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We propose a tunable nonlinear interaction for the implementation of quantumlogic operations on pairs of superconducting resonators, where thetwo-resonator interaction is mediated by a transmon quantum bit (qubit). Thisinteraction is characterized by a high on-to-off coupling ratio and allows forfast qubit-type and $d$-level system (qudit)-type operations for quantuminformation processing with multiphoton cavity states. We present analyticaland numerical calculations showing that these operations can be performed withpractically unit fidelity in absence of any dissipative phenomena, whereasphysical two-photon two-resonator operations can be realized with a fidelity of99.9% in presence of qubit and resonator decoherence. Theresonator-qubit-resonator system proposed in this Letter can be implementedusing available planar or three-dimensional microwave technology.

Multiphoton Quantum Logic Gates for Superconducting Resonators with Tunable Nonlinear Interaction