Quantum error correction

Course guarantor:

Václav Potoček

Lecturer:

Václav Potoček

Tutor:

Supervisor:

Department of Physics

Synopsis:

In this course, we will build a theory for the construction of quantum error-correcting codes. In the introductory part, necessary chapters from the classical theory will be summarized, atop of which we then present the quantum analogy. We will show how coherently stored quantum information can be made robust to loss and noise. We conclude the course by arriving at the principle of fault tolerance, based on which quantum computers are able to continuously correct errors arising at runtime and thus achieve correct results even with erroneous bits, gates or measurements

Requirements:

Syllabus of lectures:

1. Brief overview of classical theory of self-correcting codes and their bounds.

2. Error introduction during information transfer, storage, and computation. Basic decoherence channels and error models.

3. Conditions for functional error correction. Linearity of the set of correctable errors.

4. Stabilizer codes, error syndromes and their non-demolition measurement, concatenation. CSS construction.

5. Quantum counterparts of bounds for code distance. Degenerate quantum codes.

6. Clifford group. Transformation of stabilizers during operations. Encoders and decoders of stabilizer codes.

7. Operations on logical qubits.

8. The principle of fault tolerance in quantum computing.

9. GottesmanKnill theorem. Universal quantum computing on encoded qubits.

10. The threshold theorem for fault-tolerant quantum computing.

11. Topological constructions of quantum codes: surface codes, 2D and 3D color codes.

12. Fault-tolerant computing without concatenation. Magic states, their preparation and distillation.

13. Quantum LDPC codes and current state of knowledge about them.

Syllabus of tutorials:

Study Objective:

Study materials:

[1] Gottesman, D.: Stabilizer Codes and Quantum Error Correction Ph.D. thesis, California Institute of Technology 1997 https://doi.org/10.48550/arXiv.quant-ph/9705052

[2] Ball, S.: A Course in Algebraic Error-Correcting Codes Springer 2020 ISBN 9783030411527

[3] Gaitan, F.: Quantum Error Correction And Fault Tolerant Quantum Computing CRC Press

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: