Learning optimal quantum models is NP-hard

TL;DR

This paper proves that learning optimal quantum models from data is computationally intractable (NP-hard), highlighting fundamental limits on AI's ability to fully understand physical systems through quantum modeling.

Contribution

It establishes the NP-hardness of inferring optimal quantum models, showing that without heuristics, this task cannot be efficiently solved by computers.

Findings

Optimal quantum model inference is NP-hard.

Computational limits restrict AI's capacity to fully learn quantum models.

No efficient algorithms are likely to exist for this task without heuristics.

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.