论文标题
通过量子蜂窝自动机通过量子到古典的过渡
Quantum-to-classical transition via quantum cellular automata
论文作者
论文摘要
量子细胞自动机（QCA）是一个抽象模型，该模型由一系列有限维量子系统组成，这些系统通过局部统一操作在离散时间演变。在这里，我们提出了一个简单的粗粒图，其中将QCA的空间结构合并为有效的图。从模拟Dirac方程的QCA开始，我们递归应用此粗粒图，直到我们在半经典极限中获得其有效动力学，可以通过经典的细胞自动机描述。我们表明，在特定初始条件下，以前的微观离散模型的新兴结果会收敛到扩散方程和经典传输方程。因此，QCA是验证量子到古典过渡的好模型。
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.
