"Version: 20240901"--Title page verso.

Includes bibliographical references.

1. Introduction -- 2. Elements of quantum theory -- 2.1. Reminders of linear algebra -- 2.2. Postulates of quantum theory

3. Fundamentals of quantum walks -- 3.1. Quantum walks -- 3.2. Higher-dimensional spaces

4. Continuous limits and plasticity in one dimension -- 4.1. Plastic quantum walk -- 4.2. Convergence -- 4.3. Discussion and open problems

5. Plasticity in 2D, transport equations and beyond -- 5.1. Higher spatial dimensions : the plane -- 5.2. Discussion and perspectives

6. Quantum walking over triangles -- 6.1. The model -- 6.2. Discussion and open problems

7. Simulating transport on curved surfaces -- 7.1. Mimicking curved transport on the grid -- 7.2. A quantum walk over a generic two-dimensional spatial triangulation -- 7.3. Discussion and perspectives -- 8. Conclusion.

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This book provides an overview of quantum walks, limits, and transport equations. After an introduction to quantum computing, quantum simulation, and then symmetries, it then narrows down to describe quantum transport and quantum walks. It provides a review of the basics of quantum mechanics and the underlying mathematical framework. The fundamentals of quantum walks are described, followed by an overview of plastic quantum walks including limits, analysis, and interpretation of results.

Researchers, post grad students, academia in studying quantum science.

Also available in print.

Mode of access: World Wide Web.

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Giuseppe Di Molfetta is an assistant professor at Aix-Marseille University, in the Natural Computing group at the Computer Science Lab, LIS. His research focuses on Quantum Walks-based architectures and Quantum Cellular Automata, with a special emphasis on quantum simulation of physical theories, quantum algorithms and discrete geometry. He has national (Marseille, Paris, Grenoble) and international collaborations (Brazil, Japan, Germany, UK), resulting in already 34 publications in high-impact international journals (e.g., Physical Review Letters, Quantum, Quantum Information Processing, Scientific Reports, etc.).

Title from PDF title page (viewed on October 3, 2024).