From what I know, quantum computers will appear only in 10 years. The "companies of evil" (IBM, Google etc) will not allow this happen sooner.
What do you mean in appear? To be quantum computers accessible for everyone? Maybe not in 10 but in 20-30 year that may happen and then quantum will be perceive as normal as current PCs. But on another hand google's quantum computer already exists.
OP every problem is solvable, what is computer? Combination of numbers and numbers are part of math. Math can create and solve problems, so when there will be that problem, it will be solved too and as DannyHamilton correctly mentioned quantum-resistant authorization algorithm.