangled pair states and simple update (Jan Naumann) 07 12.12.2022 Toric Code and topological order (Andreas Bauer)
19.12.2022 X-mas holidays 26.12.2022
02.01.2023 No session 08 09.01.2023 AKLT and SPT (Jonáš Fuksa) 09 16.01.2023 Fermionic tensors and MPS (Andreas Bauer) 10 23.01.2023 Multiscale entanglement renormalization (Shozab Qasim) 11 30.01.2023 MPS Sampling and machine learning (Frederik Wilde) 12 13.02.2023 Closing session