A new theoretical framework shows that quantum sampling experiments with photons and fermions can be simulated on a classical computer in polynomial time whenever there is a nonzero total loss rate, however small. The result covers Fock-state boson sampling, Gaussian boson sampling with fixed uniform squeezing, and fermion sampling with magic inputs, achieving inverse-polynomial total variation error with high probability for Haar-random interferometers.

Sampling experiments are one of the main routes to demonstrating quantum computational advantage, but their robustness to experimental noise is still not well characterised. Earlier work had studied simulation bounds in specific regimes; the new approach unifies bosons and fermions under thermal loss — including pure loss as a special case — and covers both the dilute and saturated regimes of Fock-state boson sampling.

The method rests on a flatness assumption on the ideal output distribution. Under this milder condition, simulation is quasipolynomial even without Haar randomness; and with constant thermal loss per layer, the same assumption yields polynomial-time simulation up to logarithmic depth. A particularly notable result appears near full input filling: when only a bounded number of input modes remain empty, the noisy output distribution converges, as the number of modes grows, to a distribution independent of the interferometer.

The implications point to a stricter-than-expected limit on the advantage of photonic sampling architectures over classical simulation, since any nonzero experimental loss would suffice to bring the problem back into the classically tractable realm in the scenarios considered. The work also opens the way to studying which other noise models admit similar reductions and to pinning down which input or depth conditions genuinely preserve the hardness of quantum sampling.