  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.
