Quantum Control Theory Through the Lens of Non-Linear Topological Groups

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper introduces a novel approach to quantum control theory by leveraging the principles of non-linear topological groups. Traditional quantum control methods often struggle to accurately model and control systems exhibiting significant non-linearities. This research proposes a framework for mapping quantum control systems onto non-linear topological groups, capitalizing on the inherent stability and symmetry properties of these groups to achieve enhanced control precision and robustness. We demonstrate how topological invariants can be utilized to characterize the system's dynamics and derive optimal control strategies. The core of this approach lies in the ability to represent complex quantum systems within a simplified topological space, enabling efficient analysis and design of control protocols. This work provides a theoretical foundation for a new generation of quantum control techniques, particularly relevant for systems with intricate non-linear interactions.

DOI: 10.5281/zenodo.22268638

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