Neural Network-Based Discriminators for Single-Shot Readout of Superconducting Qubits in Non-Gaussian Conditions

Single-shot dispersive readout of superconducting qubits is a very important part of real-time quantum feedback and quantum error correction (QEC). Conventional discriminators such as thresholding and matched filtering are optimal under Gaussian noise assumptions, yet performance degrades in the presence of non-Gaussian effects in particular when including energy relaxation during readout and leakage to non-computational states. Neural network based discriminators have been proposed to mitigate these limitations. There is still a lack of characterization of the scenarios in which they offer a significant benefit and the mechanisms that underlie that advantage. This paper shows a controlled simulation study of six discrimination methods that get more detailed as the model gets more complex: thresholding, matched filtering, linear discriminant analysis, a multilayer perceptron operating on integrated in-phase and quadrature (IQ) features, one-dimensional convolutional neural network operating on the full time-resolved measurement trace, and a hybrid CNN. By systematically varying physically relevant parameters, we map classifier performance as a function of the ratio of readout duration to qubit relaxation time, which governs the strength of non-Gaussian effects. We demonstrate that neural network-based discriminators offer minimal or no benefits in Gaussian-dominated contexts where linear approaches are almost optimal, yet produce substantial enhancements when non-Gaussian effects are present. Specifically, a hybrid architecture combining a small temporal CNN branch with a direct skip connection for the integrated IQ features achieves assignment fidelity of about 0.98 in the stress-test scenario, which represents a significant improvement over the matched filter. This hybrid architecture, at only 686 trainable parameters, is smaller than the pure CNN yet dominates it in easy settings where the pure CNN underperforms linear baselines by <inline-formula> <tex-math notation="LaTeX">$approx 6$ </tex-math></inline-formula> percentage points, pp while retaining its advantage in hard settings. Additionally, confusion-matrix analysis reveals that this enhancement results from the capacity of temporal models to leverage within-window dynamics that are unavailable to classifiers utilizing integrated observations. Rather than recommending the hybrid as a universally superior method, we characterise the regime in which it helps: it trails the matched filter by only <inline-formula> <tex-math notation="LaTeX">approx 1.2 </tex-math></inline-formula> pp in Gaussian conditions while providing a + 5.39 pp advantage in the stress-test regime, which makes it a regime-robust default wherever the operating point is uncertain or leakage is a meaningful error channel. These results provide a predictive understanding of when neural-network-based readout is beneficial and offer practical guidance for selecting discrimination strategies in superconducting qubit systems subject to real-time constraints.