There are some promising candidate for quantum resistant cryptography signature (CMIIW), such as :
1. Lamport Signature
2. Lattice-based Cryptography
3. Multivariate-based cryptography
But AFAIK there's no serious discussion/plan of choosing/implementation of quantum resistant cryptography signature for Bitcoin.
There's no need for that right now in my opinion, most of security systems are based in the same Cryptography system as bitcoin, if there was any risky for the general cryptography system then we would have much more solutions for that.
The risks of quantum computing is already known, so it'd be dumb if people don't do anything just because it's secure for now.