Graph Theory Quantum Walk

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Graph Theory Quantum Walk

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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :

Graph Theory Quantum Walk written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Computers categories.

"Graph Theory: Quantum Walk" explores how quantum computing enhances our understanding and applications of graphs. From basic principles to advanced algorithms, the book shows how quantum mechanics revolutionizes computation in graph theory. Whether you're a student, researcher, or enthusiast, discover the exciting potential where quantum principles meet graph theory, offering new insights and computational strategies in this dynamic field.

Quantum Walks And Search Algorithms

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Author : Renato Portugal
language : en
Publisher: Springer
Release Date : 2018-08-20

Quantum Walks And Search Algorithms written by Renato Portugal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-20 with Science categories.

The revised edition of this book offers an extended overview of quantum walks and explains their role in building quantum algorithms, in particular search algorithms. Updated throughout, the book focuses on core topics including Grover's algorithm and the most important quantum walk models, such as the coined, continuous-time, and Szedgedy's quantum walk models. There is a new chapter describing the staggered quantum walk model. The chapter on spatial search algorithms has been rewritten to offer a more comprehensive approach and a new chapter describing the element distinctness algorithm has been added. There is a new appendix on graph theory highlighting the importance of graph theory to quantum walks. As before, the reader will benefit from the pedagogical elements of the book, which include exercises and references to deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks. Review of the first edition: “The book is nicely written, the concepts are introduced naturally, and many meaningful connections between them are highlighted. The author proposes a series of exercises that help the reader get some working experience with the presented concepts, facilitating a better understanding. Each chapter ends with a discussion of further references, pointing the reader to major results on the topics presented in the respective chapter.” - Florin Manea, zbMATH.

Discrete Quantum Walks On Graphs And Digraphs

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Author : Chris Godsil
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-12

Discrete Quantum Walks On Graphs And Digraphs written by Chris Godsil and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-12 with Computers categories.

Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.

Physical Implementation Of Quantum Walks

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Author : Kia Manouchehri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-23

Physical Implementation Of Quantum Walks written by Kia Manouchehri 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 2013-08-23 with Technology & Engineering categories.

Given the extensive application of random walks in virtually every science related discipline, we may be at the threshold of yet another problem solving paradigm with the advent of quantum walks. Over the past decade, quantum walks have been explored for their non-intuitive dynamics, which may hold the key to radically new quantum algorithms. This growing interest has been paralleled by a flurry of research into how one can implement quantum walks in laboratories. This book presents numerous proposals as well as actual experiments for such a physical realization, underpinned by a wide range of quantum, classical and hybrid technologies.

Quantum Walks And Pretty Good State Transfer On Paths

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Author : Christopher Martin van Bommel
language : en
Publisher:
Release Date : 2019

Quantum Walks And Pretty Good State Transfer On Paths written by Christopher Martin van Bommel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

Quantum computing is believed to provide many advantages over traditional computing, particularly considering the speed at which computations can be performed. One of the challenges that needs to be resolved in order to construct a quantum computer is the transmission of information from one part of the computer to another. Quantum walks, the quantum analogues of classical random walks, provide one potential method for resolving this challenge. In this thesis, we use techniques from algebraic graph theory and number theory to analyze the mathematical model for continuous time quantum walks on graphs. For the continuous time quantum walk model, we define a transition operator, which is a function of a Hamiltonian. We focus on the cases where the adjacency matrix or the Laplacian of a graph act as the Hamiltionian. We mainly consider quantum walks on paths as a model for spin chains, which are the underlying basis of a quantum communication protocol. For communication to be efficient, we desire states to be transferred with high fidelity, a measure of the amount of similarity between the transmitted state and the received state. At the maximum fidelity of 1, we say we have achieved perfect state transfer. Examples of perfect state transfer are relatively rare, so the concept of pretty good state transfer was introduced as a natural relaxation, which exists if fidelities arbitrarily close to 1 are obtained. Our first main result is to characterize pretty good state transfer on paths. Previously, pretty good state transfer on paths was considered mainly for the end vertices, though results for both models indicated that if there was pretty good state transfer between the end vertices, then there was pretty good state transfer between internal vertices equidistant from each end. We complete the characterization by demonstrating, for the adjacency matrix model, a family of paths where pretty good state transfer exists between internal vertices but not between end vertices, and verifying that no other example exists. For the Laplacian model, we show that there are no paths with pretty good state transfer between internal vertices but not between the end vertices. Our second main result considers initial states involving multiple vertices. Under the adjacency matrix model, we provide necessary and sufficient conditions for pretty good state transfer in a particular family of paths in terms of the eigenvalue support of the initial state. We also discuss recent results on fractional revival, which is another form of multiple qubit state transfer.

Proceedings Of The 33rd Annual Acm Symposium On Theory Of Computing

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Author :
language : en
Publisher:
Release Date : 2001

Proceedings Of The 33rd Annual Acm Symposium On Theory Of Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computable complexity categories.

Proceedings Of The Acm Symposium On Theory Of Computing

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Author :
language : en
Publisher:
Release Date : 2007

Proceedings Of The Acm Symposium On Theory Of Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Formal languages categories.

High Level Quantum Programming With Quantum Walks

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Author : Hé́ctor J. García
language : en
Publisher:
Release Date : 2007

High Level Quantum Programming With Quantum Walks written by Hé́ctor J. García and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Algorithms categories.

Quantum Information Computation

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Author :
language : en
Publisher:
Release Date : 2006

Quantum Information Computation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Information theory categories.

Quantum Communication Measurement And Computing

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Author : Stephen M. Barnett
language : en
Publisher: American Inst. of Physics
Release Date : 2004-11-19

Quantum Communication Measurement And Computing written by Stephen M. Barnett and has been published by American Inst. of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-19 with Science categories.

The papers were peer reviewed.Quantum communications, measurement and computing embodies the fledgling science of quantum information. It applies quantum physics to tackle the challenges of next generation information processing. The conference was the seventh in the series. These proceedings describe papers presented at the meeting and represent the forefront of current research. Topics include: quantum communication, measurement, quantum computation, entanglement, quantum cryptography, sources of quantum states, time, as well as dissipation and decoherence.