We discuss universal fluctuations that arise from natural quantum many-body dynamics. These fluctuations are unique to the statistics of global bitstring measurements and have been used in random circuit sampling tasks for recent quantum advantage claims. Based on such fluctuations, I will introduce a sample-efficient protocol which estimates the fidelity between an experimentally prepared state and an ideal target state, and is applicable to a wide class of analog quantum simulators. Finally, we apply this protocol in a 60-atom analog Rydberg quantum simulator, and further use our results to quantify the amount of mixed state entanglement present, finding that the experiment is competitive in this respect with state-of-the-art digital quantum devices performing random circuit evolution.
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