Adam Back suggested that the emergence of quantum computing could force Satoshi Nakamoto to move their Bitcoin to protect it, revealing whether they are alive.
I don't believe it will be reason.
If a new technical solution enforced to keep Bitcoin blockchain and bitcoins safely against quantum computers and their attacks, what's needed is Bitcoin private keys to claim new Bitcoin private keys and new bitcoins in new technical generation. The current Bitcoin blockchain and corresponding bitcoins exist on this blockchain.
I think it's misleading to say moving bitcoins from current Bitcoin blockchain to a new quantum-resistant blockchain. It's not like that.