Topological Quantum

Author : Steven H. Simon
Publisher : Oxford University Press
Page : 641 pages
File Size : 46,9 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 : Jiannis K. Pachos
Publisher : Cambridge University Press
Page : 220 pages
File Size : 52,8 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 : Jose Labastida,Marcos Marino
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 49,5 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 : Keisuke Fujii
Publisher : Springer
Page : 138 pages
File Size : 49,6 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 : Louis H. Kauffman,Randy A. Baadhio
Publisher : World Scientific
Page : 400 pages
File Size : 51,8 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 : Tudor D. Stanescu
Publisher : CRC Press
Page : 353 pages
File Size : 48,8 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 : David Thouless
Publisher : World Scientific
Page : 440 pages
File Size : 43,5 Mb
Release : 1998-03-12
Category : Science
ISBN : 9789814498036

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Topological Quantum Numbers In Nonrelativistic Physics by David Thouless Pdf

Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect, solids and liquid crystals, and topological phase transitions. The accompanying reprints include some of the classic experimental and theoretical papers in this area.Physicists — both experimental and theoretical — who are interested in the topic will find this book an invaluable reference.

Author : Thomas Kerler,Volodymyr V. Lyubashenko
Publisher : Springer
Page : 383 pages
File Size : 48,5 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540446255

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Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners by Thomas Kerler,Volodymyr V. Lyubashenko Pdf

This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.

Author : Tudor D. Stanescu
Publisher : CRC Press
Page : 380 pages
File Size : 42,5 Mb
Release : 2016-12-19
Category : Science
ISBN : 9781482245943

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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 : Thomas Klein Kvorning
Publisher : Springer
Page : 89 pages
File Size : 51,6 Mb
Release : 2018-08-12
Category : Science
ISBN : 9783319967646

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Topological Quantum Matter by Thomas Klein Kvorning Pdf

This book offers a theoretical description of topological matter in terms of effective field theories, and in particular topological field theories, focusing on two main topics: topological superconductors and topological insulators. Even though there is vast literature on these subjects, the book fills an important gap by providing a concise introduction to both topological order and symmetry-protected phases using a modern mathematical language, and developing the theoretical concepts by highlighting the physics and the physical properties of the systems. Further, it discusses in detail the topological interactions for topologically ordered matter, and the response to smooth external fields for symmetry protected matter. The book also covers more specialized topics that cannot be found elsewhere. Specifically, the response of superconductors to geometry, including the newly discovered geo-Meissner effect; and a correction to the usual Meissner effect, only present in the topologically interesting chiral superconductors.

Author : Thouless
Publisher : World Scientific
Page : 440 pages
File Size : 53,6 Mb
Release : 1998
Category : Mathematical physics
ISBN : 9789812386298

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Topological Quantum Numbers in Nonrelativistic Physics by Thouless Pdf

Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac''s argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect, solids and liquid crystals, and topological phase transitions. The accompanying reprints include some of the classic experimental and theoretical papers in this area.Physicists OCo both experimental and theoretical OCo who are interested in the topic will find this book an invaluable reference."

Author : John M. Bryden
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 44,5 Mb
Release : 2005-03-02
Category : Mathematics
ISBN : 9781402027703

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Advances in Topological Quantum Field Theory by John M. Bryden Pdf

Author : Vijay Kodiyalam
Publisher : CRC Press
Page : 74 pages
File Size : 53,8 Mb
Release : 2019-05-20
Category : Mathematics
ISBN : 9780429525070

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Topological Quantum Field Theories from Subfactors by Vijay Kodiyalam Pdf

Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible. Topological Quant

Author : Joachim Kock
Publisher : Cambridge University Press
Page : 260 pages
File Size : 53,9 Mb
Release : 2004
Category : Mathematics
ISBN : 0521540313

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Frobenius Algebras and 2-D Topological Quantum Field Theories by Joachim Kock Pdf

This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

Author : Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Publisher : Cambridge University Press
Page : 435 pages
File Size : 51,6 Mb
Release : 2010-04-29
Category : Science
ISBN : 9781139486736

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Geometric and Topological Methods for Quantum Field Theory by Hernan Ocampo,Eddy Pariguan,Sylvie Paycha Pdf

Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.