Measuring entanglement and learning noise with emergent randomness

Randomness has long been employed to characterize quantum computers with techniques like randomized benchmarking and random circuit sampling, but it is not clear how such ideas apply to the more general setting of analog quantum simulators. Here we discover time-independent Hamiltonian dynamics are far more random than they first appear by uncovering the emergence of random state ensembles hidden in the time-evolution or partial measurement of generic quantum systems. Using these findings, we import techniques for fidelity estimation from random circuit sampling for systems of up to 60 atoms with a Rydberg analog quantum simulator, reaching a regime that challenges state-of-the-art classical computers. As concrete applications of these techniques, we estimate the actual experimental mixed state entanglement entropy, and show how to learn nearly-arbitrary noise models affecting quantum systems. In total, our results reveal the hidden similarities between quantum simulators and computers, and uncover concrete means of improving near- and far-term controlled quantum systems.