Classical and Quantum Codes, 2D CFTs and Holography

Explore the intricate connections between classical and quantum codes, 2d conformal field theories (CFTs), and holography in this 59-minute lecture by Anatoly Dymarsky at QuICS. Delve into the holographic correspondence linking 2d CFTs and abelian 3d Chern-Simons theories, and discover how codes emerge as a method to parametrize condensable anyons in the 3d language. Examine the process of condensation in 3d topological field theory and its role in generating 2d CFTs at the boundary. Learn about the construction of "code CFTs" from classical codes and their natural interpretation in terms of CSS quantum codes. Investigate the holographic perspective on ensembles of codes and associated code CFTs, exploring their dual relationship to "Chern-Simons gravity." Uncover the connection between quantum gravity models and contemporary quantum information theory problems through the evaluation of averages over stabilizer states invariant under Clifford group action.