Quantum Information Theory and Computation
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 | |
Deutsch-Josza 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: