> Schrodinger's eqn being linear has nothing to do with implementing non-linear functions.
Indeed. And it's possible SH is confused by this, since she had another video about quantum chaos in asteroids where similar observation applied and she didn't address that. However...
> There's no question about how you would implement the said logic in a quantum computer - you can just do what the classical implementation does. Yeah we don't have nowhere enough qubits and it would be a gross waste of resources, but we _do_ know how to do it. Saying they don't know how to do it is a false statement at best.
Here you're being a little uncharitable. Indeed theoretically one could make the quantum computer simulate the classical computer with the non-linear weather algorithm. But the interesting point Mrs. Hossenfelder may be making here is there is no known way to make quantum computers calculate/simulate the weather evolution in a "quantum computer way", that is, not simulating discrete-state classical computer which would be wasteful and most probably not with advantage, but realizing the differential equation evolution in analog mode, using the quantum superposition capabilities. That is not known to be possible. Quantum computer may be an analog computer (continuous evolution of state), but it is not clear how to use it to integrate interesting sets of differential equations like weather models.
This paper has a very interesting claim, that they can integrate arbitrary non-linear differential equations on quantum computer, with advantage. If their analysis is correct, this makes the case for weather prediction on quantum computers much stronger.
Indeed. And it's possible SH is confused by this, since she had another video about quantum chaos in asteroids where similar observation applied and she didn't address that. However...
> There's no question about how you would implement the said logic in a quantum computer - you can just do what the classical implementation does. Yeah we don't have nowhere enough qubits and it would be a gross waste of resources, but we _do_ know how to do it. Saying they don't know how to do it is a false statement at best.
Here you're being a little uncharitable. Indeed theoretically one could make the quantum computer simulate the classical computer with the non-linear weather algorithm. But the interesting point Mrs. Hossenfelder may be making here is there is no known way to make quantum computers calculate/simulate the weather evolution in a "quantum computer way", that is, not simulating discrete-state classical computer which would be wasteful and most probably not with advantage, but realizing the differential equation evolution in analog mode, using the quantum superposition capabilities. That is not known to be possible. Quantum computer may be an analog computer (continuous evolution of state), but it is not clear how to use it to integrate interesting sets of differential equations like weather models.