Quantum Walks and Search Algorithms

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...

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Autor principal: Portugal, Renato
Format: Livre numérique
Idioma:Anglais
Publicat: New York, NY : Springer New York [20..].
Cham : Springer Nature
Edició:1st ed. 2013.
Col·lecció:Quantum Science and Technology
Accés en línia:Accès sur la plateforme de l'éditeur
Accès sur la plateforme Istex
Accès Université d'Orléans
Accès INSA CVL
Nota: Archives Springer e-books (Licence nationale)
Archives Springer e-books (Licence nationale)
Autres localisations: Voir dans le Sudoc
Edition sous un autre format:• Quantum walks and search algorithms, Renato Portugal, New York, Springer, 2013, 1 vol. (xi-222 p.), Quantum science and technology, 1-461-46335-1
• Quantum Walks and Search Algorithms, Texte imprimé, 9781461463375
• Quantum Walks and Search Algorithms, Texte imprimé, 9781489988027
• Quantum walks and search algorithms, Renato Portugal, New York, Springer, 2013, 1 vol. (xi-222 p.), Quantum science and technology, 1-461-46335-1
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505 1 |a Introduction The Postulates of Quantum Mechanics Introduction to Quantum Walks Grover's Algorithm and its Generalization Quantum Walks on Infinite Graphs Quantum Walks on Finite Graphs Limiting Distribution and Mixing Time Spatial Algorithms Hitting Time Appendix: Linear Algebra for Quantum Computation 
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520 |a 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 operaterAnalytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transformsQuantum walks on generic graphs, describing methods to calculate the limiting distribution and mixing timeSpatial 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 
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