Quantum computers and computable functions

Question

A quantum computer can possibly calcluate computable functions faster, but it can't calculate functions which a normal computer can't calculate?

If a function is not computable? Does this mean it will never be computable? Even if we change the axioms which our mathematical system is based on or we find a contradiction in it? Are we never be able to find something in the universe which can calculate these functions?

Is that right?