  Nonequilibrium dynamics of many-body systems is challenging for classical
computing, providing opportunities for demonstrating practical quantum
computational advantage with analogue quantum simulators. It is proposed to be
classically intractable to sample driven thermalized many-body states of
Bose-Hubbard systems, and further extract multi-point correlations for
characterizing quantum phases. Here, leveraging dedicated precise manipulations
and number-resolved detection through a quantum gas microscope, we implement
and sample a 32-site driven Hubbard chain in the thermalized phase. Multi-point
correlations of up to 14th-order extracted from experimental samples offer
clear distinctions between the thermalized and many-body-localized phases. In
terms of estimated computational powers, the quantum simulator is comparable to
the fastest supercomputer with currently known best algorithms. Our work paves
the way towards practical quantum advantage in simulating Floquet dynamics of
many-body systems.
