复杂元胞自动机的量子启发识别
Quantum-inspired identification of complex cellular automata
AI总结：
本研究利用量子统计记忆度量，通过分析基本元胞自动机生成结构的速率，提出一种定量区分简单与复杂ECA的新方法，并建立复杂性排序谱系。
摘要：
基本元胞自动机（ECA）是复杂系统的标志性例子。尽管它们仅由一维二进制单元串根据最近邻更新规则描述，某些ECA规则却展现出能够进行通用计算的复杂动力学。然而，精确分类哪些规则表现出复杂行为仍然是一个重大挑战。在这里，我们使用量子随机建模的工具来处理这个问题，其中量子统计记忆——使用一类量子机器对随机过程进行建模所需的记忆——可用于量化随机过程的结构。通过将ECA规则视为随机模式的变换，我们提出疑问：ECA是否生成由量子统计记忆量化的结构，如果是，生成的速度有多快？我们展示了该度量随时间增长如何正确区分简单ECA与复杂对应物。此外，它提供了一种更精细的定量识别复杂ECA的方法——提供了一个谱系，我们可以根据ECA生成结构的速率对其复杂性进行排序。
英文摘要：
Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex dynamics capable of universal computation. Yet, the classification of precisely which rules exhibit complex behaviour remains a significant challenge. Here we approach this question using tools from quantum stochastic modelling, where quantum statistical memory -- the memory required to model a stochastic process using a class of quantum machines -- can be used to quantify the structure of a stochastic process. By viewing ECA rules as transformations of stochastic patterns, we ask: Does an ECA generate structure as quantified by the quantum statistical memory, and if so, how quickly? We illustrate how the growth of this measure over time correctly distinguishes simple ECA from complex counterparts. Moreover, it provides a more refined means for quantitatively identifying complex ECAs -- providing a spectrum on which we can rank the complexity of ECA by the rate in which they generate structure.
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