  Physical modeling closes the gap between perception in terms of measurements
and abstraction in terms of theoretical models. Physical modeling is a major
objective in physics and is generally regarded as a creative process. How good
are computers at solving this task? This question is both of philosophical and
practical interest because a positive answer would allow an artificial
intelligence to understand the physical world. Quantum mechanics is the most
fundamental physical theory and there is a deep belief that nature follows the
rules of quantum mechanics. Hence, we raise the question whether computers are
able to learn optimal quantum models from measured data. Here we show that in
the absence of physical heuristics, the inference of optimal quantum models
cannot be computed efficiently (unless P = NP). This result illuminates
rigorous limits to the extent to which computers can be used to further our
understanding of nature.
