Algorithms developed to solve many-body quantum problems, like tensor
networks, can turn into powerful quantum-inspired tools to tackle problems in
the classical domain. In this work, we focus on matrix product operators, a
prominent numerical technique to study many-body quantum systems, especially in
one dimension. It has been previously shown that such a tool can be used for
classification, learning of deterministic sequence-to-sequence processes and of
generic quantum processes. We further develop a matrix product operator
algorithm to learn probabilistic sequence-to-sequence processes and apply this
algorithm to probabilistic cellular automata. This new approach can accurately
learn probabilistic cellular automata processes in different conditions, even
when the process is a probabilistic mixture of different chaotic rules. In
addition, we find that the ability to learn these dynamics is a function of the
bit-wise difference between the rules and whether one is much more likely than
the other.

利用矩阵乘积算子算法学习概率序列 - 序列过程，并将该算法应用于概率元胞自动机，可以准确学习不同条件下的概率元胞自动机过程，即使该过程是不同混沌规则的概率混合。

基于张量网络的概率元胞自动机动力学学习

Tensor-Networks-based Learning of Probabilistic Cellular Automata  Dynamics

This paper presents a probabilistic extension of the well-known cellular
automaton, Game of Life. In Game of Life, cells are placed in a grid and then
watched as they evolve throughout subsequent generations, as dictated by the
rules of the game. In our extension, called ProbLife, these rules now have
probabilities associated with them. Instead of cells being either dead or
alive, they are denoted by their chance to live. After presenting the rules of
ProbLife and its underlying characteristics, we show a concrete implementation
in ProbLog, a probabilistic logic programming system. We use this to generate
different images, as a form of rule-based generative art.

本文展示了 Game of Life 的概率扩展 ProbLife，使用与其关联的 ProbLog 构建了基于规则的生成艺术，探讨了概率元胞自动机的特征和规则。