Characterizing Midcircuit Measurements on a Superconducting Qubit Using Gate Set Tomography

Measurements that occur within the internal layers of a quantum circuit-midcircuit measurements are a useful quantum-computing primitive, most notably for quantum error correction. Midcircuit measurements have both classical and quantum outputs, so they can be subject to error modes that do not exist for measurements that terminate quantum circuits. Here we show how to characterize midcircuit measurements, modeled by quantum instruments, using a technique that we call quantum instrument linear gate set tomography (QILGST). We then apply this technique to characterize a dispersive measurement on a superconducting transmon qubit within a multiqubit system. By varying the delay time between the measurement pulse and subsequent gates, we explore the impact of residual cavity photon population on measurement error. QILGST can resolve different error modes and quantify the total error from a measurement; in our experiment, for delay times above 1000 ns we measure a total error rate (i.e., half diamond distance) of epsilon(0) = 8.1 +/- 1.4%, a readout fidelity of 97.0 +/- 0.3%, and output quantum-state fidelities of 96.7 +/- 0.6% and 93.7 +/- 0.7% when measuring 0 and 1, respectively.