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Pattern Formation in Quantum Hierarchical Cellular Neural Networks

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arXiv:2603.27063v1 Announce Type: new Abstract: We present a new class of quantum neural networks (QNNs) whose states are solutions of $p$-adic Schr\"{o}dinger 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

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Quantum Physics [Submitted on 28 Mar 2026] Pattern Formation in Quantum Hierarchical Cellular Neural Networks W. A. Zúñiga-Galindo, B. A. Zambrano-Luna, Chayapuntika Indoung 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. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.27063 [quant-ph] (or arXiv:2603.27063v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.27063 Focus to learn more Submission history From: W. A. Zuniga-Galindo [view email] [v1] Sat, 28 Mar 2026 00:39:53 UTC (566 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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