Title: Non-Standard Geometry for Quantum Simulation

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

Quantum simulation relies heavily on accurate mathematical representations of quantum systems. Traditional geometric approaches often struggle to capture the nuances of complex quantum states and their interactions, limiting the precision and scalability of simulations. This paper proposes a novel approach utilizing non-standard geometry – a mathematical framework that extends the fundamental axioms of Euclidean geometry to describe quantum states and their relationships. We introduce a new set of axioms and operations designed specifically for this purpose, aiming to significantly enhance the capabilities of quantum simulation. The core claim is that this new geometric language will facilitate the creation of more complex and accurate quantum simulations, offering a potential pathway towards advanced quantum algorithms and a deeper understanding of quantum phenomena. This work explores the foundational implications of this approach and outlines a preliminary model for its application within the field of quantum simulation.

DOI: 10.5281/zenodo.22278024

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