论文标题
$（1+1）$ d量子蜂窝自动机的异步和非平衡期过渡
Asynchronism and nonequilibrium phase transitions in $(1+1)$D quantum cellular automata
论文作者
论文摘要
概率的细胞自动机为探索经典非平衡过程提供了一个简单的框架。最近，已经提出了量子细胞自动机，它依赖于通过量子门的顺序应用沿虚拟离散的时间维度沿虚拟离散的时间维度传播。由此产生的$（1+1）$ - 尺寸时空结构使这些自动机特殊情况的馈送量子神经网络。在这里，我们展示了异步如何通过非交通门引入 - 对量子细胞自动机的集体非平衡行为产生影响。我们通过一个简单的模型来说明这一点，该模型的同步版本实现了接触过程，并在定向的渗透普遍性类别中具有非平衡相变。非交换量子门会导致“异步转变”，即一旦超过一定程度的异步性，相变行为的突然质量变化。我们的结果表明，量子效应如何导致非平衡动力学的突然变化，这可能与理解量子相关性在神经网络中的作用有关。
Probabilistic cellular automata provide a simple framework for the exploration of classical nonequilibrium processes. Recently, quantum cellular automata have been proposed that rely on the propagation of a one-dimensional quantum state along a fictitious discrete time dimension via the sequential application of quantum gates. The resulting $(1+1)$-dimensional space-time structure makes these automata special cases of feed-forward quantum neural networks. Here we show how asynchronism -- introduced via non-commuting gates -- impacts on the collective nonequilibrium behavior of quantum cellular automata. We illustrate this through a simple model, whose synchronous version implements a contact process and features a nonequilibrium phase transition in the directed percolation universality class. Non-commuting quantum gates lead to an "asynchronism transition", i.e. a sudden qualitative change in the phase transition behavior once a certain degree of asynchronicity is surpassed. Our results show how quantum effects may lead to abrupt changes of non-equilibrium dynamics, which may be relevant for understanding the role of quantum correlations in neural networks.
