Topological Quantum Computation

Author : Zhenghan Wang
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 46,7 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 : Jiannis K. Pachos
Publisher : Cambridge University Press
Page : 220 pages
File Size : 45,5 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 : Keisuke Fujii
Publisher : Springer
Page : 138 pages
File Size : 46,8 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 : Tudor D. Stanescu
Publisher : CRC Press
Page : 353 pages
File Size : 45,9 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 : Colin P. Williams
Publisher : Springer
Page : 480 pages
File Size : 50,6 Mb
Release : 2003-05-20
Category : Computers
ISBN : 9783540492085

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Quantum Computing and Quantum Communications by Colin P. Williams Pdf

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.

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 : Tudor D. Stanescu
Publisher : Unknown
Page : 128 pages
File Size : 50,5 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 : Ray LaPierre
Publisher : Springer Nature
Page : 369 pages
File Size : 43,5 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 : Bei Zeng,Xie Chen,Duan-Lu Zhou,Xiao-Gang Wen
Publisher : Springer
Page : 364 pages
File Size : 51,6 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 : Roderich Moessner,Joel E. Moore
Publisher : Cambridge University Press
Page : 393 pages
File Size : 43,5 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 : Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi,M. N. Vyalyi
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 43,7 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 : Jose Labastida,Marcos Marino
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 43,6 Mb
Release : 2007-07-18
Category : Science
ISBN : 9781402031779

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Topological Quantum Field Theory and Four Manifolds by Jose Labastida,Marcos Marino Pdf

The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.

Author : Tapio Simula
Publisher : Morgan & Claypool Publishers
Page : 160 pages
File Size : 40,7 Mb
Release : 2019-08-05
Category : Science
ISBN : 9781643271262

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Quantised Vortices by Tapio Simula Pdf

Vortices comprising swirling motion of matter are observable in classical systems at all scales ranging from atomic size to the scale of galaxies. In quantum mechanical systems, such vortices are robust entities whose behaviours are governed by the strict rules of topology. The physics of quantum vortices is pivotal to basic science of quantum turbulence and high temperature superconductors, and underpins emerging quantum technologies including topological quantum computation. This handbook is aimed at providing a dictionary style portal to the fascinating quantum world of vortices.

Author : National Academies of Sciences, Engineering, and Medicine,Division on Engineering and Physical Sciences,Intelligence Community Studies Board,Computer Science and Telecommunications Board,Committee on Technical Assessment of the Feasibility and Implications of Quantum Computing
Publisher : National Academies Press
Page : 273 pages
File Size : 41,6 Mb
Release : 2019-04-27
Category : Computers
ISBN : 9780309479691

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Quantum Computing by National Academies of Sciences, Engineering, and Medicine,Division on Engineering and Physical Sciences,Intelligence Community Studies Board,Computer Science and Telecommunications Board,Committee on Technical Assessment of the Feasibility and Implications of Quantum Computing Pdf

Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

Author : Louis Kauffman,Samuel J. Lomonaco
Publisher : CRC Press
Page : 624 pages
File Size : 48,8 Mb
Release : 2007-09-19
Category : Science
ISBN : 1584889004

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Mathematics of Quantum Computation and Quantum Technology by Louis Kauffman,Samuel J. Lomonaco Pdf

Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are equal partners in the continuing study of quantum science, Mathematics of Quantum Computation and Quantum Technology explores the rapid mathematical advancements made in this field in recent years. Novel Viewpoints on Numerous Aspects of Quantum Computing and Technology Edited by a well-respected team of experts, this volume compiles contributions from specialists across various disciplines. It contains four main parts, beginning with topics in quantum computing that include quantum algorithms and hidden subgroups, quantum search, algorithmic complexity, and quantum simulation. The next section covers quantum technology, such as mathematical tools, quantum wave functions, superconducting quantum computing interference devices (SQUIDs), and optical quantum computing. The section on quantum information deals with error correction, cryptography, entanglement, and communication. The final part explores topological quantum computation, knot theory, category algebra, and logic. The Tools You Need to Tackle the Next Generation of Quantum Technology This book facilitates both the construction of a common quantum language and the development of interdisciplinary quantum techniques, which will aid efforts in the pursuit of the ultimate goal-a "real" scalable quantum computer.