This paper investigates the stability of chaotic systems using a novel quantum algorithm designed to enhance analysis and potentially unlock new insights into their behavior. We explore the application of quantum mechanics to address challenges inherent in traditional methods, focusing on the potential for faster convergence and more precise identification of critical points. The core mechanism centers around quantum entanglement and superposition, utilized to model and analyze the system's dynamics with unprecedented fidelity. The analysis aims to provide a fundamentally new approach to understanding and predicting the stability of chaotic systems, potentially leading to breakthroughs in fields like fluid dynamics, climate modeling, and complex systems analysis. This study presents a preliminary framework demonstrating the potential for quantum-enhanced stability analysis, with a focus on identifying and quantifying key parameters that govern chaotic behavior.
Considering different quantum bit having different effective intensity in chromosome evolution, a novel quantum genetic algorithm based on potential is proposed. It makes the magnitude of rotation angle depending on the potential of a quantum bit. It generates the orientation of rotation angle according to the total potential of quantum bit in the chromosome. The character of quantum entangled interference based on potential is introduced. And convergence analysis and rationality analysis are implemented. Experimental test shows that, it can obtain better convergence rate and have less runtime on smaller population size and shorter chromosome length.