Open Quantum Dynamics Calculations with the Hierarchy Equations of Motion on Parallel Computers

TLDR

Calculating the evolution of an open quantum system in contact with a thermal environment has long been a theoretical and computational challenge, but the hierarchy equations of motion offer a powerful yet underutilized model that can now be tackled thanks to modern supercomputers with large memory and many processors. The study introduces PHI, a quantum dynamics software that solves the hierarchy equations of motion. PHI leverages concurrent processing on parallel computers, employing a specialized integrator to solve the hierarchy equations of motion for biological‑scale systems. PHI achieves strong scaling and high efficiency on large parallel machines, as demonstrated by simulating 50‑pigment excitation transfer between LH1 and LH2 complexes in purple photosynthetic bacteria.

Abstract

Calculating the evolution of an open quantum system—i.e., a system in contact with a thermal environment—has presented a theoretical and computational challenge for many years. With the advent of supercomputers containing large amounts of memory and many processors, the computational challenge posed by the previously intractable theoretical models can now be addressed. The hierarchy equations of motion present one such model and offer a powerful method that has remained underutilized so far, because of its considerable computational expense. By exploiting concurrent processing on parallel computers, the hierarchy equations of motion can be applied to biological-scale systems. Herein, we introduce the quantum dynamics software PHI that solves the hierarchical equations of motion. We describe the integrator employed by PHI and demonstrate PHI's scaling and efficiency running on large parallel computers by applying the software to the calculation of intercomplex excitation transfer between the light-harvesting complexes 1 (LH1) and 2 (LH2) of purple photosynthetic bacteria, which involves a 50-pigment system.