College Courses For Quantum Computing?

Tyler asks: "I'm currently an undergrad engineering student at a respectable school, and right now I'm pretty sure I'm majoring in CompE. I'd really like to do some work with Quantum computers in the future, but I don't know what exactly makes up a good quantum-computing engineer, so I want to take some courses over the next few years to become familiar with the science. What courses should I be taking?"