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Quantum Walks And Search Algorithms

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Quantum Walks And Search Algorithms

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Author : Renato Portugal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-16

Quantum Walks And Search Algorithms written by Renato Portugal 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 2013-02-16 with Science categories.

This book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operator Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting distribution and mixing time Spatial search algorithms, with emphasis on the abstract search algorithm (the two-dimensional lattice is used as an example) Szedgedy's quantum-walk model and a natural definition of quantum hitting time (the complete graph is used as an example) The reader will benefit from the pedagogical aspects of the book, learning faster and with more ease than would be possible from the primary research literature. Exercises and references further deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks are also provided.

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.

Quantum Walks And Search Algorithms

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Author :
language : en
Publisher: Springer
Release Date : 2013-02-19

Quantum Walks And Search Algorithms written by and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-19 with categories.

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 Computers 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.

Query Complexity

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Author : Mario Szegedy
language : en
Publisher: World Scientific Publishing Company
Release Date : 2018-06-30

Query Complexity written by Mario Szegedy and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-30 with Computers categories.

Quantum Walks For Computer Scientists

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Author : Salvador Venegas-Andraca
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

Quantum Walks For Computer Scientists written by Salvador Venegas-Andraca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.

Quantum computation, one of the latest joint ventures between physics and the theory of computation, is a scientific field whose main goals include the development of hardware and algorithms based on the quantum mechanical properties of those physical systems used to implement such algorithms. Solving difficult tasks (for example, the Satisfiability Problem and other NP-complete problems) requires the development of sophisticated algorithms, many ofwhich employ stochastic processes as their mathematical basis. Discrete random walks are a popular choice among those stochastic processes. Inspired on the success of discrete random walks in algorithm development, quantum walks, an emerging field of quantum computation, is a generalization of random walks into the quantum mechanical world. The purpose of this lecture is to provide a concise yet comprehensive introduction to quantum walks. Table of Contents: Introduction / Quantum Mechanics / Theory of Computation / Classical Random Walks / Quantum Walks / Computer Science and Quantum Walks / Conclusions

Search Algorithms And Applications

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Author : Nashat Mansour
language : en
Publisher: BoD – Books on Demand
Release Date : 2011-04-26

Search Algorithms And Applications written by Nashat Mansour and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-26 with Computers categories.

Search algorithms aim to find solutions or objects with specified properties and constraints in a large solution search space or among a collection of objects. A solution can be a set of value assignments to variables that will satisfy the constraints or a sub-structure of a given discrete structure. In addition, there are search algorithms, mostly probabilistic, that are designed for the prospective quantum computer. This book demonstrates the wide applicability of search algorithms for the purpose of developing useful and practical solutions to problems that arise in a variety of problem domains. Although it is targeted to a wide group of readers: researchers, graduate students, and practitioners, it does not offer an exhaustive coverage of search algorithms and applications. The chapters are organized into three parts: Population-based and quantum search algorithms, Search algorithms for image and video processing, and Search algorithms for engineering applications.

Introduction To Quantum Algorithms Via Linear Algebra Second Edition

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Author : Richard J. Lipton
language : en
Publisher: MIT Press
Release Date : 2021-04-06

Introduction To Quantum Algorithms Via Linear Algebra Second Edition written by Richard J. Lipton and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-06 with Science categories.

Quantum Image Processing

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Author : Fei Yan
language : en
Publisher: Springer Nature
Release Date : 2020-01-03

Quantum Image Processing written by Fei Yan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Computers categories.

This book provides a comprehensive introduction to quantum image processing, which focuses on extending conventional image processing tasks to the quantum computing frameworks. It summarizes the available quantum image representations and their operations, reviews the possible quantum image applications and their implementation, and discusses the open questions and future development trends. It offers a valuable reference resource for graduate students and researchers interested in this emerging interdisciplinary field.

Quantum Algorithms Via Linear Algebra

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Author : Richard J. Lipton
language : en
Publisher: MIT Press
Release Date : 2014-12-05

Quantum Algorithms Via Linear Algebra written by Richard J. Lipton and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Science categories.

Quantum computing explained in terms of elementary linear algebra, emphasizing computation and algorithms and requiring no background in physics. This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of all the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, this primer makes quantum algorithms accessible to students and researchers in computer science without the complications of quantum mechanical notation, physical concepts, and philosophical issues. After explaining the development of quantum operations and computations based on linear algebra, the book presents the major quantum algorithms, from seminal algorithms by Deutsch, Jozsa, and Simon through Shor's and Grover's algorithms to recent quantum walks. It covers quantum gates, computational complexity, and some graph theory. Mathematical proofs are generally short and straightforward; quantum circuits and gates are used to illuminate linear algebra; and the discussion of complexity is anchored in computational problems rather than machine models. Quantum Algorithms via Linear Algebra is suitable for classroom use or as a reference for computer scientists and mathematicians.

Quantum Walks And Search Algorithms

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