Towards Continuous-variable Quantum Neural Networks for Biomedical Imaging

TL;DR

This work assesses the feasibility of continuous-variable quantum neural networks (CV-QCNNs) for biomedical image classification by encoding PCA-reduced MedMNIST features into a small photonic CV circuit with Gaussian gates. It compares CV-QNNs to a discrete-variable QNN and a classical baseline, evaluating accuracy, robustness to Gaussian noise, and interpretability via Grad-CAM across PneumoniaMNIST, OrganAMNIST, and BreastMNIST. The findings show CV-QNNs can match classical and DV performance on these tasks, with notable robustness and distinct attention patterns, though no quantum advantage is demonstrated within the study's current configuration. The results emphasize the potential of CV quantum approaches in medical imaging and provide guidance for future enhancements, such as incorporating non-Gaussian gates, increasing circuit depth, and testing on richer datasets.

Abstract

Continuous-variable (CV) quantum computing offers a promising framework for scalable quantum machine learning, leveraging optical systems with infinite-dimensional Hilbert spaces. While discrete-variable (DV) quantum neural networks have shown remarkable progress in various computer vision tasks, CV quantum models remain comparatively underexplored. In this work, we present a feasibility study of continuous-variable quantum neural networks (CV-QCNNs) applied to biomedical image classification. Utilizing photonic circuit simulation frameworks, we construct CV quantum circuits composed of Gaussian gates, such as displacement, squeezing, rotation, and beamsplitters to emulate convolutional behavior. Our experiments are conducted on the MedMNIST dataset collection, a set of annotated medical image benchmarks for multiple diagnostic tasks. We evaluate CV-QCNN's performance in terms of classification accuracy, model expressiveness, and resilience to Gaussian noise, comparing against classical CNNs and equivalent DV quantum circuits. This study aims to identify trade-offs between DV and CV paradigms for quantum-enhanced medical imaging. Our results highlight the potential of continuous-variable models and their viability for future computer-aided diagnosis systems.

Figures (17)

• Figure 1: Comparison between original and PCA-reconstructed images for each dataset. From top to bottom: PneumoniaMNIST, BreastMNIST, and OrganAMNIST. For each dataset, the left image shows an example of the original input, while the right image shows its reconstruction using 4 principal components.
• Figure 2: The proposed 4-mode Continuous-Variable (CV) quantum circuit. Each qumode undergoes displacement ($D$) for data encoding, followed by rotational ($R$) and squeezing ($S$) gates for feature extraction. Beamsplitter ($BS$) operations entangle adjacent modes analogously to CNOT gates in DV circuits. Finally, the quadrature expectation values $\langle \hat{X} \rangle$ are measured for data decoding.
• Figure 3: The proposed 4-qubit DV quantum circuit, comprised of a set of data encoding $R_{y}(\phi)$ gates; a combination of phase $R_{z}(\phi)$ and rotational $R_{y}(\phi)$ gates for feature extraction that emulate rotational and squeezing gates from CV quantum circuits; CNOT gates that entangle data information, analogous to beam splitter gates in CV quantum systems; and data decoding via expectation values measured on the $z$-axis.
• Figure 4: Example of how TP, FP, FN, and TN are defined for a given class (here Class B) in a multiclass confusion matrix. The diagonal cell for Class B corresponds to TP, the rest of row B are FN, the rest of column B are FP, and all other cells are TN.
• Figure 5: Receiver Operating Characteristic (ROC) curve. The red line indicates the ROC curve with threshold points, the dashed gray line represents the main diagonal (random performance), and the shaded blue area corresponds to the area under the ROC curve (AUROC).