These guys have created some amazing software that will allow you to connect your PS4 Controller to your PC Computer

DS4Windows allows for the use of your Dualshock 4 controller in Windows as a Xinput device (Xbox 360 controller) making it compatible with all 360 controller ready games. DS4Windows also adds features such as trackpad to mouse support.

Automatic profile switching based on active application, Adjustable stick sensitivity and curves for pinpoint accuracy, highly configurable custom macros, button combinations for macros to extend the functionality, full trackpad to mouse support, full rumble support (with rumble compatible games).

Read more info here for mapping and other features