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We investigate theoretically the ground-state property of a two-dimensionalarray of superconducting circuits including the on-site superconducting qubits(SQs) with weak anharmonicity. In particular, we analyse the influence of thisanharmonicity on the Mott insulator to superfluid quantum phase transition. Thecomplete ground-state phase diagrams are presented under the mean fieldapproximation. Interestingly, the anharmonicity of SQs affects the Mott lobesenormously, and the single excitation Mott lobe disappears when theanharmonicity become zero. Our results can be used to guide the implementationsof quantum simulations using the superconducting circuits, which have niceintegrating and flexibility.

Superfluid-Mott-insulator transition in superconducting circuits with weak anharmonicity