Bone Cancer Detection in X-Ray Images Using Latent Equivariant Quantum Convolutional Networks with Atomic Orbital Search Optimization

Bone cancer is a life-threatening disease in which early and accurate detection plays a vital role in reducing mortality and preventing the spread of malignant cells. To address this challenge, this study proposes a novel Latent Equivariant Quantum Convolutional Neural Network with Atomic Orbital Search (LEQCNN-AOS) for enhanced bone cancer detection from X-ray images. Initially, bone X-ray images are collected from the TCIA dataset and preprocessed using the Dual Bilateral Least Squares Hybrid Filter (DBLSF), which effectively suppresses noise while preserving critical edge and structural details associated with cancerous regions. Quantum K-Means Clustering (QK-MC) is then employed for image segmentation, where image features are encoded into quantum states and swap tests are utilized to accurately cluster suspicious areas. For feature extraction, the Kolmogorov–Arnold Transformer (KAT) is introduced, combining Kolmogorov–Arnold Networks with Vision Transformers to capture complex tissue patterns through residual connections and logical activation functions. Finally, Atomic Orbital Search (AOS) optimizes LEQCNN hyperparameters by simulating electron energy transitions, ensuring an effective balance between exploration and exploitation. Experimental results demonstrate superior performance on the TCIA dataset, achieving 99.85% accuracy, 99.68% precision, and a 99.72% [Formula: see text]-score, highlighting the robustness, interpretability, and clinical potential of the proposed framework.