While there are plenty of people who have just wholesale dismissed the Hill/Viamontes paper outright, apparently because they know Shor’s algorithm works and that building a working quantum computer is obviously merely a matter of making some qubits, Van Meter is more to my thinking about the whole thing.
I have read it, but not studied it in major detail yet. I don’t know either of the authors personally, but the second author has done good work; he is certainly no dummy.
The argument is pretty straightforward, arguably naive. That doesn’t mean it’s wrong, but there are a lot of assumptions and simplifications in the work, and they need to be examined carefully.
He also says:
Anyway, I hope this at least short-circuits any rush to burn Peter Shor in effigy. He’s way too smart and sweet for that.
Here’s where I think I need to rant a bit. I’m certainly not calling for anyone to be burned in effigy or reality. I can’t testify to how sweet Peter Shor is, but I agree that he’s brilliant and I admire him.
However, Leibniz was also smart and worked in the forefront of calculation as well. His calculator had issues with propagating carry with two-digit or three-digit multipliers. That doesn’t make Leibniz any less brilliant or his achievements any less.
Peter Shor is brilliant, and his algorithms are marvelous works. If no one implements them, for whatever reasons, they won’t be any less marvelous, and he won’t be any less brilliant.
And for that matter, Hill and Viamonthes may turn out to be wrong, too. Or they may inspire someone to a tweak that makes Shor’s algorithm work (or work better).
The present spectator sport is how science works. It’s what makes it exciting.