Circuit QED realization of two-qubit photonic phase gate

Circuit QED based on superconducting circuit structure is similar to the model of interaction between cavity field and atoms, and is solidified on the substrate, so it is more suitable for integration, expansion and control. The circuit QED system consists of resonators and superconducting qubits, the length of the resonators much larger than width, so it can be regarded as a one-dimensional linear planar structure in theory. We propose a theoretical model to realizing two-qubit photonic phase gate, we use two superconducting resonators to couple a magnetic flux qutrit via two capacitors in circuit QED system, and choose an appropriate interaction time, it turns out that a two-qubit photonic phase gate can be realized by one step.