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Photonic quantum simulators are promising candidates for providing insightinto other small- to medium-sized quantum systems. The available photonicquantum technology is reaching the state where significant advantages arise forthe quantum simulation of interesting questions in Heisenberg spin systems.Here we experimentally simulate such spin systems with single photons andlinear optics. The effective Heisenberg-type interactions among individualsingle photons are realized by quantum interference at the tunable directioncoupler followed by the measurement process. The effective interactions arecharacterized by comparing the entanglement dynamics using pairwise concurrenceof a four-photon quantum system. We further show that photonic quantumsimulations of generalized Heisenberg interactions on a four-site squarelattice and a six-site checkerboard lattice are in reach of current technology.

Photonic quantum simulation of ground state configurations of Heisenberg square and checkerboard lattice spin systems