Non-Linear Quantum States: A Geometric Modeling Approach

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper explores a novel geometric modeling framework for describing non-linear quantum states. Traditional quantum mechanics often struggles to capture the complexity arising from interactions between quantum systems, particularly when these interactions exhibit non-linearity. We propose a system-theoretic approach, utilizing geometric properties of quantum states to simplify the representation of these systems. This model aims to predict system behavior by leveraging the inherent geometric structure of quantum possibilities. The core claim is that this framework provides a more intuitive and powerful way to understand and predict quantum phenomena, offering a departure from traditional quantum mechanics. This work introduces a novel method for representing and analyzing non-linear quantum states through the lens of geometric structures. The paper details the theoretical foundation, mathematical framework, and initial experimental investigations supporting this approach. We demonstrate the efficacy of this model in predicting specific quantum behaviors, highlighting its potential for advancing our understanding of complex quantum systems.

DOI: 10.5281/zenodo.22185533

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