Phase Transitions in the Classical Simulability of Open Quantum Systems

TL;DR

This paper investigates how increasing environmental coupling and temperature induce a phase transition in open quantum systems, leading to classical simulability due to entanglement saturation, limiting quantum computational advantages.

Contribution

It introduces a phase transition framework for classical simulability of open quantum systems based on entanglement saturation in Langevin unravellings.

Findings

Entanglement saturates at high environmental coupling and temperature.

Classical simulation becomes feasible for all times beyond the transition.

Limits the quantum advantage in simulating open quantum systems.

Abstract

We study the evolution of an open quantum system using a Langevin unravelling of the density matrix evolution over matrix product states. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian open system counterpart of the saturation in entanglement found in random circuits with projective or weak measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects.