Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance

TL;DR

This paper introduces an efficient numerical method leveraging permutational invariance to simulate open quantum systems with local and collective noise, enabling detailed study of collective phenomena robustness.

Contribution

The authors develop the Permutational-Invariant Quantum Solver (PIQS), an open-source Python library that significantly reduces computational complexity for simulating coupled spin-boson systems with local and collective dissipation.

Findings

Validated known collective quantum effects using PIQS

Extended analysis to local driven-dissipative scenarios

Assessed robustness of phenomena like spin squeezing and superradiance

Abstract

The permutational invariance of identical two-level systems allows for an exponential reduction in the computational resources required to study the Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of both local and collective noise. Here we take advantage of this speedup to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir. Assessing the robustness of collective effects against local dissipation is paramount to predict their presence in different physical implementations. We have developed an open-source library in Python, the Permutational-Invariant Quantum Solver (PIQS), which we use to study a variety of phenomena in driven-dissipative open quantum systems. We consider both local and collective incoherent processes in the weak, strong, and ultrastrong-coupling regimes. Using PIQS, we reproduced a series of known physical results concerning collective quantum effects and extended their study to the local driven-dissipative scenario. Our work addresses the robustness of various collective phenomena, e.g., spin squeezing, superradiance, quantum phase transitions, against local dissipation processes.