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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., 18 pages, 14 figures

Featuring excellent coherence and operated parallelly, ultracold atoms in optical lattices form a competitive candidate for quantum computation. For this, a massive number of parallel entangled atom pairs have been realized in superlattices. However, the more formidable challenge is to scale-up and detect multipartite entanglement due to the lack of manipulations over local atomic spins in retro-reflected bichromatic superlattices. Here we developed a new architecture based on a cross-angle spin-dependent superlattice for implementing layers of quantum gates over moderately-separated atoms incorporated with a quantum gas microscope for single-atom manipulation. We created and verified functional building blocks for scalable multipartite entanglement by connecting Bell pairs to one-dimensional 10-atom chains and two-dimensional plaquettes of $2\times4$ atoms. This offers a new platform towards scalable quantum computation and simulation.