# Role of Quantum Information in HEOM Trajectories

## TL;DR

This paper explores how quantum information flows in open systems, helping reduce computational costs while maintaining accuracy.

## Contribution

The study introduces a method to truncate hierarchical equations of motion based on information flow analysis.

## Key findings

- ADOs sharing a common Matsubara axis behave similarly.
- Truncating hierarchies reduces computation time without losing qualitative accuracy.

## Abstract

Open quantum systems
often operate in the non-Markovian regime
where a finite history of a trajectory is intrinsic to its evolution.
The degree of non-Markovianity for a trajectory may be measured in
terms of the amount of information flowing from the bath back into
the system. In this study, we consider how information flows through
the auxiliary density operators (ADOs) in the hierarchical equations
of motion. We consider three cases for a range of baths, underdamped,
intermediate, and overdamped. By understanding how information flows,
we are able to determine the relative importance of different ADOs
within the hierarchy. We show that ADOs sharing a common Matsubara
axis behave similarly, while ADOs on different Matsubara axes behave
differently. Using this knowledge, we are able to truncate hierarchies
significantly, thus reducing the computation time, while obtaining
qualitatively similar results. This is illustrated by comparing 2D
electronic spectra for a molecule with an underdamped vibration subsumed
into the bath spectral density.