New quantum surface codes from semi-regular tessellations

Current work presents a new approach to quantum surface codes on compact surfaces with genus g≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g \ge 2$$\end{document} using the identification of these surfaces with hyperbolic polygons and hyperbolic semi-regular tessellations. This method generalizes other contructions, and we show that this approach may give rise to codes with very good parameters. We present tables with several examples of these codes whose parameters had not been shown before.