CO 781 Topics in Quantum Information

CO 781 Topics in Quantum Information

Quantum Information Theory, Error-correction, and Cryptography
University of Waterloo
Spring 2008

Lectures: MW 10:30 to 11:50 am, Room: MC 4044
Office hours: by appointment

Lectures/notes

Homework

Announcements

May 27: Physics students may register for this course as CO 781.

May 26: There will be no lectures from June 2--11. All make up lectures are on Fridays, 10:30--11:50 am. Some classes were made up on May 16 and 23. The remaining make up classes will be announced in class, but are tentatively planned to be on July 4 and 11.

May 16: The May 16--28 lectures are being held in the IQC research room in MC, on the 5th floor (North of the IQC student office, on the side across).

Past announcements are available here.

Instructors

Debbie Leung¹ and Ashwin Nayak²

¹C&O and IQC, U. Waterloo.
Contact information: here.
²C&O and IQC, U. Waterloo, and Perimeter Institute.
Contact information: here.

Outline

In this graduate level course, we further develop three inter-related subjects: quantum information theory, error-correction, and cryptography.

Topics to be covered:

Mathematical framework: quantum states, evolution, measurement, metrics.

Error-correction: stabilizer formalism, CSS codes.

Fault-tolerance: encoded operations, concatenation, threshold theorem.

Information theory: von Neumann entropy, compression, Holevo Theorem and an in-probability bound.

Application: locally decodable codes, set-disjointness.

Quantum channels: resources and capacities.

Quantum key distribution: BB84 protocol, proof of security.

Other cryptographic protocols.

A preliminary lecture schedule appears here.

Prerequisites: We assume knowledge of basic linear algebra, theoretical computer science, and the material in a first course in quantum computation, such as CO 681, Introduction to Quantum Information Processing. Students are expected to show a fair bit of mathematical maturity.

References

Lecture notes for Theory of Quantum Information, CS 798, Advanced Research Topics, Spring 2007, taught by John Watrous.
Lectures for Quantum Error Correction, CO 781, Topics in Quantum Information, Winter 2007, taught by Daniel Gottesman. Lecture notes from an offering in Winter 2004 are available here.
Lecture notes for Quantum Information Theory, Error-correction, and Cryptography, CO 781, Topics in Quantum Information, Fall 2006, taught by Debbie Leung and Ashwin Nayak.
Classical and Quantum Computation by Kitaev, Shen, and Vyalyi, Graduate Studies in Mathematics, Vol. 47, American Mathematical Society, 2002.
Quantum Computation and Quantum Information by Nielsen and Chuang, Cambridge University Press, 2000.

Evaluation

The final mark in the course will be based on four homeworks, and a term paper. The weight given to the different components is

Homework: 60%
Term paper and presentation: 40%

To take the class under the pass/not pass option, you are expected to attend the lectures and complete three of the homeworks.

Homework

There will be four graded homework assignments in all. The homeworks will be posted here and will be due generally after two weeks. Please drop off the homework as per the instructions therein.

Each assignment consists of several questions. You are expected to attempt all of them. You should be able to solve most of the problems in the homework on your own if you have understood the lectures. However you can expect an odd question that will require additional thought. You may work on the homework in small groups (and are encouraged to do so, in case of difficulty). You may also consult us. However, you should write up the solutions on your own and mention all sources of help.

Term paper

This will consist of further reading on a topic of your choice. You will be required to make a short presentation to us and to the rest of the class. You will also be required to write a brief report on your topic. Details will be provided later in the term.