Single-Photon Dispersive Readout of a Qubit with a Photodetector: Theory Beyond the Rotating-Wave Approximation

We propose to use a single-photon pulse and a photodetector for the dispersive readout of a qubit. The scheme avoids the shot noise errors. However, another source of errors makes it challenging to perform a single-photon readout. To boost its performance, we propose to detune the qubit and the resonator further than usual, while coupling them stronger. The Bloch-Siegert shift then should be taken into account. It is shown how it can improve the readout. We provide simple analytical estimates for the readout contrast. Results of more complicated calculations that take the qubit relaxation into account are also presented. A contrast more than 75% can be achieved in 1μs for ideal detector and photon source.