Decodable Quantum LDPC Codes Beyond the Square Root Distance Barrier Using High Dimensional Expander

Explore the intricacies of decodable quantum LDPC codes in this IEEE conference talk. Delve into the world of quantum error correction, focusing on CSS (Calderbank, Shor, Steane) codes and their representation as 2-complexes. Examine geometric approaches, including LSV (Lubotzky, Samuels, Vishne) complexes, and their role in surpassing the square root distance barrier. Investigate the balancing of distances and the decoding process for LSV complexes. Gain insights from experts Shai Evra, Tali Kaufman, and Gilles Zemor as they discuss advanced concepts in quantum coding theory and high-dimensional expanders.

Intro
Classical codes
CSS (Calderbank, Shor, Steane) codes A quantum CSS code is given by two orthogonal subspaces
CSS codes as 2-complexes A CSS code given by parity check matrices
Geometric 2-complexes
Boundaries
Towards better complexes
Geometrical approach (II)
LSV (Lubotzky, Samuels, Vishne) complexes (1) These are explicit bounded degree simplicial complexes, which are highly complicated objects (both locally and globally).
Link of a vertex
Decoding LSV complexes (1)
Balancing distances (1) TA
LSV 3-complexes
Final remarks