论文标题
使用（1 + 1）D量子蜂窝自动机探索大规模量子神经网络中的集体效应
Using (1 + 1)D Quantum Cellular Automata for Exploring Collective Effects in Large Scale Quantum Neural Networks
论文作者
论文摘要
量子机学习领域的核心是量子感知和神经网络体系结构的设计。在这方面，一个关键问题是量子影响对此类模型处理信息的方式的影响。在这里，我们通过建立$（1+1）d $量子蜂窝自动机之间的连接来解决这个问题，该自动机通过连续应用局部量子门和经常性的量子神经网络实现了离散的非质量量子多体动力学，该动力学通过互联互体互连相邻的层来处理它，从而通过将其馈送来处理信息。这种关系允许研究量子神经网络中的信息的处理，以相等的细胞自动机动力学的特性来研究。我们通过构建允许引入量子效应的一类量子门（感知）来利用这一点，例如与连贯的汉密尔顿进化相关的量子效应，并与连续时间lindblad动力学建立了严格的链接。我们进一步分析了特定量子细胞自动机的通用特性，并在量子效应变化时确定临界行为的变化，表明它们确实可以影响大规模神经网络中信息处理的基础的集体动力学行为。
Central to the field of quantum machine learning is the design of quantum perceptrons and neural network architectures. A key question in this regard is the impact of quantum effects on the way in which such models process information. Here, we approach this question by establishing a connection between $(1+1)D$ quantum cellular automata, which implement a discrete nonequilibrium quantum many-body dynamics through the successive application of local quantum gates, and recurrent quantum neural networks, which process information by feeding it through perceptrons interconnecting adjacent layers. This relation allows the processing of information in quantum neural networks to be studied in terms of the properties of their equivalent cellular automaton dynamics. We exploit this by constructing a class of quantum gates (perceptrons) that allow for the introduction of quantum effects, such as those associated with a coherent Hamiltonian evolution, and establish a rigorous link to continuous-time Lindblad dynamics. We further analyse the universal properties of a specific quantum cellular automaton, and identify a change of critical behavior when quantum effects are varied, demonstrating that they can indeed affect the collective dynamical behavior underlying the processing of information in large-scale neural networks.
