Quantum Information Theory and Computation
instructor | nicolas macris |
office | inr 134 |
phone | +4121 6938114 |
nicolas.macris@epfl.ch | |
lectures | wednesday 9h00-10h45, room INR 113 |
exercises | flexible but usually on fridays 14h15-16h00 |
Special announcements
No prerequisites in quantum mechanics and/or information theory are be needed.
Course notes and homeworks are posted weekly.
This is a 4 credit course. Exam form is oral.
Choose mini-projects for the exams from the email I sent. You are also welcome to propose your own project, but we have to agree. Please decide before the last lecture on Dec 21 and send an email. We will have to fix a date between Jan 16 and Feb 3.
Objectives
The support of information is material. Today one is able to manipulate matter at the nanoscale were quantum behavior becomes important. It is possible that
ultimately information processing will have to take into account the laws of quantum physics. This course introduces the theoretical concepts and methods that have been developed in the last 25 years to take advantage of guenuine quantum resources. We will see how the concepts of bit, entropy, and Shannon's theory are 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.
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, Exercises |
---|---|
Experiments with light, analyzers and polarizers | chapter1homework1 |
Mathematical formalism of quantum mechanics | chapter2 homework2 |
Quantum key distribution protocols | chapter3 homework3 |
Quantum entanglement | chapter4homework4 |
Part 2: Quantum Information Theory | Notes, Exercises |
Density matrix formalism | chapter5homework5 |
Quantum entropy | chapter6 homework6 |
Accessible information | chapter7 |
Source coding theorem | chapter8homework8 |
Channel capacity theorems | |
Part 3: Computation and Error Correction | Notes, Exercises |
Models of computation | homework9 |
Deutsch-Josza problem | |
Hidden subgroup, period finding and QFT | homework10 |
Circuit and complexity of QFT | |
Factoring algorithm (Shor) | |
Search algorithm (Grover) | |
Quantum error correction | |
Papers
- 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).
- A review on quantum cryptography reviews of modern physics (2002)
- Recent hacking of a QKD system based on BB84
Exam
Oral. Modalities to be discussed in class. Homeworks are not graded.
Books related to the lectures
- 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).
- For an emphasis on computer science aspects Quantum computing, by Mika Hirvensalo, Springer Verlag (2001).
For a more physical introduction
- A small pedagogic book A short introduction to quantum information and quantum computation, by Michel Le Bellac, Cambridge University Press (2006).
To learn quantum mechanics seriously
- Quantum Mechanics by Albert Messiah, ed Dover (two volumes bound as one).
- Feynman lectures on Physics, vol 3 by Richard P. Feynman, Robert B. Leighton, Matthew Sands (1998) Addison Wesley.