This research project investigates the trainability of parameterized quantum circuits (PQCs), which are at the heart of most quantum machine learning (QML) variational algorithms. Specifically, it seeks to determine whether PQCs can be designed to guarantee trainability while achieving sufficient expressiveness and maintaining quantumness (non-dequantizable) to offer a quantum advantage over classical machine learning algorithms. Hence, to investigate this question, this work proposed a theoretical analysis of the mathematical structure of PQCs, examining how their expressibility and degree of entanglement influence trainability and dequantization in practical QML applications.