Clustering is a well-established unsupervised machine-learning approach to classify data automatically. In large datasets, the classical version of such algorithms performs well only if significant computing resources are available (e.g., GPU). An alternative approach relies on integrating a quantum processing unit (QPU) to alleviate the computing cost. This is achieved through the QPU’s ability to exploit quantum effects, such as superposition and entanglement, to natively parallelize computation or approximate multidimensional distributions for probabilistic computing (Born rule). In this paper, we propose first a clustering algorithm adapted to a hybrid CPU-QPU architecture while considering the current limitations of noisy intermediate-scale quantum (NISQ) technology. Secondly, we propose a quantum algorithm that exploits the probabilistic nature of quantum physics to make the most of our QPU’s potential. Our approach leverage on ideas from generative machine-learning algorithm and variational quantum algorithms (VQA) to design an hybrid QPU-CPU algorithm based on a mixture of so-called quantum circuits Born machines (QCBM). We hope to achieve accurate data clustering and acceleration on the NISQ architectures scheduled to be available in the next few years. Finally, we analyse our results and summarize the lessons learned from exploiting a CPU-QPU architecture for data clustering.