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Instinctively, I want to think that post-quantum crypto means both ends. That is to say, if it transpires that quantum computing can break all pre-quantum encryption schemes, it ought to follow that there will be post-quantum encryption schemes that it can't.

I don't understand quantum computing well enough to know if that's a reliable instinct though. Is it anywhere near the mark?

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No, that's not really correct. The theoretical capability of a quantum computer to "collapse" to optimal routes to solutions during computation does not imply the existence of cryptographic trapdoor functions which are likewise intractable. More concisely: the existence of a quantum computer does not imply the existence of problems it cannot solve. They're orthogonal things.

That being said, Mahadev's recent research constructing a quantum verification protocol using the LWE is exciting along similar lines to what you're thinking. It allows us to say with authority that one of the following must be true:

1. LWE protocols are not post-quantum resistant, or

2. Quantum verification is possible via LWE-based cryptography.

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