  The hierarchical equations of motion (HEOM) approach can describe the reduced
dynamics of a system simultaneously coupled to multiple bosonic and fermionic
environments. The complexity of exactly describing the system-environment
interaction with the HEOM method usually results in time-consuming calculations
and a large memory cost. Here, we introduce an open-source software package
called HierarchicalEOM.jl: a Julia framework integrating the HEOM approach.
HierarchicalEOM.jl features a collection of methods to compute bosonic and
fermionic spectra, stationary states, and the full dynamics in the extended
space of all auxiliary density operators (ADOs). The required handling of the
ADOs multi-indexes is achieved through a user-friendly interface. We exemplify
the functionalities of the package by analyzing a single impurity Anderson
model, and an ultra-strongly coupled charge-cavity system interacting with
bosonic and fermionic reservoirs. HierarchicalEOM.jl achieves a significant
speedup with respect to the corresponding method in the Quantum Toolbox in
Python (QuTiP), upon which this package is founded.
