[AlyssaRowan]

And indeed (from my skim-read, and please bearing in mind that I know very little about quantum computing) the paper seems to combine that same Grover's algorithm used to speed up just about any brute-force search with ECM, to find small primes more efficiently than Shor's algorithm in this case.

Then it constructs a 1 terabyte RSA parameter, so big neither algorithm can currently attack it using a computer (quantum or otherwise) of practical size, as all known quantum attacks (including the new presented) would still need over a 2¹⁰⁰ workfactor; the 2³¹ factors they would need to find are each 4096 bits long themselves, if I'm reading it right?

Needless to say, that is a trifle on the heavy side and definitely isn't your first practical choice (those would be lattice-, code- or hash-based primitives), but it is possible, and that's impressive (to me) by itself! Nice work.