Quantum State Geometry Optimization via Non-Linear Topological Algorithms

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Quantum state geometry optimization is a rapidly growing field with significant potential for advancing quantum computing and quantum information processing. This paper explores the application of non-linear topological algorithms to optimize quantum state representations and algorithms. We propose a novel framework where the quantum state itself is treated as a topological space, allowing for the manipulation of its geometry through topological transformations. This framework will enhance algorithmic efficiency and generalization capabilities compared to traditional optimization techniques. The core mechanism involves designing and implementing specific topological transformations that directly influence the quantum state's properties, leading to improved performance. We present a preliminary design of an algorithm leveraging this approach, demonstrating its potential for enhancing quantum circuit design and optimization.

DOI: 10.5281/zenodo.22314263

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