So like 17 doublings? Obviously very rough and uncertain, but Moore's law equivalent for qbits seems to be a doubling every ~5 years.

That implies bitcoin keys will be insecure in about 85 years, no?

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Probably sooner, if enough time and resources are allocated towards brute forcing a specific wallet (1000 days to steal 50 BTC from one of Satoshi's UTXOs).

But cryptography will also improve in the meantime.

Cryptography will improve, but I imagine the difficult part would be hard forking bitcoin at that stage. You would have to give some huge (decade long) window for people to move to the new system in anticipation of this happening, and then burn all the coins that don't move.