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This research demonstrates that BosonSampling remains classically simulable in polynomial time whenever a constant fraction of photons survive, significantly expanding the known limits where quantum advantage is provably unattainable. By bridging the gap between theoretical models and experimental realities like linear photon loss, the study provides a crucial benchmark for assessing the robustness of near-term photonic quantum devices.
Polynomial-Time Classical Simulation of BosonSampling under Any Constant-Fraction Photon Loss
arXiv:2610.27065v1 Announce Type: new Abstract: Understanding how photon loss changes the classical complexity of BosonSampling is central to assessing the robustness of near-term photonic quantum advantage. In this work, we present a polynomial-time classical simulation algorithm for lossy BosonSampling that applies whenever a constant fraction of the input photons survives. We consider the standard fixed-loss model, where $N$ input photons propagate through an $M$-mode interferometer and exactly $N-n$ photons are lost uniformly at random, leaving $n$ surviving photons at the output. For any constant surviving fraction $n/N\in(0,1)$, the algorithm samples from a distribution within total variation distance $\varepsilon$ of the fixed-loss BosonSampling distribution with probability at least $1-\delta$ over Haar-random interferometers, in time $\operatorname{poly}(M,N,\varepsilon^{-1},\delta^{-1})$. We further extend the fixed-loss analysis to the uniform-transmission-loss model and obtain analogous polynomial-time simulability for any fixed transmission rate $\eta\in(0,1)$. These results substantially extend the known provably simulable regime of $n=O(\sqrt{\varepsilon N})$ surviving photons or $\eta=O(\sqrt{\varepsilon/N})$ transmission rate, and demonstrate that even the experimentally relevant linear-survival regime can admit efficient classical simulation under the conditions considered here.
Abstract:Understanding how photon loss changes the classical complexity of BosonSampling is central to assessing the robustness of near-term photonic quantum advantage. In this work, we present a polynomial-time classical simulation algorithm for lossy BosonSampling that applies whenever a constant fraction of the input photons survives. We consider the standard fixed-loss model, where $N$ input photons propagate through an $M$-mode interferometer and exactly $N-n$ photons are lost uniformly at random, leaving $n$ surviving photons at the output. For any constant surviving fraction $n/N\in(0,1)$, the algorithm samples from a distribution within total variation distance $\varepsilon$ of the fixed-loss BosonSampling distribution with probability at least $1-\delta$ over Haar-random interferometers, in time $\operatorname{poly}(M,N,\varepsilon^{-1},\delta^{-1})$. We further extend the fixed-loss analysis to the uniform-transmission-loss model and obtain analogous polynomial-time simulability for any fixed transmission rate $\eta\in(0,1)$. These results substantially extend the known provably simulable regime of $n=O(\sqrt{\varepsilon N})$ surviving photons or $\eta=O(\sqrt{\varepsilon/N})$ transmission rate, and demonstrate that even the experimentally relevant linear-survival regime can admit efficient classical simulation under the conditions considered here.
arXiv:2610.27065 [quant-ph]
(or arXiv:2610.27065v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.27065 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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