Well... It does work, technically. It's just that the button mappings are a bit mixed up (Circle and X switched, Triangle and Square switched, Select/Start switched with L3/R3, Right Stick directions turned sideways, etc.). Unlike the PS3 controller, though, the PS4 controller has official Windows support, according to Sony.

I do have a PS1 controller and USB adapter, actually, but the PS4 controller is much more responsive and feels much better in my hands, so I'd prefer to use that if I could just map the stupid buttons.