Cory Fields posted this proposal to the Bitcoin Developers Mailing List:

As soon as a quantum computer is demonstrated to be able to break bitcoin keys, these new rules apply:

1. Every legacy address must have a thirty day timelock when it is spent
2. Every legacy address spent must also include an equivalent number of sats from a quantum resistant address as collateral.
3. If someone can reveal a proof (from before some arbitrary date or blockheight) that they knew the keys to the legacy coins being spent, they get both the legacy coins and the collateral.
4. If no one reveals such a proof, the legacy coins can be spent as normal after the timelock expires.

I believe the goal here is to create a situation where it becomes dangerous for thieves to try to sweep coins in quantum-vulnerable addresses because they never can be sure that the real owner hasn't hidden a proof of their ownership.

Of course, one question here might be: if we're requiring people to make a transaction hiding a proof of their ownership in a new quantum-resistant address, why don't they just spend all their coins to new quantum resistant-addresses and be done with it?

This scheme is especially interesting because it actually incentivizes Alice to bait a quantum attacker pre-qday in order to double her vulnerable coins later, and thus makes quantum attackers wary of stealing coins as they may be secretly guarded by mines. It also muddies the waters so that on qday, it's not possible to analyze how many coins are vulnerable to theft.

This is the landmine. Often in these discussions about what to do with quantum-vulnerable addresses, the question comes up of what will happen to all the people who don't learn about the issue or for whatever reason don't move their coins. This proposal attempts to create a scenario where it is so risky to steal quantum vulnerable coins that attackers will generally avoid it.

Unfortunately, there is this wrinkle: what happens to someone who doesn't have enough coins in quantum-resistant addresses to make up the collateral? Unless I missed it, there isn't any path to spend for a person who hasn't got equivalent coins in quantum-resistant addresses. This seems like a pretty major flaw, as it still only delivers the freedom to spend quantum-vulnerable coins to people who acted before quantum attackers arrive -- and those are all people who could have just moved their coins anyway.

I like the landmine concept, but I don't think it solves the real problem, at least not in its current iteration. But I like that instead of trying to categorically solve the problem, this proposal think about how to create incentives that make it unprofitable to steal coins with a quantum computer.

Cory Fields also proposes an auction mechanism whereby people could bid on coins that are known to be lost or otherwise remain vulnerable to quantum attackers. It was complicated enough that I didn't quite wrap my head around it.