Lectures On Quantum Computation Quantum Error Correcting Codes And Information Theory
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Lectures On Quantum Computation Quantum Error Correcting Codes And Information Theory
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Author : K. R. Parthasarathy
language : en
Publisher:
Release Date : 2006
Lectures On Quantum Computation Quantum Error Correcting Codes And Information Theory written by K. R. Parthasarathy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
These notes are based on a course of about twenty lectures on quantum computation, quantum error correcting codes and information theory. The topics include a comparative description of the basic features of classical probability theory on finite sample spaces and quantum probability theory on finite dimensional complex Hilbert spaces, quantum gates and cicuits, simple examples of circuits arising from quantum teleportation, communication through EPR pairs and arithmetical computations on a quantum computer, more sophisticated examples of such circuits in the context of Fourier transform and phase estimation, a detailed account of the order finding algorithm as well as the celebrated Shor's algorithm for factorising a positive integer into its prime factors. There is a leisurely discussion of quantum error correcting codes with the Knill-Laflamme criterion for error correction and a number of examples of such codes whose construction is based on the Weyl commutation relations for finite abelian groups. The reader may find here a brief introduction to the basic ideas of classical information theory as developed by Shannon,properties of von Neumann's quantum entropy and relative entropy as well as a proof of Schumacher's noiseless quantum coding theorem. The Holevo bound for transmission of classical information through encoding by quantum states followed by measurements is derived. The only background assumed of the reader is linear algebra on finite dimensional complex vector spaces and elementary classical probability theory on finite sample spaces.These notes are aimed at mathematicians and computer scientists who are curious to know the mystery behind a quantum computer and the possibility of communicating information using the principles of elementary quantum theory.
The Functional Analysis Of Quantum Information Theory
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Author : Ved Prakash Gupta
language : en
Publisher: Springer
Release Date : 2015-05-28
The Functional Analysis Of Quantum Information Theory written by Ved Prakash Gupta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-28 with Science categories.
This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting.
A Tribute To C S Seshadri
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Author : Venkatrama Lakshmibai
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-24
A Tribute To C S Seshadri written by Venkatrama Lakshmibai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-24 with Mathematics categories.
C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.
Lecture Notes For Physics 229 Quantum Information And Computation
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Author : John Preskill
language : en
Publisher:
Release Date : 2015-01-12
Lecture Notes For Physics 229 Quantum Information And Computation written by John Preskill and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-12 with categories.
Lecture Notes for Physics 229:Quantum Information and ComputationBy John Preskill
Quantum Codes For Topological Quantum Computation
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Author : Clarice Dias de Albuquerque
language : en
Publisher: Springer Nature
Release Date : 2022-08-04
Quantum Codes For Topological Quantum Computation written by Clarice Dias de Albuquerque and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-04 with Science categories.
This book offers a structured algebraic and geometric approach to the classification and construction of quantum codes for topological quantum computation. It combines key concepts in linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics, and classical and quantum coding theory to help readers understand and develop quantum codes for topological quantum computation. One possible approach to building a quantum computer is based on surface codes, operated as stabilizer codes. The surface codes evolved from Kitaev's toric codes, as a means to developing models for topological order by using qubits distributed on the surface of a toroid. A significant advantage of surface codes is their relative tolerance to local errors. A second approach is based on color codes, which are topological stabilizer codes defined on a tessellation with geometrically local stabilizer generators. This book provides basic geometric concepts, like surface geometry, hyperbolic geometry and tessellation, as well as basic algebraic concepts, like stabilizer formalism, for the construction of the most promising classes of quantum error-correcting codes such as surfaces codes and color codes. The book is intended for senior undergraduate and graduate students in Electrical Engineering and Mathematics with an understanding of the basic concepts of linear algebra and quantum mechanics.
Diversities In Quantum Computation And Quantum Information
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Author : Mikio Nakahara
language : en
Publisher: World Scientific
Release Date : 2013
Diversities In Quantum Computation And Quantum Information written by Mikio Nakahara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
This book is a collection of lecture notes and contributions in "Summer School on Diversities in Quantum Computation/Information" held on 1-5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relativistic quantum information, quantum computing of link polynomials, quantum algorithms, etc. Each lecture note is written in a self-contained manner so that it may be used as a textbook for one semester graduate course or advanced undergraduate course. Contributions report current research subjects also in a self-contained manner. We believe that these articles are accessible to the readers form various disciplines.
Lectures On Quantum Information
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Author : Dagmar Bruss
language : en
Publisher: Wiley-VCH
Release Date : 2007
Lectures On Quantum Information written by Dagmar Bruss and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Computers categories.
Quantum Information Processing is a young and rapidly growing field of research at the intersection of physics, mathematics, and computer science. Its ultimate goal is to harness quantum physics to conceive -- and ultimately build -- "quantum" computers that would dramatically overtake the capabilities of today's "classical" computers. One example of the power of a quantum computer is its ability to efficiently find the prime factors of a larger integer, thus shaking the supposedly secure foundations of standard encryption schemes. This comprehensive textbook on the rapidly advancing field introduces readers to the fundamental concepts of information theory and quantum entanglement, taking into account the current state of research and development. It thus covers all current concepts in quantum computing, both theoretical and experimental, before moving on to the latest implementations of quantum computing and communication protocols. With its series of exercises, this is ideal reading for students and lecturers in physics and informatics, as well as experimental and theoretical physicists, and physicists in industry. Dagmar Bruß graduated at RWTH University Aachen, Germany, and received her PhD in theoretical particle physics from the University of Heidelberg in 1994. As a research fellow at the University of Oxford she started to work in quantum information theory. Another fellowship at ISI Torino, Italy, followed. While being a research assistant at the University of Hannover she completed her habilitation. Since 2004 Professor Bruß has been holding a chair at the Institute of Theoretical Physics at the Heinrich-Heine-University Düsseldorf, Germany. Gerd Leuchs studied physics and mathematics at the University of Cologne, Germany, and received his Ph.D. in 1978. After two research visits at the University of Colorado in Boulder, USA, he headed the German gravitational wave detection group from 1985 to 1989. He became technical director at Nanomach AG in Switzerland. Since 1994 Professor Leuchs has been holding the chair for optics at the Friedrich-Alexander-University of Erlangen-Nuremberg, Germany. His fields of research span the range from modern aspects of classical optics to quantum optics and quantum information. Since 2003 he has been Director of the Max Planck Research Group for Optics, Information and Photonics at Erlangen.
Math Unlimited
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Author : R. Sujatha
language : en
Publisher: CRC Press
Release Date : 2011-11-11
Math Unlimited written by R. Sujatha and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-11 with Mathematics categories.
This collection of essays spans pure and applied mathematics. Readers interested in mathematical research and historical aspects of mathematics will appreciate the enlightening content of the material. Highlighting the pervasive nature of mathematics today in a host of different areas, the book also covers the spread of mathematical ideas and techn
An Introduction To Quantum Computing
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Author : Phillip Kaye
language : en
Publisher: OUP Oxford
Release Date : 2006-11-17
An Introduction To Quantum Computing written by Phillip Kaye and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-17 with Computers categories.
This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as quantum mechanics and computational complexity is not required.
Quantum Information And Quantum Computing
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Author : Mikio Nakahara
language : en
Publisher: World Scientific
Release Date : 2013
Quantum Information And Quantum Computing written by Mikio Nakahara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
The open research center project "Interdisciplinary fundamental research toward realization of a quantum computer" has been supported by the Ministry of Education, Japan for five years. This is a collection of the research outcomes by the members engaged in the project. To make the presentation self-contained, it starts with an overview by Mikio Nakahara, which serves as a concise introduction to quantum information and quantum computing. Subsequent contributions include subjects from physics, chemistry, mathematics, and information science, reflecting upon the wide variety of scientists working under this project. These contributions introduce NMR quantum computing and related techniques, number theory and coding theory, quantum error correction, photosynthesis, non-classical correlations and entanglement, neutral atom quantum computer, among others. Each of the contributions will serve as a short introduction to these cutting edge research fields.