Geometric Topology-Driven Quantum Algorithm Design (GTQAD)

Jincheng Zhang

Published Aug 29, 2026• 0 citations

Abstract

Quantum computation, while promising, faces significant challenges in terms of scalability and resource requirements. Traditional algorithm design methods often struggle to efficiently explore complex quantum systems, limiting the potential for practical quantum advantage. Geometric Topology, specifically topological quantum field theory (TQFT), presents a compelling alternative, offering a framework for designing quantum algorithms with inherent efficiency improvements. This paper introduces Geometric Topology-Driven Quantum Algorithm Design (GTQAD), a novel methodology leveraging geometric topology to optimize quantum circuit design, aiming to address the limitations of current approaches and unlock further progress in quantum computation. We present a core mechanism for leveraging TQFT to create more efficient quantum circuits, demonstrating its potential to reduce computational complexity and improve overall performance. The proposed approach focuses on constructing circuits that exhibit topological properties, leading to increased robustness and reduced overhead.

DOI: 10.5281/zenodo.22158622

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