Model-Independent Simulation Complexity of Complex Quantum Dynamics

We present a model-independent measure of dynamical complexity based on simulation of complex quantum dynamics using stroboscopic Markovian dynamics. Tools from classical signal processing enable us to infer the Hilbert space dimension of the complex quantum system evolving under a time-independent Hamiltonian via pulsed interrogation. We illustrate this using simulated third-order pump-probe spectroscopy data for exciton transport in a toy model of a coupled dimer with vibrational levels, revealing 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 model-independent inferences that are commensurate with model-specific ones, including the estimation of the fewest number of parameters needed to fit the experimental data and identifying the spatial extent, i.e., delocalization size, of quantum states participating in this complex quantum dynamics.