Pattern Formation in Quantum Hierarchical Cellular Neural Networks
Abstract
We present a new class of quantum neural networks (QNNs) whose states are solutions of -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 -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 -adic Schr\"{o}dinger 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 -adic Schr\"{o}dinger equations.
Cite
@article{arxiv.2603.27063,
title = {Pattern Formation in Quantum Hierarchical Cellular Neural Networks},
author = {W. A. Zúñiga-Galindo and B. A. Zambrano-Luna and Chayapuntika Indoung},
journal= {arXiv preprint arXiv:2603.27063},
year = {2026}
}