Workload prediction is critical to ensuring quality of service in distributed edge cloud platforms (ECP). However, this task faces multiple challenges due to the inherent uncertainties within ECP. On the one hand, ECP aggregates heterogeneous infrastructure resources, whose static attributes are difficult to effectively represent and utilize. On the other hand, the dynamic switching of applications deployed on edge servers leads to diverse workload patterns. These uncertainties make server workload prediction in ECP challenging. Inspired by quantum theory in modeling uncertainty, we make an important attempt to design a Quantum-Driven workload Prediction model based on Transformer (QDPformer). Specifically, we introduce fundamental concepts such as quantum states and density matrices to model various uncertain features in ECP. Additionally, we present an improved quantum attention mechanism based on quantum measurement and quantum evolution that enables QDPformer to simulate dynamic changes in servers, significantly enhancing the model’s predictive performance. Experimental results on real ECP datasets show that QDPformer achieves up to a 24.52% reduction in mean squared error (MSE) compared with the baseline models.