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arXiv · 2012.04237

Quantum-to-classical transition via quantum cellular automata

Pedro C. S. Costa
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Abstract

A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial structure of the QCA is merged into effective ones. Starting with a QCA that simulates the Dirac equation, we apply this coarse-graining map recursively until we get its effective dynamics in the semiclassical limit, which can be described by a classical cellular automaton. We show that the emergent-effective result of the former microscopic discrete model converges to the diffusion equation and to a classical transport equation under a specific initial condition. Therefore, QCA is a good model to validate the quantum-to-classical transition.

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Pedro C. S. Costa. 2021-08-01. Quantum-to-classical transition via quantum cellular automata. https://doi.org/10.1007/s11128-021-03175-0

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