The hope is that quantum computers will give us an exponential speed up on some problems, which could (again, hopefully) allow us to solve some NP hard problems. This can be extremely useful for scientific computing (e.g. protein folding) and engineering, where computers have to solve complex NP-hard optimisation problems.
It could also be possible to use the technology developed for the precise control and measurement of qubits to "rebuild" natural phenomena like the interaction of chemical molecules, something which is currently extremely hard to simulate.
It could also be possible to use the technology developed for the precise control and measurement of qubits to "rebuild" natural phenomena like the interaction of chemical molecules, something which is currently extremely hard to simulate.