instructor  nicolas macris 
office  inr 134 
phone  +4121 6938114 
nicolas.macris@epfl.ch  
lectures  tuesday 10h15 – 12h, room INR 113 
exercises  friday 10h15 – 12h, room INR 113 
Special announcements
Do not forget to choose exam subjects among the list given in class. We have to agree on subjects before the Christmas break.
From now on notes are manuscript and may contain a greater amount of mistakes (sorry). In the pdf “chap 12” on page 16 there is at least one mistake: the true lower bound for the Euler function is \phi \geq \frac{r}{4\ln\ln r}, r\geq 19. The “r” in the numerator has to be propagated in the rest of the notes (easy exercise !).
Objectives
It appears that today one is able to manipulate matter at the nanoscale, so that although the technology does not yet exist, information processing may have to take into account the laws of quantum physics. This course introduces the theoretical concepts and methods that have been developped in the last two decades to take advantage of guenuine quantum ressources. We will see how the concepts of bit and entropy, and Shannon’s theory can extended to the quantum domain. We will emphasize the role of entanglement which is a distinctly quantum feature. We will also see how useful quantum parallelism can be in the theory of quantum computation. No prerequisite in quantum mechanics is needed.
Outline: the course is divided in three parts

Introduction to quantum mechanics, Qbits and quantum cryptography.

Quantum information theory.

Quantum computation, and quantum error correcting codes.
Part 1: QM, Qbits, Cryptography  Notes, Exercices  

Experiments with light, analyzers and polarizers  chap 1, ex1  
Mathematical formalism of quantum mechanics  chap 2, ex2, ex3  
Quantum key distribution protocols  chap 3, ex4  
Quantum entanglement  chap 4, ex5, ex6  
Part 2: Quantum Information Theory  Notes, Exercises  
Density matrix formalism  chap 5, ex7  
Quantum entropy  chap 6, ex8  
Accessible information  chap 7  
Source coding theorem  chap 8  
Channel capacity theorems  chap 9, ex9  
Part 3: Computation and Error Correction  Notes, Exercises  
Models of computation  chap 10, ex10  
DeutschJosza problem  chap 11  
Hidden subgroup, period finding and QFT  chap 12  
Circuit and complexity of QFT  chap 12bis  
Factoring algorithm (Shor)  chap 13  
Search algorithm (Grover)  chap 14  
Quantum error correction  
Course notes and homework
In principle, are posted weekly.
Exam
Oral seminar presentations by students.
Additional reading material
Books

A rather complete reference Quantum Computation and Quantum Information, by Michael A. Nielsen and Isaac L. Chuang, Cambridge University Press (2004).

A book that covers quantum computing An introduction to quantum computing, by Phillip Kaye, Raymond Laflamme and Michele Mosca, Oxford University Press (2007).

A small pedagogic book written by a phycisist A short introduction to quantum information and quantum computation, by Michel Le Bellac, Cambridge University Press (2006).

A collection of reprinted articles can be found in Quantum computation and quantum information theory eds C. Macchiavello, G.M.Palma, A.Zeilinger world scientific (2000).

For an emphasis on computer science aspects Quantum computing, by Mika Hirvensalo, Springer Verlag (2001).

See the Feynman lectures on Physics, vol 3 by Richard P. Feynman, Robert B. Leighton, Matthew Sands (1998) Addison Wesley.

For those who want to seriously learn quantum physics Quantum Mechanics by Albert Messiah, ed Dover (two volumes bound as one).
Papers: