Boson sampling is fragile to loss

Abstract

Boson sampling experiments aim to demonstrate quantum computational advantage with increasing numbers of interfering photons. A central question is whether their computational hardness survives under photon loss. We show that even an arbitrarily small nonzero uniform loss rate permits efficient classical sampling in the average case when the rate remains fixed as the system grows. We exploit how loss suppresses correlations involving many photons to approximate the full output distribution using low correlation orders. The resulting samplers run in time polynomial in system size and inverse total variation error, with the error averaged over Haar random interferometers. The results apply to Fock state boson sampling with single-photon states in distinct input modes and arbitrary additional vacuum inputs, and to Gaussian boson sampling with equal squeezing of bounded strength in every input mode. Classical sampling is efficient even when the mean detected photon number grows linearly with system size, showing that large photon counts alone do not ensure computational hardness.