Quantum Codes For Topological Quantum Computation
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Quantum Computation With Topological Codes
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Author : Keisuke Fujii
language : en
Publisher: Springer
Release Date : 2015-12-15
Quantum Computation With Topological Codes written by Keisuke Fujii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-15 with Science categories.
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
Quantum Codes For Topological Quantum Computation
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Author : Clarice Dias de Albuquerque
language : en
Publisher: Springer Nature
Release Date : 2022-08-04
Quantum Codes For Topological Quantum Computation written by Clarice Dias de Albuquerque and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-04 with Science categories.
This book offers a structured algebraic and geometric approach to the classification and construction of quantum codes for topological quantum computation. It combines key concepts in linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics, and classical and quantum coding theory to help readers understand and develop quantum codes for topological quantum computation. One possible approach to building a quantum computer is based on surface codes, operated as stabilizer codes. The surface codes evolved from Kitaev's toric codes, as a means to developing models for topological order by using qubits distributed on the surface of a toroid. A significant advantage of surface codes is their relative tolerance to local errors. A second approach is based on color codes, which are topological stabilizer codes defined on a tessellation with geometrically local stabilizer generators. This book provides basic geometric concepts, like surface geometry, hyperbolic geometry and tessellation, as well as basic algebraic concepts, like stabilizer formalism, for the construction of the most promising classes of quantum error-correcting codes such as surfaces codes and color codes. The book is intended for senior undergraduate and graduate students in Electrical Engineering and Mathematics with an understanding of the basic concepts of linear algebra and quantum mechanics.
Quantum Computation With Topological Codes
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Author : Keisuke Fujii
language : en
Publisher:
Release Date : 2015
Quantum Computation With Topological Codes written by Keisuke Fujii and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
Introduction To Topological Quantum Computation
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Author : Jiannis K. Pachos
language : en
Publisher: Cambridge University Press
Release Date : 2012-04-12
Introduction To Topological Quantum Computation written by Jiannis K. Pachos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-12 with Computers categories.
Ideal for graduate students and researchers from various sub-disciplines, this book provides an excellent introduction to topological quantum computation.
Topological Quantum Computation
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Author : Zhenghan Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Topological Quantum Computation written by Zhenghan Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.
Quantum Computing And Quantum Communications
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Author : Colin P. Williams
language : en
Publisher: Springer
Release Date : 2003-05-20
Quantum Computing And Quantum Communications written by Colin P. Williams and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-20 with Computers categories.
This book contains selected papers presented at the First NASA International Conference on Quantum Computing and Quantum Communications, QCQC'98, held in Palm Springs, California, USA in February 1998. As the record of the first large-scale meeting entirely devoted to quantum computing and communications, this book is a unique survey of the state-of-the-art in the area. The 43 carefully reviewed papers are organized in topical sections on entanglement and quantum algorithms, quantum cryptography, quantum copying and quantum information theory, quantum error correction and fault-tolerant quantum computing, and embodiments of quantum computers.
Quantum Information Processing And Quantum Error Correction
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Author : Ivan Djordjevic
language : en
Publisher: Academic Press
Release Date : 2012-04-16
Quantum Information Processing And Quantum Error Correction written by Ivan Djordjevic and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-16 with Computers categories.
Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice. This book is ideal for the electronics, photonics and computer engineer who requires an easy- to-understand foundation on the principles of quantum information processing and quantum error correction, together with insight into how to develop quantum electronic and photonic circuits. Readers of this book will be ready for further study in this area, and will be prepared to perform independent research. The reader completed the book will be able design the information processing circuits, stabilizer codes, Calderbank-Shor-Steane (CSS) codes, subsystem codes, topological codes and entanglement-assisted quantum error correction codes; and propose corresponding physical implementation. The reader completed the book will be proficient in quantum fault-tolerant design as well. Unique Features Unique in covering both quantum information processing and quantum error correction - everything in one book that an engineer needs to understand and implement quantum-level circuits. Gives an intuitive understanding by not assuming knowledge of quantum mechanics, thereby avoiding heavy mathematics. In-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits. Provides the right balance among the quantum mechanics, quantum error correction, quantum computing and quantum communication. Dr. Djordjevic is an Assistant Professor in the Department of Electrical and Computer Engineering of College of Engineering, University of Arizona, with a joint appointment in the College of Optical Sciences. Prior to this appointment in August 2006, he was with University of Arizona, Tucson, USA (as a Research Assistant Professor); University of the West of England, Bristol, UK; University of Bristol, Bristol, UK; Tyco Telecommunications, Eatontown, USA; and National Technical University of Athens, Athens, Greece. His current research interests include optical networks, error control coding, constrained coding, coded modulation, turbo equalization, OFDM applications, and quantum error correction. He presently directs the Optical Communications Systems Laboratory (OCSL) within the ECE Department at the University of Arizona. Provides everything an engineer needs in one tutorial-based introduction to understand and implement quantum-level circuits Avoids the heavy use of mathematics by not assuming the previous knowledge of quantum mechanics Provides in-depth coverage of the design and implementation of quantum information processing and quantum error correction circuits
Quantum Error Correction
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Author : Daniel A. Lidar
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-12
Quantum Error Correction written by Daniel A. Lidar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-12 with Computers categories.
Focusing on methods for quantum error correction, this book is invaluable for graduate students and experts in quantum information science.
Introduction To Quantum Computation And Information
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Author : Hoi-Kwong Lo
language : en
Publisher: World Scientific
Release Date : 1998
Introduction To Quantum Computation And Information written by Hoi-Kwong Lo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Technology & Engineering categories.
"The book fills a gap between the turgid prose of the burgeoning research literature and the superficial accounts in the popular press." Nature, 1999 "The concepts introduced in this book and the forecast of future directions provided should continue to provide a good primer for the exciting breakthrough anticipated in this field." Mathematics Abstracts, 2001 "Despite its age, this book remains an excellent way to learn the basics of quantum information." Quantum Information and Computation, 2002
Introduction To Topological Quantum Matter Quantum Computation
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Author : Tudor D. Stanescu
language : en
Publisher: CRC Press
Release Date : 2016-12-19
Introduction To Topological Quantum Matter Quantum Computation written by Tudor D. Stanescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-19 with Science categories.
What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.