The way to pick locks fast is as follows:
Start turning the left analog stick SLOWLY in the direction indicated, and push it out against the very outside of the circle, as soon as you hear the click, reverse directions (slowly), and then again when yo uhear the next click. It shoudl only take 3 clicks if done properly.
Swirling the analog stick around fastly will do it eventually, but the proper slow-turn-until-click way is the fastest.