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.
Автор: Cardona Alexander Название: Geometric, Algebraic and Topological Methods for Quantum Fie ISBN: 9814460044 ISBN-13(EAN): 9789814460040 Издательство: World Scientific Publishing Рейтинг: Цена: 21226.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory.This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.
Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.
Quantum dynamics underlies macroscopic systems exhibiting some kind of ordering, such as superconductors, ferromagnets and crystals. Even large scale structures in the Universe and ordering in biological systems appear to be the manifestation of microscopic dynamics ruling their elementary components. The scope of this book is to answer questions such as: how it happens that the mesoscopic/macroscopic scale and stability characterizing those systems are dynamically generated out of the microscopic scale of fluctuating quantum components; how quantum particles coexist and interact with classically behaving macroscopic objects, e.g. vortices, magnetic domains and other topological defects. The quantum origin of topological defects and their interaction with quanta is a crucial issue for the understanding of symmetry breaking phase transitions and structure formation in a wide range of systems from condensed matter to cosmology. Deliberately not discussing other important problems, primarily renormalization problems, this book provides answers to such questions in a unitary, self-consistent physical and mathematical framework, which makes it unique in the panorama of existing texts on a similar subject. Crystals, ferromagnets and superconductors appear to be macroscopic quantum systems, i.e. their macroscopic properties cannot be explained without recourse to the underlying quantum dynamics. Recognizing that quantum field dynamics is not confined to the microscopic world is one of the achievements of this book, also marking its difference from other texts. The combined use of algebraic methods, and operator and functional formalism constitutes another distinctive, valuable feature.
Автор: Keisuke Fujii Название: Quantum Computation with Topological Codes ISBN: 9812879951 ISBN-13(EAN): 9789812879950 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: Thomas Klein Kvorning Название: Topological Quantum Matter ISBN: 3030072460 ISBN-13(EAN): 9783030072469 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Нет в наличии.
Описание: 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.
Автор: Hernan Ocampo; Sylvie Paycha; Andr?s Vargas Название: Geometric and Topological Methods for Quantum Field Theory ISBN: 3642063519 ISBN-13(EAN): 9783642063510 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory.
Автор: Simula Tapio Название: Quantised Vortices: A Handbook of Topological Excitations ISBN: 164327127X ISBN-13(EAN): 9781643271279 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 13999.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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.
Описание: This thesis extends our understanding of systems of independent electrons by developing a generalization of Bloch’s Theorem which is applicable whenever translational symmetry is broken solely due to arbitrary boundary conditions. The thesis begins with a historical overview of topological condensed matter physics, placing the work in context, before introducing the generalized form of Bloch's Theorem. A cornerstone of electronic band structure and transport theory in crystalline matter, Bloch's Theorem is generalized via a reformulation of the diagonalization problem in terms of corner-modified block-Toeplitz matrices and, physically, by allowing the crystal momentum to take complex values. This formulation provides exact expressions for all the energy eigenvalues and eigenstates of the single-particle Hamiltonian. By precisely capturing the interplay between bulk and boundary properties, this affords an exact analysis of several prototypical models relevant to symmetry-protected topological phases of matter, including a characterization of zero-energy localized boundary excitations in both topological insulators and superconductors. Notably, in combination with suitable matrix factorization techniques, the generalized Bloch Hamiltonian is also shown to provide a natural starting point for a unified derivation of bulk-boundary correspondence for all symmetry classes in one dimension.
Автор: Dario Bercioux; J?r?me Cayssol; Maia G. Vergniory; Название: Topological Matter ISBN: 3030094774 ISBN-13(EAN): 9783030094775 Издательство: Springer Рейтинг: Цена: 16070.00 р. Наличие на складе: Нет в наличии.
Описание: This book covers basic and advanced aspects in the field of Topological Matter. The chapters are based on the lectures presented during the Topological Matter School 2017. It provides graduate level content introducing the basic concepts of the field, including an introductory session on group theory and topological classification of matter. Different topological phases such as Weyls semi-metals, Majoranas fermions and topological superconductivity are also covered. A review chapter on the major experimental achievements in the field is also provided. The book is suitable not only for master, graduate and young postdoctoral researchers, but also to senior scientists who want to acquaint themselves with the subject.
Автор: Li Jin-Jin Название: Generalized Optomechanics and Its Applications ISBN: 9814417033 ISBN-13(EAN): 9789814417037 Издательство: World Scientific Publishing Рейтинг: Цена: 12830.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A mechanical oscillator coupled to the optical field in a cavity is a typical cavity optomechanical system. This book introduces the quantum optical properties of optomechanical system, such as linear and nonlinear effects.
Автор: Tapio Simula Название: Quantised Vortices: A Handbook of Topological Excitations ISBN: 1643271237 ISBN-13(EAN): 9781643271231 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 10811.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
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