Usually we only bring up Turing machines for decidability, ie when the only thing that matters is whether it takes finite or infinite amounts of time.
(Yes, I know, you can also calculate exact runtimes with Turing machines, but nobody really cares, I think?)
I guess you mean to say classical computer or so?
> [...] and no number of Intel CPUs will let us overcome that barrier.
Or at least that's everybody's best guess. On similar footing to the empirical evidence for P != NP. It's still theoretically possible that BQP = BPP, if memory serves right. (https://en.wikipedia.org/wiki/BQP vs https://en.wikipedia.org/wiki/BPP_(complexity))
Most of the time the different ways to model computing only have a polynomial slowdown to emulate each other. In that sense, quantum computers are different from Turing machines: the best way we know to emulate quantum computers on Turing machines has exponential slow downs.
So, basically a lack of computing resources. QCs aren't generally that much faster than classical ones, but in this particular case they are--understandably so, given the universe runs on quantum mechanics. Turing machines are not good enough for this, and no number of Intel CPUs will let us overcome that barrier.
Physicists try really hard anyway, but the approximations are... Well. As I said, awful.