Quantum Walks, Limits, and Transport Equations

In mathematics, a classical random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. Quantum walks are the quantum equivalent of the classical. Most quantum walk models are defined on graphs, which is a discrete structure, and the time-evolution can be discrete or continuous. The question that arises is how can quantum walks be used to model the usual quantum mechanical equations? This book lithely deals with this problem.

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.