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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.
Key Features:
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Introduces the subject.
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Presents an overview of quantum walks and plastic quantum walks.
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Demonstrates quantum walk-based simulation schemes.
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Includes the plasticity of a circuit, i.e. the property that allows quantum walks to be convergent in continuous time and continuous or discrete space.
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Discusses limits, analysis, and interpretation of results.
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 (eg. Physical Review Letters, Quantum, Quantum Information Processing, Scientific Reports,...).
Preface
Acknowledgements
Author Biography
1 Introduction
2 Elements of quantum theory
3 Fundamentals of Quantum Walks
4 Continuous limits and plasticity in one dimension
5 Plasticity in 2D, transport equations and beyond
6 Quantum walking over triangles
7 Simulating transport on curved surfaces
8 Conclusion