While at BYU I wrote an Honors Thesis titled Modeling the Quantum Computer on the Classical Computer. As an intro to the topic, I'll include my abstract here.
Information is traditionally stored in computers as 1s and 0s called bits and manipulated by classical gates. Similarly, information can be stored at the quantum level in qubits and manipulated by quantum gates. Programs can then be written for quantum computers by assembling networks of these quantum gates. If realized, such programs would be able to achieve an exponential speedup over classical algorithms by taking advantage of quantum effects such as interference, superposition, and entanglement.
Because of the difficulty of maintaining quantum coherence, quantum networks will not be operational for some time. I propose to simulate these networks on a classical computer. Although such a simulator does not produce an exponential speedup, it allows the user to test quantum gate networks before implementing them in hardware. The operation of an n-bit quantum computer simulator I have developed is described. The advantages and limitations of the simulator, as well as possible applications, are then discussed.
If you want more information you can read a paper I recently co-authored, or even the complete text of my thesis. Feel free to mail me if you want more information on my research.