Several months ago there is a paper appears calling Disentangling Hype from Practicality: On Realistically Achieving Quantum Advantage. It seems it is a real challenge to transfer data from quantum to classical register faster than classical cpu/gpu does this with RAM.
Could it be the show stopper for quantum computation?
I wouldn't say it's a show stopper. The paper argues data upload into a quantum computer is really difficult so large data problems are not the way to go. But what we would like sometimes is the ability to generalize from a small amount of data so that we can do some generative modeling for example. In that case small amount of data is desirable and if you have a good quantum algorithm you are in the game. So then the question becomes whether we have good quantum algorithms for generative modeling and the answer I think so far is no, see here .
Good quantum algorithms in ML are hard to come by since you must avoid de-quantization i.e good classical surrogate models.
But all this says nothing about Quantum Dynamics, Energy Estimation, Differential Equations where do have provable speedups.
