Characterizing mid-circuit measurements on a superconducting qubit using gate set tomography

TL;DR

This paper introduces a new method called QILGST to characterize mid-circuit measurements in superconducting qubits, revealing detailed error modes and quantifying measurement errors crucial for quantum error correction.

Contribution

The paper develops and applies QILGST, a novel technique for characterizing quantum instruments in mid-circuit measurements, providing detailed error analysis in superconducting qubit systems.

Findings

Measured a total error rate of 8.1% at delay times above 1000 ns.

Achieved a readout fidelity of 97.0%.

Obtained output state fidelities of 96.7% and 93.7% for states 0 and 1.

Abstract

Measurements that occur within the internal layers of a quantum circuit -- mid-circuit measurements -- are an important quantum computing primitive, most notably for quantum error correction. Mid-circuit 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 mid-circuit measurements, modelled 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 measured a total error rate (i.e., half diamond distance) of $\epsilon_{\diamond} = 8.1 \pm 1.4 \%$, a readout fidelity of $97.0 \pm 0.3\%$, and output quantum state fidelities of $96.7 \pm 0.6\%$ and $93.7 \pm 0.7\%$ when measuring $0$ and $1$, respectively.