Perovskites-compounds with the CaTiO3-type crystal structure-show outstanding performance in photovoltaics and multiparameter optical emitters due to their large oscillator strength, strong solar absorption, and excellent charge-transport properties. However, the ability to realize and control many-body quantum states in perovskites, which would extend their application from classical optoelectronic materials to ultrafast quantum operation, remains an open research topic. Here, we generate a cooperative quantum state of excitons in a quantum dot ensemble based on a lead halide perovskite, and we control the ultrafast radiation of excitonic quantum ensembles by introducing optical microcavites. The stimulated radiation of excitonic quantum ensemble in a superlattice microcavity is demonstrated to not be limited by the classical population-inversion condition, leading to a picosecond radiative duration time to dissipate all of the in-phase dipoles. Such a perovskite-assembly superlattice microcavity with a tunable radiation rate promises potential applications in ultrafast, photoelectric-compatible quantum processors.