Tensor-networks-based learning of probabilistic cellular automata dynamics
Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle issues in the classical domain. This work focuses on matrix product operators, a prominent numerical technique to study many-body quantum systems, especially in one...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2024-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.043202 |
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| _version_ | 1846157054651138048 |
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| author | Heitor P. Casagrande Bo Xing William J. Munro Chu Guo Dario Poletti |
| author_facet | Heitor P. Casagrande Bo Xing William J. Munro Chu Guo Dario Poletti |
| author_sort | Heitor P. Casagrande |
| collection | DOAJ |
| description | Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle issues in the classical domain. This work focuses 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 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 bitwise difference between the rules and whether one is much more likely than the other. |
| format | Article |
| id | doaj-art-d0bfbf44256d45cf9f80778f7d119f3b |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-d0bfbf44256d45cf9f80778f7d119f3b2024-11-25T15:03:23ZengAmerican Physical SocietyPhysical Review Research2643-15642024-11-016404320210.1103/PhysRevResearch.6.043202Tensor-networks-based learning of probabilistic cellular automata dynamicsHeitor P. CasagrandeBo XingWilliam J. MunroChu GuoDario PolettiAlgorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle issues in the classical domain. This work focuses 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 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 bitwise difference between the rules and whether one is much more likely than the other.http://doi.org/10.1103/PhysRevResearch.6.043202 |
| spellingShingle | Heitor P. Casagrande Bo Xing William J. Munro Chu Guo Dario Poletti Tensor-networks-based learning of probabilistic cellular automata dynamics Physical Review Research |
| title | Tensor-networks-based learning of probabilistic cellular automata dynamics |
| title_full | Tensor-networks-based learning of probabilistic cellular automata dynamics |
| title_fullStr | Tensor-networks-based learning of probabilistic cellular automata dynamics |
| title_full_unstemmed | Tensor-networks-based learning of probabilistic cellular automata dynamics |
| title_short | Tensor-networks-based learning of probabilistic cellular automata dynamics |
| title_sort | tensor networks based learning of probabilistic cellular automata dynamics |
| url | http://doi.org/10.1103/PhysRevResearch.6.043202 |
| work_keys_str_mv | AT heitorpcasagrande tensornetworksbasedlearningofprobabilisticcellularautomatadynamics AT boxing tensornetworksbasedlearningofprobabilisticcellularautomatadynamics AT williamjmunro tensornetworksbasedlearningofprobabilisticcellularautomatadynamics AT chuguo tensornetworksbasedlearningofprobabilisticcellularautomatadynamics AT dariopoletti tensornetworksbasedlearningofprobabilisticcellularautomatadynamics |