Pattern Formation in Quantum Hierarchical Cellular Neural Networks
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Quantum Physics arXiv:2603.27063 (quant-ph) [Submitted on 28 Mar 2026] Title:Pattern Formation in Quantum Hierarchical Cellular Neural Networks Authors:W. A. Zúñiga-Galindo, B. A. Zambrano-Luna, Chayapuntika Indoung View a PDF of the paper titled Pattern Formation in Quantum Hierarchical Cellular Neural Networks, by W. A. Z\'u\~niga-Galindo and 2 other authors View PDF HTML (experimental) Abstract: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 arXiv-issued DOI via DataCite (pending registration) Submission history From: W. A. Zuniga-Galindo [view email] [v1] Sat, 28 Mar 2026 00:39:53 UTC (566 KB) Full-text links: Access Paper: View a PDF of the paper titled Pattern Formation in Quantum Hierarchical Cellular Neural Networks, by W. A. Z\'u\~niga-Galindo and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)