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Network traffic prediction, a critical application of time series analysis, is essential for network management and optimization. Traditional statistical models and machine learning methods have been employed for network traffic prediction, where recent advancements in multi-layer perception mixer architectures, particularly TSMixer, have achieved state-of-the-art performance. However, TSMixer faces challenges with periodic signals and long-term predictions. To address these limitations, we propose a Quantum TSMixer (QTSMixer) model, a hybrid quantum-classical approach that leverages quantum neural networks for enhanced feature extraction related to periodic signals and long-term dependencies. By introducing trainable parameters to control the strength of the quantum components, the hybrid structure of multi-layer perception and quantum neural network is generated. QTSMixer's cross-domain application potential and practical application capability are demonstrated through empirical analysis on real-world datasets, in which QTSMixer outperforms TSMixer by 6.72% in the long-term network traffic prediction dataset. In the future, the development of QTSMixer can be further explored in other fields, such as financial market analysis and weather prediction.