TENSO: Software Package for Numerically Exact Open Quantum Dynamics Based on Efficient Tree Tensor Network Decomposition of the Hierarchical Equations of Motion.

TENSO is a versatile and powerful open-source software package for numerically exact simulations of the dynamics of quantum systems immersed in structured thermal environments. It is based on a tree tensor network decomposition of the hierarchical equations of motion (HEOM) that efficiently curtails its curse of dimensionality with bath complexity. As such, TENSO enables exact non-Markovian open-quantum-dynamics simulations even with complex environments typical of chemistry and quantum information science. TENSO allows for time-dependent drive in the system and for noncommuting fluctuations. More generally, TENSO efficiently propagates the dynamics for any method with a generator of the dynamics that can be expressed in a sum-of-products form, including the HEOM and multilayer multiconfigurational time-dependent Hartree methods. TENSO enables simulations using tensor trees and trains of arbitrary order and implements three propagation strategies for the coupled master equations: two fixed rank methods that require a constant memory footprint during the dynamics and one adaptive rank method with a variable memory footprint controlled by the target level of computational error. In contrast to the accompanying theory and algorithmic paper [ J. Chem. Phys.2025, 163, 104109. ], the focus here is on the practical usage and applications of TENSO with underlying theoretical concepts introduced only as needed.