E2 210 - Quantum Error-Correcting Codes

ECE Dept | IISc

E2 210
Quantum Error-Correcting Codes

January-April 2025

LecturesHomeworkCourse OutlineReferences

Instructor

Navin Kashyap
Office: SP 2.17

Teaching Assistants

TBD

Lectures

Tuesdays and Thursdays, 5:30-7:00pm
Venue: Room MP20, ECE Dept.
The first lecture will be on Thursday, January 2.

Homework Assignments

Homework assignments will be posted at regular intervals on the MS Teams site for this course.

Exams

There will be one midterm exam, to be tentatively held on Tuesday, March 4, during class hours.

Grading

The course grade will be based on the following: 25% for homework assignments, 25% for the midterm, and 50% for a course project that will involve a written report and presentation.

Pre-requisites

A solid background in linear algebra is a must. In addition, it would help considerably to have taken at least one of the following:

a course on classical error-correcting codes (E2 205 or equivalent)
a course on quantum computation (QT 207 or equivalent)

Course Outline

This course is intended to serve as an entry into the field of quantum error-correction. The theory is developed from the basics, assuming only the postulates of quantum mechanics.

The following topics will be covered:

Basics of quantum computation: qubits, quantum states, quantum gates, measurement, density matrices, trace, partial trace; the no-cloning theorem
Quantum noise models: bit flips and phase flips, depolarizing channel, amplitude damping, phase damping
Quantum error-correction: quantum codes; the Knill-Laflamme conditions; Pauli error basis; discretization of quantum errors
Constructions: Shor's code, CSS codes, stabilizer codes, topological codes (surface codes, color codes), quantum LDPC codes
Bounds: quantum Hamming bound, quantum Singleton bound, quantum Gilbert-Varshamov bound
Entanglement-assisted quantum error-correcting codes
Fault-tolerant quantum computation

References

M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010 (10th Anniversary Edition)

D.A. Lidar and T.A. Brun (eds.), Quantum Error Correction Cambridge University Press, 2013.

John Preskill, Lecture notes on quantum error correcting codes, Physics 219 course website, Caltech

Daniel Gottesman's course on Quantum Error Correction and Fault Tolerance, Perimeter Institute, Waterloo, Ontario, Canada

Dan Browne, Lectures on topological codes and quantum computation, University College London

A lot of the material covered in class will be drawn from papers from the literature, and some classic PhD theses:

Daniel Gottesman, Stabilizer Codes and Quantum Error Correction, PhD thesis, Caltech, 1997.

Min-Hsiu Hsieh, Entanglement-Assisted Coding Theory, PhD thesis, University of Southern California, 2008.

Mark Wilde, Quantum Coding with Entanglement, PhD thesis, University of Southern California, 2008.

A.R. Calderbank, E.M. Rains, P.W. Shor and N.J.A. Sloane, "Quantum Error Correction via Codes over GF(4)", IEEE Trans. Inform. Theory, July 1998.

A. Ketkar, A. Klappenecker, S. Kumar, P.K. Sarvepalli, "Nonbinary Stabilizer Codes Over Finite Fields, IEEE Trans. Inform. Theory, Nov. 2006.

M.M. Wilde and T.A. Brun, "Optimal entanglement formulas for entanglement-assisted quantum coding", Physical Review A, June 2008.

[Instructor | Lectures | Homework | Course Outline | References | MS Teams site]

E2 210 Quantum Error-Correcting Codes

January-April 2025

E2 210
Quantum Error-Correcting Codes