Existing multi-modal sentiment analysis (MSA) methods typically achieve interaction by connecting different layers or designing special structures, but rarely consider the synergistic effects among data. Moreover, most sentiment analysis research tends to focus solely on single sentiment polarity analysis, without considering the intensity and directional attributes of emotions. Addressing these issues, we propose a framework called Hierarchical Graph Contrastive Learning based on Quantum Neural Network (HGCL-QNN) to remedy these shortcomings. Specifically, a graph structure is established within and between modalities. In the quantum fuzzy neural network module, fuzzy quantum encoding is implemented by using complex-valued, then quantum superposition and entanglement are utilized to consider the intensity and directional attributes of emotions while analyzing emotional polarity. In the quantum multi-modal fusion neural network module, methods such as amplitude encoding and quantum entanglement are employed to further integrate information from different modalities, thereby enhancing the model's power to express emotional information. To enhance the model's understanding of fine-grained and global features, and to better align and integrate features from different modalities, hierarchical graph contrastive learning is employed on different levels. The experimental results demonstrate that HGCL-QNN outperforms the existing baseline methods on MOSI and MOSEI datasets, achieving significant efficacy improvements.