I'm not trying to be evasive. I'm directly saying quantum computers won't factor interesting numbers for years. That's more typically described as biting the bullet.

There are several experiments that claim to factor 15 with a quantum computer (e.g. [1][2]). But beware these experiments cheat to various degrees (e.g. instead of performing period finding against multiplication mod 15 they do some simpler process known to have the same period). Even without cheating, 15 is a huge outlier in the simplicity of the modular arithmetic. For example, I think 15 is the only odd semiprime where you can implement modular multiplication by a constant using nothing but bit flips and bit swaps. Being so close to a power of 2 also doesn't hurt.

Beware there's a constant annoying trickle of claims of factoring numbers larger than 15 with quantum computers, but using completely irrelevant methods where there's no reason to expect the costs to scale subexponentially. For example, Zapata (the quantum startup that recently went bankrupt) had one of those [3].

[1]: https://www.nature.com/articles/414883a

[2]: https://arxiv.org/abs/1202.5707

[3]: https://scottaaronson.blog/?p=4447

Thank you for the reply and links. Good stuff.