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This research introduces a stochastic unravelling method that preserves weak permutation symmetry for systems of N emitters coupled to common modes, significantly reducing computational costs from O(N^5) to O(N). By enabling efficient large-N simulations even for d-level systems like qutrits (d=3), the work expands the feasible scale for modeling exact quantum dynamics in complex many-body setups.
Permutation-symmetric quantum trajectories
arXiv:2605.11103v3 Announce Type: replace Abstract: We show how one may perform a stochastic unravelling which respects weak permutation symmetry for general models of $N$ emitters coupled to a common system (e.g. a cavity mode). Our work extends prior work by Zhang et al. [2018 New J. Phys. 20 112001] which provided an efficient quantum jump approach for a restricted subset of such problems. For problems involving $2$-level emitters, such an unravelling reduces the computational cost from $\mathcal{O}(N^5)$ to $\mathcal{O}(N^2)$, and with additional refinements, allows reduction to $\mathcal{O}(N)$. This significantly increases the range of system sizes for which one can model exact quantum dynamics of such systems. We further show how the method can also be applied to $d$-level systems, with computational effort scaling as $\mathcal{O}(N^{d(d-1)/2})$, and we show it allows large-$N$ simulations for $d=3$.
Abstract:We show how one may perform a stochastic unravelling which respects weak permutation symmetry for general models of $N$ emitters coupled to a common system (e.g. a cavity mode). Our work extends prior work by Zhang et al. [2018 New J. Phys. 20 112001] which provided an efficient quantum jump approach for a restricted subset of such problems. For problems involving $2$-level emitters, such an unravelling reduces the computational cost from $\mathcal{O}(N^5)$ to $\mathcal{O}(N^2)$, and with additional refinements, allows reduction to $\mathcal{O}(N)$. This significantly increases the range of system sizes for which one can model exact quantum dynamics of such systems. We further show how the method can also be applied to $d$-level systems, with computational effort scaling as $\mathcal{O}(N^{d(d-1)/2})$, and we show it allows large-$N$ simulations for $d=3$.
Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Gases (cond-mat.quant-gas)
arXiv:2605.11103 [quant-ph]
(or arXiv:2605.11103v3 [quant-ph] for this version)
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