Boson Sampling is Robust to Small Errors in the Network Matrix

TL;DR

This paper shows that BosonSampling remains accurate despite small errors in the optical network matrix, with the output distribution's deviation proportional to the error magnitude and number of photons.

Contribution

It provides a theoretical bound on the robustness of BosonSampling to small matrix deviations, establishing tolerances for optical network components.

Findings

Output distribution within psilon n of the desired distribution

Derived sufficient tolerances for beamsplitters and phase shifters

Robustness applies to errors in the implemented unitary matrix

Abstract

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.