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The quantum many-body systems give us a rich field which potentially yields unexpected phenomena. Especially, their dynamics have attracted much attention due to the recent progress of the experimental realizations. The striking examples are the quantum computations since both of the quantum annealing and the gate-type quantum devices can be regarded as the controlled dynamics of the quantum many-body systems. In this talk, I would like to discuss our recent studies on the dynamics for quantum many-body systems, including the photo-induced superconductivity as well as the simulations of the gate-type quantum computations.