We propose a tunable nonlinear interaction for the implementation of quantum logic operations on pairs of superconducting resonators, where the two-resonator interaction is mediated by a transmon quantum bit (qubit). This interaction is characterized by a high on-to-off coupling ratio and allows for fast qubit-type and $d$-level system (qudit)-type operations for quantum information processing with multiphoton cavity states. We present analytical and numerical calculations showing that these operations can be performed with practically unit fidelity in absence of any dissipative phenomena, whereas physical two-photon two-resonator operations can be realized with a fidelity of 99.9% in presence of qubit and resonator decoherence. The resonator-qubit-resonator system proposed in this Letter can be implemented using available planar or three-dimensional microwave technology.
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