  Family-Vicsek scaling is one of the most essential scale-invariant laws
emerging in surface-roughness growth of classical systems. In this Letter, we
theoretically elucidate the emergence of the Family-Vicsek scaling even in a
strongly interacting quantum bosonic system by introducing a surface-height
operator. This operator is comprised of a summation of local particle-number
operators at a simultaneous time, and thus the observation of the surface
roughness in the quantum many-body system and its scaling behavior are
accessible to current experiments of ultracold atoms.
