C&O 639: Quantum Error Correction
Instructor: Daniel Gottesman
(dgottesman@perimeterinstitute.ca, 569-7600x427)
Location: MC 4039, University of Waterloo
Time: TTh 10-11:20
Term: Winter 2004
Office Hours: None, but e-mail me to set up a time to talk with
me at the Perimeter Institute (35 King Street N)
Course web page:
http://perimeterinstitute.ca/people/researchers/dgottesman/CO639-2004
The course is now complete, and lecture notes for roughly the
first two-thirds of the course are available below (covering the
basics of quantum error correction and fault-tolerance, but omitting
the last part of the course on miscellaneous advanced topics).
Problem Sets
- Problem Set 1: PDF (63K),
PS (131K)
- Problem Set 2: PDF (55K),
PS (115K)
- Problem Set 3: PDF (74K),
PS (158K)
- Problem Set 4: PDF (55K),
PS (113K)
- Problem Set 5: PDF (77K),
PS (161K)
Errata: In Problem 2, \alpha should generate GF(p)\0. In 2a, the code can
correct p-\mu-1 erasure errors. In Problem 3, there are many wrong factors
of 2.
Solution Sets
- Solution Set 1: PDF (81K),
PS (117K)
- Solution Set 2: PDF (88K),
PS (184K)
- Solution Set 3: PDF (110K),
PS (254K)
- Solution Set 4: PDF (86K),
PS (177K)
- Solution Set 5: PDF (120K),
PS (261K)
Scribe Notes
- Lecture 1: PDF (139K)
- Lecture 2: PDF (121K)
- Lecture 3: PDF (61K)
- Lecture 4: PDF (87K)
- Lecture 5: PDF (43K)
- Lecture 6: PDF (157K)
- Lecture 7: PDF (66K)
- Lecture 8: PDF (143K)
- Lecture 9: PDF (107K)
- Lecture 10: PDF (61K)
- Lecture 11: PDF (193K)
- Lecture 12: PDF (114K)
- Lecture 13: PDF (126K)
- Lecture 14: PDF (80K)
- Lecture 15: PDF (365K)
- Lecture 16: PDF (96K)
- Lecture 17: PDF (40K)
Supplementary Materials
- Introduction to group theory: PDF
(96K)
Syllabus (tentative)
- 4 weeks: Basics of quantum error correction (stabilizer
codes, CSS codes, specific code constructions, Clifford group, upper
and lower bounds on quantum error correction)
- 3 weeks: Fault-tolerance (fault-tolerant error measurement,
fault-tolerant gate design, the threshold for fault-tolerant quantum
computation)
- 5 weeks: Miscellaneous additional topics (As time permits:
higher-dimensional codes, entanglement purification protocols, quantum
channel capacity, topological fault-tolerance, decoherence-free
subspaces, relationships with quantum cryptography, ...)
Grading
- 40%: Problem sets
- 50%: Final paper/project
- 10%: Scribe notes
Problem sets will be assigned once every two weeks.
The final project should involve reading two or three
research papers on additional topics beyond those covered
in the course, and writing up a digested version of them,
ideally with a small extension of the results.
One student each lecture will be assigned to take notes and
write them up in TeX for distribution to the rest of the class.
When you complete the notes (which should be within 2 weeks after
the lecture), give the TeX source to me and I will edit it and post
the notes on the class web page.