# BoFiN-HEOM: HEOM solver for Bosonic and Fermionic systems¶

BoFiN-HEOM is a “Hierarchical Equations of Motion” solver for quantum systems coupled to Bosonic or Fermionic environments. The HEOM method was originally developed by Tanimura and Kubo [Tanimura_1989] .

BoFiN-HEOM is designed to be as generic as possible. It relies on the QuTiP package, and is provided in two versions :

• BoFiN : Pure Python version of the HEOM solver. Has a BosonicHEOMSolver and FermionicHEOMSolver class. It can be found here .
• BoFiN-fast : Hybrid C++ - Python version, of the HEOM solver. Here the backend for RHS construction of the HEOM solver written in C++. It is otherwise completely identical (both in user interface and functionality) to the pure Python version. It can be found here .

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.

The provided example notebooks explain some common choices of environmental parameterization. See Installation Instructions for details on how to set up both versions.