Quantum Information (2015)

Name of course:

Quantum Information


ECTS credits: 5


Course parameters:

Language: English

Level of course: PhD or Master

Time of year: Q3 2015

No. of hours: 35 in-class contact hours, 80 hours out-of-class preparation and exercises, 20 hours out-of-class preparation for the final exam presentation, 135 hours in total

Capacity limits: 30 participants


Objectives of the course:

The course will lay the foundations for an in-depth understanding of the physics of quantum information theory. It will provide the necessary tools to follow current research and applications in the field of quantum computing, quantum communication and quantum information, and to evaluate the differences between classical and quantum methods. Methodologically, the course will be a practical application of quantum mechanics and linear algebra.


Learning outcomes and competences:

At the end of the course, the student should be able to:

  • Describe quantum states of single and multiple qubits and qudits
  • Differentiate between entangled and separable states
  • Use the density matrix representation
  • Apply and practically implement classical cryptography schemes and evaluate their vulnerability to quantum computers
  • Construct quantum gates for a given task
  • Describe the nonlocality of quantum states using Bell’s theorem and the Greenberg-Horne-Zeilinger state
  • Reproduce arguments for the contextuality of quantum mechanics
  • Describe Grover’s search algorithm, Shor’s Factorization algorithm and explain the source of the quantum speed-up
  • Apply simple error-correcting models

 

Compulsory programme:

To be admitted to the final exam, the participant needs to achieve 60% of the points in the six exercise sheets that include written problem sets and programming tasks. The programming tasks will be evaluated in a peer-reviewed manner, and each participant will be requested to evaluate a certain number of her/his peers’ codes.


Course contents:

The first part of the course will lay the conceptual foundations:

  •  Review of quantum mechanics: Hilbert space, basis states, operators, transformations, measurements, single and multi-qubit states, density matrices, entanglement
  • Gates (classical vs. quantum): single (qu)bit gates, multi-(qu)bit gates, universal set of gates
  • Classical information theory

The second part of the course will describe the non-classical features of quantum information theory:

  • Only Quantum: No cloning theorem, Bell’s theorem, contextuality, teleportation
  • Classical and quantum communication: classical public-private key encryption RSA, quantum key distribution
  • Computational complexity theory
  • Quantum algorithms: Deutsch Jozsa algorithm, Shor’s factorization algorithm, Grover’s search algorithm, adiabatic quantum computing and the d-wave machine
  • Error correction: Sources of error, quantum error correction, fault tolerant computing

 

Prerequisites:

Quantum mechanics and linear algebra, basic programming skills


Name of lecturer:

Malte Tichy


Type of course/teaching methods:

To concentrate on interactive elements and in-depth discussions, the participants will be asked to read book-chapters and excerpts of the lecture notes before each class.

- 4 hours of class each week will be devoted to the syllabus within highly interactive lectures that include, e.g., group work, discussions and quizzes

- 1 hour each week will be devoted to the discussion of the written exercises and the programming tasks


Literature:

  • Quantum Computation and Quantum Information, Michael Nielsen and Isaac Chuang. Cambridge University Press
  • Scientific articles will be handed out during the course
  • Lecture notes will be provided and lecture slides will be made available

 

Course homepage: None yet, but the course material will be made available on Blackboard or AULA.


Course assessment:

The final oral exam includes a presentation of an assigned paper (10 minutes) followed by 15 minutes of questions and problems concerning the full course content.


Provider: Department of Physics and Astronomy


Time: 01 January to 30 March 2014


Place: Campus, 8000 Aarhus C


Registration:

Deadline for registration is January 23rd, 2015. Information regarding admission will be sent out no later than January 25th, 2015.

 

For registration and questions please contact Malte Tichy, e-mail: tichy@phys.au.dk

 

 

 

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Revised 20.06.2016