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© 2020

Quantum Error Correction

Symmetric, Asymmetric, Synchronizable, and Convolutional Codes

Textbook
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Part of the Quantum Science and Technology book series (QST)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Giuliano Gadioli La Guardia
    Pages 1-16
  3. Giuliano Gadioli La Guardia
    Pages 17-23
  4. Giuliano Gadioli La Guardia
    Pages 25-41
  5. Giuliano Gadioli La Guardia
    Pages 43-56
  6. Giuliano Gadioli La Guardia
    Pages 57-124
  7. Giuliano Gadioli La Guardia
    Pages 125-161
  8. Giuliano Gadioli La Guardia
    Pages 163-211
  9. Back Matter
    Pages 213-227

About this book

Introduction

This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS) construction, the Hermitian, and the Steane’s enlargement construction to certain classes of classical codes. These quantum codes have good parameters and have been introduced recently in the literature. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes.

Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it equips the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference.

Keywords

quantum codes CSS construction Hermitian construction Steane's construction asymmetric quantum codes quantum convolutional codes asymmetric quantum convolutional codes quantum error correction

Authors and affiliations

  1. 1.Department of Mathematics and StatisticsPonta Grossa State UniversityPonta GrossaBrazil

About the authors

Giuliano G. La Guardia received a Master's degree in pure mathematics in 1998 and a PhD in electrical engineering in 2008, both from the State University of Campinas (UNICAMP), São Paulo, Brazil. Since 1999 he has been with the Department of Mathematics and Statistics at the State University of Ponta Grossa, where he is an Associate Professor. His research areas include quantum and classical coding theory, matroid theory, category theory and dynamical systems theory.

Bibliographic information