Quantum Systems and Computing | Non-Archimedean Analysis and Applications

Abstract:
The mini symposium aims at bringing together researchers in non-archimedean analysis and applications, in order to present the state of the art of new developments in non-archimedean analysis and applications in the Sciences, Engineering and Economics. Having initially diffusion processes over the p-adic number field, now non-linear dynamics (e.g. an analogue of Navier-Stokes or the porous medium equation), as well as other p-adic domains like p-adic analytic manifolds are now included. First applied and further developped in mathematical physics, the methods are now part of computer science, biology, earth sciences and other domains. Bringing together researchers in quantum systems and computing aims at fostering new insights and ideas towards a deeper understanding of general hierarchical structures in this domain overlapping with mathematics. 

Confirmed Speakers:
Brian Zambrano-Luna: U Alberta
David Weisbart: UCR
Ilaria Svampa: U Köln
Vincenzo Parisi: IIT Genoa
Speaker: Wilson Zuniga-Galindo: University of Texas Rio Grande Valley
Title: p-Adic Quantum Cellular Neural Networks
Abstract: We present a new class of quantum neural networks (QNNs) whose states are solutions to p-adic Schrödinger equations with a non-local potential that governs the interaction between 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, hierarchical discrete 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 to the new p-adic Schrödinger equations. The talk is based on the preprint:
W. A. Zúñiga-Galindo, B. A. Zambrano-Luna, Chayapuntika Indoung. Pattern Formation in Quantum Hierarchical Cellular Neural Networks. https://doi.org/10.48550/arXiv.2603.27063