The Brilliant Satoshi Nakamoto responded to Quantum Computer FUD 11 years ago

  1. “SHA-256 is very strong. It's not like the incremental step from MD5 to SHA1. It can last several decades unless there's some massive breakthrough attack.”
  2. “If SHA-256 became completely broken, I think we could come to some agreement about what the honest block chain was before the trouble started, lock that in and continue from there with a new hash function.”

Source: https://bitcointalk.org/index.php?topic=191.msg1585#msg1585

And keep in mind that this is worst case situation, as if Quantum computers came unsuspectedly years earlier- I think lamport signature or other solutions could easily be implemented before any trouble comes.

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