Quantum Walks and Search Algorithms

This book explores quantum walks, which are important in building quantum algorithms. Coverage includes Grover's algorithm; Analytical solutions of quantum walks using Fourier transforms; Quantum walks on generic graphs; Spatial search algorithms and more.

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.

Offers an expanded introduction to the field of quantum walks Covers key topics in quantum computation including Grover's algorithm Includes a new chapter on the Element Distinctness Algorithm

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).

Résumé

"The text is easy to read and very instructive, this book can be best recommended." (K.-E. Hellwig, zbMATH 1457.81004, 2021)

Contenu

1 Introduction.- 2 The Postulates of Quantum Mechanics.- 3 Introduction to Quantum Walks.- 4 Grover's Algorithm and Its Generalization.- 5 Coined Walks on Infinite Lattices.- 6 Coined Walks with Cyclic Boundary Conditions.- 7 Coined Quantum Walks on Graphs.- 8 Staggered Model.- 9 Spatial Search Algorithms.- 10 Element Distinctness.- 11 Szegedy's Quantum Walk.- A Linear Algebra for Quantum Computation.- B Graph Theory for Quantum Walk.- C Classical Hitting Time.