Passive quantum error correction of linear optics networks through error averaging

We propose and investigate a method of error detection and noise correction for bosonic linear networks using a method of unitary averaging. The proposed error averaging does not rely on ancillary photons or control and feed-forward correction circuits, remaining entirely passive in its operation. We construct a general mathematical framework for this technique then give a series of proof of principle examples including numerical analysis. Two methods for the construction of averaging are then compared to determine the most effective manner of implementation and probe the related error thresholds. Finally we discuss some of the potential uses of this scheme.