Introduction

Lectures

• A short introduction to classical error-correcting codes: Lecture 1 and Exercise Session 1
  1) A first example: the repetition code
  2) Linear codes to detect and correct errors
  3) Dual representation of linear codes
  4) Hamming and minimum distances
  
  

• Introduction to quantum error correcting codes: Lecture 2 and Exercise Session 2
  1) A first quantum error correcting code: Shor's code
  2) Calderbank-Shor-Steane (CSS) codes
  3) Stabilizer codes
  4) Threshold theorem
  
  

• An introduction to quantum information theory: Lecture 3 and Exercise Session 3
  1) Typical sequences
  2) Shannon's compression theorem
  3) Von Neumann entropy
  4) Quantum typical subspace theorem
  5) Schumacher's compression theorem
  

• About classical and quantum random walks: Lecture 4 and Exercise Session 4
  1) Usefulness of random walks
  2) Markov chains
  3) Random walks on graphs
  4) Quantum random walks
  5) Application: finding collisions
  
  

Final exam

• Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States,
  A. Chefles and S. M. Barnett.


• On the distinguishability of random quantum states,
  A. Montanaro.


• Kitaev's toric code, Section 5,
  in the lecture notes by Gilles Zemor.


• Achieving the Holevo Capacity of a Pure State Classical-Quantum Channel via Unambiguous State Discrimination,
  by M. Takeoka, H. Krovi and S. Guha.


• HHL algorithm Chapter 10,
  in the lecture notes by Ronald de Wolf.

Bibliography (books and lectures notes used for this course)

• “Quantum Computation and Quantum Information”, Michael A. Nielsen and Isaac L. Chuang; Cambridge
• Lectures notes by Ronald de Wolf: https://arxiv.org/abs/1907.09415
• Lecture notes by Gilles Zemor: https://www.math.u-bordeaux.fr/~gzemor/QuantumCodes.pdf