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 $1000\mathrm{ns}$ we measure a total error rate (i.e., half diamond distance) of ${ϵ}_{\diamond }=8.1\pm 1.4\mathrm{\%}$, a readout fidelity of $97.0\pm 0.3\mathrm{\%}$, and output quantum-state fidelities of $96.7\pm 0.6\mathrm{\%}$ and $93.7\pm 0.7\mathrm{\%}$ when measuring $0$ and $1$, respectively.

• Received 17 March 2021
• Revised 4 November 2021
• Accepted 18 November 2021

DOI:https://doi.org/10.1103/PhysRevApplied.17.014014