I think that the big challenge is to recast any classical computations as quantum computations with a superpolynomial speedup.

I think that all classical problems can be cast as quantum computations because quantum computation is just computation - I believe that one can implement a turning machine using quantum gates, so arbitrary computation is possible with quantum gates.

The superpolynomial speedups are the thing.. I wonder if these will be limited to a class of computations that have no physical realization - just pure maths.