Boson Sampling is Robust to Small Errors in the Network Matrix

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 $\tilde{U}$ that is within $\epsilon$ of the desired matrix $U$ in operator norm leads to an output distribution that is within $\epsilon n$ 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.