250120 VO Quantum Information, Quantum Computing, and Quantum Algorithms (2020W)

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

Associated to the lecture is a two-hour tutorial/exercise session (course 250122).