Low-Rank Adaptation (LoRA) enables efficient fine-tuning of pre-trained language models via low-rank matrix approximation, which is effective in many scenarios. However, its low-rank representation capacity is constrained in complex tasks or high-rank dependency settings, potentially limiting model adaptability. Addressing the expressive bottleneck of classical low-rank approximation in fine-tuning large language models, this paper proposes a parameter-efficient fine-tuning method based on a Quantum Weighted Tensor Hybrid Network (QWTHN), which leverages Quantum Neural Network (QNN). The study investigates quantum-classical hybrid parameter-efficient fine-tuning in low-rank spaces. QWTHN decomposes pre-trained weights into quantum neural network and tensor network representations, utilizing quantum state superposition and other methods to break through classical rank limitations. Experiments show that the proposed quantum fine-tuning technique for large models approaches or even surpasses the parameter efficiency of LoRA. On the CPsyCounD and R1-Distill-SFT datasets, QWTHN, compared to classical LoRA, reduces training loss by up to 15% while using 76% fewer parameters, and achieves an 8.4% performance improvement on the CPsyCounD test set. This research not only realizes lightweight and efficient adaptation of quantum resources to billion-parameter models but also validates the practical path of quantum hardware driven by large model tasks, laying the first engineering-ready technical foundation for future quantum-enhanced AGI systems.