hktuotroi

But parent was stating something very different, that today quantum factoring is only asymptotically better that classical one, when that is clearly not the case.

Isn't quantum factoring proven to be exponentially faster than the best known classical one?

The only question is we don't know if there is a better classical factoring algorithm.

Wikipedia:

> On a quantum computer, to factor an integer N, Shor's algorithm runs in polynomial time. This is almost exponentially faster than the most efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time

They didn't say 2.5 days on a laptop. They probably mean on a bunch of datacenters together. That is expensive.

Google implied their supremacy over all of the world computers combined together.