  We present an empirical analysis of the scaling of the minimal quantum
circuit depth required for a variational quantum simulation (VQS) method to
obtain a solution to the time evolution of a quantum system within a predefined
error tolerance. In a comparison against a non-variational method based on
Trotterized time evolution, we observe a better scaling of the depth
requirements using the VQS approach with respect to both the size of the system
and the simulated time. Results are also put into perspective by discussing the
corresponding classical complexity required for VQS. Our results allow us to
identify a possible advantage region for VQS over Trotterization.
