  We present a model-independent measure of dynamical complexity based on
simulating complex quantum dynamics using stroboscopic Markovian dynamics.
Tools from classical signal processing enable us to infer the Hilbert space
dimension of a complex quantum system evolving under a time-independent
Hamiltonian via pulsed interrogation. We evaluate our model-independent
simulation complexity (MISC) for the spin-boson model and simulated third-order
pump-probe spectroscopy data for exciton transport in coupled dimers with
vibrational levels. The former provides insights into coherence and population
dynamics in the two-level system while the latter reveals the dimension of the
singly-excited manifold of the dimer. Finally, we probe the complexity of
excitonic transport in light harvesting 2 (LH2) and Fenna-Matthews-Olson (FMO)
complexes using data from two recent nonlinear ultrafast optical spectroscopy
experiments. For the latter we make some model-independent inferences that are
commensurate with model-specific ones. This includes estimating the fewest
number of parameters needed to fit the experimental data and identifying the
spatial extent, i.e., delocalization size, of quantum states occurring in this
complex quantum dynamics.
