I have installed Qt Creator using Ubuntu Software Center but when I try to run it nothing happens. There is no error message, no new process, no new window.
You may be running QtCreator on an old CPU that's missing SSE2 instructions, hence the "illegal instruction" message. See this question on archlinux:https://bugs.archlinux.org/task/34228 .
However, I don't know if it possible to recompile recent QtCreator (2.7) so that it doesn't use SSE2 instructions.