Benchmarking the quality of multiplexed qubit readout beyond assignment fidelity

TL;DR

This work extends readout benchmarking for superconducting qubits beyond assignment fidelity by employing detector tomography to fully characterize multiqubit readout, including coherent and correlated errors. By linking the information-extraction rate to quantum infidelity I(ρ,σ) and comparing it with assignment fidelities, it provides a more comprehensive benchmark and validates infidelity-thresholding as a practical validation tool. The authors demonstrate two- and three-qubit tomography under readout-error mitigation, optimize the allocation of shots between detector tomography and state tomography, and quantify readout correlations, showing that correlations can be a useful diagnostic and optimization target. The results show scalable improvement in state reconstruction (≈30× for three qubits) and establish correlation coefficients as a meaningful metric for optimizing multiplexed readout in larger devices with few-qubit benchmarking capabilities.

Abstract

The accurate measurement of quantum two-level objects (qubits) is crucial for developing quantum computers. Over the last decade, the measure of choice for benchmarking readout routines for superconducting qubits has been assignment fidelity. However, this method only focuses on the preparation of computational basis states and therefore does not provide a complete characterization of the readout. Here, we expand the focus to the use of detector tomography to fully characterize multiqubit readout of superconducting transmon qubits. The impact of different readout parameters on the rate of information extraction is studied using quantum state reconstruction infidelity as a proxy. The results are then compared with assignment fidelities, showing good agreement for separable two-qubit states. We therefore propose the rate of infidelity convergence as a validation tool for assignment fidelity and a more comprehensive benchmark for single- and multiqubit readout optimization. To make the best use of experimental resources, we investigate the most efficient distribution of a limited shot budget between detector tomography and state reconstruction within the context of single- and two-qubit experiments. To address the growing interest in three-qubit gates and test scalability of the validation tool, we perform three-qubit quantum state tomography that goes beyond conventional readout-error-mitigation methods and find a factor of 30 reduction in quantum infidelity. Our results demonstrate that qubit readout correlations are not induced by a significantly reduced state distinguishability. Consequently, correlation coefficients can serve as a valuable tool in qubit readout optimization.

Figures (12)

• Figure 1: Resonator spectroscopy of the four-qubit system. At sufficiently low readout powers, each qubit couples coherently to its resonator, enabling dispersive readout. Systems A, B and C are two-qubit systems of neighboring resonator-qubit systems. An important feature is the closeness of resonators in System C, symbolized by the orange color. From left to right, the corresponding qubits are q0, q1, q2, and q3.
• Figure 2: Mean infidelity curves crossing different threshold values (corresponding to infidelity values of 0.10, 0.15, and 0.20). Two different readout parameters are examined, where blue curves are with and red curves are without quantum readout-error mitigation (QREM). The curves are created using a Bayesian mean estimator of the reconstructed quantum states. Only readout-error-mitigated infidelities reliably cross the given thresholds, where the lowest threshold was only crossed by the QREM curves. Each curve is averaged over 16 Haar random initial states, and the shaded area indicates the interquartile range.
• Figure 3: Comparison of quantum-state-tomography-based readout benchmark with assignment fidelities for varying readout amplitudes. The vertical dashed red line indicates optimal readout amplitude. Top: The number of two-qubit state tomography shots required to reach infidelity thresholds of 0.10, 0.15 and 0.20 for various readout amplitudes. The error bars are bootstrapped standard deviations. For very low readout powers, the distinguishability of the basis states is significantly reduced. For very high readout amplitudes, the measurement process excites higher states in the system, which the state classifier cannot correctly take into account. Each point uses 558 000 shots. Bottom: Mean and product of single-shot assignment fidelities. Each point uses 2000 shots.
• Figure 4: Comparison of quantum-state-tomography-based readout benchmark with assignment fidelities for varying amplification. The vertical dashed red line indicates optimal pump power. Top: The number of shots in state tomography needed to reach 0.10, 0.15, and 0.20 reconstruction infidelity. The error bars show bootstrapped standard deviations. Each point uses 558 000 shots. Bottom: Sum and product of assignment fidelities for the performed experiments. State separation increases with pump power up to approximately $6.5\,\text{dBm}$, after which it drops sharply. The error bars show propagated standard deviations from the assignment fidelity. Each point uses 2000 shots.
• Figure 5: Reachable infidelities for different distributions of a given shot budget in readout-error-mitigated state reconstruction. The plotted infidelities refer to the final infidelity at the end of quantum state reconstruction. The blue triangles correspond to the mean infidelities, while the spread in each case is shown with teal circles. The red horizontal line indicates the mean final infidelity at which the full budget was used for standard state tomography. The identified optimal shot ratio is marked in green. Top: Single qubit, shot budget of 10 000, averaged over 40 Haar random states. Bottom: Two-qubit reconstruction with a shot budget of 40 000, averaged over ten Haar random states.