Quantum Error Correction Symmetric, Asymmetric, Synchronizable, and
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 cons
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Giuliano Gadioli La Guardia
Quantum Error Correction Symmetric, Asymmetric, Synchronizable, and Convolutional Codes
Quantum Science and Technology Series Editors Raymond Laflamme, Waterloo, ON, Canada Gaby Lenhart, Sophia Antipolis, France Daniel Lidar, Los Angeles, CA, USA Arno Rauschenbeutel, Vienna University of Technology, Vienna, Austria Renato Renner, Institut für Theoretische Physik, ETH Zürich, Zürich, Switzerland Maximilian Schlosshauer, Department of Physics, University of Portland, Portland, OR, USA Jingbo Wang, Department of Physics, University of Western Australia, Crawley, WA, Australia Yaakov S. Weinstein, Quantum Information Science Group, The MITRE Corporation, Princeton, NJ, USA H. M. Wiseman, Brisbane, QLD, Australia
The book series Quantum Science and Technology is dedicated to one of today’s most active and rapidly expanding fields of research and development. In particular, the series will be a showcase for the growing number of experimental implementations and practical applications of quantum systems. These will include, but are not restricted to: quantum information processing, quantum computing, and quantum simulation; quantum communication and quantum cryptography; entanglement and other quantum resources; quantum interfaces and hybrid quantum systems; quantum memories and quantum repeaters; measurement-based quantum control and quantum feedback; quantum nanomechanics, quantum optomechanics and quantum transducers; quantum sensing and quantum metrology; as well as quantum effects in biology. Last but not least, the series will include books on the theoretical and mathematical questions relevant to designing and understanding these systems and devices, as well as foundational issues concerning the quantum phenomena themselves. Written and edited by leading experts, the treatments will be designed for graduate students and other researchers already working in, or intending to enter the field of quantum science and technology.
More information about this series at http://www.springer.com/series/10039
Giuliano Gadioli La Guardia
Quantum Error Correction Symmetric, Asymmetric, Synchronizable, and Convolutional Codes
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Giuliano Gadioli La Guardia Department of Mathematics and Statistics Ponta Grossa State University Ponta Grossa, Paraná, Brazil
ISSN 2364-9054 ISSN 2364-9062 (electronic) Quantum Science and Technology ISBN 978-3-030-48550-4 ISBN 978-3-030-48551-1 (eBook) https://doi.org/10.1007/978-3-030-48551-1 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks,
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