Hyperbolic quantum color codes

TL;DR

This paper introduces a novel method for constructing hyperbolic quantum color codes on high-genus surfaces, resulting in codes with improved parameters and a family with asymptotically optimal encoding rate.

Contribution

It presents a new approach to quantum color codes using hyperbolic tessellations, providing examples with previously unknown parameters and a family with high encoding rate.

Findings

Codes with improved parameters on hyperbolic surfaces

Examples of codes with parameters not shown before

A family of codes with asymptotic encoding rate approaching 1

Abstract

Current work presents a new approach to quantum color codes on compact surfaces with genus $g \geq 2$ 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 $n \rightarrow \infty$.