  We investigate theoretically the ground-state property of a two-dimensional
array of superconducting circuits including the on-site superconducting qubits
(SQs) with weak anharmonicity. In particular, we analyse the influence of this
anharmonicity on the Mott insulator to superfluid quantum phase transition. The
complete ground-state phase diagrams are presented under the mean field
approximation. Interestingly, the anharmonicity of SQs affects the Mott lobes
enormously, and the single excitation Mott lobe disappears when the
anharmonicity become zero. Our results can be used to guide the implementations
of quantum simulations using the superconducting circuits, which have nice
integrating and flexibility.
