Looking at the SQIsign I algorithm, which has "palatable" signature sizes but an astronomically high verification cost, I got the following shower thought: Could it be possible to introduce a post-quantum option based on optional verification?
Basically how today OP_RETURN tokens like Counterparty or Runes work: miners and full nodes would not need to verify the transactions. Instead it would be the users when they transfer and/or accept these coins; they would verify that there's a coherent chain of signatures until a point where an "old style Bitcoin" was burnt and exchanged to a "post-quantum Bitcoin" (a bit similar to how Counterparty was distributed originally).
Once hardware speeds have accelerated to the point that verification is no longer a problem, the verification could be turned mandatory again (i.e. a proof of verification added to the blocks), at the same time those "tokens" would then be recognized as "real Bitcoins".
That is an awesome idea! The concept of optional verification for a post-quantum option does have some merit, especially considering the potential congestion and high costs related to verification with algorithms like SQIsign.
Your comparison to how OP_RETURN tokens work is apt; it could create a more flexible system where user-initiated verification offloads some of the burden from miners and full nodes. This would allow users to accept and verify transactions at their discretion, reducing the immediate costs associated with heavy verification processes.
The vision of eventually upgrading to a mandatory verification model, once hardware becomes sufficiently advanced, aligns with Bitcoin’s ethos of evolving and improving with time.
However, we will need to carefully consider the implications for security and the potential for users to by mistake accept invalid "post-quantum Bitcoins" if proper checks are not enforced from the start. And, ensuring that the conversion from “old style” to “post-quantum” is smooth and secure would be important to maintain trust in the system.
Overall, it is a fascinating area to explore further, and discussions like this are vital for fostering innovation in the blockchain space.