Learning optimal quantum models is NP-hard

Abstract

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.