I take it you mean Qt, the cross-platform application design API, not Apple's QuickTime video format (which would make little sense)?
Microsoft provides its own proprietary APIs for dealing with Windows and doing the sorts of things that Qt does. Some of it is just in the basic "Windows SDK", and the rest is covered by parts of DirectX.
You're going to have to ask more specific questions if you want better answers. Also, as noted, this should really be in Software.