  Whether noisy quantum devices without error correction can provide quantum
advantage over classical computers is a critical issue of current quantum
computation. In this work, the random quantum circuits, which are used as the
paradigm model to demonstrate quantum advantage, are simulated with
depolarizing noise on experiment relevant two-dimensional architecture. With
comprehensive numerical simulation and theoretical analysis, we find that the
maximum achievable operator entanglement entropy, which indicates maximal
simulation cost, has area law scaling with the system size for constant noise
rate. On the other hand, we also find that the maximum achievable operator
entanglement entropy has power law scaling with the noise rate for fixed system
size, and the volume law scaling can be obtained only if the noise rate
decreases when system size increase.
