Ultracold atoms in optical lattices have been successfully used as analog quantum simulators for Hubbard-type models. In particular, it has been established that they can exhibit better performance for non-equilibrium dynamics in generic systems than numerical simulations with classical computers. Nevertheless, since those quantum simulators are analog, comparison with theories is essential in order to make simulated results reliable. In this talk, I will report recent development of ultracold-atom quantum simulators at Kyoto University especially from a theoretical viewpoint. Specifically, I focus on the Bose-Hubbard system, and discuss dynamics subjected to a sudden quench across the quantum phase transition from a Mott insulator to a superfluid  and effects of the two-body loss on the transition .
 Y. Takasu et al., in preparation.
 T. Tomita et al., Science Adv. 3, e1701513 (2017).