  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.
