There is only a draft BIP with the tentative number 360. I had opened a thread about that discussion.

It's however unlikely the BIP will be implemented soon. The problem is that the developers don't consider the current post quantum algorithms to be mature enough, and for example @achow101 (a Bitcoin developer) has stated in that thread that he'd prefer to choose a single, battle-tested algorithm, instead of letting the users decide which algorithm to use (that can be dangerous because many users have no idea about the safety of the different algorithms and their particular challenges and potential vulnerabilities).

I personally think that it is reasonable to wait a couple of years more, because quantum computers with hundreds of thousands of logical qubits would be needed to crack a Bitcoin key in several years, and millions if it should happen in a few days. That's imo at least a decade, if not a century away. (And afaik you can't just connect several 1000-qubit-machines to create a million-qubit supercomputer.) And until quantum computers can crack keys in a few minutes, there is a simple strategy to make coins "almost" quantum safe: don't re-use your addresses, and thus no public key is exposed.

The best way to stay up to date about development issues is to follow the Bitcoin-dev mailing list. There was a quite long discussion about the proposed BIP360.