Could nonlinear quantum mechanics be found by future quantum computers? How could working quantum computers test if nonlinear quantum mechanics or another nonlinear theory is at work at deeper levels or fundamental level?
 A: This is hard to say. Given that nonlinearities would be interpreted at first as a broken computer, presumably the answer would require many different quantum computers based on different technologies running into similar barriers vis-a-vis their quantum coherence times and the delicacy of their operations. By collecting many different physical systems with apparently the same boundary, you would start to get the idea that it's not just one physical realization of quantum mechanics that needs a more complicated model, but rather that you have found a deeper mystery which has an effective theory that is linear for typical quantum regimes, but becomes nonlinear in some corner case.
Fortunately there are lots of different proposals for quantum computers, unfortunately they're all kind of mediocre. When quantum computing breaks out it will probably be just one of these technologies passing a certain cost-benefit threshold and edging all of the others out of the market within a few decades. So we're speculating on something that would have to be a century or two off or so, even if quantum computing really “lands” in the next few decades. Maybe that is pessimistic, but given that we're 70 or 80 years into the silicon revolution and everyone is still talking the silicon silicon silicon, I think it's realistic.
A: No. Models are not fundamental. A quantum computer can, in the end, tell you only about the properties of the model it computes. It cannot tell you whether that corresponds to reality. You need an experiment.
A: In principle yes. If the computer relies on a given linear model to work as expected, and we find it behaves strangely, then the computer has found nonlinear quantum behaviour.
A: The computational model used in a quantum computer has no bearing to how quantum mechanics work, just like a computer made from solid state transistors is no tool for exploring solid state states and transitions.
It may be suited better for juggling the kind of computational tasks required to model quantum mechanical processes, but that does not provide insights into quantum mechanical processes.
The only means to discover quantum mechanical novelties is when the computer is regularly returning results inconsistent with the expectations of its implementation, just like randomly flipped bits in a classic computer may tell of its susceptibility to cosmic radiation.
