Introduction To Topological Quantum Computation

Author : Tudor D. Stanescu
Publisher : CRC Press
Page : 353 pages
File Size : 46,7 Mb
Release : 2016-12-19
Category : Science
ISBN : 9781351722285

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Introduction to Topological Quantum Matter & Quantum Computation by Tudor D. Stanescu Pdf

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.

Author : Jiannis K. Pachos
Publisher : Cambridge University Press
Page : 220 pages
File Size : 45,7 Mb
Release : 2012-04-12
Category : Computers
ISBN : 9781107005044

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Introduction to Topological Quantum Computation by Jiannis K. Pachos Pdf

Ideal for graduate students and researchers from various sub-disciplines, this book provides an excellent introduction to topological quantum computation.

Author : Steven H. Simon
Publisher : Oxford University Press
Page : 641 pages
File Size : 42,9 Mb
Release : 2023-09-29
Category : Electronic
ISBN : 9780198886723

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Topological Quantum by Steven H. Simon Pdf

At the intersection of physics, mathematics, and computer science, an exciting new field of study has formed, known as "Topological Quantum." This research field examines the deep connections between the theory of knots, special types of subatomic particles known as anyons, certain phases of matter, and quantum computation. This book elucidates this nexus, drawing in topics ranging from quantum gravity to topology to experimental condensed matter physics. Topological quantum has increasingly been a focus point in the fields of condensed matter physics and quantum information over the last few decades, and the forefront of research now builds on the basic ideas presented in this book. The material is presented in a down-to-earth and entertaining way that is far less abstract than most of what is in the literature. While introducing the crucial concepts and placing them in context, the subject is presented without resort to the highly mathematical category theory that underlies the field. Requiring only an elementary background in quantum mechanics, this book is appropriate for all readers, from advanced undergraduates to the professional practitioner. This book will be of interest to mathematicians and computer scientists as well as physicists working on a wide range of topics. Those interested in working in these field will find this book to be an invaluable introduction as well as a crucial reference.

Author : Zhenghan Wang
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 48,7 Mb
Release : 2010
Category : Complex manifolds
ISBN : 9780821849309

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Topological Quantum Computation by Zhenghan Wang Pdf

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.

Author : Keisuke Fujii
Publisher : Springer
Page : 138 pages
File Size : 43,5 Mb
Release : 2015-12-15
Category : Science
ISBN : 9789812879967

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Quantum Computation with Topological Codes by Keisuke Fujii Pdf

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.

Author : Ray LaPierre
Publisher : Springer Nature
Page : 369 pages
File Size : 50,7 Mb
Release : 2021-09-27
Category : Science
ISBN : 9783030693183

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Introduction to Quantum Computing by Ray LaPierre Pdf

This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future.

Author : Tudor D. Stanescu
Publisher : Unknown
Page : 128 pages
File Size : 40,5 Mb
Release : 2017
Category : Quantum computing
ISBN : 1351722530

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Introduction to Topological Quantum Matter & Quantum Computation by Tudor D. Stanescu Pdf

Author : Roderich Moessner,Joel E. Moore
Publisher : Cambridge University Press
Page : 393 pages
File Size : 41,6 Mb
Release : 2021-04-29
Category : Mathematics
ISBN : 9781107105539

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Topological Phases of Matter by Roderich Moessner,Joel E. Moore Pdf

This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 55,9 Mb
Release : 2006-02-04
Category : Science
ISBN : 9783540312642

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Topology in Condensed Matter by Michael I. Monastyrsky Pdf

This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

Author : John Watrous
Publisher : Unknown
Page : 599 pages
File Size : 48,7 Mb
Release : 2018-04-26
Category : Computers
ISBN : 9781107180567

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The Theory of Quantum Information by John Watrous Pdf

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.

Author : Bei Zeng,Xie Chen,Duan-Lu Zhou,Xiao-Gang Wen
Publisher : Springer
Page : 364 pages
File Size : 53,9 Mb
Release : 2019-03-28
Category : Computers
ISBN : 9781493990849

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Quantum Information Meets Quantum Matter by Bei Zeng,Xie Chen,Duan-Lu Zhou,Xiao-Gang Wen Pdf

This book approaches condensed matter physics from the perspective of quantum information science, focusing on systems with strong interaction and unconventional order for which the usual condensed matter methods like the Landau paradigm or the free fermion framework break down. Concepts and tools in quantum information science such as entanglement, quantum circuits, and the tensor network representation prove to be highly useful in studying such systems. The goal of this book is to introduce these techniques and show how they lead to a new systematic way of characterizing and classifying quantum phases in condensed matter systems. The first part of the book introduces some basic concepts in quantum information theory which are then used to study the central topic explained in Part II: local Hamiltonians and their ground states. Part III focuses on one of the major new phenomena in strongly interacting systems, the topological order, and shows how it can essentially be defined and characterized in terms of entanglement. Part IV shows that the key entanglement structure of topological states can be captured using the tensor network representation, which provides a powerful tool in the classification of quantum phases. Finally, Part V discusses the exciting prospect at the intersection of quantum information and condensed matter physics – the unification of information and matter. Intended for graduate students and researchers in condensed matter physics, quantum information science and related fields, the book is self-contained and no prior knowledge of these topics is assumed.

Author : Venkateswaran Kasirajan
Publisher : Springer Nature
Page : 463 pages
File Size : 47,8 Mb
Release : 2021-06-21
Category : Computers
ISBN : 9783030636890

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Fundamentals of Quantum Computing by Venkateswaran Kasirajan Pdf

This introductory book on quantum computing includes an emphasis on the development of algorithms. Appropriate for both university students as well as software developers interested in programming a quantum computer, this practical approach to modern quantum computing takes the reader through the required background and up to the latest developments. Beginning with introductory chapters on the required math and quantum mechanics, Fundamentals of Quantum Computing proceeds to describe four leading qubit modalities and explains the core principles of quantum computing in detail. Providing a step-by-step derivation of math and source code, some of the well-known quantum algorithms are explained in simple ways so the reader can try them either on IBM Q or Microsoft QDK. The book also includes a chapter on adiabatic quantum computing and modern concepts such as topological quantum computing and surface codes. Features: o Foundational chapters that build the necessary background on math and quantum mechanics. o Examples and illustrations throughout provide a practical approach to quantum programming with end-of-chapter exercises. o Detailed treatment on four leading qubit modalities -- trapped-ion, superconducting transmons, topological qubits, and quantum dots -- teaches how qubits work so that readers can understand how quantum computers work under the hood and devise efficient algorithms and error correction codes. Also introduces protected qubits - 0-π qubits, fluxon parity protected qubits, and charge-parity protected qubits. o Principles of quantum computing, such as quantum superposition principle, quantum entanglement, quantum teleportation, no-cloning theorem, quantum parallelism, and quantum interference are explained in detail. A dedicated chapter on quantum algorithm explores both oracle-based, and Quantum Fourier Transform-based algorithms in detail with step-by-step math and working code that runs on IBM QisKit and Microsoft QDK. Topics on EPR Paradox, Quantum Key Distribution protocols, Density Matrix formalism, and Stabilizer formalism are intriguing. While focusing on the universal gate model of quantum computing, this book also introduces adiabatic quantum computing and quantum annealing. This book includes a section on fault-tolerant quantum computing to make the discussions complete. The topics on Quantum Error Correction, Surface codes such as Toric code and Planar code, and protected qubits help explain how fault tolerance can be built at the system level.

Author : Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi,M. N. Vyalyi
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 48,9 Mb
Release : 2002
Category : Computational complexity
ISBN : 9780821832295

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Classical and Quantum Computation by Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi,M. N. Vyalyi Pdf

An introduction to a rapidly developing topic: the theory of quantum computing. Following the basics of classical theory of computation, the book provides an exposition of quantum computation theory. In concluding sections, related topics, including parallel quantum computation, are discussed.

Author : Louis H. Kauffman,Randy A. Baadhio
Publisher : World Scientific
Page : 400 pages
File Size : 41,5 Mb
Release : 1993
Category : Mathematics
ISBN : 981022575X

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Quantum Topology by Louis H. Kauffman,Randy A. Baadhio Pdf

This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.

Author : Mikio Nakahara
Publisher : World Scientific
Page : 194 pages
File Size : 43,9 Mb
Release : 2013
Category : Computers
ISBN : 9789814425223

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Quantum Information and Quantum Computing by Mikio Nakahara Pdf

The open research center project "Interdisciplinary fundamental research toward realization of a quantum computer" has been supported by the Ministry of Education, Japan for five years. This is a collection of the research outcomes by the members engaged in the project. To make the presentation self-contained, it starts with an overview by Mikio Nakahara, which serves as a concise introduction to quantum information and quantum computing. Subsequent contributions include subjects from physics, chemistry, mathematics, and information science, reflecting upon the wide variety of scientists working under this project. These contributions introduce NMR quantum computing and related techniques, number theory and coding theory, quantum error correction, photosynthesis, non-classical correlations and entanglement, neutral atom quantum computer, among others. Each of the contributions will serve as a short introduction to these cutting edge research fields.