Application of machine learning techniques to the description of open quantum systems.

Abstract

This work focuses on using classical machine learning (ML) models to study the quantum dynamics of excitation energy transfer (EET) within strongly coupled open quantum systems relevant to light harvesting complexes (LHCs). Direct evidence for long-lived quantum coherence has been found to play an important role in EET processes during the first step of photosynthesis in certain LHCs where excitation energy is transmitted from the antenna pigments to the reaction center in which photochemical reactions are initiated [1–3]. The numerically exact method used to simulate the dynamics in this work is the hierarchical equations of motion (HEOM) adapted by Ishizaki and Fleming to suit the quantum biological regime [4–6]. In the case of an open quantum system, such as a photosynthetic pigment-protein complex, evolving over time we can generate a set of time dependent observables that depict the coherent movement of electronic excitations through the system by solving a suitable set of quantum dynamic equations such as the HEOM. We have focused on solving two problems, the first being the inverse problem. That is, the objective is to determine whether a trained ML model can perform Hamiltonian tomography by using the time dependence of the observables as inputs. We demonstrate the capability of the convolutional neural network (CNN) to solve the inverse problem. That is, the trained CNN can accurately describe the system under study by predicting the parameters of the system Hamiltonian when given the aforementioned time dependent data. The models developed can predict Hamiltonian parameters such as excited state energies and inter-site couplings of a system up to 99.28% accuracy. The second use of the same data set of observables involves time-series analysis. Although various analytical solutions for the dynamics of open quantum systems such as the HEOM have been developed, these often require immense computational resources. We demonstrate that models such as SARIMA, CatBoost, Prophet, convolutional and recurrent neural networks can predict the long-time dynamics provided that the initial short-time dynamics is given. Our results suggest that SARIMA can serve as a computationally inexpensive yet accurate way to predict long-time dynamics.