Current work presents a new approach to quantum surface codes on compact surfaces with
genus g≥ 2 using the identification of these surfaces with hyperbolic polygons and …

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 …

In the last three decades, several constructions of quantum error-correcting codes were
presented in the literature. Among these codes, there are the asymmetric ones, ie, quantum …

The use of properties of quantum mechanics theoretically allows faster quantum
computation than classic computation to obtain solutions of certain computational problems …

Given the importance of hyperbolic quantum color codes and Euclidean quantum color
codes, this paper considers the study of the former codes on compact surfaces with …

We propose a procedure for constructing new classes of codes, called polygonal color
codes. This technique expands the triangular color codes introduced by Bombin and Martin …

Due to the negative curvature of the hyperbolic plane, we may find several types of groups of
symmetries of patterns built on such a plane, which implies in the existence of infinitely many …

This book is intended to be an introductory material on topological quantum codes, with the
necessary elements from a mathematical and engineering point of view, aimed at …

In this paper we construct two classes of binary quantum error-correcting codes on closed
orientable surfaces. These codes are derived from self-dual orientable embeddings of …

The study of error-correcting quantum codes associated with combinatorial objects is an
active area of research. These codes play an important role in several results in …