Actually Steve the only time that large caches/memory/storage come into their own is during the ‘training’ phase (think on it as a massive curve fit with random jumps to get rid of false results). The pretrained models can be, and usually are, quite small. For example the smart phone camera systems that recognise faces.
At this time so-called quantum computers do not really help as the difficult bit is selecting the data on which the set is trained. (hence the problems in it currently being relatively easy to add ‘malign’ data).
The use of neural networks with their hidden layers makes interpretation and understanding of ‘how’ the model works very difficult and investigation of ways of making such models spit out ‘why’ it gets a particular answer is a major research subject. For example ‘why’ the relatively useless police face id program spits out so many false answers if non-white people are involved, or why a bit of carefully applied face paint (not a mask!) makes someone invisible to the camera (identifies as not a person).
.
