Hm, they seem to be making huge theoretical claims: it seems they're claiming it outperforms classical Turing machine methods by an exponential (non-polynomial)

Hm, they seem to be making huge theoretical claims: it seems they're claiming it outperforms classical Turing machine methods by an exponential (non-polynomial) factor. I think this would be a violation of Church-Turing thesis and in of itself quite revolutionary. It's odd this conclusion didn't receive more attention. On the surface, since they're not using full quantum coherence properties, it seems this should be possible to simulate in a classical computer just fine (in "polynomial time" in some sense) which make it unclear to me why the exponential speedup should exist. Nonetheless, I think this kind of machine could be useful and more efficient even without any exponential advantages (which to be frank I'm dubious of).