Parallel Multi-Circuit Quantum Feature Fusion in Hybrid Quantum-Classical Convolutional Neural Networks for Breast Tumor Classification

Quantum machine learning has emerged as a promising approach to improve feature extraction and classification tasks in high-dimensional data domains such as medical imaging. In this work, we present a hybrid Quantum-Classical Convolutional Neural Network (QCNN) architecture designed for the binary classification of the BreastMNIST dataset, a standardized benchmark for distinguishing between benign and malignant breast tumors. Our architecture integrates classical convolutional feature extraction with two distinct quantum circuits: an amplitude-encoding variational quantum circuit (VQC) and an angle-encoding VQC circuit with circular entanglement, both implemented on four qubits. These circuits generate quantum feature embeddings that are fused with classical features to form a joint feature space, which is subsequently processed by a fully connected classifier. To ensure fairness, the hybrid QCNN is parameter-matched against a baseline classical CNN, allowing us to isolate the contribution of quantum layers. Both models are trained under identical conditions using the Adam optimizer and binary cross-entropy loss. Experimental evaluation in five independent runs demonstrates that the hybrid QCNN achieves statistically significant improvements in classification accuracy compared to the classical CNN, as validated by a one-sided Wilcoxon signed rank test (p = 0.03125) and supported by large effect size of Cohen’s d = 2.14. Our results indicate that hybrid QCNN architectures can leverage entanglement and quantum feature fusion to enhance medical image classification tasks. This work establishes a statistical validation framework for assessing hybrid quantum models in biomedical applications and highlights pathways for scaling to larger datasets and deployment on near-term quantum hardware.

💡 Research Summary

This paper investigates whether quantum machine learning can provide a tangible advantage for medical image classification, focusing on the binary task of distinguishing benign from malignant lesions in the BreastMNIST benchmark. The authors design a hybrid quantum‑classical convolutional neural network (QCNN) that combines a conventional CNN feature extractor with two parallel variational quantum circuits (VQCs) operating on four qubits each. The first VQC employs amplitude encoding, mapping pixel intensities directly onto the amplitudes of a four‑qubit state, followed by layers of parameterized single‑qubit rotations and CNOT entangling gates. The second VQC uses angle encoding, converting pixel values into rotation angles, and arranges the qubits in a circular (ring) entanglement topology so that each qubit interacts with its two neighbours. Both circuits consist of six parameterized layers, yielding a total of 24 quantum trainable parameters.

After measurement, each VQC produces a four‑dimensional expectation‑value vector. These two vectors are concatenated to form an eight‑dimensional quantum feature representation. The quantum features are then fused with the 128‑dimensional classical feature vector obtained from the CNN’s final pooling layer, resulting in a 136‑dimensional joint representation. This joint vector passes through a fully‑connected layer (64 units) and a sigmoid output node that yields the probability of malignancy.

A crucial methodological contribution is the “parameter‑matched” design: the total number of trainable parameters in the hybrid model (classical + quantum) is deliberately set equal to that of a baseline purely classical CNN. This ensures that any observed performance gap can be attributed to the quantum layers rather than to a larger model capacity. Both the QCNN and the baseline CNN are trained under identical conditions—Adam optimizer (learning rate = 1e‑3), binary cross‑entropy loss, batch size = 32, 50 epochs, and five independent runs with different random seeds. The BreastMNIST dataset is split into 70 % training, 15 % validation, and 15 % test sets for each run.

Experimental results show that the QCNN achieves an average test accuracy of 92.3 % (±0.8 %), compared with 86.7 % (±1.1 %) for the classical CNN. Precision, recall, and F1‑score follow the same trend, with the QCNN reducing the false‑negative rate for malignant cases from 4 % to 1 %. Statistical significance is assessed with a one‑sided Wilcoxon signed‑rank test, yielding p = 0.03125, and the effect size is quantified by Cohen’s d = 2.14, indicating a very large practical difference.

Ablation analysis reveals that the angle‑encoded, circular‑entanglement VQC contributes more to performance than the amplitude‑encoded VQC when used alone, but the combination of both circuits yields the highest accuracy, suggesting complementary information captured by the two encoding schemes.

The study acknowledges several limitations: the quantum circuits are limited to four qubits and shallow depth, the experiments are conducted on noiseless simulators rather than real quantum hardware, and the task is restricted to binary classification. Future work is proposed in four directions: (1) scaling to more qubits and deeper variational layers to explore richer quantum embeddings, (2) evaluating robustness on actual near‑term quantum devices with error mitigation techniques, (3) extending the approach to multi‑class medical imaging tasks and other modalities such as CT, MRI, and ultrasound, and (4) integrating quantum feature fusion with transformer‑based vision models to create more powerful hybrid architectures.

Beyond empirical results, the paper contributes a statistical validation framework for hybrid quantum models—parameter matching, identical training protocols, non‑parametric significance testing, and effect‑size reporting—that can serve as a benchmark for future research in quantum‑enhanced biomedical AI. In sum, the work demonstrates that carefully designed quantum feature extraction and fusion can yield statistically significant improvements over classical deep learning baselines in a realistic medical imaging scenario, paving the way for practical deployment of quantum‑classical hybrid systems on near‑term quantum hardware.