  We numerically investigate the scaling properties of a one-dimensional
driven-dissipative condensate described by a stochastic complex Ginzburg-Landau
equation (SCGLE). We directly extract the static and dynamical scaling
exponents from the dynamics of the condensate's phase field, and find that both
coincide with the ones of the one-dimensional Kardar-Parisi-Zhang (KPZ)
equation. We furthermore calculate the spatial and the temporal two-point
correlation functions of the condensate field itself. The decay of the temporal
two-point correlator assumes a stretched-exponential form, providing further
quantitative evidence for an effective KPZ description. Moreover, we confirm
the observability of this non-equilibrium scaling for typical current
experimental setups with exciton-polariton systems, if cavities with a reduced
$Q$ factor are used.
