System characterization of dispersive readout in superconducting qubits

Designing quantum systems with the measurement speed and accuracy needed for quantum error correction using superconducting qubits requires iterative design and testing informed by accurate models and characterization tools. We introduce a single protocol, with few prerequisite calibrations, to measure the dispersive shift, resonator linewidth, and drive power used in the dispersive readout of superconducting qubits. We find that the resonator linewidth is poorly controlled, with a factor of 2 variation between the maximum and minimum measured values, and this variation is likely to require focused attention in future quantum error correction experiments. We also introduce a protocol for measuring the efficiency of the readout system using the same power levels as are used in typical qubit readout, and without the need to measure the qubit dephasing. We routinely run these protocols on chips with tens of qubits to a hundred qubits, driven by automation software with little human interaction. Using the extracted system parameters, we find that a model based on these parameters predicts the readout signal-to-noise ratio to within 10% over a device with 54 qubits.