How to verify the computation happened in off-chain(ZKVM) is a problem. And now we would love to use a fraud-proof to solve it. A Bisection protocol used in Arbitrum.
So, we could verify a single instruction of ZKVM on Bitcoin. It's easy to implement it based on the current opcodes set in Bitcoin.
We're a bit of a long way from seeing an implementation of zk-proofs validating a contract on Bitcoin (as opposed to zk-proofs validating network state, for which work is already happening right now). But it's highly expected that any development of a ZKVM will be done as a separate program, and maybe as an alternative to Lightning Network.
I don't think much thought was given to how LN would interoperate with these other systems though.
Yeah, In terms of the cost and programmability, it's very hard to run a zk-verify contract on Bitcoin directly now. And tbh, it's much harder to support these by changing the bitcoin. So We have to find another way to solve it. The fraud proof may be used to achieve it. Instead of executing the zk-verify program on the bitcoin, we can just execute one step of zk-verify on the bitcoin. The one-step means the one instruction of VM. It could be easy to implement by using the current opcodes in Bitcoin.