  In this paper, we propose a framework to study the combined effect of several
factors that contribute to the barren plateau problem in quantum neural
networks (QNNs), which is a critical challenge in quantum machine learning
(QML). These factors include data encoding, qubit entanglement, and ansatz
expressibility. To investigate this joint effect in a real-world context, we
focus on hybrid quantum neural networks (HQNNs) for multi-class classification.
Our proposed framework aims to analyze the impact of these factors on the
training landscape of HQNNs. Our findings show that the barren plateau problem
in HQNNs is dependent on the expressibility of the underlying ansatz and the
type of data encoding. Furthermore, we observe that entanglement also plays a
role in the barren plateau problem. By evaluating the performance of HQNNs with
various evaluation metrics for classification tasks, we provide recommendations
for different constraint scenarios, highlighting the significance of our
framework for the practical success of QNNs.
