Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915034835189760 |
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| author | Casagrande, Heitor P. Xing, Bo Munro, William J. Guo, Chu Poletti, Dario |
| author_facet | Casagrande, Heitor P. Xing, Bo Munro, William J. Guo, Chu Poletti, Dario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics Casagrande, Heitor P. Xing, Bo Munro, William J. Guo, Chu Poletti, Dario Statistical Mechanics Machine Learning Quantum Physics 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. |
| title | Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics |
| topic | Statistical Mechanics Machine Learning Quantum Physics |
| url | https://arxiv.org/abs/2404.11768 |