Quantum electrodynamics of non-demolition detection of single microwave photon by superconducting qubit array

By consistently applying the formalism of quantum electrodynamics we developed a comprehensive theoretical framework describing the interaction of single microwave photons with an array of superconducting transmon qubits in a wave guide cavity resonator. In particular, we analyze the effects of microwave photons on the arrays response to a weak probe signal exciting the resonator. The study reveals that a high quality factor cavities provide better spectral resolution of the response, while cavities with moderate quality factor allow better sensitivity for a single photon detection. Remarkably, our analysis showed that a single-photon signal can be detected by even a sole qubit in cavity under the realistic range of system parameters. We also discuss how quantum properties of the photons and electrodynamical properties of resonators affect the response of qubits array. Our results provide an efficient theoretical background for informing the development and design of quantum devices consisting of arrays of qubits, especially for those using a cavity where an explicit expression for the transmission or reflection is required.