Machine learning for Hamiltonian tomography of photosynthetic excitation energy transfer complexes*

Classical machine learning (ML) models are used to study the quantum dynamics of excitation energy transfer (EET) within light harvesting complexes (LHCs). The numerically exact method used to simulate the dynamics is the hierarchical of equations of motion (HEOM) [2-4]. 

 

In the process of an open quantum system, such as a LHCs, 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 the HEOM. We have focused on solving the inverse problem. That is, to determine whether a trained ML model can perform Hamiltonian tomography by using the time dependence of the observables as inputs.

 

We explicitly solve the HEOM to generate training and testing datasets for supervised ML tasks where elements of reduced density matrices are translated into features for the model and corresponding excited state energies and electronic couplings of the Frenkel Hamiltonian are used as labels. The parameters of the Hamiltonians were sampled around the same order of magnitude as those that are typical of LHCs. The developed models have been able to make predictions with up to 99.28% accuracy [5]. 

 

[1] G. S. Engel et al., Nature, 446, 782 (2007)

[2] Y. Tanimura, J. Chem. Phys., 153, 020901 (2020)

[3] Y. Tanimura and R. Kubo, J. Phys. Soc. Jap., 58, 1199 (1989)

[4] A. Ishizaki and G. R. Fleming, J. Chem. Phys., 130, 234111 (2009)

[5] K. Naicker, I. Sinayskiy and F. Petruccione, Phys. Rev. R., 4, 033175 (2022)