Single particle detection is one of the most fundamental issues in quantum mechanics as it addresses the question of quantum measurement. An accurate quantum description of a detector would avoid the use of the Born rule (or von Neumann postulate) about the probabilities of different outcomes, leading to the controversial interpretation of the collapse of the wave packet or the Schrodinger's cat.

In this talk, we apply consistently the formalism of quantum electrodynamics and we developed a comprehensive theoretical framework describing the interaction of single microwave photons with an array of superconducting transmon qubits in a waveguide cavity resonator. In particular, we analyse the effects of microwave

photons on the array’s 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 microwave radiation 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.