4. Conclusions

The HEOM approach is now available in the modular open-source Libra software, starting from the version v4.8.1. This version is available at the Zenodo server42 as well as from the Quantum Dynamics Hub GitHub Libra software repository https://github.com/Quantum-Dynamics-Hub/libra-code. The current work provides a comprehensive account on the underlying theoretical foundations and terminology of the method, the key algorithms used, and the important implementation details and use guidance. The detailed examples to run the calculations presented in this work are available at the Zenodo server43 as well as from the GitHub data repository https://github.com/AkimovLab/Project_HEOM.
The present implementation features a user-friendly design of the Python-level modules for HEOM calculation, which shall facilitate the use of this method in Jupyter- or Python-based calculations. Our current implementation considers a number of acceleration features, such as using the scaled HEOM method, filtering the HEOM, using the concept of active equation lists, which are updated periodically to remove the propagation of ADMs when the ADM’s time derivatives are negligible. A nearly trivial OpenMP parallelization is incorporated in the step of computing ADM’s time-derivatives and leads to expected acceleration of the computations. We have provided examples of using the code for propagating reduced density matrices to describe quantum dynamics of open systems. We have illustrated the capabilities of the present HEOM implementation in computing spectral line shapes. We have provided a number of examples on the expected qualitative changes in the dynamics of quantum systems in response to variation of various properties of the bath. We have provided some computational scalability and execution time benchmarks to guide the potential users of this software in feasibility of various types of calculations.