Deploying deep learning models for Fine-Grained Visual Classification (FGVC) on resource-constrained edge devices remains a significant challenge. While deep architectures achieve high accuracy on benchmarks like CUB-200-2011, their computational cost is often prohibitive. Conversely, shallow networks (e.g., AlexNet, VGG) offer efficiency but fail to distinguish visually similar sub-categories. This is because standard Global Average Pooling (GAP) heads capture only first-order statistics, missing the subtle high-order feature interactions required for FGVC. While Bilinear CNNs address this, they suffer from high feature dimensionality and instability during training. To bridge this gap, we propose the Quantum-inspired Interaction Classifier (QuIC). Drawing inspiration from quantum mechanics, QuIC models feature channels as interacting quantum states and captures second-order feature covariance via a learnable observable operator. Designed as a lightweight, plug-and-play module, QuIC supports stable, single-stage end-to-end training without exploding feature dimensions. Experimental results demonstrate that QuIC significantly revitalizes shallow backbones: it boosts the Top-1 accuracy of VGG16 by nearly 20% and outperforms state-of-the-art attention mechanisms (SE-Block) on ResNet18. Qualitative analysis, including t-SNE visualization, further confirms that QuIC resolves ambiguous cases by explicitly attending to fine-grained discriminative features and enforcing compact intra-class clustering.