General method for extracting the quantum efficiency of dispersive qubit readout in circuit QED*

We present and demonstrate a general 3-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of non-steady-state homodyne measurement. We derive analytically that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. To demonstrate generality, we extract the quantum efficiency as a function of the readout drive frequency and for different drive envelopes. We use the proven method to optimally bias a Josephon travelling-wave parametric amplifier and to quantify the different noise contributions in the readout amplification chain. This method allows in-situ characterization and optimization of the quantum efficiency in extensible multi-qubit architectures.