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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.27063 |
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| _version_ | 1866912986511179776 |
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| author | Zúñiga-Galindo, W. A. Zambrano-Luna, B. A. Indoung, Chayapuntika |
| author_facet | Zúñiga-Galindo, W. A. Zambrano-Luna, B. A. Indoung, Chayapuntika |
| contents | We present a new class of quantum neural networks (QNNs) whose states are solutions of $p$-adic Schrödinger equations with a non-local potential that controls the interaction between the neurons. These equations are obtained as Wick rotations of the state equations of $p$-adic cellular neural networks (CNNs). The CNNs are continuous limits of discrete hierarchical neural networks (NNs). The CNNs are bio-inspired in the Wilson-Cowan model, which describes the macroscopic dynamics of large populations of neurons. We provide a detailed study of the discretization of the new $p$-adic Schrödinger equations, which allows the construction of new QNNs on simple graphs. We also conduct detailed numerical simulations, offering a clear insight into the functioning of the new QNNs. At a mathematical level, we show the existence of local solutions for the new $p$ -adic Schrödinger equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27063 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pattern Formation in Quantum Hierarchical Cellular Neural Networks Zúñiga-Galindo, W. A. Zambrano-Luna, B. A. Indoung, Chayapuntika Quantum Physics We present a new class of quantum neural networks (QNNs) whose states are solutions of $p$-adic Schrödinger equations with a non-local potential that controls the interaction between the neurons. These equations are obtained as Wick rotations of the state equations of $p$-adic cellular neural networks (CNNs). The CNNs are continuous limits of discrete hierarchical neural networks (NNs). The CNNs are bio-inspired in the Wilson-Cowan model, which describes the macroscopic dynamics of large populations of neurons. We provide a detailed study of the discretization of the new $p$-adic Schrödinger equations, which allows the construction of new QNNs on simple graphs. We also conduct detailed numerical simulations, offering a clear insight into the functioning of the new QNNs. At a mathematical level, we show the existence of local solutions for the new $p$ -adic Schrödinger equations. |
| title | Pattern Formation in Quantum Hierarchical Cellular Neural Networks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.27063 |