# Optimized auxiliary oscillators for the simulation of general open quantum systems

## TL;DR

This paper introduces a systematic method to construct few-body damped harmonic oscillator networks that accurately simulate general bosonic environments in open quantum systems, enabling efficient and flexible modeling of non-Markovian effects.

## Contribution

The paper presents a novel algorithm for designing effective oscillator networks that replicate complex environments with controlled error, applicable to a wide range of open quantum systems.

## Key findings

- Accurately reproduces environment effects with few oscillators
- Enables efficient simulation of non-Markovian dynamics
- Applicable at arbitrary temperatures, including zero

## Abstract

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly non-perturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present a study based on current research in the context of coherent transport in biological aggregates as a more realistic example of its use; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.