Lecture "Quantum Information, Quantum Computing, and Quantum Algorithms" (winter term 2023/24)
Lecturers: Norbert Schuch, András Molnár
Tutorials: András Molnár, José Garre Rubio
Overview
Quantum Information Theory is concerned with how we can process information and perform computations in a world which is governed by the laws of quantum mechanics, like the world we live in. The lecture will provide an in-depth introduction to the field of Quantum Information Theory, with a special focus on Quantum Computing and Quantum Algorithms, taught from a mathematical perspective. In particular, no prior knowledge of quantum mechanics or any other physics will be required; solid foundations in linear algebra will be both necessary and sufficient to attend the lecture. The focus of the lecture will be on the underlying concepts and the key mathematical questions of Quantum Information and Computation, but depending on interest, a birds-eye view on the main challenges and approaches towards building a real quantum computer can be included.
Planned topics include:
- The basic formalism: States, evolution, and measurement
- Mixed states, completely positive maps, and POVM measurements
- Entanglement theory
- Quantum cryptography
- Quantum computation
- Quantum algorithms
- Quantum error correction
- Quantum complexity theory
- Topological quantum computing
The lecture course consists of a four-hour lecture (250078 VO), and an associated two-hour tutorial/exercise session (250042 PS).
Prerequisites
No prior knowledge of quantum mechanics or any other physics will be required. Solid foundations in linear algebra will be both necessary and sufficient to attend the lecture.
Course material
Lecture notes
- Introduction and Linear Algebra
- The formalism of Quantum Theory
- Entanglement
- Quantum Computing and Quantum Algorithms
- Quantum Error Correction
Exercise sheets
- Sheet 1 (posted 13.10., discussed 17./18.10.)
- Sheet 2 (posted 20.10., discussed 24./25.10.)
- Sheet 3 (posted 3.11., discussed 7./8.11.)
- Sheet 4 (posted 10.11., discussed 14./15.11.)
- Sheet 5 (posted 17.11., discussed 21./22.11.)
- Sheet 6 (posted 24.11., discussed 28./29.11.)
- Sheet 7 (posted 1.12., discussed 5./6.12.)
- Sheet 8 (posted 6.12., discussed 12./13.12.)
- Sheet 9 (posted 19.12., discussed 9./10.1.)
- Sheet 10 (posted 12.1., discussed 16./17.1.)
- Sheet 11 (posted 19.1., discussed 23./24.1.)
Literature
Main texts
- J. Preskill, Quantum Computation lecture notes.
- M. Nielsen and I. Chuang, Quantum Information and Computation. (Cambridge University Press, 2010)
Additional texts and lecture notes
- Mark Wilde, From Classical to Quantum Shannon Theory.
- Reinhard Werner, Quantum Information Theory - an Invitation.
- Michael Wolf, Mathematical Introduction to Quantum Information Processing.
Further reading
- A. Peres, Quantum Theory: Concepts and Methods (Kluver Academic Press, 2002)
Organisatorial issues
The lecture takes place Monday 16:45–18:15 and Friday 11:30–13:00 in Hörsaal 11 (Oskar-Morgenstern-Platz 1, 2nd floor). The first lecture is on 2.10.. For the tutorial/proseminar, there will be two groups; please see ufind for further information, including time and location. If you are interested in participating in the lecture/tutorial but cannot register formally, please get in touch with the corresponding lecturer.
The examination/grading modalities for both the lecture and the tutorial will be communicated on moodle.