It's not clear how your perception of quantum computing would lead to 'faster horses' in the current view of NN architectures - keep mind that the common view of 'exploring many paths simultaneously' is at best an oversimplification (https://scottaaronson.blog/?p=2026).

That said, perhaps advances in computing fundamentals would lead to something entirely new (and not at all horselike).

If you can tie in a loss function for a neural network into the quantum excitement state of a quantum system, then presumably, letting the system settle at the energy minimum would be equivalent to a training step, but perhaps much faster.