This study prospectively explores the application of Transformer neural network models to predict the entangled two-component quantum states, aiming to contribute to the sustainable development of the field of quantum computing. Quantum entanglement is a fundamental and critical phenomenon in quantum mechanics, and its unique properties grant quantum computers exceptional computational efficiency for specific problems. However, traditional quantum computing methods often face challenges of excessive consumption of computational resources when dealing with complex quantum systems, which contradicts the goals of pursuing efficiency and reducing resource consumption in sustainable development. To address this challenge, this study aims to shorten computation time and improve the energy efficiency of quantum computing by training deep learning models to decompose quantum density matrices. The results of the study indicate that the Transformer model performs satisfactorily on the training set, but there is still room for improvement on the test set. Nonetheless, the preliminary outcomes of this research provide a new direction for the sustainable development of quantum computing, with future expectations for enhancing its ability to solve practical problems while reducing resource consumption through model optimization and algorithm improvements. The results of this study not only hold academic value for the field of quantum computing but also serve as a reference for the future development of green computing and sustainable technology. By improving computational efficiency and reducing energy consumption, we hope that this research can facilitate the development of environmentally friendly and efficient computing technologies, promoting the application of quantum computing in sustainable development and leading to more environmentally friendly solutions for future technological innovations.