Ordinary computer can't model even a small quantum system exactly in finite time because it has to deal with infinite-dimension matrices to do it. In other hands, quantum computer could model any quantum system of the same size by one-to-one mapping of degrees of freedom. So you could build a quantum computer that just models your computer and do anything you could do on your ordinary computer on the quantum one.

If you are interested in the subject try to read this book http://www.amazon.com/Programming-Universe-Quantum-Computer-... (you can skip the parts about the Universe as quantum computer because they are controversial and a kind of metaphysics, just read a few first chapters to pick up the idea of quantum computations).