Quantum Walks and Search Algorithms

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

Auteur
Dr. Renato Portugal is a full researcher at the National Laboratory of Scientific Computing (LNCC). He received the Howard E. Brandt paper award in 2017. He is member of the editorial board of the journal Natural Computing. 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, Brazil. He received his doctoral degree at the Brazilian Center for Research in Physics. He has published over 150 articles in Scientific Journals and refereed proceedings, with an h-index of 19, and three books. 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).

Contenu
1 Introduction2 The Postulates of Quantum Mechanics3 Introduction to Quantum Walks4 Grover's Algorithm and Its Generalization5 Coined Walks on Infinite Lattices6 Coined Walks with Cyclic Boundary Conditions7 Coined Quantum Walks on Graphs8 Staggered Model9 Spatial Search Algorithms10 Element Distinctness
11 Szegedy's Quantum WalkA Linear Algebra for Quantum ComputationB Graph Theory for Quantum WalkC Classical Hitting Time