Boson Sampling is Robust to Small Errors in the Network Matrix

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We demonstrate the robustness of BosonSampling to imperfections in the linear optical network that cause a small deviation in the matrix it implements. We show that applying a noisy matrix U that is within ε of the desired matrix U in operator norm leads to an output distribution that is within εn of the desired distribution in variation distance, where n is the number of photons. This lets us derive a sufficient tolerance each beamsplitters and phaseshifters in the network. This result considers only errors that result from the network encoding a different unitary than desired, and not other sources of noise such as photon loss and partial distinguishability.