Title: Topological Quantum Entanglement for Computational Complexity Theory

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Abstract: This paper explores the application of Topological Data Analysis (TDA) to characterize and quantify entanglement-based computational complexity. Traditional complexity theory often focuses on the resources required for computation, while this approach seeks to leverage the unique properties of entanglement – particularly its topological nature – to uncover potential computational barriers. We propose a novel method for representing entanglement as a graph and then utilizing TDA to identify patterns and bounds within this graph. The core claim is that this method offers a fundamentally different perspective on complexity, potentially revealing new computational complexities that are inaccessible through conventional approaches. The paper details the development of a new entanglement graph representation, the introduction of topological properties as a key identifier, and the application of TDA to derive computational complexity bounds. We demonstrate the effectiveness of this approach through theoretical analysis and preliminary numerical experiments, suggesting a significant advance in understanding and potentially manipulating the landscape of computational complexity.

DOI: 10.5281/zenodo.22192739

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