Certification of Gaussian Boson Sampling via graph theory

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.

arXiv comment9 pages, 5 figures

References in corpus (47)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum computational advantage using photons
• Strong quantum computational advantage using a superconducting quantum processor
• Universal Linear Optics
• Quantum Computational Supremacy
• Quantum circuits with many photons on a programmable nanophotonic chip
• Gaussian Boson Sampling
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Strawberry Fields: A Software Platform for Photonic Quantum Computing
• Efficient experimental validation of photonic boson sampling against the uniform distribution
• Boson Sampling from Gaussian States
• Generation and sampling of quantum states of light in a silicon chip
• A detailed study of Gaussian Boson Sampling
• No imminent quantum supremacy by boson sampling
• Using Gaussian Boson Sampling to Find Dense Subgraphs
• Sampling of partially distinguishable bosons and the relation to the multidimensional permanent
• Applications of Near-Term Photonic Quantum Computers: Software and Algorithms
• Quantum Computational Advantage via High-Dimensional Gaussian Boson Sampling
• Efficient algorithm for boson sampling with partially distinguishable photons
• Simulating boson sampling in lossy architectures
• The Boundary for Quantum Advantage in Gaussian Boson Sampling
• What can quantum optics say about computational complexity theory?
• A quantum hardware-induced graph kernel based on Gaussian Boson Sampling
• 20-Mode Universal Quantum Photonic Processor
• Regimes of classical simulability for noisy Gaussian boson sampling
• A Statistical Benchmark for BosonSampling
• Experimental statistical signature of many-body quantum interference
• Classical simulation of photonic linear optics with lost particles
• General rules for bosonic bunching in multimode interferometers
• Experimental Gaussian Boson Sampling
• Quantum approximate optimization with Gaussian boson sampling
• Exact simulation of Gaussian Boson Sampling in polynomial space and exponential time
• Graph isomorphism and Gaussian boson sampling
• Reconfigurable continuously-coupled 3D photonic circuit for Boson Sampling experiments
• Classical simulation of lossy boson sampling using matrix product operators
• Pattern recognition techniques for Boson Sampling validation
• Classical simulation of boson sampling based on graph structure
• Experimental generalized quantum suppression law in Sylvester interferometers
• Witnessing genuine multi-photon indistinguishability
• Classical simulation of linear optics subject to nonuniform losses
• Benchmarking of Gaussian boson sampling using two-point correlators
• Simulating complex networks in phase space: Gaussian boson sampling
• Simulability of Imperfect Gaussian and Superposition Boson Sampling
• Classically simulating near-term partially-distinguishable and lossy boson sampling
• A quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices
• Simulating macroscopic quantum correlations in linear networks

Cited by in corpus (6)

• Gaussian Boson Sampling with Pseudo-Photon-Number Resolving Detectors and Quantum Computational Advantage
• Benchmarking a boson sampler with Hamming nets
• Validation of a noisy Gaussian boson sampler via graph theory
• Optical Quantum Computing
• Sample space filling analysis for boson sampling validation
• Realistic photon-number resolution in Gaussian boson sampling