Quantum-Inspired Feature Representations for Depression Subtype Classification: A Synthetic Benchmark Study

Depression is a clinically heterogeneous disorder comprising subtypes such as melancholic, atypical, anxious, and unspecified, each characterized by distinct symptom profiles and treatment responses. Accurate identification of these subtypes is essential for precision psychiatry and optimizing therapeutic outcomes. This study investigates the potential of quantum-inspired feature representations to enhance the classification of depression subtypes from clinical data. A synthetic dataset of 5000 patients was generated, simulating realistic demographic, psychometric, behavioural, and biological variables (e.g., BDI, HRSD, cortisol, sleep, anxiety, BMI). Using standardized and quantum-transformed features, we trained and evaluated four classification models: Random Forest, Support Vector Machine (SVM), XGBoost, and a multi-layer neural network. Quantum-inspired features were derived via parameterized quantum circuits with amplitude encoding and entanglement, yielding fixed-length state vector representations. Performance was assessed using accuracy, weighted F1-score, ROC AUC, and confusion matrices on a held-out test set. Across all models, original clinical features consistently outperformed quantum-transformed features in classification accuracy and subtype separability. Statistical tests confirmed significant performance degradation with quantum features (p < 0.001). Despite this, our framework establishes a reproducible pipeline for benchmarking quantum-inspired machine learning in psychiatry. The findings highlight both the current limitations and future potential of quantum-based representations in modelling complex mental health phenotypes. This work serves as a foundation for integrating emerging quantum learning paradigms with clinically relevant, multi-class psychiatric classification tasks.