Define "connect MQ to the cloud". In MQ the only thing an MQ client or QMgr connects to to exchange MQ messages is a QMgr. So one can connect from a cloud-hosted app to a QMgr. Or one can virtualize a QMgr and host it in the cloud through Docker, Workload Deployer, Pure, VMWare, etc. It isn't clear from the question if one of these is what is required or something else altogether.