ℹ️Satoshi Nakamoto proposed two solutions in case quantum computing threatened Bitcoin:

1 - Freeze the blockchain in the last safe state and continue with a new hash function.

2 - Update the software to use a new hash from a specific block, ensuring that everyone updates in time.

1 - “If SHA-256 is broken, we could agree on the state of the blockchain before the problems start, lock it, and continue from there with a new hash function.”

2 “If the hash breakage is gradual, we could transition to a new hash in an orderly fashion. The software would be programmed to start using a new hash after a certain block.

Everyone would have to update by that time.  

The software could save the new hash of all old blocks to ensure that a different block with the same old hash could not be used.”

First image: Satoshi quote. Second image: Neven's law, quantum computing evolution.