What type of Grad School if I'm interested in Quantum Computing?
You should aim for whichever department has people working on the topic.

Quantum Computing is somewhat multidisciplinary, and not present in every university. So, before applying, check where are the quantum computing groups and follow them. Your background seems to be a good fit for either side.

By the way, I wouldn't be surprised if there was somewhere a department dedicated to quantum computing. Recently I saw a "department of glycoscience".