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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.27063 |
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Table of Contents:
- 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.