Quantum-Enhanced Gradient Descent for Differential Geometry

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

Quantum-Enhanced Gradient Descent for Differential Geometry (QGDE) explores the potential of leveraging quantum tunneling principles to accelerate gradient descent within the context of differential geometry. Current gradient descent algorithms, while widely used, can be computationally intensive, particularly when dealing with complex geometries and high-dimensional spaces. This research proposes a novel approach that introduces a 'quantum tunneling adjustment' step within the gradient descent algorithm, aiming to effectively overcome these computational bottlenecks and enhance the speed and accuracy of finding solutions. Quantum tunneling, a phenomenon where particles pass through barriers that they classically shouldn't be able to overcome, offers a potential pathway to significantly accelerate the optimization process. This paper provides a detailed investigation of this concept, outlining the theoretical underpinnings, proposed implementation, and preliminary results demonstrating a demonstrable improvement in convergence speed compared to traditional gradient descent.

DOI: 10.5281/zenodo.22507436

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