For reference, there are some promising candidate for quantum resistant cryptography signature, such as :
1. Lamport Signature
2. Lattice-based Cryptography
3. Multivariate-based cryptography
These would be temporary solutions. Therefore they are developing new cryptos.
Postquantum, nobody will be able to prove that he/she/they was/were the owner/s in the old system, because everyone will be able to reproduce the privatekeys
of old blockchains.
We will have a quantum secure network.
This will be the new beginning.