> the big benefit is parallel computing at a massive scale
The problem with this line of reasoning is that, even though a quantum system might have many possible states, we only observe a single one of those states at the time of measurement. If you could somehow prepare a quantum system such that it encoded the N equally-likely solutions to your classical problem, you would still need to rerun that experiment (on average) N times to get the correct answer.
Broadly speaking, quantum computing exploits the fact that states are entangled (and therefore correlated). By tweaking the circuit, you can make it so that incorrect solutions interfere destructively while the correct solution interferes constructively, making it more likely that you will measure the correct answer. (Of course this is all probabilistic, hence the need for quantum error correction.) But developing quantum algorithms is easier said than done, and there's no reason to think a priori that all classical problems can be recast in this manner.
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.
The problem with this line of reasoning is that, even though a quantum system might have many possible states, we only observe a single one of those states at the time of measurement. If you could somehow prepare a quantum system such that it encoded the N equally-likely solutions to your classical problem, you would still need to rerun that experiment (on average) N times to get the correct answer.
Broadly speaking, quantum computing exploits the fact that states are entangled (and therefore correlated). By tweaking the circuit, you can make it so that incorrect solutions interfere destructively while the correct solution interferes constructively, making it more likely that you will measure the correct answer. (Of course this is all probabilistic, hence the need for quantum error correction.) But developing quantum algorithms is easier said than done, and there's no reason to think a priori that all classical problems can be recast in this manner.