Geometric Topology for Quantum State Simulation: Mapping Quantum States to Fractal Landscapes

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

Quantum state simulation presents a significant challenge in quantum computing and quantum information science. Traditional methods often struggle to capture the intricate entanglement patterns inherent in quantum systems. This paper introduces a novel geometric topology approach – mapping quantum states to fractal landscapes – as a potential solution. We propose a method for representing quantum states as a continuous space of fractal shapes, allowing for the visualization and analysis of entanglement. This framework offers a fundamentally new perspective on simulating quantum phenomena, potentially leading to enhanced visualization and understanding of quantum entanglement. The core mechanism relies on the inherent properties of fractals to represent and analyze quantum states, offering a potential pathway to more accurate and insightful simulations.

DOI: 10.5281/zenodo.22593970

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