Fig. 1: Schematic of graph representations in different dimensions.
From: Multi-particle quantum walks on 3D integrated photonic chip
a Single-layer triangular lattice. The central site is connected to six surrounding sites, and all connections have the same coupling strength C. b, c Sketch of high-dimensional graph representations of a single-layer lattice spanned by 2-photon and 3-photon injection. Each node represents a multi-particle state, and every edge represents a possible transition between multi-particle states. All the nodes are divided into three groups: collision-free events (blue), two-photon bunching events (green) and three-photon bunching event (red). d Two-layer triangular lattice. The experimental structure consists of 19 sites. e, f Expanded graph representations of a two-layer lattice spanned by 2-photon and 3-photon injection, corresponding to 361 nodes, 1596 edges and 6859 nodes, 45,486 edges, respectively
