Model-Independent Simulation Complexity of Complex Quantum Dynamics

TL;DR

This paper introduces a model-independent measure of quantum dynamical complexity using classical signal processing, applied to various quantum systems to infer their Hilbert space dimensions and quantum state properties.

Contribution

It develops a novel, model-independent method to quantify quantum dynamical complexity and applies it to multiple complex quantum systems, including light-harvesting complexes.

Findings

Successfully inferred Hilbert space dimensions of quantum systems.

Estimated the delocalization size of quantum states in biological complexes.

Provided model-independent insights consistent with traditional model-based analyses.

Abstract

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.