Maybe we have to agree to disagree. While each node within a neural net is effected in conventional code, the overall result is far from linear.
Linear systems require essentially closed-form solutions, with the programmer building the system to take account of all possible options, and required to know those outcomes before building the system.
The neural net uses the multiple training data across a series of nodes to identify patterns that were previously non-obvious. That seems to me to be non-linear.
As for qunatum computing - I fail to see how nayone could see that as linear. Yes, the box of tricks needs programming using conventional code, but the outcome of simultaneously exploring all possible states is as non-linear as you can get.
What you are really saying (it seems to me) is that anything coded in a conventional linear language is, by definition linear, only because those languages are linear. And in fact, any high-level language will have to be linear because it needs to be parsed down to machine code by the OS.
Thus, you seem to be saying, that any piece of high-level code produces a linear result and therefore only is suited to linear processes.
I don't accept that assumption, but as I said, I think we'll have to agree to differ on that one.