If you are after shortest turnaround times, then definitely look into the schedules of Asian carriers as they tend to use larger aircraft than those airlines closer to home. In particular, Thai Airways uses 747s on its Bangkok to Phuket route and the aircraft is turned around in just 70 minutes. Similarly, Asiana Airlines operates 747s on its Seoul to Tokyo (Narita) route. This is turned around in 80 minutes.

Whilst you didn’t ask for turnaround times of a 747, this is currently (until tomorrow anyway) the largest passenger aircraft in service. If a 747 can be turned around in such a short space of time, then the turnaround time for something smaller, whether an A330 or A320, could be a lot shorter.