Topological Quantum
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.
1143759699
Topological Quantum
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.
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Topological Quantum

Topological Quantum

by Steven H. Simon
Topological Quantum

Topological Quantum

by Steven H. Simon

Overview

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.

Product Details

ISBN-13: 9780198886723
Publisher: Oxford University Press
Publication date: 12/29/2023
Pages: 640
Product dimensions: 9.40(w) x 8.00(h) x 2.00(d)

About the Author

Steven H. Simon, Theoretical Physics Professor, Oxford University

Steven H. Simon is a theoretical physics professor at Oxford University and a professorial fellow of Somerville College, Oxford. Before coming to Oxford he was director of theoretical physics research at Bell Laboratories. He has served on the UK EPSRC Physical Sciences Strategic Advisory Board. He is known for his work on Topological Phases of Matter, Topological Quantum Computation, and Fractional Quantum Hall Effect. He is the author of a popular introductory book on solid state physics, entitled The Oxford Solid State Basics which has been used at over a hundred universities worldwide.

Table of Contents

1.. Introduction and Ancient History2.. Kauffman Bracket Invariant and Relation to PhysicsI Anyons and Topological Quantum Field Theories3.. Particle Quantum Statistics4.. Aharonov-Bohm Effect and Charge-Flux Composites5.. Chern-Simons Theory Basics6.. Short Digression on Quantum Gravity7.. Defining Topological Quantum Field TheoryII Anyon Basics8.. Fusion and Structure of Hilbert Space9.. Change of Basis and F-Matrices10.. Exchanging Identical Particles11.. Computing with AnyonsIII Anyon Diagrammatics12.. Planar Diagrams13.. Braiding Diagrams14.. Seeking Isotopy15.. Twists16.. Nice Theories with Planar or Three-Dimensional Isotopy17.. Further StructureIV Some Examples: Planar Diagrams and Anyon Theories18.. Some Simple Examples19.. Anyons From Discrete Groups Elements20.. Bosons and Fermions from Group Representati21.. Quantum Groups (In Brief)22.. Temperly-Lieb Algebra and Jones-Kauffman AnyonsV Applications of TQFT Diagrammatics23.. State Sum TQFTs24.. Formal Construction of “Chern-Simons” TQFT: Surgery and More Complicated Manifolds25.. Anyon CondensationVI Toric Code Basics26.. Introducing Quantum Error Correction27.. Introducing the Toric Code28.. The Toric Code as a Phase of Matter and a TQFT29.. Robustness of Topologically-Ordered Matter30.. Abstracting the Toric Code: Introduction to Tube AlgebraVII More General Loop-Gas and String-Net Models31.. Kitaev Quantum Double Model32.. Doubled-Semion Model33.. Levin-Wen String-NetVIII Entanglement and Symmetries34.. Topological Entanglement35.. SPT Phases of Matter36.. Anyon Permuting SymmetryIX Further Thoughts37.. 37 Experiments (In Brief)38.. Final Comments39.. Appendix: Kac and Other Resources for TQFTs40.. Appendix: Some Mathematical BasicsIndex
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