Many old, hard problems are still hard even on quantum computers (SAT, TSP, etc. cannot be solved in polynomial time on quantum computers). Factoring can be done in polynomial time on quantum computers. FFT can be made even faster. But again, some classic, hard problems still stand. So don't worry, quantum computers are not magic solutions to all hard problems, just some.
> Is there a quantum computing-proof encryption algorithm
This is still an area of active research. For instance, there are learning-with-errors-based cryptosystems: https://en.wikipedia.org/wiki/Learning_with_errors#Use_in_cr...
But such systems are based on the assumption that "this type of problem is probably hard even with quantum computers". I believe we don't have anything more "quantum-proof" than that..
And of course, there are cryptosystems with unconditional security. Such as OTP.