Figure 4

Orbits under the symmetry group for the model \(\pmb{\{H_{2}, S_{z}\}}\) on a \(\pmb{3\times3}\) square lattice. The 2D-TFIM Hamiltonian on this lattice has \(\sigma_{z}\) operators on each site and the links represent the \(\sigma_{x}^{i}\sigma_{x}^{j}\) couplings between sites. Lattice sites and couplings that lie in the same orbit (under the reflections and rotations that leave the quantum simulation model unchanged) are identically colored. There are five distinct orbits in this example.