CO 781 Topics in Quantum Information

CO 781 Topics in Quantum Information
Quantum Information Theory, Error-correction, and Cryptography
University of Waterloo
Fall 2006

Lectures: MWF 11:30 to 12:20 pm, Room: MC 5158A
Office hours: by appointment

Announcements

Schedule/Lecture Notes

Homework

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 will further develop three inter-related topics: quantum information theory, error-correction, and cryptography.

Preliminary list of topics:

Mathematical framework: quantum states, 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: communication complexity of set-disjointness.

Quantum channels: resources and capacities.

Quantum key distribution: BB84 protocol, proof of security.

Other cryptographic protocols: bounded-storage model, bit-commitment.

Schedule: We will see these topics roughly in the order given above. We will try to post the precise subject matter of a lecture here in advance.

Prerequisites: We will assume knowledge of basic linear algebra, theoretical computer science, and the material in a first course in quantum computation, such as CO 481, Introduction to Quantum Information Processing. Students will be expected to show a fair bit of mathematical maturity.

Text

The book Quantum Computation and Quantum Information, by Nielsen and Chuang (Cambridge University Press) is a helpful reference, as are the lecture notes from CO 639 Quantum Error Correction taught by Daniel Gottesman in Winter 2004. We will also develop lecture notes as we go along.

Evaluation

The final mark in the course will be based on the scribe notes you prepare, homework, and a term paper. The weight given to the different components is

Scribe notes: 20%
Homework: 60%
Term paper: 20%

To take the class under the pass/not pass option, you would be required to attend the lectures, scribe lecture notes, and complete half of the homework requirement.

Scribe notes

You will be required to take notes for some number of lectures of your choice. Preparing lecture notes will help you understand the lecture material more thoroughly, and give you another opportunity to think about the material. Notes are expected to be handed in within a week of the lecture being scribed. The notes are to be transcribed in Latex in the template provided here.

Homework

There will be three graded homework assignments in all. There will be a homework assignment essentially every month. The homework will be posted on the web and will be due three weeks later. We will collect the homework in class the day they are due.

Each assignment will consist of four to five questions. You are required 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 me. 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 possibly to the rest of the class. You will also be required to write a short report on your topic.

Feedback

Please pass on your comments, criticism, and opinions on the course to us; these are always welcome. If you prefer not to reveal your identity, you could use a free anonymous remailer available on the web.