The ability to interpret human emotions, particularly genuine smiles arising from positive cognitive states, is crucial for effective communication and accurately distinguishing between genuine and fake smiles in online interactions remains a challenge. This paper proposes a novel approach leveraging Quantum-inspired Fermionic Operator Representation (Quantum-FER) to classify smiles and potentially infer underlying cognitive states. Our methodology employs a machine learning framework to preprocess facial images from a standard dataset. The pre-processed data is then encoded into quantum states using Quantum encoding techniques. Subsequently, a TensorFlow Quantum-based model is trained to classify smiles as genuine or fake. The system outputs the percentages of genuine and fake smile detections, enabling robust classification. This research explores the potential of Quantum-FER in deciphering the link between facial expressions and human cognition, paving the way for more nuanced understanding of online interactions. In our experiments, the model achieved a precision of 0.95, recall of 0.91, and F1-score of 0.93 for detecting non-smiling faces. For smiling faces, the precision, recall, and F1-score were 0.80, 0.88, and 0.84, respectively. Overall, trained model loss has been reduced to 0.74 to 0.23 and accuracy increased from 0.73 to 0.92.