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

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.