What cannot be learned in the quantum universe?

Recent advances have significantly enhanced our understanding of what can be efficiently learned in the quantum universe. However, certain fundamental aspects remain resistant to efficient learning using known algorithms. This talk explores several of fundamental properties—including time, causal structure, topological order, and noise—and demonstrates how they can be provably hard to learn. These results stem from our recent work on how to construct random unitaries (with Ma, forthcoming) and generate them in extremely low depth (with Schuster and Haferkamp, arXiv:2407.07754). Examining these "unlearnable" aspects of our world sheds light on the fundamental limits of scientific inquiry in the quantum realm.