Quantum Information Theory and Computation

instructor nicolas macris
office inr 134
phone +4121 6938114
email 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

 

  1. Introduction to quantum mechanics, Qbits and quantum cryptography.
  2. Quantum information theory.
  3. 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).

 

 

  • Recent hacking of a QKD system based on BB84

nature comm (2011)

Exam

Oral. Modalities to be discussed in class. Homeworks are not graded.

 

  • 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.