# A quantum hardware-induced graph kernel based on Gaussian Boson Sampling

## TL;DR

This paper introduces a novel quantum hardware-based graph kernel using Gaussian Boson Sampling, demonstrating its effectiveness for graph similarity and providing theoretical insights into its performance, with promising applications in quantum computing.

## Contribution

It presents a new quantum hardware-inspired graph kernel leveraging Gaussian Boson Sampling, linking quantum sampling distributions to graph matchings for improved similarity measures.

## Key findings

- Kernel performs well on benchmark datasets
- Links Gaussian Boson Sampling to graph matchings
- Provides theoretical motivation for kernel effectiveness

## Abstract

A device called a 'Gaussian Boson Sampler' has initially been proposed as a near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on these results we construct a feature map and graph similarity measure or 'graph kernel' using samples from the device. We show that the kernel performs well compared to standard graph kernels on typical benchmark datasets, and provide a theoretical motivation for this success, linking the distribution of a Gaussian Boson Sampler to the number of matchings in subgraphs. Our results contribute to a new way of thinking about kernels as a (quantum) hardware-efficient feature mapping, and lead to an interesting application for near-term quantum computing.