GUI library for HMI Cortex M
Using Qt in a microcontroller project is infeasible. It requires megabytes of RAM and ROM and a full-fledged OS. There is support for embedded systems but it is limited to Nokia phone OSes, embedded Linux and Windows CE. See storage requirements for embedded Linux for example (note that these aren't RAM requirements). Qt has been used successfully on ARM9, ARM11 and Cortex-A systems such as FriendlyARM boards, BeagleBoard etc. (note that many of these have OpenGL ES hardware acceleration, too). Extra convenient support for Raspberry Pi is upcoming. If you actually need Qt, consider an ARM CPU-based (as opposed to a MCU-based) system running Linux.

If you do need to run a GUI on a microcontroller, see the answer linked to by embedded.kyle for realistic alternatives.