论文标题
两个空间维度的量子细胞自动机和量子场理论
Quantum cellular automata and quantum field theory in two spatial dimensions
论文作者
论文摘要
在晶格上的量子行走可以在长波长极限下引起单粒子相对论的波动方程。在进入多个颗粒时，量子细胞自动机（QCA）是量子步行的天然概括。在一个空间维度中，可以将量子行走“促进”到QCA，该QCA在长波长的极限下会导致非互动费米子的狄拉克量子场理论（QFT）。该QCA/QFT对应既具有理论和实际应用，但是在两个或多个空间维度中类似结构存在障碍。在这里，我们表明一种采用限制在完全反对称子空间的可区分颗粒的构造方法在两个空间维度中产生QCA，从而导致2D Dirac QFT。概括为3D会带来一些其他并发症，但没有概念上的障碍。我们研究了这种构建如何逃避“不走”，从而导致早期工作。
Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial dimension, the quantum walk can be "promoted" to a QCA that, in the long-wavelength limit, gives rise to the Dirac quantum field theory (QFT) for noninteracting fermions. This QCA/QFT correspondence has both theoretical and practical applications, but there are obstacles to similar constructions in two or more spatial dimensions. Here we show that a method of construction employing distinguishable particles confined to the completely antisymmetric subspace yields a QCA in two spatial dimensions that gives rise to the 2D Dirac QFT. Generalizing to 3D will entail some additional complications, but no conceptual barriers. We examine how this construction evades the "no go" results in earlier work.
