I wasn't talking about non-linearity other than the one you mention. That should be abundantly obvious from what I posted.

You can't have quantum computation without measurement, and thus without non-linearity. Quantum computation is not simply "doing the computation in each possible world", it also is some trick to extract (collapse) the information into one particular world, and I don't think we currently understand fully what that means, but it's certainly non-linear. After all the information is often in the amplitude.

Conversely there are measurement based models for quantum computation that rely purely on the non-linear process.