Methods in Quantum Error Correction
CS-632 / 30 crédits
Enseignant(s): Conrad Jonathan, Viazovska Maryna, Vidick Thomas Georges Pierre
Langue: Anglais
Frequency
Every year
Summary
This course discusses mathematical methods of quantum error correction in the style via presentation and discussion of research papers. It covers basic algebraic and geometric properties of quantum error correcting codes and fault tolerance theory and prepares for research in this field.
Content
In this seminar we discuss the basics and mathematical methods of quantum error correction (QEC) via tutorials and reading-club style presentations and discussions. We cover number theoretical- and algebraic methods in QEC and fault tolerance theory to understand their geometric aspects.
- Quantum error correction theory: Conditions, Recoverability, Geometry.
- Semidefinite optimization of quantum error correcting codes.
- Stabilizer codes in finite and infinite dimensions: Symplectic lattices
- Invariants of quantum error correcting codes: Weight enumerators
- Coding theory: parameter bounds and existence results
- Code constructions: Kitaevs quantum double model, homological codes, the toric code.
- Application of Quantum error correction to complexity
By the end of the course, the student must be able to understand and present basic methods in quantum error correction
Keywords
Quantum Error Correction, Coding theory
Learning Prerequisites
Recommended courses
Knowledge of basic linear algebra required. An introduction to quantum computation such as CS-308 introduction to quantum computation COM-309, PHYS-541 are recommended but not required.
Resources
Bibliography
Textbooks:
M. Nielsen and I. Chuang, Quantum Computation and Quantum Information. D.Lidar and T. Brun, Quantum Error Correction.
Moodle Link
Dans les plans d'études
- Forme de l'examen: Exposé (session libre)
- Matière examinée: Methods in Quantum Error Correction
- Cours: 6 Heure(s)
- Exercices: 6 Heure(s)
- TP: 24 Heure(s)
- Type: optionnel
- Forme de l'examen: Exposé (session libre)
- Matière examinée: Methods in Quantum Error Correction
- Cours: 6 Heure(s)
- Exercices: 6 Heure(s)
- TP: 24 Heure(s)
- Type: optionnel