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arXiv · 2404.11768

Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics

Heitor P. Casagrande·Bo Xing·William J. Munro·Chu Guo·Dario Poletti
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Abstract

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.

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Heitor P. Casagrande, Bo Xing, William J. Munro, Chu Guo, Dario Poletti. 2024-04-17. Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics. https://doi.org/10.1103/physrevresearch.6.043202

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