If a problem can be reduced to efficiently sampling from the summation of an exponentially large number of FFT's, then a quantum computer will destroy a classical computer.
If a task can't be efficiently reduced to such a problem, then a QC probably won't ever help at all; the square root time advantage from grover's algorithm is too easily overwhelmed by simple engineering factors.
“We give new evidence that quantum computers—moreover, rudimentary quantum computers
built entirely out of linear-optical elements—cannot be efficiently simulated by classical comput-
ers. In particular, we define a model of computation in which identical photons are generated,
sent through a linear-optical network, then nonadaptively measured to count the number of
photons in each mode. This model is not known or believed to be universal for quantum com-
putation, and indeed, we discuss the prospects for realizing the model using current technology.
On the other hand, we prove that the model is able to solve sampling problems and search
problems that are classically intractable under plausible assumptions.”
If a task can't be efficiently reduced to such a problem, then a QC probably won't ever help at all; the square root time advantage from grover's algorithm is too easily overwhelmed by simple engineering factors.