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Integer factorization for codebreaking is a military or criminal application, not a commercial one. Someone will make money doing it, but it won't be contributing to society in the way we normally mean when talking about commerce. It would be like saying nukes have commercial applications.

"Quantum simulation" is too vague to speak to applicability in any domain. There is no proven or empirically demonstrated exponential speedup on any simulation problem with known commercial applications.



This paper claims quantum computer can integrate arbitrary non-linear differential equations with quantum advantage:

https://arxiv.org/pdf/2011.06571.pdf

It does seems too good to be true.


I found a layman's explanation at Quanta Magazine: https://www.quantamagazine.org/new-quantum-algorithms-finall...

The two caveats are

1. Only works for "mildly" nonlinear equations

2. Results are in quantum world and have to be translated back into normal deterministic world results, and this hasn't been figured out yet




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