Phase transitions in the classical simulability of open quantum systems

• Published in: Scientific reports Vol. 13; no. 1; p. 8866
• Main Authors: Azad, F., Hallam, A., Morley, J., Green, A. G.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 31.05.2023; Nature Publishing Group; Nature Portfolio
• Subjects: 639/705; 639/766; Friction; Humanities and Social Sciences; multidisciplinary; Open systems; Phase transitions; Science; Science (multidisciplinary)
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-023-35336-9

We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. 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. Moreover, if a quantum simulator is in this phase, it cannot simulate with quantum advantage.