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)
3. Quantum error correcting codes (5 Sep)
   QECC - definition, linearity of errors, necessary and sufficient conditions for qecc: Knill-Laflamme Conditions
   Ref: Got (Chap 2.4-2.5), Wri (Lecture 3-4)
   
   10-19 Sep: No lectures
4. Knill-Laflamme Conditions (24 Sep)
   Review QECC definition, Knill-Laflamme Conditions: necessary and sufficient conditions for QECC, t-weight errors
   Ref: Got (Chap 2.4-2.5), Wri (Lecture 4-5)
5. Knill-Laflamme Conditions (Contd) (26 Sep)
   Consequences of Knill-Laflamme Conditions: distance, degeneracy, error detection, classical linear codes, introduction to stabilizer codes
   Ref: Got (Chap 2.5, 3.1-3.3), Wri (Lecture 5-6)
6. Stabilizer Codes (1 Oct)
   Stabilizer of a code, Centralizer, distance of a stabilizer code
   Ref: Got (Chap 3.1-3.3), Wri (Lecture 6-7)
7. Stabilizer Codes (contd) (3 Oct)
   Stabiizer codes (recap of last lecture), distance and degeneracy of stabilizer codes, binary symplectic representation
   Ref: Got (Chap 3), Wri (Lecture 6-7)

Tentative Schedule (for remaining lectures)

8. 8 Oct: Binary Symplectic Representation and GF(4) codes
9. 10 Oct: CSS Codes
10. 15 Oct: bounds on QECCs
11. 17 Oct: qudit codes, toric codes
12. 22 Oct: Clifford group
13. 24 Oct: Clifford group
14. 29 Oct: fault tolerance
15. 31 Oct: fault tolerance
16. Other topics: topological codes

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.

This page has been accessed at least times since 24 Aug, 2025.