The drug design process currently requires considerable time and resources to develop each new compound that enters the market. This work develops an application of hybrid quantum generative models based on the integration of parameterized quantum circuits into known molecular generative adversarial networks and proposes quantum cycle architectures that improve model performance and stability during training. Through extensive experimentation on benchmark drug design datasets, quantum machine 9 (QM9) and PubChemQC 9 (PC9), the introduced models are shown to outperform the previously achieved scores. Most prominently, the new scores indicate an increase of up to 30% in the quantitative estimation of druglikeness. The new hybrid quantum machine learning algorithms, as well as the achieved scores of pharmacokinetic properties, contribute to the development of fast and accurate drug discovery processes.