BosonSampling is robust against small errors in the network matrix

We demonstrate the robustness of BosonSampling against imperfections in the linear optical network that cause a small deviation in the matrix it implements. We show that applying a noisy matrix (U) over tilde that is within is an element of of the desired matrix U in operator norm leads to an output distribution that is within is an element of n of the desired distribution in variation distance, where n is the number of photons. This lets us derive a sufficient tolerance for beam splitters and phase shifters in the network. This result only concerns errors that result from the network encoding a different unitary than desired and not from other sources of noise such as photon loss and partial distinguishability.