Asynchronism and nonequilibrium phase transitions in(1+1)-dimensional quantum cellular automata,Physical Review E

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Asynchronism and nonequilibrium phase transitions in(1+1)-dimensional quantum cellular automata
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-13 , DOI: 10.1103/physreve.106.l032103
Edward Gillman _{1,

2} , Federico Carollo ₃ , Igor Lesanovsky _{1,

2,

3}

Affiliation

Probabilistic cellular automata provide a simple framework for exploring 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 recurrent quantum neural networks which can implement broad classes of classical nonequilibrium processes. Here, we present a general prescription by which these models can be extended into genuinely quantum nonequilibrium models via the systematic inclusion of asynchronism. This is illustrated for the classical contact process, where the resulting model is closely linked to the quantum contact process (QCP), developed in the framework of open quantum systems. Studying the mean-field behavior of the model, we find evidence of an “asynchronism transition,” i.e., a sudden qualitative change in the phase transition behavior once a certain degree of asynchronicity is surpassed, a phenomenon we link to observations in the QCP.

中文翻译：

(1+1)维量子元胞自动机中的异步和非平衡相变

概率元胞自动机为探索经典的非平衡过程提供了一个简单的框架。最近，已经提出了量子元胞自动机，它依赖于通过量子门的顺序应用沿虚构的离散时间维度传播一维量子态。所结果的

(1 + 1)

维时空结构使这些自动机成为递归量子神经网络的特例，可以实现广泛的经典非平衡过程。在这里，我们提出了一个通用处方，通过系统地包含异步性，这些模型可以扩展到真正的量子非平衡模型。这在经典接触过程中得到了说明，其中产生的模型与在开放量子系统框架中开发的量子接触过程 (QCP) 密切相关。研究模型的平均场行为，我们发现了“异步转变”的证据，即一旦超过一定程度的异步性，相转变行为的突然质变，我们将这种现象与 QCP 中的观察联系起来。

更新日期：2022-09-13

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