# Experimental kernel-based quantum machine learning in finite feature space

## TL;DR

This paper demonstrates an optical quantum machine learning setup that uses kernel methods in a finite-dimensional quantum feature space, showing improved scalability and effective classification.

## Contribution

It introduces a hybrid optical quantum machine learning approach with optimized feature maps for finite-dimensional kernels, enhancing scalability and classification performance.

## Key findings

- Kernel-based quantum classifiers achieve viable decision boundaries.
- Optimized feature maps improve kernel resolution in finite spaces.
- Exponential scaling advantage over previous kernel methods.

## Abstract

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed on a classical computer. Our two-photon proposal encodes data points in a discrete, eight-dimensional feature Hilbert space. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels' ability to separate points, i.e., their resolution, under the constraint of finite, fixed Hilbert space dimension. Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classification tasks in feature space. We demonstrate such kernel-based quantum machine learning using specialized multiphoton quantum optical circuits. The deployed kernel exhibits exponentially better scaling in the required number of qubits than a direct generalization of kernels described in the literature.