quantum walks and search algorithms quantum science and technology

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Quantum Walks And Search Algorithms

Author : Renato Portugal
ISBN : 9781461463368
Genre : Science
File Size : 30. 60 MB
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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 Algorithms Via Linear Algebra

Author : Richard J. Lipton
ISBN : 9780262028394
Genre : Science
File Size : 43. 69 MB
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Quantum computing explained in terms of elementary linear algebra, emphasizing computation and algorithms and requiring no background in physics.

Physical Implementation Of Quantum Walks

Author : Kia Manouchehri
ISBN : 9783642360145
Genre : Computers
File Size : 21. 96 MB
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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.

Physical Implementation Of Quantum Walks

Author : Kia Manouchehri
ISBN : 9783642360145
Genre : Computers
File Size : 58. 90 MB
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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.

Foundations Of Quantum Programming

Author : Mingsheng Ying
ISBN : 9780128025468
Genre : Computers
File Size : 51. 92 MB
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Foundations of Quantum Programming discusses how new programming methodologies and technologies developed for current computers can be extended to exploit the unique power of quantum computers, which promise dramatic advantages in processing speed over currently available computer systems. Governments and industries around the globe are now investing vast amounts of money with the expectation of building practical quantum computers. Drawing upon years of experience and research in quantum computing research and using numerous examples and illustrations, Mingsheng Ying has created a very useful reference on quantum programming languages and important tools and techniques required for quantum programming, making the book a valuable resource for academics, researchers, and developers. Demystifies the theory of quantum programming using a step-by-step approach Covers the interdisciplinary nature of quantum programming by providing examples from many different fields including, engineering, computer science, medicine, and life sciences Includes techniques and tools to solve complex control flow patterns and synchronize computations Presents a coherent and self-contained treatment that will be valuable for academics and industrial researchers and developers

Multi Photon Quantum Information Science And Technology In Integrated Optics

Author : Jonathan C.F. Matthews
ISBN : 9783642328695
Genre : Science
File Size : 72. 74 MB
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Photons are an attractive option for testing fundamental quantum physics and developing new quantum-enhanced technology, including highly advanced computers and simulators, as well as precision sensing beyond shot-noise. Traditionally, bulk optical components have been bolted onto optical benches to realize metre-scale quantum circuits. However this approach is ultimately proving unwieldy for increasing the complexity and for scaling up to practical quantum technologies based on photons. The work presented here demonstrates a series of quantum photonic devices based on waveguide circuits embedded in miniature monolithic chips. This represents a paradigm shift in the underlying architecture of quantum optics and provides key building blocks for all-optical and hybrid quantum technologies.

Theory And Applications Of Models Of Computation

Author : Manindra Agrawal
ISBN : 9783540792284
Genre : Computers
File Size : 86. 19 MB
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This proceedings volume examines all major areas in computer science, mathematics (especially logic) and the physical sciences, especially computation, algorithms, complexity and computability theory.

Computer Science Theory And Applications

Author : Farid M. Ablaev
ISBN : 9783642131820
Genre : Computers
File Size : 60. 91 MB
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Quantum Computer Science

Author : N. David Mermin
ISBN : 1139466801
Genre : Science
File Size : 41. 71 MB
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In the 1990's it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction to quantum computation, developing the basic elements of this new branch of computational theory without assuming any background in physics. It begins with an introduction to the quantum theory from a computer-science perspective. It illustrates the quantum-computational approach with several elementary examples of quantum speed-up, before moving to the major applications: Shor's factoring algorithm, Grover's search algorithm, and quantum error correction. The book is intended primarily for computer scientists who know nothing about quantum theory, but will also be of interest to physicists who want to learn the theory of quantum computation, and philosophers of science interested in quantum foundational issues. It evolved during six years of teaching the subject to undergraduates and graduate students in computer science, mathematics, engineering, and physics, at Cornell University.

Quantum Walks For Computer Scientists

Author : Salvador Elías Venegas-Andraca
ISBN : 9781598296563
Genre : Computers
File Size : 67. 74 MB
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"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 of which 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."--BOOK JACKET.

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