## Lecture "Quantum Information, Quantum Computing, and Quantum Algorithms" (winter term 2022/23)

Lecturer: Norbert Schuch

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 the 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 Shannon theory
- 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
- The formalism: States, measurements, and evolution
- Entanglement
- Quantum Computing and Quantum Algorithms
- Quantum Error Correction

#### Exercise sheets

- Sheet 1 (posted 14.10., discussed 19./24.10.)
- Sheet 2 (posted 28.10., discussed 7./9.11.)
- Sheet 3 (posted 9.11., discussed 14./16.11.)
- Sheet 4 (posted 16.11., discussed 21./23.11.)
- Sheet 5 (posted 23.11., discussed 28./30.11.)
- Sheet 6 (posted 30.11., discussed 5./7.12.)
- Sheet 7 (posted 7.12., discussed 12./14.12.)
- Sheet 8 (posted 19.12., discussed 9./11.1.)
- Sheet 9 (posted 11.1., discussed 16./18.1.)
- Sheet 10 (posted 18.1., discussed 23./25.1.)

### 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 13:15-14:45 in Hörsaal 13, and Friday, 9:45-11:15 in Hörsaal 11 (Oskar-Morgenstern-Platz 1, 2nd floor). The first lecture is on 3.10..

For the tutorial/proseminar, there will be two groups, one on Monday 8:00-9:30, and one on Wednesday 8:00-9:30 (see ufind for locations). If you are interested in participating in the lecture/tutorial but cannot register formally, please get in touch with me.

The examination/grading modalities for both the lecture and the tutorial will be communicated on moodle.