Quantum State Transformation via Non-Linear Geometry

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

Quantum state transformation represents a fundamental challenge in quantum information theory, demanding precise manipulation of quantum states. Traditional approaches often rely on deterministic transformations, limiting their applicability. This paper explores the potential of utilizing non-linear geometry to fundamentally alter quantum state transformations, introducing a novel algorithm capable of precise control and the discovery of hidden advantages within these transformations. We propose a framework based on quantum geometry, specifically leveraging the concept of non-linear transformations to achieve a shift in the state space. The core mechanism involves designing a specialized algorithm that iteratively modifies the quantum state through geometric processes, enabling a degree of flexibility not achievable with conventional methods. This research investigates the theoretical and practical implications of this approach, aiming to push the boundaries of quantum state manipulation and uncover novel computational pathways. We demonstrate the feasibility of this design through a simplified, yet illustrative, example, highlighting the potential for significant advancements in quantum information processing.

DOI: 10.5281/zenodo.22268867

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