Quantum computing often scares away many potential researchers from computer science because of the apparent background need in quantum mechanics and the alien looking notation used in papers on the topic.

This paper will give an overview of quantum computation from the point of view of a complexity theorist. We will see that one can think of BQP as yet another complexity class and study its power without focusing on the physical aspects behind it.

Dieter van Melkebeek gave many useful comments on an earlier draft of this paper.