Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2202.07711 · Quantum Science and Technology

Certification of Gaussian Boson Sampling via graphs feature vectors and kernels

Taira Giordani, Valerio Mannucci, Nicolò Spagnolo, Marco Fumero, Arianna Rampini, Emanuele Rodolà, Fabio Sciarrino

Published Sep 30, 2022• 9 citations
arXivHTMLPDF

Abstract

Abstract Gaussian Boson Sampling (GBS) is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling (BS) 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 GBS 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 GBS 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 GBS 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 are presented. The first method exploits the distributions of graph feature vectors and classification via neural networks. The second approach investigates the distributions of graph kernels. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers.

DOI
10.1088/2058-9565/ac969b

Related papers

Validation of a noisy Gaussian boson sampler via graph theory

Denis Stanev, Taira Giordani, Nicolò Spagnolo +1 more

Quantum photonic processors are emerging as promising platforms to prove preliminary evidence of quantum computational advantage toward the realization of universal quantum computers. In the context of nonuniversal noisy intermediate quantum devices, photonic-based sampling machines solving the Gaussian boson sampling (GBS) problem currently play a central role in the experimental demonstration of quantum computational advantage. A relevant issue is the validation of the sampling process in the presence of experimental noise, such as photon losses, which could undermine the hardness of simulating the experiment. We test the capability of a validation protocol that exploits the connection between GBS and graph perfect match counting to perform such an assessment in a noisy scenario. In particular, we use as a test bench the recently developed machine Borealis, a large-scale sampling machine that has been made available online for external users, and address its operation in the presence of noise. The employed approach to validation is also shown to provide connections with the open question on the effective advantage of using noisy GBS devices for graph similarity and isomorphism problems and thus provides an effective method for certification of quantum hardware.

arXiv:2306.12120•Advanced Photonics Nexus•Jan 9, 2025•2 citations

Measuring the similarity of graphs with a Gaussian boson sampler

Maria Schuld, Kamil Brádler, Robert Israel +2 more

Gaussian boson samplers (GBSs) have initially been proposed as a near-term demonstration of classically intractable quantum computation. We show here that they have a potential practical application: Samples from these devices can be used to construct a feature vector that embeds a graph in Euclidean space, where similarity measures between graphs---so-called graph kernels---can be naturally defined. This is crucial for machine learning with graph-structured data, and we show that the GBS-induced kernel performs remarkably well in classification benchmark tasks. We provide a theoretical motivation for this success, linking the extracted features to the number of $r$ matchings in subgraphs. Our results contribute to a new way of thinking about kernels as a quantum hardware-efficient feature mapping, and lead to a promising application for near-term quantum computing.

arXiv:1905.12646•Physical Review A•Mar 11, 2020•92 citations

Gaussian Boson Sampling to Accelerate NP-Complete Vertex-Minor Graph Classification

Mushkan Sureka, Saikat Guha

Gaussian Boson Sampling (GBS) generates random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations of quantum supremacy using GBS, Boson Sampling, and instantaneous quantum polynomial (IQP) algorithms, systematic evaluations of the power of these quantum-enhanced random samplers when applied to provably hard problems, and performance comparisons with best-known classical algorithms have been lacking. We propose a hybrid quantum-classical algorithm using the GBS for the NP-complete problem of determining if two graphs are a vertex minor of one another. The graphs are encoded in GBS and the generated random samples serve as feature vectors in a support vector machine (SVM) classifier. We find a graph embedding that allows trading between the one-shot classification accuracy and the amount of input squeezing, a hard-to-produce quantum resource, followed by repeated trials and a majority vote to reach an overall desired accuracy. We introduce a new classical algorithm based on graph spectra, which we show outperforms various well-known graph-similarity algorithms. We compare the performance of our algorithm with this classical algorithm and analyze their time versus problem-size scaling, to yield a desired classification accuracy. Our simulation results suggest that with a near-term realizable GBS device—5 dB pulsed squeezers, 12-mode unitary, and reasonable assumptions on coupling efficiency, on-chip losses, and detection efficiency of photon number resolving detectors—we can solve 12-node vertex-minor instances with about 103fold lower time compared to a powerful desktop computer.

arXiv:2402.03524•IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 15, 2024•0 citations

Solving Graph Problems Using Gaussian Boson Sampling

Yu‐Hao Deng, Si-Qiu Gong, Yi-Chao Gu +21 more

Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed that the generated samples from the GBS could be harnessed to enhance the classical stochastic algorithms in searching some graph features. Here, we use Jiǔzhāng, a noisy intermediate-scale quantum computer, to solve graph problems. The samples are generated from a 144-mode fully connected photonic processor, with photon click up to 80 in the quantum computational advantage regime. We investigate the open question of whether the GBS enhancement over the classical stochastic algorithms persists-and how it scales-with an increasing system size on noisy quantum devices in the computationally interesting regime. We experimentally observe the presence of GBS enhancement with a large photon-click number and a robustness of the enhancement under certain noise. Our work is a step toward testing real-world problems using the existing noisy intermediate-scale quantum computers and hopes to stimulate the development of more efficient classical and quantum-inspired algorithms.

arXiv:2302.00936•Physical Review Letters•May 9, 2023•60 citations

Sample efficient graph classification using binary Gaussian boson sampling

Amanuel Anteneh, Olivier Pfister

We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS), a near-term model of quantum computing. However, unlike the currently proposed algorithms for this problem, our GBS setup requires only binary (light or no light) detectors, as opposed to photon-number-resolving detectors. Binary detectors are technologically simpler and can operate near room temperature, making our algorithm much less complex and costly to implement physically. We also investigate the connection between graph theory and the Torontonian matrix function which characterizes the probabilities of binary GBS detection events.

arXiv:2301.01232•Physical Review A•Dec 11, 2023•3 citations

Gaussian boson sampling: Benchmarking quantum advantage

Ned Goodman, Alexander S. Dellios, Margaret D. Reid +1 more

Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors, and how do they affect the complexity of the problem solved? Large-scale Gaussian boson sampling (GBS) experiments give an example in which random numbers are generated. Despite classical hardness, these have computable benchmarks for checking data validity. While there are other quantum computing architectures, Gaussian boson sampling is uniquely testable at all scales. Several large, pioneering quantum computing (QC) experiments have been carried out to investigate quantum advantage. Here, we introduce a highly scalable but classical algorithm that can solve GBS approximately. Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes. This algorithm outperforms all previous classical, approximate algorithms and scales efficiently to larger experiments. Our results show that effects beyond losses can cause the errors that allow classical simulability. This work will lead to more precise algorithms and is a step towards understanding how QC quantum advantage is affected by the underlying physics.

quant-pharXiv:2604.12330•Apr 15, 2026•0 citations
Abstract Gaussian Boson Sampling (GBS) is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling (BS) 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 GBS 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 GBS 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 GBS 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 are presented. The first method exploits the distributions of graph feature vectors and classification via neural networks. The second approach investigates the distributions of graph kernels. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers.
Quantum photonic processors are emerging as promising platforms to prove preliminary evidence of quantum computational advantage toward the realization of universal quantum computers. In the context of nonuniversal noisy intermediate quantum devices, photonic-based sampling machines solving the Gaussian boson sampling (GBS) problem currently play a central role in the experimental demonstration of quantum computational advantage. A relevant issue is the validation of the sampling process in the presence of experimental noise, such as photon losses, which could undermine the hardness of simulating the experiment. We test the capability of a validation protocol that exploits the connection between GBS and graph perfect match counting to perform such an assessment in a noisy scenario. In particular, we use as a test bench the recently developed machine Borealis, a large-scale sampling machine that has been made available online for external users, and address its operation in the presence of noise. The employed approach to validation is also shown to provide connections with the open question on the effective advantage of using noisy GBS devices for graph similarity and isomorphism problems and thus provides an effective method for certification of quantum hardware.
Gaussian boson samplers (GBSs) have initially been proposed as a near-term demonstration of classically intractable quantum computation. We show here that they have a potential practical application: Samples from these devices can be used to construct a feature vector that embeds a graph in Euclidean space, where similarity measures between graphs---so-called graph kernels---can be naturally defined. This is crucial for machine learning with graph-structured data, and we show that the GBS-induced kernel performs remarkably well in classification benchmark tasks. We provide a theoretical motivation for this success, linking the extracted features to the number of rrr matchings in subgraphs. Our results contribute to a new way of thinking about kernels as a quantum hardware-efficient feature mapping, and lead to a promising application for near-term quantum computing.
Gaussian Boson Sampling (GBS) generates random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations of quantum supremacy using GBS, Boson Sampling, and instantaneous quantum polynomial (IQP) algorithms, systematic evaluations of the power of these quantum-enhanced random samplers when applied to provably hard problems, and performance comparisons with best-known classical algorithms have been lacking. We propose a hybrid quantum-classical algorithm using the GBS for the NP-complete problem of determining if two graphs are a vertex minor of one another. The graphs are encoded in GBS and the generated random samples serve as feature vectors in a support vector machine (SVM) classifier. We find a graph embedding that allows trading between the one-shot classification accuracy and the amount of input squeezing, a hard-to-produce quantum resource, followed by repeated trials and a majority vote to reach an overall desired accuracy. We introduce a new classical algorithm based on graph spectra, which we show outperforms various well-known graph-similarity algorithms. We compare the performance of our algorithm with this classical algorithm and analyze their time versus problem-size scaling, to yield a desired classification accuracy. Our simulation results suggest that with a near-term realizable GBS device—5 dB pulsed squeezers, 12-mode unitary, and reasonable assumptions on coupling efficiency, on-chip losses, and detection efficiency of photon number resolving detectors—we can solve 12-node vertex-minor instances with about 103fold lower time compared to a powerful desktop computer.
Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed that the generated samples from the GBS could be harnessed to enhance the classical stochastic algorithms in searching some graph features. Here, we use Jiǔzhāng, a noisy intermediate-scale quantum computer, to solve graph problems. The samples are generated from a 144-mode fully connected photonic processor, with photon click up to 80 in the quantum computational advantage regime. We investigate the open question of whether the GBS enhancement over the classical stochastic algorithms persists-and how it scales-with an increasing system size on noisy quantum devices in the computationally interesting regime. We experimentally observe the presence of GBS enhancement with a large photon-click number and a robustness of the enhancement under certain noise. Our work is a step toward testing real-world problems using the existing noisy intermediate-scale quantum computers and hopes to stimulate the development of more efficient classical and quantum-inspired algorithms.
We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS), a near-term model of quantum computing. However, unlike the currently proposed algorithms for this problem, our GBS setup requires only binary (light or no light) detectors, as opposed to photon-number-resolving detectors. Binary detectors are technologically simpler and can operate near room temperature, making our algorithm much less complex and costly to implement physically. We also investigate the connection between graph theory and the Torontonian matrix function which characterizes the probabilities of binary GBS detection events.
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors, and how do they affect the complexity of the problem solved? Large-scale Gaussian boson sampling (GBS) experiments give an example in which random numbers are generated. Despite classical hardness, these have computable benchmarks for checking data validity. While there are other quantum computing architectures, Gaussian boson sampling is uniquely testable at all scales. Several large, pioneering quantum computing (QC) experiments have been carried out to investigate quantum advantage. Here, we introduce a highly scalable but classical algorithm that can solve GBS approximately. Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes. This algorithm outperforms all previous classical, approximate algorithms and scales efficiently to larger experiments. Our results show that effects beyond losses can cause the errors that allow classical simulability. This work will lead to more precise algorithms and is a step towards understanding how QC quantum advantage is affected by the underlying physics.