Quantum Information and Computation

instructor nicolas macris
office inr 134
phone +4121 6938114
email nicolas.macris@epfl.ch
lectures monday 8h15-10h00, room BC 03

Special announcements

No prerequisites in quantum mechanics and/or information theory are needed.
A draft of course notes will be updated weekly here draftDec14.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.

A subset of the following topics will be treated in class.

Part 1: QM, Qbits, Cryptography
Experiments with light, analyzers and polarizers
Mathematical formalism of quantum mechanics
Quantum key distribution protocols
Quantum entanglement
Part 2: Quantum Information Theory
Density matrix formalism
Quantum entropy
Accessible information
Source coding theorem
Quantum channel models
Channel capacity theorems
Part 3: Computation and Error Correction
Models of computation and Deutsch-Josza problem
Hidden subgroup problem
Period finding, Quantum Fourier Transform and Shor algorithm
Search algorithm (Grover)
Adiabatic quantum computation
Quantum error correction

Topics for oral presentations (January 24, 2019)

1) Security proof for BB84: Phys Rev Letters, 85, no 2, July 10 (2000) pp 441-444  [Taken by Eleonora Testa]

2) QKD based on Bell’s theorem: A. K. Ekert, Phys. Rev. Lett. 67, 661 ~1991!. [Taken by Jun Wang]

3) Three party QKD: Physics Letters A 354 (2006) 67–70  [Taken by Mark Sutherland]

4) Strong subadditivity of entropy proof: Journal of Mathematical Physics 14, 1938 (1973) [Taken by Novak Kaluderovic]

5) Quantum source coding: Phys. Rev. A 51, 2738 – Published 1 April 1995 [Taken by Sichen Mi. Will present in afternoon]

6) Sending entanglement through noisy quantum channels: Physical Review A, vol 54, number 4 (1996) page 2614 – 2628

7) Grover’s algorithm. Chapter 12 from course notes. [Taken by Samuel Bosch. Will present after lunch]

8) Quantum error correction A: Chapter from Nielsen and Chuang (Shor’s code, Stabilizer formalism) [Taken by Giulia Meuli.  Will present in the morning]

9) Quantum error correction B: Chapter from Nielsen and Chuang (Shor’s code, Calderbank-Steane-Shor CSS codes)

10) Adiabatic quantum computing A: Review of modern physics, vol 90, (2018) pp 015002-1 — Section II on grover and Deutch Josza from adiabatic perspective. [Taken by Bruno Schmitt]

11) Adiabatic quantum computing A: Review of modern physics, vol 90, (2018) pp 015002-1 — Section IV on universality and equivalence with circuit model.

12) Solving linear systems of equations (in special cases): Phys.Rev.Lett vol 103, 150502 (2009) [Taken by Jakab Tardos]

13) Quantum walks: arXiv:quant-ph/0403120   [Taken by Sadra Boreiri]

14) Quantum Amplitude Amplification and Estimation: arXiv:quant-ph/0005055   [Taken by Alexandre Carlier]

15) Quantum communication complexity [Taken by Garg Paritosh] :

https://homepages.cwi.nl/~rdewolf/qcommcompl.pdf

  Papers

  • A collection of reprinted Communication Theory Laboratory, School of Computer and Communication Sciences, \'{E}cole Polytechnique F\'{e}d\'{e}rale de Lausanne (EPFL), Lausanne, CH-1015, Switzerlandarticles 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.