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 selfcontained 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, twodimensional 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 twodimensional lattice is used as an example)* Szedgedy's quantumwalk 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.
About Renato Portugal
Dr. Renato Portugal is Researcher in the Department of Computer Science at the National Laboratory for Scientific Computing (LNCC). His past positions include Visiting Professor in the Department of Applied Mathematics and the Symbolic Computation Group at the University of Waterloo, Visiting Professor in the Department of Physics at Queen's University of Kingston, and Researcher at the Brazilian Center for Research in Physics. He received his D.Sc. at the Centro Brasileiro de Pesquisas Fisicas, CBPF, Brazil. He has published 40 articles in Scientific Journals, 3 books, and over 30 papers in refereed proceedings. He has developed 7 software packages, including his latest: The Invar Package in 2007. He was General Chair of the WorkshopSchool of Quantum Information and Computation (WECIQ 2010), and Chair of the Programme Committee for the WorkshopSchool of Quantum Information and Computation (WECIQ 2006).Details Book
Author  :  Renato Portugal 
Publisher  :  SpringerVerlag New York Inc. 
Data Published  :  17 January 2013 
ISBN  :  1489988025 
EAN  :  9781489988027 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  222 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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