What bit to use to cut a hole in quartz counter top?
You will cut this as it is granite and use a diamond tip hole bit (see example that I have used).  Not an endorsement because I cut a hole in granite 3-4 times a year but they worked fine for me. 

Quartz is a little easier to cut than granite but I would still go diamond.  Also make sure you have someone pouring water on the scene, take you time, put little to no pressure on the bit after it starts, and if things are going too slow reverse and pull the bit out and try again (let it cool and clear out debris).