Quantum Walks and Search Algorithms

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 Workshop-School of Quantum Information and Computation (WECIQ 2010), and Chair of the Programme Committee for the Workshop-School of Quantum Information and Computation (WECIQ 2006).

From the reviews: "The reviewed book is a pedagogically oriented survey of the main results regarding quantum walks and quantum search algorithms. ... 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, Vol. 1275, 2014)

• 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.