This is a problem we face training activists and journalists in a number of countries. Esp places like China, Russia etc. We have to work hard to help people get the idea that a lot of the encrypted, password protected stuff etc they send now is potentially at risk in 5-10+ years. To a certain extent (but different context obviously), the lessons of the Venona Project comes to mind.
IIRC that's one of the big things the NSA's data center was doing - storing Tor traffic with the assumption QC could break the public key crypto and either see where it was going/coming from or maybe even what was being sent (traffic itself)?
Take what I say with a grain of salt, I'm not a cryptographer.
It's my understanding the onion routing (what went where) could be cracked since it uses public key. The data itself may be fine because it uses private key, but if you sent the private key using a public key then you may be burned (IIRC there's a protocol where you send the symmetric key using public key crypto then fall back to private key since it's faster)
