Quantum-Inspired Geometry for Computational Complexity

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum-inspired geometry proposes a novel framework for quantifying computational complexity by leveraging the properties of quantum phenomena. This paper explores the concept of a "Quantum Complexity Metric" – a quantifiable measure derived from the inherent characteristics of quantum states and entanglement – to provide an alternative to traditional complexity measures. We delve into the potential benefits of this approach, emphasizing its ability to identify patterns and bottlenecks in algorithm performance. The research focuses on establishing a rigorous mathematical foundation for this metric, outlining its operational principles and demonstrating its potential to enhance our understanding of computational limitations. Specifically, we will address the challenges of quantifying entanglement and its connection to computational cost, and we will present preliminary results utilizing a simplified, yet illustrative, model. Ultimately, this work aims to advance the field by suggesting a fundamentally new approach to analyzing complexity, potentially leading to more efficient algorithms and deeper insights into the boundaries of computation.

DOI: 10.5281/zenodo.22198868

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