Discrete Quantum Walks on Graphs and Digraphs

Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.

Chris Godsil (Author), Hanmeng Zhan (Author)

9781009261685, Cambridge University Press

Paperback / softback, published 12 January 2023

300 pages
23 x 15.2 x 0.9 cm, 0.23 kg

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 mathematicians and as a detailed reference for computer scientists and physicists working on quantum information theory.

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.

Subject Areas: Algorithms & data structures [UMB], Combinatorics & graph theory [PBV], Algebra [PBF], Set theory [PBCH]