Quantum simulation scheme of two-dimensional xy-model Hamiltonian with controllable coupling

We study a scheme of quantum simulator for two-dimensional xy -model Hamiltonian. Previously, the quantum simulator for a coupled cavity array spin model has been explored, but the coupling strength is fixed by the system parameters. In the present scheme, several cavity resonators can be coupled with each other simultaneously via an ancilla qubit. In the two-dimensional Kagome lattice of the resonators, the hopping of resonator photonic modes gives rise to the tight-binding Hamiltonian which in turn can be transformed to the quantum xy -model Hamiltonian. We employ the transmon as an ancilla qubit to achieve in situ controllable xy -coupling strength.