Quantum Information and Computation

instructor nicolas macris
office inr 134
phone +4121 6938114
email [email protected]
lectures monday 17h15-19h00, room BC 04

Special announcements

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

This is a 4 credit course. Exam form is study of papers and oral presentations.

 

Course starts on Sept 27 IN PRESENCE and you are strongly encouraged to come in class. However the following zoom link is tentatively available https://epfl.zoom.us/j/64467034624

Objectives

The support of information is material. Today one is able to manipulate matter at the nano scale were quantum behavior becomes important. 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 decades to take advantage of genuine 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, qubits and quantum cryptography.
  2. Quantum information theory.
  3. Quantum computation, and quantum error correcting codes.

The following topics will be treated in class. Extra topics will be discussed as papers studies and oral presentations by students.

Part 1: QM, Qbits, Cryptography  
   
Introduction: 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 von Neumann entropy  
Inequalities  
Accessible information and Holevo quantity  
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 and Simon’s algorithm  
Period finding, Quantum Fourier Transform and Shor’s algorithm  
Search algorithm (Grover)  
Quantum error correction  

Topics for oral presentations: Friday February 4. Duration 30 min slides or blackboard + 10 min questions.

  1. 8h15 – 9h00:  Ozan YakarSending entanglement through noisy quantum channels: Physical Review A, vol 54, number 4 (1996) page 2614 – 2628 PhysRevA.54.2614
  2. 9h00 – 9h45:  Fabio Bersano Quantum error correction: Chapter from Nielsen and Chuang (Shor’s code, Stabilizer formalism) 
  3. 10h00 – 10h45:  Federico Stella  Quantum communication complexity https://homepages.cwi.nl/~rdewolf/qcommcompl.pdf
  4. 10h45 – 11h30:  David Honzátko Quantum ML with continuous variables PhysRevResearch.1.033063
  5. 13h15 – 14h00:  Simon Guilloud 
    Formal verification of quantum algorithms using quantum Hoare logic https://lcs.ios.ac.cn/~bzhan/cav2019.pdf
  6. 14h00 – 14h45:  Louis Coulon  Quantum Approximate Optimization Algorithm QAOA Algo
  7. 15h00 – 15h45:  Maystre Gilbert Theodore [1]: https://www.sciencedirect.com/science/article/pii/S030439750100144X [2]: “An introduction to Quantum Computing” by Kaye, Laflamme and Mosca
  8. 15h45 – 16h00: Antoine Bodin  Stamatopoulos, N., Egger, D. J., Sun, Y., Zoufal, C., Iten, R., Shen, N., & Woerner, S. (2020). Option pricing using quantum computers. Quantum, 4, 291
    https://quantum-journal.org/papers/q-2020-07-06-291/pdf/

Other topics not taken…

9) Three party QKD: Physics Letters A 354 (2006) 67–70 1 S2.0 S0375960106001228 Main

10) Adiabatic quantum computing: Review of modern physics, vol 90, (2018) pp 015002-1 — Sections II and III (in particular Grover, Deutch Josza, Bernstein-Vazirani from adiabatic perspective) RevModPhys.90.015002

11) Solving linear systems of equations (in special cases): Phys.Rev.Lett vol 103, 150502 (2009)lon version:  Arxiv 0811.3171

12) Quantum Amplitude Amplification and Estimation: Amplitude Amplification

13) Algorithm for the solution of the Dirac equation on digital quantum computers PhysRevA.95.042343

14) Artificial neural networks for solving many body problems Neural Networks For QC

15) Quantum natural gradient Quantum Natural Gradient

  Papers

  • A collection of classical reprints 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.