Analog computers can outperform digital computers in some tasks, like integrating a continuous function, matrix multiplication, signal interpolation and filtering and so on, but not in all cases. In Bitcoin, we use SHA-256 that is designed with a digital computer in mind, and will almost certainly be better done in one.
If you ignore SHA-256, you can build a PoW system optimized to analog computers, like BIP-052 OPoW, but this requires changing Bitcoin protocol.
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