This study presents a novel framework to develop a present-day technique that will be used for the Attention Deficit Hyperactivity Disorder (ADHD) diagnosis. It is derived from Quantum Machine Learning (QML) using electroencephalograms (EEG). ADHD is still among the most frequent neurodevelopmental disorders that arises in kids, greatly influencing their cognition. In order to overcome the problems posed by conventional diagnostic methods, this research implements feature extraction using the Quantum Convolutional Neural Network (QCNN) which efficiently captures complex patterns across the time, frequency, and time-frequency domains. The holistic preprocessing pipeline involves bandpass filtering from 1 to 40 Hz, artifact removal using Independent Component Analysis (ICA), and segmentation of 2-second epochs with 50% overlap. The quantum feature extraction method outperforms the traditional methods with an accuracy of 98.1% compared to the Fast Fourier Transform and Wavelet Transform. Using Particle Swarm Optimization for feature selection, 36 critical features were selected. The mean powers in the frontal theta band (importance score: 0.92) and in the central beta band (0.89) were the most significant characteristics. The robustness of the proposed framework is validated using 10-fold cross-validation that gave an accuracy of 96.3±1.6% cross-folds.Quantum-enhanced Gradient Boosting model achieves the highest performance (accuracy: 97.2%, precision: 98.1%, recall: 95.7%, F1-score: 96.9%) in the comparative analysis across seven machine learning classifiers These results show significant improvements over existing methods in both accuracy and computational efficiency. It provided a promising foundation for clinical diagnosis of ADHD using quantum machine learning techniques.