Recent progress on quantum LDPC codes

Gilles Zémor (University of Bordeaux)

It is commonly assumed that quantum computers will eventually have to rely on error correcting codes of LDPC type, hence the interest into their research, among other motivations. Many mysteries surround our current knowledge, among them whether we have hit a fundamental limit for the minimum distance of LDPC codes or whether we just don’t know how to go beyond. We shall discuss recent constructions of quantum LDPC codes that achieve a minimum distance slightly above the square root of the block length and that rely on higher-dimensional simplicial complexes.