This is incorrect. Assume nested virtualization. Extrapolate to infinity. On a computer, understood to be one like ours, it follows that there is now a machine that executes in finite steps will have arrived past infinity. Moreover, there are higher countings of infinity and these would of necessity be within such a virtualization. So it can't even reasonably be expected to compute everything even if you just have a very small sub-set of everything.

Well, I did say "anything" and not "everything".

Only on quantum computers of sufficient size. And we are far from having idea about how to actually build them.

Huh? It is my understanding that the current understanding is that quantum computers cannot compute anything that ordinary computers can. They can just compute certain things faster.

A quantum computer can be simulated on a normal computer, just inefficiently.

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).