Permutation-symmetric quantum trajectories

TL;DR

This paper introduces a permutation-symmetric stochastic unraveling method for quantum models with N emitters, significantly reducing computational costs and enabling large-N simulations for complex systems.

Contribution

The authors develop a new stochastic unraveling technique that respects permutation symmetry, drastically lowering computational complexity for modeling quantum dynamics.

Findings

Reduces computational cost from O(N^5) to O(N^2) for 2-level emitters.

Further refinements lower complexity to O(N), enabling larger system simulations.

Extends the method to d-level systems with complexity O(N^{d(d-1)/2}), allowing large-N simulations for d=3.

Abstract

We show how one may perform a stochastic unraveling which respects weak permutation symmetry for models of $N$ emitters coupled to a common system (e.g. a cavity mode). 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.