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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.05461 |
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| _version_ | 1866929681225220096 |
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| author | Wagner, Elisabeth Dell'Anna, Federico Nigmatullin, Ramil Brennen, Gavin K. |
| author_facet | Wagner, Elisabeth Dell'Anna, Federico Nigmatullin, Ramil Brennen, Gavin K. |
| contents | The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the number density and one that performs majority voting. For number preserving DC, two QCAs are introduced that reach the fixed point solution in a time scaling quadratically with the system size. One of the QCAs is based on a known classical probabilistic cellular automaton which has been studied in the context of DC. The second is a new quantum model that is designed to demonstrate additional quantum features and is restricted to only two-body interactions. Both can be generated by continuous-time Lindblad dynamics. A third QCA is a hybrid rule defined by both discrete-time and continuous-time three-body interactions that is shown to solve the majority voting problem within a time that scales linearly with the system size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density Classification with Non-Unitary Quantum Cellular Automata Wagner, Elisabeth Dell'Anna, Federico Nigmatullin, Ramil Brennen, Gavin K. Quantum Physics The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the number density and one that performs majority voting. For number preserving DC, two QCAs are introduced that reach the fixed point solution in a time scaling quadratically with the system size. One of the QCAs is based on a known classical probabilistic cellular automaton which has been studied in the context of DC. The second is a new quantum model that is designed to demonstrate additional quantum features and is restricted to only two-body interactions. Both can be generated by continuous-time Lindblad dynamics. A third QCA is a hybrid rule defined by both discrete-time and continuous-time three-body interactions that is shown to solve the majority voting problem within a time that scales linearly with the system size. |
| title | Density Classification with Non-Unitary Quantum Cellular Automata |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.05461 |