Aims

The aim of the module is

• to introduce basic ideas of quantum computation and quantum information;
• to study quantum mechanics in a finite-dimensional space in its own right;
• to explain that information is physical and explore the consequences thereof;
• to complement the traditional approach to quantum mechanics based on particle dynamics;
• to see the interplay between mathematics and physics at work in a currently active research field.

Learning objectives

At the end of the module you should

• be familiar with quantum mechanics in finite-dimensional spaces;
• appreciate the differences between classical and quantum mechanical processing of information;
• understand paradigms of quantum information theory such as the no-cloning theorem, teleportation, and basic quantum algorithms;
• be able to understand and construct simple quantum circuits;
• be aware of quantum parallelism.

Syllabus

In recent years, a quantum mechanical theory of information has emerged. It is based on the idea that, ultimately, all processing of information requires physical objects to carry it. If implemented microscopically, the quantum mechanical nature of the carriers needs to be taken into account. This new perspective not only imposes restrictions but also opens up new, classically unexpected ways to process information.

The first part of the module will present quantum mechanics in finite-dimensional spaces where most of quantum information processing takes place. Concepts such as general measurements and entanglement will be introduced. The second part will focus on quantum information proper, i.e. on quantum circuits, teleportation, and basic but surprisingly efficient quantum algorithms. Other topics such as quantum cryptography, error correction, other quantum algorithms, or the subtle properties of entanglement will be discussed if time permits.

Recommended texts

• N. David Mermin: Quantum Computer Science (Cambridge University Press, Cambridge 2007) (SK 30 MER)
• MA Nielsen, I L Chang: Quantum Computation and Quantum Information (Cambridge University Press, Cambridge 2000) (SK 30 NIE)
• G Alber: Quantum Information - An introduction to basic theoretical concepts and experiments (Springer, London 2001) (SK 30 ALB)

Teaching

• Autumn Term
• 2 lectures per week
• weekly seminars
• optional mini-presentations

Assessment

Coursework (10%) plus 120 min closed examination in Wk 1 of the Spring Term (90%). Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Elective information

This module introduces the theory of quantum information. After  a self-contained presentation of non-relativistic quantum mechanics in finite spaces, basic paradigms of the theory of quantum information proper will be discussed.

Please check prerequisites carefully before asking to take this module as an elective.

Prerequisites

Linear Algebra,
Quantum Mechanics