Select Page

Quantum Error-Correcting
Codes
From its theoretical underpinnings to effective computations An introductory course to

An introductory course to Quantum Error-Correcting Codes: From its theoretical underpinnings to effective computations

Sign in
BGSMath Course
From September 15, 2026
to October 06, 2026

Venue: Universitat Politècnica de Catalunya (UPC)

Room: 

Registration deadline 13 / 09 / 2026

Introduction

It is recognized that quantum error-correcting coding (QECC) is a crucial technique to ensure the possibility of successful quantum computing.
The main goal of the course is to present a working understanding of the key ingredients involved in QECC:

(1) The mathematics of error-correcting coding (ECC), focused on the codes that are deemed more promising for QECC;

(2) The mathematical models of quantum computing, the difficulties that hinder their physical realization, and the role of QECC to overcome them; and

(3) The effective management of ECC and QECC, mainly the algorithmics and programming that concur in their construction, coding and decoding.

Altogether, it is a promising research area in which talent is in short supply and hence it is quite reasonable to expect that inquiring into any aspect of those ingredients should bring valuable fruits. Suitable for graduate students in domains such as Mathematics, Physics, Computer Science, Telecommunications engineering, or High-performance computing.

LECTURERS

Simeon Ball

UPC – CRM

Sebastià Xambó

UPC

SCHEDULE & PROGRAM

Session Date Time
1 Tuesday 15 September 2026 15:00 → 17:00
2 Thursday 17 September 2026 15:00 → 17:00
3 Tuesday 22 September 2026 15:00 → 17:00
4 Tuesday 29 September 2026 15:00 → 17:00
5 Thursday 1 October 2026 15:00 → 17:00
6 Tuesday 6 October 2026 15:00 → 17:00

1. Error-correcting coding (4 h)

    • Summary of general error-correcting coding notions
    • Alternating codes: construction, coding and decoding
    • Low-density parity-check codes: construction and iterative decoding
    • Other useful codes

2. Quantum computing (3 h)

    • Qubits and q-registers (Hilbert space)
    • Quantum gates and teleportation
    • Shor’s modular order-finding and integer factoring algorithms

3. Quantum error-correcting codes (5 h)

    • Error operators and quantum codes
    • Stabilizer codes
    • Syndrome decoding
    • Logical operators
    • Symplectic self-orthogonal subspaces
    • Stabilizer codes as graphs

REFERENCES

# Reference
[1] S. Ball: A Course in Algebraic Error-Correcting Codes. Birkhäuser, 2020.
[2] S. Ball, A. Centelles, F. Huber: Quantum error-correcting codes and their geometries. Ann. Inst. Henri Poincaré D 10 (2023), no. 2, 337–405. arxiv.org/abs/2007.05992
[3] S. Ball, S. Xambó: Chapters 5, 8 and Appendix B of [5].
[4] S. Xambó: Block Error-Correcting Codes: A Computational Primer. Springer, 2003.
[5] S. Xambó: Error-Correcting Codes: A Computational Primer (draft of 2nd edition of [4]). Chapters 1–4 revised; new chapters: 0 (Preliminary flashes), 5 (Low-density parity-check codes), 6 (Code-based post-quantum cryptography), 7 (Convolutional codes), 8 (Codes for quantum computing); Appendix A (Probability, entropy and information), Appendix B (Quantum computing), Appendix C (the computational PyM system).
[6] A. R. Calderbank, P. Shor: Good quantum error-correcting codes exist. Physical Review A 54.2, 1996. arxiv.org/pdf/quant-ph/9512032
[7] A. M. Steane: Error correcting codes in quantum theory. Physical Review Letters 77.5, 1996.
[8] A. J. Scott: Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions. arxiv.org/pdf/quant-ph/0310137
[9] A. Ketkar, A. Klappenecker, S. Kumar, P. K. Sarvepalli: Nonbinary stabilizer codes over finite fields. arxiv.org/abs/quant-ph/0508070
[10] V. Guruswami: Expander codes and their decoding. CMU Spring, 2010.
[11] S. J. Johnson: Iterative Error Correction: Turbo, LDPC and RA codes. Cambridge University Press, 2010.
[12] T. A. Brun: Quantum Error Correction, 2013. arxiv.org/pdf/1910.03672
[13] S. Evra, T. Kaufman, G. Zémor: Decodable quantum LDPC codes beyond the √n distance barrier using high-dimensional expanders. SIAM Journal on Computing 53.6, 2022, FOCS20-276–FOCS20-316. arxiv.org/pdf/2004.07935
[14] N. P. Breuckmann, J. N. Eberhardt: Quantum low-density parity-check codes. PRX Quantum 2.4, 2021.
[15] J. Roffe: Towards practical quantum LDPC codes. quantum-journal.org/views/qv-2021-11-30-63
[16] A. Leverrier, G. Zémor: Quantum Tanner codes. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), IEEE, 2022, 872–883. arxiv.org/pdf/2202.13641
[17] S. M. Girvin: Introduction to quantum error correction and fault tolerance. SciPost Physics Lecture Notes, 2023. scipost.org/SciPostPhysLectNotes.70/pdf
[18] H. Cao, F. Pan, D. Feng, Y. Wang, P. Zhang: Generative decoding for quantum error-correcting codes, 2025. arxiv.org/pdf/2503.21374
[19] B. Vasic, V. Savin, M. Pacenti, S. Borah, N. Raveendran: Quantum low-density parity-check codes, 2025. arxiv.org/pdf/2510.14090
[20] I. Mahmud, A. Abdelhadi: Quantum codes, a comprehensive survey of techniques, challenges, and future directions, 2025. ieeexplore.ieee.org
[21] M. Sy: Demystifying 5G polar and LDPC codes, a comprehensive review and foundations, 2025. arxiv.org/pdf/2502.11053
[22] Riverlane QEC Report 2025. riverlane.com/quantum-error-correction-report-2025

LIST OF PARTICIPANTS

Name Institution

 

For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat​​

 

CRM Events code of conduct

All activities organized by the CRM are required to comply with the following Code of Conduct.

CRM Code of Conduct

scam warning

We are aware of a number of current scams targeting participants at CRM activities concerning registration or accommodation bookings. If you are approached by a third party (eg travellerpoint.org, Conference Committee, Global Travel Experts or Royal Visit) asking for booking or payment details, please ignore them.

Please remember:
i) CRM never uses third parties to do our administration for events: messages will come directly from CRM staff
ii) CRM will never ask participants for credit card or bank details
iii) If you have any doubt about an email you receive please get in touch

Sustainable Events

We are committed to organising sustainable events that minimise environmental impact and create a positive legacy for the host community. We support organisers in designing events aligned with the UN 2030 Sustainable Development Goals, reducing negative environmental impacts and promoting responsible practices.

All materials provided during our activities are responsibly sourced, including recycled pens and plastic-free badges. We work with responsible suppliers, and our catering partners use fully compostable materials while offering vegetarian and vegan options, with at least one event day being fully vegetarian.