Quantum physics is - in some sense - strictly more complex than classical physics and therefore simulating quantum physical systems with classical systems, for example a classical computer, causes exponentially growing costs. Besides that quantum physics is non-local and can not be simulated at all if you have only access to local state. There is a prize of a million dollar waiting for you if you can demonstrate the opposite [1].

[1] http://www.science20.com/alpha_meme/quantum_randi_challenge_...