Fig. 1: Relation between linear-optical circuit and bipartite graph.
From: Classical simulability of constant-depth linear-optical circuits with noise
a Linear-optical circuit with input photons on red dots and vacuum on empty dots on the left and output modes on blue dots on the right. Input and output modes are coupled by beam-splitter arrays with depth d = 3, which make the input photons propagate through the dotted lines. b The corresponding bipartite graph. c When the second and third photons get lost, the corresponding vertices are removed from the graph. Consequently, the resultant bipartite graph is divided into two disconnected bipartite graphs.
