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Nonequilibrium dynamics of many-body systems is challenging for classicalcomputing, providing opportunities for demonstrating practical quantumcomputational advantage with analogue quantum simulators. It is proposed to beclassically intractable to sample driven thermalized many-body states ofBose-Hubbard systems, and further extract multi-point correlations forcharacterizing quantum phases. Here, leveraging dedicated precise manipulationsand number-resolved detection through a quantum gas microscope, we implementand sample a 32-site driven Hubbard chain in the thermalized phase. Multi-pointcorrelations of up to 14th-order extracted from experimental samples offerclear distinctions between the thermalized and many-body-localized phases. Interms of estimated computational powers, the quantum simulator is comparable tothe fastest supercomputer with currently known best algorithms. Our work pavesthe way towards practical quantum advantage in simulating Floquet dynamics ofmany-body systems.

Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System