Basically, quantum computers can solve problems of the BQP class in a time that is a polynomial function of input size. These same problems, on a traditional co

Basically, quantum computers can solve problems of the BQP class in a time that is a polynomial function of input size. These same problems, on a traditional computer, can take exponential time. It is hard to tell with certainty what can be done with quantum computers, but having powerful quantum computers will certainly open new fields of research, like trying to figure out if quantum algorithms for NP-class problems have better complexity than classical algorithms. Simply finding subexponential algorithms for problems that would have required exponential time on a traditional computer, may prove valuable. Basically, outside of the immediately available problems, this opens up an entirely new complexity class from which to attempt to crack other classes of complexity. Trying to break NP-problems with turing machines, if not successful in an academic sense, has proved immensely valuable and profitable. By getting another architecture, we get a shot at similar breakthroughs.