Based on your statement (I don't recall offhand), it might be said that it is widely believed RSA and ECC algorithms are vulnerable in a world where quantum computing is plausible. The safety of other systems would require a more rigorous proof; the absence of known vulnerability does not imply safety.

I am not an expert in this field, but the understanding I have from the last time I spent an afternoon reading about it might be summarized as:

* Known/Suspected vulnerable systems use "classically-hard" problems with vulnerability based on small key (or subkey) size.

* Most of the 'theoretically more secure' systems make the working set size large enough, and complex enough, to eclipse the scope of stable quantum computers.

* Thus, the two attack vectors to consider for 'post quantum' cryptography are currently unthinkably large systems or weaknesses in algorithms that allow for attacking a subset which does fit within a quantum system.

If my understanding/memory is incorrect updates would be very helpful.