Briefly, the new work uses Kitaev’s version of Shor’s factoring algorithm, running on an ion-trap quantum computer with five calcium ions, to prove that, with at least 90% confidence, 15 equals 3×5. Now, one might object that the “15=3×5 theorem” has by now been demonstrated many times using quantum computing ...It is still cheating to say they factored 15 "scalably", because the method does not scale up to larger numbers.
Nevertheless, as far as I can tell, the new work is a genuine milestone in experimental QC, because it dispenses with most of the precompilation tricks that previous demonstrations of Shor’s algorithm used. “Precompilation tricks” are a fancier term for “cheating”: i.e., optimizing a quantum circuit in ways that would only make sense if you already assumed that 15 was, indeed, 3×5. So, what’s new is that a QC has now factored 15 “scalably”: that is, with much less cheating than before.
Of course, as I’m sure the authors would acknowledge, the word “scalable” in their title admits multiple interpretations, rather like the word “possible.” ...
In conclusion, let me suggest the following principle:
I will not assign a nonzero probability to something like 3×5=7, for which there’s no explanatory theory telling me how it possibly could be true. That doesn’t mean that I’ll assign a zero probability — i.e., that I’ll accept a bet with infinite odds on anything that strikes me (perhaps mistakenly) as a logical or metaphysical impossibility. It just means that I’ll refuse to bet at all.
In the make-believe quantum world, anything is possible. Everything is just probabilities. If it doesn't happen here, then it happens in some parallel universe.
Scott admits that no one has demonstrated quantum computing, but he like to study, so he likes to believe it is possible. And even if it is not possible, it is a rewarding thing to study. And he cannot positively rule it out, just as he cannot rule out 3×5=7.
Speaking of possibilities, it is possible that the elusive dark matter is black holes. Until the LIGO discovery, we only knew about star-sized black holes and giant million-star black holes. The star-sized ones show up as part of a binary star where the other star is visible. The big ones are at the nucleus of galaxies, and could be essential for galaxy formation.
Common sense would indicate that there must be some intermediate sizes. The LIGO team claims they say 2 30-Sun black holes collide. This could be a freak event, or there could be billions of them scattered all over the place, and we would never notice. If the latter, they could be the dark matter whose gravity is essential to holding galaxies together.
I posted some skepticism about LIGO, but we could soon have a lot more data to settle the question. Maybe another country with build a LIGO, and not build in the capability to fake results.
Update: Sean M. Carroll responds to the possibility that LIGO discovered the missing dark matter.