Quantum Information theory and Computation

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 !).

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.

1. Introduction to quantum mechanics, Qbits and quantum cryptography.
2. Quantum information theory.
3. Quantum computation, and quantum error correcting codes.

In principle, are posted weekly.

Oral seminar presentations by students.

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:

• Entanglement Asssited Capacity

• Quantum Gaussian Channels

• Review on Entropy

• http://www.idquantique.com/
• http://www.magiqtech.com/
• http://www.vjquantuminfo.org/quantuminfo/lect9quantinfo0910.pdf