Gaussian continuous-variable quantum neural networks for MedMNIST classification

Continuous-variable (CV) quantum computing offers a promising framework for potentially scalable quantum machine learning by leveraging optical systems with infinite-dimensional Hilbert spaces. Although discrete-variable (DV) quantum neural networks (QNNs) have shown remarkable progress in various computer vision tasks, CV quantum models remain comparatively underexplored. In this paper, we present a feasibility study of small-scale Gaussian CV QNNs applied to biomedical image classification. Utilizing photonic quantum circuits through Gaussian simulation, we constructed CV quantum circuits composed of Gaussian gates, such as displacement, squeezing, rotation, and beam splitters, to emulate neural networks and convolutional behaviors. We evaluate the CV QNN on three MedMNIST benchmarks (PneumoniaMNIST, BreastMNIST, and OrganAMNIST) in terms of statistical classification performance, model expressiveness and reliability, model complexity, and noise resilience, and we also compare the results against a same-scale DV QNN baseline and classical NN counterpart under the same principal component analysis (PCA)-compressed input setting. On the test sets, the CV QNN reached F1 scores of 84.29%, 75.64%, and 45.63%, and the area under the receiver operating characteristic curves were up to 92%, which are comparable to those of the evaluated DV and classical counterparts. Any higher performance observed relative to the shallow 4-qubit DV baseline in some cases should therefore not be interpreted as a general superiority of CV over DV architectures. Under the limited setting of threefold cross-validation with one fixed random seed, Friedman and Bonferroni-corrected Wilcoxon tests did not detect statistically significant differences in F1 scores among the three models ( p>0.05). This study examines the trade-offs between DV and CV paradigms for quantum-enhanced medical imaging under a small-scale configuration. Overall, the results suggest that small-scale Gaussian CV models can be a viable direction for future computer-aided diagnosis systems within the PCA-compressed, Gaussian-only, and limited statistical setting considered in this study.