BoFiN-HEOM (C++ version) : A Bosonic and Fermionic hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics

Neill Lambert, Tarun Raheja, Shahnawaz Ahmed, Alexander Pitchford, Franco Nori

Abstract

The “hierarchical equations of motion” (HEOM) method is a powerful numerical approach to solve the dynamics and steady-state of a quantum system coupled to a non-Markovian and non-perturbative environment. Originally developed in the context of physical chemistry, it has also been extended and applied to problems in solid-state physics, optics, single-molecule electronics,and biological physics. Here we present a numerical library in Python, integrated with the powerful QuTiP platform, which implements the HEOM for both Bosonic and Fermionic environments. Wedemonstrate it’s utility with a series of examples. For the Bosonic case, we present examples for fitting arbitrary spectral densities, modelling a Fenna-Matthews-Olsen photosynthetic complex,and simulating dynamical decoupling of a spin from its environment. For the Fermionic case, we present an integrable single-impurity example, used as a benchmark of the code, and a more complex example of an impurity strongly coupled to a single vibronic mode, with applications in single-molecule electronics.

C++ HEOM Solver

We have developed two packaged versions of the HEOM solver :

• BoFiN : Pure Python version of the HEOM solver. Has a BosonicHEOMSolver and FermionicHEOMSolver.
• BoFiN-Fast : Hybrid C++ - Python version, with backend for RHS construction of the HEOM solver written in C++. Otherwise completely identical in user interface and functionality to the pure Python version.

This repository contains the hybrid Python-C++ version of the solver. It should be noted that the C++ version dramatically speeds up RHS construction, with respect to the Python version. We have noted more than 10x speedup using the C++ version for some hard Fermionic HEOM problems.

OTHER VERSION

The pure Python solver can be found here : https://github.com/tehruhn/bofin

Installing dependencies & setting up

For uniformity across platforms, we recommend using Conda environments to keep the setup clean, and to install dependencies painlessly (since pip install is known to have issues on Mac OS). Once you have Conda installed, make a fresh Python 3 environment called bofin_env, and then switch to it :

conda create -n bofin_env python=3.8
conda activate bofin_env

In your bofin_env environment, install requirements using :

conda install numpy scipy cython
conda install -c conda-forge qutip

This will ensure painless setup across Windows, Linux and Mac OS.

Installing the BoFiN-HEOM package

Clone the repository using git clone.

Once you have the dependencies installed, from the parent repository folder, run the following commands :

python3 setup.py build_ext --inplace
pip3 install -e .

This installs the hybrid Python - C++ version of the HEOM solvers. These are identical in usage and functionality to the Python solvers.

Usage example

# import the hybrid Python - C++ Bosonic HEOM Solver
from bofinfast.heom import BosonicHEOMSolver as BosonicHEOMSolverCPP

Documentation

The documentation can be found at https://bofin-heom.readthedocs.io/en/main/ .

Example notebooks

There are several example notebooks illustrating usage of the code, in the examples folder. Note how RHS constuction is much faster in pure C++.