Your question is so broad that it is impossible to give any kind of answer.

Qt uses an event-driven architecture to respond to hardware and GUI inputs. If you write an application in such a way that Qt can never service its event loop (for example, a compute-intensive application that never gives execution control back to Qt), then the GUI will be frozen and the event loop cannot respond to inputs that generate events (like input ready to read on a serial port or mouse clicks).

There are no particular problems using a GPU in a Qt application as long as you return control from the GPU side frequently enough to keep the GUI "alive". Alternatively, you could run the GPU code from a non-GUI thread and use inter-thread signals and slots to feed data back to the GUI for display.