What device can switch ON and OFF different pads independently?
Since this post already has an arduino tag I'm going to suggest that you use an arduino (e.g. micro) as the brain of your device.
Why?


very flexible
has 20 i/o pins (can be switched on or off)
switches in a matter of µs (should easily be fast enough)
easy to learn
open source
rather cheap.


An active output has 5V but limited current. So if you want to use the signal to drive heavier loads (e.g. leds) you would also add something to your outputs that can handle higher currents.
There are many options and tutorials depending on your needs (transistors, driver-chips, FETs, Relais …). 



As others mentioned there are many more options to consider (other MCUs, complex timer circuits…) but this seems to be a practical solution.