Current work presents a new approach to quantum color codes on compact surfaces with genus g≥2 using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance d=4 and the encoding rate asymptotically going to 1 while n→∞.
@article{arxiv.1804.06382,
title = {Hyperbolic quantum color codes},
author = {Eduardo Brandani da Silva and Waldir Silva Soares},
journal= {arXiv preprint arXiv:1804.06382},
year = {2018}
}