"Discrete quantum walks are quantum analogues of classical random walks. They are an important tool in quantum computing and a number of algorithms can be viewed as discrete quantum walks, in particular Grover's search algorithm. These walks are constructed on an underlying graph, and so there is a relation between properties of walks and properties of the graph. This book studies the mathematical problems that arise from this connection, and the different classes of walks that arise. Written at a level suitable for graduate students in mathematics, the only prerequisites are linear algebra and basic graph theory; no prior knowledge of physics is required. The text serves as an introduction to this important and rapidly developing area for mathematiciansand as a detailed reference for computer scientists and physicists working on quantum information theory"--
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Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.
Preface;
1. Grover search;
2. Two reflections;
3. Applications;
4. Averaging:
5. Covers and embeddings;
6. Vertex-face walks;
7. Shunts;
8. 1-Dimensional walks; References; Glossary; Index.
Chris Godsil is Distinguished Professor Emeritus at the University of Waterloo. He has written three books: Algebraic Combinatorics (1993), Algebraic Graph Theory (2004, co-authored with Gordon Royle) and The Erdos-Ko-Rado Theorem: Algebraic Approaches (2015, co-authored with Karen Meagher). Hanmeng Zhan is Postdoc Fellow at Simon Fraser University. For her thesis on discrete quantum walks via algebraic graph theory, she received two awards from University of Waterloo: the University Finalist for the Governor General's Gold Medal and the Inaugural Mathematics Doctoral Prize.
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