I believe that she was using the term "linear" in the computational/signal processing sense, not that of computing.
In electronics, in a linear system, you can decompose a complex waveform and analyze its response to each frequency discretely, and when you recompose them, you get a correct answer.
In a non-linear system, such as a mixer, no such analysis is possible, you have to consider all of the frequencies, and their levels at the same time.
Also consider that most algorithms are founded on a deterministic computational method.
I believe the point is that quantum computers allow you to manipulate a linear combination of bits, whereas simulating the weather would require non-linear combinations. It's unclear how a QC would help simulate something like that better than a classical computer.
Quantum algorithms are nonlinear. If someone is saying "quantum mechanics is a linear theory" as a counterargument to anything QC related. Then that person has no idea what they are talking about. Because they likely never cared to learn event the basics of QC.
"New Quantum Algorithms Finally Crack Nonlinear Equations. Two teams found different ways for quantum computers to process nonlinear systems by first disguising them as linear ones."
In electronics, in a linear system, you can decompose a complex waveform and analyze its response to each frequency discretely, and when you recompose them, you get a correct answer.
In a non-linear system, such as a mixer, no such analysis is possible, you have to consider all of the frequencies, and their levels at the same time.
Also consider that most algorithms are founded on a deterministic computational method.