Permutation-symmetric quantum trajectories
Elliot W. Lloyd, Aleksandra A. Ziolkowska, Jonathan Keeling
TLDR
This paper introduces a permutation-symmetric stochastic unraveling method, drastically reducing the computational cost for modeling N-emitter quantum systems.
Key contributions
- Introduces a stochastic unraveling method respecting weak permutation symmetry for N-emitter systems.
- Reduces computational cost for 2-level emitters from O(N^5) to O(N^2), or O(N) with refinements.
- Extends method to d-level systems, achieving O(N^(d(d-1)/2)) scaling.
- Enables large-N simulations for d=3 systems, significantly expanding modelable system sizes.
Why it matters
This method significantly expands the range of system sizes for which exact quantum dynamics can be modeled. It makes previously intractable large-N simulations feasible, advancing our ability to study complex quantum systems.
Original 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.
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