Quantum Walks via Quantum Cellular Automata for Simulating Quantum Computation

Abstract

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The quantum walk is a subset of classical random walks. Considerable research has lately been conducted on quantum walks in relation to quantum computing. The walk may be thought of as a type of quantum cellular automata. In a broader sense, there is a one-to-one link between them. Furthermore, we look at another type of quantum cellular automata that may be thought of as a quantum version of stochastic cellular automata. The quantum walk formalism is a widely used and quite practical paradigm for modelling quantum systems such as Dirac equation simulations, discrete dynamics in both the low and high energy regimes, and the development of a multitude of quantum algorithms. The walker in a QW moves in a quantum superposition of pathways, and the ensuing interference serves as the foundation for a broad range of quantum algorithms, including quantum search, graph isomorphism issues, and rating nodes in a network.