  There are several different proposals, relating holographic complexity to the
gravitational objects defined on the Wheeler-DeWitt patch. In this paper, we
investigate the evolution of complexity following a global quantum quench for
these proposals. We find that surprisingly they all reproduce known properties
of complexity, such as the switchback effect. However, each of these proposals
also has its own characteristic features during the dynamical evolution, which
may serve as a powerful tool to distinguish the various holographic duals of
complexity.
