Currently, the on-premises Quick Fields desktop application is able to connect to Cloud repositories - both for capturing documents to reprocess and for storing processed documents. Please contact your Regional Manager for more information about available options. 

If you're looking for a more 'truly cloud' option that runs the processing on Cloud, currently this is on our roadmap, but we still have a lot of work to do to make it happen, so we don't have a specific estimate yet. Like with Workflow, it will likely have a limited feature set for the initial Cloud release. If there are certain existing Quick Fields features/processes you'd especially like to see prioritized for the initial Cloud release, feel free to let us know.