On the Importance of Fundamental Properties in Quantum-Classical Machine Learning Models

TL;DR

This paper systematically investigates how quantum circuit design choices, such as ansatz depth and feature mapping, influence the performance of hybrid quantum-classical neural networks on classification tasks, providing practical design insights.

Contribution

It offers a comprehensive analysis of the impact of ansatz depth and feature encoding on model performance, highlighting the importance of multi-axis Pauli rotations for effective learning.

Findings

Increasing ansatz depth improves generalization up to a point.

Multi-axis Pauli rotations are essential for successful quantum encoding.

Data distribution analysis reveals how quantum features evolve through the network.

Abstract

We present a systematic study of how quantum circuit design, specifically the depth of the variational ansatz and the choice of quantum feature mapping, affects the performance of hybrid quantum-classical neural networks on a causal classification task. The architecture combines a convolutional neural network for classical feature extraction with a parameterized quantum circuit acting as the quantum layer. We evaluate multiple ansatz depths and nine different feature maps. Results show that increasing the number of ansatz repetitions improves generalization and training stability, though benefits tend to plateau beyond a certain depth. The choice of feature mapping is even more critical: only encodings with multi-axis Pauli rotations enable successful learning, while simpler maps lead to underfitting or loss of class separability. Principal Component Analysis and silhouette scores reveal how data distributions evolve across network stages. These findings offer practical guidance for designing quantum circuits in hybrid models. All source codes and evaluation tools are publicly available.