Quantum error correction is an indispensable ingredient for scalable quantum computing. In
this Perspective we discuss a particular class of quantum codes called “quantum low-density …

Storing quantum information in a quantum error correction code can protect it from errors,
but the ability to transform the stored quantum information in a fault tolerant way is equally …

Theory of quantum information and computation has been extensively investigated in the
last two decades (see the textbook [121] by Nielsen and Chuang and the references [25, 53 …

We introduce homological measurement, a framework for measuring the logical Pauli
operators encoded in CSS stabilizer codes. The framework is based on the algebraic …

The framework of this thesis is fault-tolerant quantum algorithms. Grover's algorithm and
quantum walks are described in Chapter 2. We start by highlighting the central role that …

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 …

In this work, we present new constructions for topological subsystem codes using semi-
regular Euclidean and hyperbolic tessellations. They give us new families of codes, and we …

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 …