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

TL;DR

TENSO is an open-source software that enables numerically exact simulations of open quantum system dynamics in complex environments using an efficient tree tensor network approach, applicable to chemistry and quantum information science.

Contribution

It introduces a versatile software package that implements an efficient tree tensor network decomposition of HEOM for exact quantum dynamics simulations in structured environments.

Findings

Allows for non-Markovian quantum dynamics simulations with complex environments.

Supports time-dependent drives and non-commuting fluctuations.

Provides fixed-rank and adaptive-rank propagation methods.

Abstract

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 curbs 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 non-commuting 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 multi-layer 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. 163, 104109 (2025)] the focus here is on the practical usage and applications of TENSO with underlying theoretical concepts introduced only as needed.