The Emergence of Geometric Topology in Quantum Computation: A Novel Validation Method

Jincheng Zhang

Published Sep 4, 2026• 0 citations

Abstract

This paper explores the intersection of geometric topology and quantum computation, focusing on the dynamic properties of quantum computation intrinsically linked through self-linking geometry. We introduce the concept of "self-linking geometric topology" to frame quantum algorithms as evolving geometric structures, and investigate how this approach validates quantum computations through self-similarity and topological properties. The core mechanism involves utilizing self-linking geometry to characterize the evolution of quantum states and identify critical points within the quantum algorithm. This research offers a novel validation method for quantum algorithms, potentially leading to improved algorithm design and robustness.

DOI: 10.5281/zenodo.22295794

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