Q would pop into your lab and your office quite often, especially when you were hard at work. He wouldn't do it to bother you or interrupt per se, he just liked to watch you do your work and he liked to spend time with you when you were doing what you loved. He loved to watch your face set in concentration and your eyes light up when you made an advancement.

Q would be fascinated by your fascination of the natural world. As a Q, he just knows most things about the world, and he'd enjoy watching you figure it out. He wouldn't tell you the answers to your scientific questions, though he would encourage you to continue with your research and might point you in the right direction from time to time.

You would probably be very interested in Q's powers and how they work. You'd ask him many questions about the Q and would try to piece together what it means to be a Q scientifically. You'd write papers about the Q from a scientific perspective and would be the first to study them in such detail. Q would feel honoured to be the centre of your research and would answer any questions you asked.

Q would offer to bring you to different locations to study around the universe. Anywhere from a planet in the early stages of evolution to a sun about to go supernova. He'd love to bring you anywhere you wanted to conduct research at. This would of course give you an advantage over other scientists. You'd have the opportunity to study various locations and visit planets that would otherwise take ages to get to.

People would speculate and question whether you were dating Q simply to advance your studies. You'd be quick to tell them no, but you'd be able to understand where they're coming from. While you wouldn't use Q for his powers or take advantage of his ability to help you with your studies, you would definitely be very grateful and feel lucky to have him around.