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:2306.12120 · Advanced Photonics Nexus

Validation of a noisy Gaussian boson sampler via graph theory

Denis Stanev, Taira Giordani, Nicolò Spagnolo, Fabio Sciarrino

Published Jan 9, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1117/1.apn.4.1.016011

Related papers

Certification of Gaussian Boson Sampling via graphs feature vectors and kernels

Taira Giordani, Valerio Mannucci, Nicolò Spagnolo +4 more

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.

arXiv:2202.07711•Quantum Science and Technology•Sep 30, 2022•9 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

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

Validation tests of Gaussian boson samplers with photon-number resolving detectors

Alexander S. Dellios, M. D. Reid, P. D. Drummond

Abstract An important challenge with the current generation of noisy, large-scale quantum computers is the question of validation. Does the hardware generate correct answers? If not, what are the errors? This issue is often combined with questions of computational advantage, but it is a fundamentally distinct issue. In current experiments, complete validation of the output statistics is generally not possible because it is exponentially hard to do so. Here, we apply phase-space simulation methods to partially verify recent experiments on Gaussian boson sampling (GBS) implementing photon-number resolving detectors. The positive-P phase-space distribution is employed, as it uses probabilistic sampling to reduce complexity. It is ∼ 10 18 times faster than direct classical simulation for experiments on 288 modes where quantum computational advantage is claimed. When combined with binning and marginalization to improve statistics, multiple validation tests are efficiently computable, of which some tests can be carried out on experimental data. We show that the data as a whole has discrepancies with theoretical predictions for perfect squeezing. However, a modification of the GBS parameters greatly improves agreement for some tests. We suggest that such validation tests could form the basis of feedback methods to improve GBS experiments.

arXiv:2411.11228•Quantum Science and Technology•Aug 21, 2025•2 citations

Employing Integrated Quantum Photonic Computers for Gaussian Boson Sampling

Mehrdad Ghasemi, Hassan Kaatuzian, Houshyar Noshad +3 more

Gaussian boson sampling (GBS) is a tool for demonstrating quantum computational utilities and also exhibits mathematical connections to specific graph-related and quantum chemistry problems. It has been suggested that the samples generated from GBS could be utilized to improve stochastic algorithms in searching for certain graph features. In this study, we employed X8, a noisy intermediate-scale quantum computer, to address graph problems. The samples were produced from a 4-mode quantum photonic processor. This research represents a step toward analyzing Gaussian boson sampling as a tool for solving real-world problems using existing noisy intermediate-scale quantum computers and aims to encourage the development of quantum algorithms.

•May 14, 2024•1 citation

A Quantum-Inspired Algorithm for Graph Isomorphism

Innes L. Maxwell, Stefan N. van den Hoven, Jelmer J. Renema

The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical quantum advantage remain elusive in this era, it provides space to develop and analyze the advantages and limitations of systems and their ability to solve problems. In this work, we critically assess a proposed quantum algorithm for the graph isomorphism problem, implemented on a photonic quantum device. Inspired by the nature of this quantum algorithm, we formulate a necessary condition for the isomorphism of graphs encoded in Gaussian boson samplers and a classical algorithm to test for it. Our classical algorithm makes use of efficiently computable statistical properties of a quantum sampling system to show a pair of graphs fail to meet our necessary condition and thus cannot be isomorphic. We analyze our algorithm in the context of the inspiring, sampler-based quantum algorithm of Bràdler et. al., the classical color refinement algorithm, and the state-of-the-art quasi-polynomial Babai algorithm.

quant-pharXiv:2512.24423•Jan 1, 2026•0 citations
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.
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.
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.
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.
Abstract An important challenge with the current generation of noisy, large-scale quantum computers is the question of validation. Does the hardware generate correct answers? If not, what are the errors? This issue is often combined with questions of computational advantage, but it is a fundamentally distinct issue. In current experiments, complete validation of the output statistics is generally not possible because it is exponentially hard to do so. Here, we apply phase-space simulation methods to partially verify recent experiments on Gaussian boson sampling (GBS) implementing photon-number resolving detectors. The positive-P phase-space distribution is employed, as it uses probabilistic sampling to reduce complexity. It is ∼ 10 18 times faster than direct classical simulation for experiments on 288 modes where quantum computational advantage is claimed. When combined with binning and marginalization to improve statistics, multiple validation tests are efficiently computable, of which some tests can be carried out on experimental data. We show that the data as a whole has discrepancies with theoretical predictions for perfect squeezing. However, a modification of the GBS parameters greatly improves agreement for some tests. We suggest that such validation tests could form the basis of feedback methods to improve GBS experiments.
Gaussian boson sampling (GBS) is a tool for demonstrating quantum computational utilities and also exhibits mathematical connections to specific graph-related and quantum chemistry problems. It has been suggested that the samples generated from GBS could be utilized to improve stochastic algorithms in searching for certain graph features. In this study, we employed X8, a noisy intermediate-scale quantum computer, to address graph problems. The samples were produced from a 4-mode quantum photonic processor. This research represents a step toward analyzing Gaussian boson sampling as a tool for solving real-world problems using existing noisy intermediate-scale quantum computers and aims to encourage the development of quantum algorithms.
The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical quantum advantage remain elusive in this era, it provides space to develop and analyze the advantages and limitations of systems and their ability to solve problems. In this work, we critically assess a proposed quantum algorithm for the graph isomorphism problem, implemented on a photonic quantum device. Inspired by the nature of this quantum algorithm, we formulate a necessary condition for the isomorphism of graphs encoded in Gaussian boson samplers and a classical algorithm to test for it. Our classical algorithm makes use of efficiently computable statistical properties of a quantum sampling system to show a pair of graphs fail to meet our necessary condition and thus cannot be isomorphic. We analyze our algorithm in the context of the inspiring, sampler-based quantum algorithm of Bràdler et. al., the classical color refinement algorithm, and the state-of-the-art quasi-polynomial Babai algorithm.