First of all, I haven't the slightest idea how a quantum computer actually works but I understand that it is theoretically possible to make them and they could, in theory, be used to compute things that a classical computer would take too long to compute. (i.e. large combinatorial problems like cracking some code). So if this quantum computer exists, and you give it some initial input which represents instructions to solve some massive combinatorial problem that classical computers cannot solve (in a reasonable time), then in this situation you would not be able to model the system (the quantum computer) with a classical computer (i.e. a turing machine) in a reasonable way because if you did then you would solve the combinatorial problem which you can't solve on classical computers! My question is: Can classical computers be used to model quantum physics accurately (in a reasonable time)? Or is a quantum computer just a weird case that computers can't be used to model? And I may be jumping ahead of myself here, but presuming classical computers can't model quantum phenomena, could a quantum computer model quantum phenomena? I'm reading Roger Penrose's book "The Emperor's new Mind", this is what lead me to ask this question. Thanks a lot :) note: I notice the ambiguities of "reasonable time" and "in a reasonable way". I would guess a proper way of asking this questions would involve Big O notation but I'm not experienced enough in maths/physics/computation theory to phrase my question in that way.