A Computational Non-commutative Geometry Program for Disordered Topological Insulators

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Publisher : Springer
ISBN 13 : 3319550233
Total Pages : 123 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis A Computational Non-commutative Geometry Program for Disordered Topological Insulators by : Emil Prodan

Download or read book A Computational Non-commutative Geometry Program for Disordered Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2017-03-17 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder.In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of non-commutative Brillouin torus, and a list of known formulas for various physical response functions is presented. In the second part, auxiliary algebras are introduced and a canonical finite-volume approximation of the non-commutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. In the third part upper bounds on the numerical errors are derived and it is proved that the canonical-finite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation.The book is intended for graduate students and researchers in numerical and mathematical physics.

Cyclic Cohomology at 40: Achievements and Future Prospects

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Publisher : American Mathematical Society
ISBN 13 : 1470469774
Total Pages : 592 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Cyclic Cohomology at 40: Achievements and Future Prospects by : A. Connes

Download or read book Cyclic Cohomology at 40: Achievements and Future Prospects written by A. Connes and published by American Mathematical Society. This book was released on 2023-02-23 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.

Geometric Methods in Physics XXXVIII

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Publisher : Springer Nature
ISBN 13 : 3030533050
Total Pages : 373 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Geometric Methods in Physics XXXVIII by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXVIII written by Piotr Kielanowski and published by Springer Nature. This book was released on 2020-10-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems

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Publisher : Springer Nature
ISBN 13 : 3031122011
Total Pages : 225 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems by : Hermann Schulz-Baldes

Download or read book Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems written by Hermann Schulz-Baldes and published by Springer Nature. This book was released on 2022-12-31 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems. This book is intended for advanced students in mathematical physics and researchers alike.

Bulk and Boundary Invariants for Complex Topological Insulators

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Publisher : Springer
ISBN 13 : 3319293516
Total Pages : 217 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Bulk and Boundary Invariants for Complex Topological Insulators by : Emil Prodan

Download or read book Bulk and Boundary Invariants for Complex Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2016-02-05 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.

Coarse Geometry of Topological Groups

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Publisher : Cambridge University Press
ISBN 13 : 110884247X
Total Pages : 309 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Coarse Geometry of Topological Groups by : Christian Rosendal

Download or read book Coarse Geometry of Topological Groups written by Christian Rosendal and published by Cambridge University Press. This book was released on 2021-12-16 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.

The Role of Topology in Materials

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Publisher :
ISBN 13 : 9783319765976
Total Pages : 297 pages
Book Rating : 4.7/5 (659 download)

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Book Synopsis The Role of Topology in Materials by : Sanju Gupta

Download or read book The Role of Topology in Materials written by Sanju Gupta and published by . This book was released on 2018 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure-property-function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.

Condensed Matter Field Theory

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Publisher : Cambridge University Press
ISBN 13 : 0521769752
Total Pages : 785 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Condensed Matter Field Theory by : Alexander Altland

Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Statistical Mechanics

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Publisher : OUP Oxford
ISBN 13 : 0191566217
Total Pages : 374 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Statistical Mechanics by : James Sethna

Download or read book Statistical Mechanics written by James Sethna and published by OUP Oxford. This book was released on 2006-04-07 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.

The Mathematics and Topology of Fullerenes

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Publisher : Springer Science & Business Media
ISBN 13 : 9400702213
Total Pages : 294 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis The Mathematics and Topology of Fullerenes by : Franco Cataldo

Download or read book The Mathematics and Topology of Fullerenes written by Franco Cataldo and published by Springer Science & Business Media. This book was released on 2011-12-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.

Toeplitz Operators and Index Theory in Several Complex Variables

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Publisher : Springer Science & Business Media
ISBN 13 : 9783764352820
Total Pages : 512 pages
Book Rating : 4.3/5 (528 download)

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Book Synopsis Toeplitz Operators and Index Theory in Several Complex Variables by : Harald Upmeier

Download or read book Toeplitz Operators and Index Theory in Several Complex Variables written by Harald Upmeier and published by Springer Science & Business Media. This book was released on 1995-01-26 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 4. 1 Bergman-Toeplitz Operators Over Bounded Domains 242 4. 2 Hardy-Toeplitz Operators Over Strictly Domains Pseudoconvex 250 Groupoid C* -Algebras 4. 3 256 4. 4 Hardy-Toeplitz Operators Over Tubular Domains 267 4. 5 Bergman-Toeplitz Operators Over Tubular Domains 278 4. 6 Hardy-Toeplitz Operators Over Polycircular Domains 284 4. 7 Bergman-Toeplitz Operators Over Polycircular Domains 290 4. 8 Hopf C* -Algebras 299 4. 9 Actions and Coactions on C* -Algebras 310 4. 10 Hardy-Toeplitz Operators Over K-circular Domains 316 4. 11 Hardy-Toeplitz Operators Over Symmetric Domains 325 4. 12 Bergman-Toeplitz Operators Over Symmetric Domains 361 5. Index Theory for Multivariable Toeplitz Operators 5. 0 Introduction 371 5. 1 K-Theory for Topological Spaces 372 5. 2 Index Theory for Strictly Pseudoconvex Domains 384 5. 3 C*-Algebras K-Theory for 394 5. 4 Index Theory for Symmetric Domains 400 5. 5 Index Theory for Tubular Domains 432 5. 6 Index Theory for Polycircular Domains 455 References 462 Index of Symbols and Notations 471 In trod uction Toeplitz operators on the classical Hardy space (on the I-torus) and the closely related Wiener-Hopf operators (on the half-line) form a central part of operator theory, with many applications e. g. , to function theory on the unit disk and to the theory of integral equations.

Building Electro-Optical Systems

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Publisher : John Wiley & Sons
ISBN 13 : 111821109X
Total Pages : 750 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Building Electro-Optical Systems by : Philip C. D. Hobbs

Download or read book Building Electro-Optical Systems written by Philip C. D. Hobbs and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "Now a new laboratory bible for optics researchers has joined the list: it is Phil Hobbs's Building Electro-Optical Systems: Making It All Work." —Tony Siegman, Optics & Photonics News Building a modern electro-optical instrument may be the most interdisciplinary job in all of engineering. Be it a DVD player or a laboratory one-off, it involves physics, electrical engineering, optical engineering, and computer science interacting in complex ways. This book will help all kinds of technical people sort through the complexity and build electro-optical systems that just work, with maximum insight and minimum trial and error. Written in an engaging and conversational style, this Second Edition has been updated and expanded over the previous edition to reflect technical advances and a great many conversations with working designers. Key features of this new edition include: Expanded coverage of detectors, lasers, photon budgets, signal processing scheme planning, and front ends Coverage of everything from basic theory and measurement principles to design debugging and integration of optical and electronic systems Supplementary material is available on an ftp site, including an additional chapter on thermal Control and Chapter problems highly relevant to real-world design Extensive coverage of high performance optical detection and laser noise cancellation Each chapter is full of useful lore from the author's years of experience building advanced instruments. For more background, an appendix lists 100 good books in all relevant areas, introductory as well as advanced. Building Electro-Optical Systems: Making It All Work, Second Edition is essential reading for researchers, students, and professionals who have systems to build.

K-Theory for Operator Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 1461395720
Total Pages : 347 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis K-Theory for Operator Algebras by : Bruce Blackadar

Download or read book K-Theory for Operator Algebras written by Bruce Blackadar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.

Electronic Transport in Mesoscopic Systems

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Publisher : Cambridge University Press
ISBN 13 : 1139643010
Total Pages : 398 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis Electronic Transport in Mesoscopic Systems by : Supriyo Datta

Download or read book Electronic Transport in Mesoscopic Systems written by Supriyo Datta and published by Cambridge University Press. This book was released on 1997-05-15 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in semiconductor technology have made possible the fabrication of structures whose dimensions are much smaller than the mean free path of an electron. This book gives a thorough account of the theory of electronic transport in such mesoscopic systems. After an initial chapter covering fundamental concepts, the transmission function formalism is presented, and used to describe three key topics in mesoscopic physics: the quantum Hall effect; localisation; and double-barrier tunnelling. Other sections include a discussion of optical analogies to mesoscopic phenomena, and the book concludes with a description of the non-equilibrium Green's function formalism and its relation to the transmission formalism. Complete with problems and solutions, the book will be of great interest to graduate students of mesoscopic physics and nanoelectronic device engineering, as well as to established researchers in these fields.

Modern Condensed Matter

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Publisher :
ISBN 13 : 9780957481190
Total Pages : 15 pages
Book Rating : 4.4/5 (811 download)

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Book Synopsis Modern Condensed Matter by :

Download or read book Modern Condensed Matter written by and published by . This book was released on 2020 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamentals of Quantum Computing

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Publisher : Springer Nature
ISBN 13 : 3030636895
Total Pages : 463 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Fundamentals of Quantum Computing by : Venkateswaran Kasirajan

Download or read book Fundamentals of Quantum Computing written by Venkateswaran Kasirajan and published by Springer Nature. This book was released on 2021-06-21 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to K-Theory for C*-Algebras

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Publisher : Cambridge University Press
ISBN 13 : 9780521789448
Total Pages : 260 pages
Book Rating : 4.7/5 (894 download)

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Book Synopsis An Introduction to K-Theory for C*-Algebras by : M. Rørdam

Download or read book An Introduction to K-Theory for C*-Algebras written by M. Rørdam and published by Cambridge University Press. This book was released on 2000-07-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.