[choffman]

I'm not sure that anyone can speak to what happens to crypto in a post quantum world.

Mixing does not happen on a server - that would be an atrocious violation of privacy. Monero (and other cryptonote coins ) use ring signatures - https://lab.getmonero.org/pubs/MRL-0004.pdf

There is also work being done to employ gmaxwell's Confidential Transactions: https://github.com/ShenNoether/MiniNero/blob/master/RingCT0....