We call this improving your jump. Here is a set that my coach has me do as crit season heats up.
From a standing start (or as close as you can manage), do 10 sets of 15" intervals. Five from the small (or middle ring), say 39x16 or so. Hit it hard and wind it up as fast as you can go. Don't shift. You should feel like you're spinning as fast as possible at the end of the 15".
Now do five from the big ring, say 53x15 or so. Again, hit it hard and don't shift. On these you'll really struggle to turn the pedals over for the first five or so revs. Then focus on getting on top of the gear and turning the mash into spin.
These are inherently high intensity intervals so I wouldn't do these more often than twice a week, at least to start.