Anyone more in this field know if this has been reviewed by others, or the likelihood of it standing in the way of practical quantum computers?
It sounds pretty damning to QC if true.
Gil Kalai has been beating this particular drum/dead horse for decades at this point. Having read the paper, it seems pretty consistent with his previous work ... it all crucially hinges on the postulate that, somehow, noise will prevent this from working, but he has yet to actually come up with a solid explanation for how.
(Even this paper, ultimately, relies on Conjecture 4, which essentially comes down to saying that "Well, we've proven this one particular system runs into noise issues, so we're just going to assume that some grand physical principle will cause this to extend to every possible small noisy quantum system.")
I'm not "in the field" nor do I have a clue about quantum computing, but I recognize the name Gil Kalai from the comments section of Scott Aaronson's blog.