In theory, quantum computers could provide dramatic speedups for certain linear algebra operations (eg. matrix inversion, eigenvalue estimation). The catch is that many NN training algorithms need all the data to be stored in qRAM so the QC can access matrices efficiently. Loading in a massive dataset will likely be more difficult than the computations, eliminating the quantum advantage. This is analogous to having an extraordinarily fast processor attached to a slow af hard drive inside a neutrino storm.