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.
- 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
- Professor: Jonathan Conrad
- Professor: Maryna Viazovska
- Professor: Thomas Vidick
- Professor: Aurèle Barrière
- Professor: Clément Pit-Claudel
- Teacher: Yawen Guan
- Teacher: Alexandre Pinazza
