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

Silvie Illésová, Tomasz Rybotycki, Piotr Gawron, Martin Beseda

TL;DR

The paper analyzes how fundamental quantum-layer properties—namely ansatz depth and feature-map encoding—affect the performance of hybrid quantum-classical networks on a causal classification task. Using a CNN for classical feature extraction and a quantum layer with a TwoLocal ansatz, the authors evaluate nine feature maps on 8×8 cause-effect heatmaps, revealing that deeper ansätze improve generalization and training stability with diminishing returns beyond a few repetitions. Crucially, only multi-axis Pauli-rotational feature maps enable effective learning, while simpler encodings lead to underfitting or dimensional collapse, as shown by PCA and silhouette analyses across model stages. The work provides practical design guidance for quantum circuit construction in hybrid models and releases code for reproducibility, highlighting both opportunities and limitations for extending these findings to broader architectures and datasets.

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.

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

TL;DR

The paper analyzes how fundamental quantum-layer properties—namely ansatz depth and feature-map encoding—affect the performance of hybrid quantum-classical networks on a causal classification task. Using a CNN for classical feature extraction and a quantum layer with a TwoLocal ansatz, the authors evaluate nine feature maps on 8×8 cause-effect heatmaps, revealing that deeper ansätze improve generalization and training stability with diminishing returns beyond a few repetitions. Crucially, only multi-axis Pauli-rotational feature maps enable effective learning, while simpler encodings lead to underfitting or dimensional collapse, as shown by PCA and silhouette analyses across model stages. The work provides practical design guidance for quantum circuit construction in hybrid models and releases code for reproducibility, highlighting both opportunities and limitations for extending these findings to broader architectures and datasets.

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.

Paper Structure

This paper contains 14 sections, 29 equations, 11 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. cnn
  4. QNN
  5. Dataset
  6. Training
  7. Performance metrics
  8. Results
  9. Effect of Ansatz Depth on Learning Dynamics
  10. Impact of Feature Mapping on Hybrid Model Performance
  11. Conclusions
  12. Acknowledgments
  13. Tables
  14. Feature Mappings

Figures (11)

  • Figure 1: Step-wise architecture of the hybrid quantum-classical model. Classical processing (blue) extracts and projects features, quantum processing (purple) performs parameterized evolution, and the final classifier outputs class probabilities.
  • Figure 2: One repetition (depth = 1) of a TwoLocal ansatz with $R_y$ and $R_z$ rotations and linear CNOT entanglement for $n_q = 3$ qubits.
  • Figure 3: Training and validation accuracy curves for models with 1, 2, 3, and 5 ansatz repetitions.
  • Figure 4: Absolute generalization gap during training across different ansatz depths.
  • Figure 5: Bloch sphere, which is used to visualize the single qubit state
  • ...and 6 more figures