Core Claim: This research proposes a novel quantum-adaptive topology deformation algorithm designed to efficiently handle complex geometric structures and improve computational efficiency.

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

The study of topology and its applications is a cornerstone of modern mathematics and science. Traditional methods often struggle with the inherent complexity of geometric structures, limiting the scalability of existing techniques. This paper introduces a new approach leveraging quantum self-adaptation to address these challenges. We present a quantum-based algorithm for topology deformation, demonstrating its potential to significantly enhance computational efficiency, particularly in scenarios involving intricate geometric configurations. The core of our innovation lies in the utilization of quantum self-adaptation, which allows the algorithm to dynamically adjust the topology of a geometric structure during the deformation process. This dynamic adjustment is achieved through a carefully designed quantum state evolution, resulting in a substantially faster and more robust computation compared to classical methods. The presented algorithm exhibits promising results across a range of geometric examples, offering a fundamentally different pathway toward improved topology analysis. The study also explores the underlying principles and potential challenges associated with implementing this quantum-adaptive topology deformation algorithm, providing insights into its future development and application prospects.

DOI: 10.5281/zenodo.22203082

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