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Quantum Walks And Search Algorithms
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Book Synopsis Quantum Walks and Search Algorithms by : Renato Portugal
Download or read book Quantum Walks and Search Algorithms written by Renato Portugal and published by Springer Science & Business Media. This book was released on 2013-02-16 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Walks and Search Algorithms by : Renato Portugal
Download or read book Quantum Walks and Search Algorithms written by Renato Portugal and published by Springer. This book was released on 2018-08-20 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Walks and Search Algorithms by :
Download or read book Quantum Walks and Search Algorithms written by and published by Springer. This book was released on 2013-02-19 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Physical Implementation of Quantum Walks by : Kia Manouchehri
Download or read book Physical Implementation of Quantum Walks written by Kia Manouchehri and published by Springer Science & Business Media. This book was released on 2013-08-23 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Query Complexity written by Mario Szegedy and published by World Scientific Publishing Company. This book was released on 2018-06-30 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Primer on Quantum Computing by : Franklin de Lima Marquezino
Download or read book A Primer on Quantum Computing written by Franklin de Lima Marquezino and published by Springer. This book was released on 2019-06-25 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about quantum computing and quantum algorithms. The book starts with a chapter introducing the basic rules of quantum mechanics and how they can be used to build quantum circuits and perform computations. Further, Grover's algorithm is presented for unstructured search discussing its consequences and applications. Next, important techniques are discussed such as Quantum Fourier Transform and quantum phase estimation. Finally, Shor's algorithm for integer factorization is explained. At last, quantum walks are explained in detail covering both the discrete and continuous time models,and applications of this techniques are described for the design and analyses of quantum algorithms.
Book Synopsis Quantum Walks for Computer Scientists by : Salvador Venegas-Andraca
Download or read book Quantum Walks for Computer Scientists written by Salvador Venegas-Andraca and published by Morgan & Claypool Publishers. This book was released on 2008-10-08 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Quantum Computing: An Applied Approach by : Jack D. Hidary
Download or read book Quantum Computing: An Applied Approach written by Jack D. Hidary and published by Springer Nature. This book was released on 2021-09-29 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first to bring these elements together in an updated manner. This work is suitable for both academic coursework and corporate technical training. The second edition includes extensive updates and revisions, both to textual content and to the code. Sections have been added on quantum machine learning, quantum error correction, Dirac notation and more. This new edition benefits from the input of the many faculty, students, corporate engineering teams, and independent readers who have used the first edition. This volume comprises three books under one cover: Part I outlines the necessary foundations of quantum computing and quantum circuits. Part II walks through the canon of quantum computing algorithms and provides code on a range of quantum computing methods in current use. Part III covers the mathematical toolkit required to master quantum computing. Additional resources include a table of operators and circuit elements and a companion GitHub site providing code and updates. Jack D. Hidary is a research scientist in quantum computing and in AI at Alphabet X, formerly Google X.
Book Synopsis Randomization and Approximation Techniques in Computer Science by : Jose D.P. Rolim
Download or read book Randomization and Approximation Techniques in Computer Science written by Jose D.P. Rolim and published by Springer. This book was released on 2003-08-03 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002, held in Cambridge, MA, USA in September 2002. The 21 revised full papers presented were carefully reviewed and selected from 48 submissions. Among the topics addressed are coding, geometric computations, graph colorings, random hypergraphs, graph computations, lattice computations, proof systems, probabilistic algorithms, derandomization, constraint satisfaction, and web graphs analysis.
Book Synopsis Introduction to Quantum Algorithms via Linear Algebra, second edition by : Richard J. Lipton
Download or read book Introduction to Quantum Algorithms via Linear Algebra, second edition written by Richard J. Lipton and published by MIT Press. This book was released on 2021-04-06 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, it makes quantum algorithms accessible to students and researchers in computer science who have not taken courses in quantum physics or delved into fine details of quantum effects, apparatus, circuits, or theory.
Book Synopsis Quantum Walks for Computer Scientists by : Salvador Venegas-Andraca
Download or read book Quantum Walks for Computer Scientists written by Salvador Venegas-Andraca and published by Springer Nature. This book was released on 2022-05-31 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Quantum Image Processing by : Fei Yan
Download or read book Quantum Image Processing written by Fei Yan and published by Springer Nature. This book was released on 2020-01-03 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Computing for Programmers by : Robert Hundt
Download or read book Quantum Computing for Programmers written by Robert Hundt and published by Cambridge University Press. This book was released on 2022-03-31 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Takes readers from the basics to detailed derivations and open-source implementations of more than 25 fundamental quantum algorithms.
Book Synopsis Discrete Quantum Walks on Graphs and Digraphs by : Christopher David Godsil
Download or read book Discrete Quantum Walks on Graphs and Digraphs written by Christopher David Godsil and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Discrete quantum walks are quantum analogues of classical random walks. They are an important tool in quantum computing and a number of algorithms can be viewed as discrete quantum walks, in particular Grover's search algorithm. These walks are constructed on an underlying graph, and so there is a relation between properties of walks and properties of the graph. This book studies the mathematical problems that arise from this connection, and the different classes of walks that arise. Written at a level suitable for graduate students in mathematics, the only prerequisites are linear algebra and basic graph theory; no prior knowledge of physics is required. The text serves as an introduction to this important and rapidly developing area for mathematicians and as a detailed reference for computer scientists and physicists working on quantum information theory"--
Book Synopsis Quantum Computation and Quantum Information by : Michael A. Nielsen
Download or read book Quantum Computation and Quantum Information written by Michael A. Nielsen and published by Cambridge University Press. This book was released on 2010-12-09 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.
Book Synopsis Quantum Algorithms via Linear Algebra by : Richard J. Lipton
Download or read book Quantum Algorithms via Linear Algebra written by Richard J. Lipton and published by MIT Press. This book was released on 2014-12-05 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of Quantum Programming by : Mingsheng Ying
Download or read book Foundations of Quantum Programming written by Mingsheng Ying and published by Elsevier. This book was released on 2024-05-01 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers promise dramatic advantages in processing speed over currently available computer systems. Quantum computing offers great promise in a wide variety of computing and scientific research, including Quantum cryptography, machine learning, computational biology, renewable energy, computer-aided drug design, generative chemistry, and any scientific or enterprise application that requires computation speed or reach beyond the limits of current conventional computer systems. Foundations of Quantum Programming, Second Edition discusses how programming methodologies and technologies developed for current computers can be extended for quantum computers, along with new programming methodologies and technologies that can effectively exploit the unique power of quantum computing. The Second Edition includes two new chapters describing programming models and methodologies for parallel and distributed quantum computers. The author has also included two new chapters to introduce Quantum Machine Learning and its programming models – parameterized and differential quantum programming. In addition, the First Edition's preliminaries chapter has been split into three chapters, with two sections for quantum Turing machines and random access stored program machines added to give the reader a more complete picture of quantum computational models. Finally, several other new techniques are introduced in the Second Edition, including invariants of quantum programs and their generation algorithms, and abstract interpretation of quantum programs. Demystifies the theory of quantum programming using a step-by-step approach Includes methodologies, techniques, and tools for the development, analysis, and verification of quantum programs and quantum cryptographic protocols Covers the interdisciplinary nature of quantum programming by providing preliminaries from quantum mechanics, mathematics, and computer science, and pointing out its potential applications to quantum engineering and physics Presents a coherent and self-contained treatment that will be valuable for academic and industrial researchers and developers Adds new developments such as parallel and distributed quantum programming; and introduces several new program analysis techniques such as invariants generation and abstract interpretation
