My (admittedly fuzzy) understanding is that while running a DNN is a very parallel problem, training it (back-propagation, in particular) is not and is thought

My (admittedly fuzzy) understanding is that while running a DNN is a very parallel problem, training it (back-propagation, in particular) is not and is thought to be susceptible to quantum speedup. Google's work in quantum computing is motivated by the same application.