Quantum information and computation

Introduction

• Basic principles of quantum mechanics (pure and mixed states, unitary evolution)
• Quantum measurements (projective and positive operator valued measure)
• Notion of quantum bit
• Quantum no-cloning theorem

Quantum entanglement 

• Separability vs entanglement of pure and mixed states
• Nonlocality (EPR paradox and Bell inequalities)
• Dense coding and teleportation

Quantum information theory

• Basic notions of classical information theory
• Quantum source coding (von Neumann entropy)

Quantum cryptography

• BB84 protocol for quantum key distribution
• Entanglement-based quantum key distribution

Quantum computing

• Quantum circuits and universal gates
• Phase kickback: Deutsch-Jozsa’s algorithm
• Amplitude amplification: Grover’s search algorithm
• Quantum Fourier transform: Shor’s factoring algorithm

Quantum error correction

• Decoherence
• Classical error correction
• 3-qubit repetition code
• Shor’s 9-qubit code
• Fault tolerance (basics)

The final objectives are

• to familiarise the students with the basic properties of quantum information, in particular how it differs from classical information and how it can be processed keeping quantum coherence;
• to expose how these properties can be exploited in different communication and computation applications, analyzing in particular the notion of quantum algorithms;
• to confront the students with current challenges in the field of quantum information and computation, both from a physics and computer science perspective.

Learning outcomes:

At the end of the course students are able to

• understand the basics of quantum information theory and its main applications;
• solve simple problems in quantum information and computation;
• design and analyse simple quantum algorithms using basic tools such as phase kickback and amplitude amplification.

• Theory courses
• Exercice sessions

References, bibliography, and recommended reading

• Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000
• John Preskill. Lecture notes for the course “Physics 219/Computer Science 219” at Caltech. See in particular chapter 6 for quantum computation: http://www.theory.caltech.edu/~preskill/ph219/index.html#lecture
• David Mermin. Quantum Computer Science; An introduction. Cambridge Univ Press, 2007

Course notes

• Université virtuelle

Contacts

Ognyan ORESHKOV (Ognyan.Oreshkov@ulb.be)

Campus

Solbosch

Method(s) of evaluation

• Oral examination

Oral examination

Final assessment: open book oral exam

Mark calculation method (including weighting of intermediary marks)

The oral exam is graded on a total of 20.

Language(s) of evaluation

• english