[honzaik]

well, it depends on the size of the quantum computer. of course you can make large enough RSA keys (depends whats your security margin/assumptions) but the problem is that the size/computational increase is exponential whereas the solving speed scales polynomially.

https://eprint.iacr.org/2017/351

[maginx]

The size/computational complexity of usage also only grows as a polynomial with RSA. But even with this in mind, a quantum computer that can crack in polynomial time is still problematic. While you can increase the key size, the operator of the quantum computer could enlarge his computer, a true cat-and-mouse game. Unlike the current situation where usage complexity grows as a polynomial, while cracking grows exponentially. This difference is the reason why we can pick key sizes where signing/decryption takes a millisecond while cracking it takes (presumably) billions of years.