Quantum Information Theory and Computation

instructor nicolas macris
office inr 134
phone +4121 6938114
email nicolas.macris@epfl.ch
lectures thursday 9h15-11h00, room INM 203

 

Special announcements

No prerequisites in quantum mechanics and/or information theory are needed.
A draft of course notes will be updated weekly here current-draft.pdf
This is a 4 credit course. Exam form is oral.

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  
   
Experiments with light, analyzers and polarizers homework-19Sept.pdf
Mathematical formalism of quantum mechanics homework-26Sept.pdf
Quantum key distribution protocols homework-17Oct.pdf
Quantum entanglement homework-31Oct.pdf
Part 2: Quantum Information Theory  
   
Density matrix formalism homework-7nov.pdf
Quantum entropy homework-14nov.pdf
Accessible information  
Source coding theorem homework-21nov.pdf
Channel capacity theorems  
   
Part 3: Computation and Error Correction  
   
Models of computation and Deutsch-Josza problem homework-29nov-2013.pdf
Hidden subgroup, period finding, QFT, and Shor algorithm homework-12Dec-2013.pdf
Search algorithm (Grover)  
Quantum error correction  

 

Solutions of Problems

Exam – Presentation Subjects

Subject 1: Security of BB84, securityBB84.pdf and Chuang-Nielsen sec 12.6

Subject 2: Quantum random walks, quantum-random-walk.pdf

Subject 3: Proof of Strong Subadditivity, Chuang-Nielsen sec 11.4 + appendix 6 (Lieb’s theorem)

Subject 4: Holevo-Schumacher-Westmoreland theorem (classical-quantum capacity) Chuang-Nielsen sec 12.3.2 pp 554-561 (plus notion of quantum channel)

Subject 5: Entanglement Assisted Capacity, entanglement-assisted-cap.pdf

Subject 6: Error Correcting Codes, Nielsen-Chuang chap 10 and in particular sec 10.5

Subject 7: Entanglement as a Physical Resource, Nilesen-Chuang sec 12.5 and in particular sec 12.5.2

Subject 8: Quantum Fano Inequality and Quantum Data Processing, Chuang and Nielsen sec 12.4.1 + sec 12.4.2

Subject 9: Linear Optical Computing with Photonic Qubits, ReviewModPhys2007.pdf

Subject 10: Bit Commitment, review.pdf, kent1.pdf, kent2.pdf

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 nature comm (2011)

 

 

  • 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.