We demonstrate that quantum vision transformers (QViTs), vision transformers (ViTs) with self-attention (SA) mechanisms replaced by quantum self-attention (QSA) mechanisms, can match state-of-the-art (SOTA) biomedical image classifiers while using 99.99% fewer parameters. QSAs are produced by replacing linear SA layers with parameterised quantum neural networks (QNNs), producing a QSA mechanism and reducing parameter scaling from \(\mathcal {O}(n^2)\) to \(\mathcal {O}(n)\) . On RetinaMNIST, our ultra parameter-efficient QViT outperforms 13/14 SOTA methods including CNNs and ViTs, achieving 56.5% accuracy, just 0.88% below the top MedMamba model while using 99.99% fewer parameters (1K vs 14.5M) and 89% fewer GFLOPs. We present the first investigation of knowledge distillation (KD) from classical to quantum vision transformers in biomedical image classification, showing that QViTs maintain comparable performance to classical ViTs across eight diverse datasets spanning multiple modalities, with improved QSA parameter-efficiency. Our higher-qubit architecture benefitted more from KD pre-training, suggesting a scaling relationship between QSA parameters and KD effectiveness. These findings establish QSA as a practical architectural choice toward parameter-efficient biomedical image analysis (Code available at https://github.com/surgical-vision/QViT-KD.git ).