A fundamental result of information theory and thermodynamics is that computation generates heat, as your knees may have noticed. Further, it has been proven that, in a classical computer, deleting data necessarily produces a small amount of waste heat. A new theoretical result shows that in a quantum computer deleting data actually cools the device under the right circumstances. The result can be checked by experiment and has possible practical applications; it leads as well to a new understanding of entropy in thermodynamics and information theory.