A single photon transistor based on superconducting systems

We present a realistic scheme for how to construct a single-photon transistor where the presence or absence of a single microwave photon controls the propagation of a subsequent strong signal signal field. The proposal is designed to work with existing superconducting artificial atoms coupled to cavities. We study analytically and numerically the efficiency and the gain of our proposal and show that current transmon qubits allow for error probabilities ~1% and gains of the order of hundreds.