May classical pseudo random generators be predictable by powerful quantum computers in the future or is it proven that this is not possible?
If they are predictable, do scientists know whether there exist PRGs that are unpredictable by quantum computers?
The security of a classical Cryptographic Pseudo-Random Number Generator (CPRNG) is always based on some hardness assumption, such as "factoring is hard" or "colliding the SHA-256 function is hard".
Quantum computers make some computational problems easier. That violates some of the old hardness assumptions. But not all of them.
For example, blum blum shub is likely broken by quantum computers, but no one knows how to break lattice-based cryptography with quantum computers. Showing you can break all classical CPRNGs with quantum computers is tantamount to showing that BQP=NP, which is not expected to be the case.
Even if quantum computers did break all classical CPRNGs, they happen to also fill that hole. They enable the creation of "Einstein-certified" random numbers.
