QMC has no API as the QMC is simply a web page served from the web server inside the QMS.
The QMS service has an API, but I don't think it offers a Rest interface nor a JSON interface. It's just a web service with its own set of commands and replies.
For more details on how to interface to this particular service, see. QlikView Management API - Getting Started and Examples or QlikView Version 11 SDK