Previous implementations

The current HEOM implementation in QuTiP is the latest in a succession of HEOM implementations by various contributors:


The original HEOM solver was implemented by Neill Lambert, Anubhav Vardhan, and Alexander Pitchford and is still available as qutip.nonmarkov.dlheom_solver.HSolverDL and only directly provided support for the Drude-Lorentz bath although there was the possibility of sub-classing the solver to implement other baths.

A compatible interface using the current implementation is available under the same name in qutip.nonmarkov.heom.HSolverDL.


BoFiN-HEOM (the bosonic and fermionic HEOM solver) was a much more flexible re-write of the original QuTiP HSolverDL that added support for both bosonic and fermionic baths and for baths to be specified directly via their correlation function expansion coefficients. Its authors were Neill Lambert, Tarun Raheja, Shahnawaz Ahmed, and Alexander Pitchford.

BoFiN was written outside of QuTiP and is can still be found in its original repository at

The construction of the right-hand side matrix for BoFiN was slow, so BoFiN-fast, a hybrid C++ and Python implementation, was written that performed the right-hand side construction in C++. It was otherwise identical to the pure Python version. BoFiN-fast can be found at

BoFiN also came with an extensive set of example notebooks that are available at

Current implementation

The current implementation is a rewrite of BoFiN in pure Python. It’s right-hand side construction has similar speed to BoFiN-fast, but is written in pure Python. Built-in implementations of a variety of different baths are provided, and a single solver is used for both fermionic and bosonic baths. Multiple baths of the same kind (either fermionic or bosonic) may be specified in a single problem, and there is good support for working with the auxiliary density operator (ADO) state and extracting information from it.

The code was written by Neill Lambert and Simon Cross.