# Direct probing of the simulation complexity of open quantum many-body dynamics

## TL;DR

This paper investigates the computational complexity of simulating open quantum many-body systems, revealing how dissipation influences correlation length, mixing time, and the disparity between quantum and classical simulation resources.

## Contribution

It provides a detailed analysis of how dissipation affects the complexity of open quantum system simulations, highlighting differences between quantum and classical methods.

## Key findings

- Dissipation impacts correlation length and mixing time differently over time.
- Classical tensor network complexity does not decrease with stronger dissipation.
- Quantum and classical resource scaling diverge in the presence of dissipation.

## Abstract

Simulating open quantum systems is key to understanding non-equilibrium processes, as persistent influence from the environment induces dissipation and can give rise to steady-state phase transitions. A common strategy is to embed the system-environment into a larger unitary framework, but this obscures the intrinsic complexity of the reduced system dynamics. Here, we investigate the computational complexity of simulating open quantum systems, focusing on two physically relevant parameters -- correlation length and mixing time -- and explore whether it can be comparable (or even lower) to that of simulating their closed counterparts. In particular, we study the role of dissipation in simulating open-system dynamics using both quantum and classical methods, where the classical complexity is characterised by the bond dimension and operator entanglement entropy. Our results show that dissipation affects correlation length and mixing time in distinct ways at intermediate and long timescales. Moreover, we observe numerically that in classical tensor network simulations, classical complexity does not decrease with stronger dissipation, revealing a separation between quantum and classical resource scaling.