论文标题
粗粒量子细胞自动机
Coarse-grained quantum cellular automata
论文作者
论文摘要
人们可以将某些物理发展视为微观离散模型的新兴结果。受经典的粗粒程序的启发，我们为遵循Goldilocks规则的粗粒色量子蜂窝自动机提供了一个简单的程序。该过程包括（i）时空将量子蜂窝自动机（QCA）分组为$ n $的单元格； （ii）将单元格的状态投射到其边界上，并将它们与精细的动态联系起来； （iii）描述边境国家的整体动态，我们呼吁信号； （iv）为不同尺寸的$ n $构建粗粒动力学。这种简单的玩具模型的副产品是Stokes Law的一般离散类似物。此外，我们证明，在时空限制中，自动机融合到了无狄拉克的汉密尔顿人。我们在这里介绍的QCA可以通过当今的量子平台（例如Rydberg阵列，被困离子和超导QBIT）实现。我们希望我们的研究能够为以有限分辨率的那些系统有更丰富的了解铺平道路。
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular automata that follow Goldilocks rules. The procedure consists in (i) space-time grouping the quantum cellular automaton (QCA) in cells of size $N$; (ii) projecting the states of a cell onto its borders, connecting them with the fine dynamics; (iii) describing the overall dynamics by the border states, that we call signals; and (iv) constructing the coarse-grained dynamics for different sizes $N$ of the cells. A byproduct of this simple toy-model is a general discrete analog of the Stokes law. Moreover we prove that in the spacetime limit, the automaton converges to a Dirac free Hamiltonian. The QCA we introduce here can be implemented by present-day quantum platforms, such as Rydberg arrays, trapped ions, and superconducting qbits. We hope our study can pave the way to a richer understanding of those systems with limited resolution.
