# Analysis and synthesis of feature map for kernel-based quantum classifier

## TL;DR

This paper introduces a method to analyze and synthesize feature maps for kernel-based quantum classifiers, enabling better understanding and construction of feature maps for improved classification performance.

## Contribution

It provides a general formula for lower bounds of training accuracy and a synthesis approach to combine kernels for enhanced quantum classifier feature maps.

## Key findings

- The method effectively evaluates feature map suitability for datasets.
- Demonstrated the approach on 2-qubit classifiers with 2D datasets.
- Synthesis of kernels improves classifier performance.

## Abstract

A method for analyzing the feature map for the kernel-based quantum classifier is developed; that is, we give a general formula for computing a lower bound of the exact training accuracy, which helps us to see whether the selected feature map is suitable for linearly separating the dataset. We show a proof of concept demonstration of this method for a class of 2-qubit classifier, with several 2-dimensional dataset. Also, a synthesis method, that combines different kernels to construct a better-performing feature map in a lager feature space, is presented.