CSS.427.1: A minicourse on Quantum Coding Theory - Monsoon Semester (2025-26)

Time: Wed & Friday 11:30-13:00
Location: A201
Instructors:
Homepage: https://www.tcs.tifr.res.in/~prahladh/teaching/2025-26/qecc/

Course Announcement

Lectures

1. Introduction to Quantum Error Correction (29 Aug)
   Administrivia, why error correction (classical and quantum)?, brief history of quantum error correction and fault tolerance, Shor's 9-quibit code
   Ref: Got (Chap 1-2), Wri (Lecture 1-2)
2. How is noise modeled? (3 Sep)
   Shor's 9-qubit code (correcting 1-bit X and Z-errors, general 1-quibit errors); quantum channel (CPTP operator, Krauss representation, examples); qecc -- definition
   Ref: Got (Chap 1, 2.3-2.4), Wri (Lecture 2-3)

Tentative Schedule (for remaining lectures)

3. 5 Sep: quantum error correction, Knill-Laflamme conditions
   10-19 Sep: No lectures
4. 24 Sep: stabilizer codes
5. 26 Sep: CSS codes and GF(4) codes
6. 1 Oct: bounds on QECCs
7. 3 Oct: qudit codes, toric codes
8. 8 Oct: Clifford group
9. 10 Oct: Clifford group
10. 15 Oct: fault tolerance
11. 17 Oct: fault tolerance
12. 22 Oct: topological codes
13. 24 Oct: chain complexes and quantum LDPC codes
14. 29 Oct: chain complexes and quantum LDPC codes
15. 31 Oct: other topics

Requirements

Students taking the course for credit will be expected to:

• Problems Sets (2 problem sets)
• Project / Paper Presentation
• Participate actively in class
• Grading Policy:
  • Problems Sets - 50%
  • Class Participation - 10%
  • Project / Paper Presentation -- 40%

References

[Got]

Daniel Gottesman, "Surviving as a Quantum Computer in a Classical World", (draft of book), 2024.

[Wri]

John Wright, "CS 294: Quantum Coding Theory", Berkeley, Spring 2024.

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