Unitary Quantum Cellular Automata for Density Classification
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911198354604032 |
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| author | Costa, Pedro C. S. Sanders, Yuval R. Balbi, Pedro Paulo Brennen, Gavin K. |
| author_facet | Costa, Pedro C. S. Sanders, Yuval R. Balbi, Pedro Paulo Brennen, Gavin K. |
| contents | We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. While there is no one-dimensional two-state, radius $r \geq 1$, deterministic CA with periodic boundary conditions that solves the DCT perfectly, we explore whether a unitary quantum model can succeed. We employ the Partitioned Unitary Quantum Cellular Automaton (PUQCA), a number-conserving model, and, via evolutionary search, find solutions to the DCT where the success condition is stipulated in terms of measurement probabilities rather than convergence to fixed-point configurations. Finally, we identify a classically simulable regime of the PUQCA in which we find rules that solve the DCT at fixed system sizes and analyze their performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitary Quantum Cellular Automata for Density Classification Costa, Pedro C. S. Sanders, Yuval R. Balbi, Pedro Paulo Brennen, Gavin K. Quantum Physics We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. While there is no one-dimensional two-state, radius $r \geq 1$, deterministic CA with periodic boundary conditions that solves the DCT perfectly, we explore whether a unitary quantum model can succeed. We employ the Partitioned Unitary Quantum Cellular Automaton (PUQCA), a number-conserving model, and, via evolutionary search, find solutions to the DCT where the success condition is stipulated in terms of measurement probabilities rather than convergence to fixed-point configurations. Finally, we identify a classically simulable regime of the PUQCA in which we find rules that solve the DCT at fixed system sizes and analyze their performance. |
| title | Unitary Quantum Cellular Automata for Density Classification |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.06947 |