Quantum Software Engineering (QSE) is a research area practiced by tech firms. Quantum developers face challenges in optimizing quantum computing and QSE concepts. They use Stack Overflow (SO) to discuss challenges and label posts with specialized quantum tags, which often refer to technical aspects rather than developer posts. Categorizing questions based on quantum concepts can help identify frequent QSE challenges. We conducted studies to classify questions into various challenges. We extracted 2829 questions from Q&A platforms using quantum-related tags. Posts were analyzed to identify frequent challenges and develop a novel grounded theory. Challenges include Tooling, Theoretical, Learning, Conceptual, Errors, and API Usage. Through content analysis and grounded theory, discussions were annotated with common challenges to develop a ground truth dataset. ChatGPT validated human annotations and resolved disagreements. Fine-tuned transformer algorithms, including BERT, DistilBERT, and RoBERTa, classified discussions into common challenges. We achieved an average accuracy of 95% with BERT DistilBERT, compared to fine-tuned Deep and Machine Learning (D&ML) classifiers, including Feedforward Neural Networks (FNN), Convolutional Neural Networks (CNN), and Long Short-Term Memory networks (LSTM), which achieved accuracies of 89%, 86%, and 84%, respectively. The Transformer-based approach outperforms the D&ML-based approach with a 6\% increase in accuracy by processing actual discussions, i.e., without data augmentation. We applied SHAP (SHapley Additive exPlanations) for model interpretability, revealing how linguistic features drive predictions and enhancing transparency in classification. These findings can help quantum vendors and forums better organize discussions for improved access and readability. However,empirical evaluation studies with actual developers and vendors are needed.