Quantum computing could be used for solving systems of linear equations more efficiently for example, having applications in image/video processing, weather predictions and all kinds of analysis - solving such equations with classic computers is done in something like O(n^3) or O(Cn^2) with a huge C, but quantum computers could reduce this to O(log n) or something like that. This is really cool, because doing simulations of complex systems, like weather modelling, involves a huge number number of equations and variables (think billions, or even trillions).

It isn't far fetched to think of evolved quantum algorithms for making better predictions than we currently do. On the other hand, some people kind of have the impression that with quantum computers suddenly NP won't be an issue anymore. Which is simply not true. Most problems we have will simply go unsolved and quantum computers will introduce problems of their own.