Pattern formation in quantum hierarchical cellular neural networks

Authors

• Wilson A. Zuniga-Galindo, The University of Texas Rio Grande ValleyFollow
• B. A. Zambrano-Luna, Universidad Sergio Arboleda
• Chayapuntika Indoung, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

11-1-2026

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 p -adic CNNs arise as continuous limits of large discrete hierarchical neural networks (NNs). The CNNs are bio-inspired by 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 global solutions for the new p -adic Schrödinger equations.

Comments

Copyright

Recommended Citation

Zúñiga-Galindo, W. A., B. A. Zambrano-Luna, and Chayapuntika Indoung. “Pattern Formation in Quantum Hierarchical Cellular Neural Networks.” Communications in Nonlinear Science and Numerical Simulation 163 (November 2026): 110715. https://doi.org/10.1016/j.cnsns.2026.110715.

Publication Title

Communications in Nonlinear Science and Numerical Simulation

DOI

10.1016/j.cnsns.2026.110715