I'm saying - you can get accurate, complete, or fast - pick two.
A simple quantum computer could be modelled in a regular computer ... technically they are doing it, functionally, right now: oh look!
If you want to model the QM processes that would lead to the components of a quantum computer - again, fine. Provided you keep it simple. It is models like these that lead us to think that quantum computers are possible in the first place and it's probably how we'll design the first ones.
We don't normally think of using a very small quantum computer as a pocket calculator, just like we don't use our ultra-miniaturization to make smaller 8086 processors - so we'd think of quantum computers in terms of their promise. Very big, very fast.
It will help refine your question if you consider where your line of reasoning was going.
 Mind you, we never thought that the processing power we have now would be used to post pictures of cats at each other either.