As I understand it...
Currently, computers attack certain complex problems by iterating through all possible solutions, one at a time, which can take a very long time.
A quantum computer could instantly be in all possible solutions at once, and then persuaded to give you the best solution.
Example:
Cracking an encrypted message without having the decryption key theoretically means trying all possible keys (passwords), which can take a long time (like millenia).
A quantum computer could apply all possible keys at once, and promptly give you the one that works.
That's one thing I love about Free Republic--so many intelligent, well informed people here! ~S