Title: Topology-Enhanced Quantum Algorithm Verification

Jincheng Zhang

Published Sep 2, 2026• 0 citations

Abstract

Quantum algorithms promise revolutionary advancements across diverse fields, yet their verification remains a significant challenge. Traditional verification methods often rely on exhaustive testing, which is computationally expensive and impractical for complex algorithms. This research proposes a novel approach leveraging topological concepts to proactively identify potential errors and vulnerabilities within quantum algorithms, significantly improving the accuracy and efficiency of the verification process. This work details the development of a method for analyzing the topological structure of quantum circuits, identifying anomalous regions indicative of errors, and ultimately providing a more robust verification framework. We introduce a novel topological analysis technique that incorporates the principles of graph theory and measure theory to effectively assess algorithm integrity. The core claim is that this method enhances the accuracy of quantum algorithm verification by detecting subtle errors that traditional approaches miss. This paper presents a comprehensive overview of the proposed method, including detailed mathematical formulations, illustrative examples, and a discussion of its potential impact on the future of quantum algorithm verification. The focus is on providing a practical, mathematically grounded solution to a critical problem within the quantum realm.

DOI: 10.5281/zenodo.22253870

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