# Comparative performance analysis of quantum feature maps for quantum kernel-based machine learning

## TL;DR

This paper compares different quantum feature maps to improve machine learning models using quantum kernels.

## Contribution

The study introduces a new high-order feature map and evaluates its performance against existing ones in quantum kernel-based learning.

## Key findings

- A new high-order feature map improves quantum kernel performance on nonlinear datasets.
- Hyperparameter tuning enhances decision boundaries and kernel expressivity.
- Quantum kernels outperform classical models on certain complex classification tasks.

## Abstract

Quantum algorithms have become a popular research domain in recent times for discovering quantum-enhanced solutions in machine learning applications. Quantum kernels are one of the directions that establish such quantum-enhanced solutions to some extent. This work presents a detailed analysis of the quantum kernel approach leveraging feature maps and relevant hyperparameters to develop enhanced quantum kernels. The study includes a new high-order feature map and assesses five existing state-of-the-art feature maps for enhanced quantum kernel classifiers. Additionally, the significance of the rotational factor as a hyperparameter is highlighted for improving kernel performance. Also, it is analyzed whether different hyperparameter-tuned feature maps can lead to enhanced decision boundaries, demonstrating kernel expressivity. The analysis is undertaken on classification tasks using four different nonlinear datasets of distinct complexity. Comparative evaluations are also made with traditional machine learning models—Support Vector Machines (Linear and RBF), Naïve Bayes, Linear Discriminant Analysis, Decision Tree, Random Forest, Adaptive Boosting, and MLP. Overall, the study demonstrates that a well-tuned quantum feature map can enhance the generalization ability of quantum kernels, making them more effective for broader quantum-enhanced machine learning applications.