This paper investigates the application of quantum machine learning to End-to-End (E2E) communication systems in wireless fading scenarios. We introduce a novel hybrid quantum-classical autoencoder architecture that combines parameterized quantum circuits with classical deep neural networks (DNNs). Specifically, we propose a hybrid quantum-classical autoencoder (QAE) framework to optimize the E2E communication system. Our results demonstrate the feasibility of the proposed hybrid system, and reveal that it is the first work that can achieve comparable block error rate (BLER) performance to classical DNN-based and conventional channel coding schemes, while significantly reducing the number of trainable parameters. Additionally, the proposed QAE exhibits steady and superior BLER convergence over the classical autoencoder baseline.