I'm sure you mean infeasible. "Impossible" goes back to a problem's decidability. If a problem is undecidable, there's no way you're going to find its solution by switching computational models; classical computers can do anything a quantum computer can do, just "slower".

Not if they use up all the energy in the visible universe or they need so much power they collapse and form a black hole.

Real quantum computers should be able to do calculations that are that powerful, assuming we can prove the best classical algorithms are really exponential.