Certification of Gaussian Boson Sampling via graph theory

TL;DR

This paper introduces a graph-theoretic method to verify Gaussian Boson Sampling experiments, leveraging graph features and kernels to benchmark the quantum device’s performance and authenticity.

Contribution

It proposes a novel graph-based benchmarking approach for Gaussian Boson Sampling, connecting graph properties to quantum sampling verification.

Findings

Graph feature vectors serve as signatures of correct sampling.

Graph kernels effectively distinguish genuine from incorrect samples.

The method offers a scalable benchmarking tool for large Gaussian Boson Samplers.

Abstract

Gaussian Boson Sampling is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling problem. Nowadays, it represents a paradigmatic quantum platform to reach the quantum advantage regime in a specific computational model. Indeed, thanks to the implementation in photonics-based processors, the latest Gaussian Boson Sampling experiments have reached a level of complexity where the quantum apparatus has solved the task faster than currently up-to-date classical strategies. In addition, recent studies have identified possible applications beyond the inherent sampling task. In particular, a direct connection between photon counting of a genuine Gaussian Boson Sampling device and the number of perfect matchings in a graph has been established. In this work, we propose to exploit such a connection to benchmark Gaussian Boson Sampling experiments. We interpret the properties of the feature vectors of the graph encoded in the device as a signature of correct sampling from the true input state. Within this framework, two approaches that exploit the distributions of graph feature vectors and graph kernels are presented. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers.