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arXiv:2510.06300

Extended validations on photon number resolving detector based Gaussian boson sampling with low noises

Ji Yang, Wu, Yongzheng, Shi Wang, Jie Hou, Zijian Wang, Jiang, Bo

Published Oct 7, 2025• 0 citations
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Abstract

Gaussian boson sampling (GBS) is a variety of boson sampling overcoming the stable single-photon preparation difficulty of the later. However, like those in the original version, noises in GBS will also result in the deviation of output patterns and the reduction of classical simulation complexity. We extend the pattern recognition validation, together with the correlation approach as a comparison, on GBS using photon number resolving detectors, with noises of both photon loss and distinguishability, to quantificationally evaluate noise levels. As for the classical simulation with noises to be used during validations, it is actually a simulation of mixed states where we employ an existing photon-pair strategy to realize polynomial speedup locally. Furthermore, we use an output-binning strategy to realize validation speedup. Our simulation indicates that the pattern recognition protocol is useful for noise evaluations of GBS even when noises are sufficiently low.

DOI
10.48550/arxiv.2510.06300

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Gaussian boson sampling (GBS) is a variety of boson sampling overcoming the stable single-photon preparation difficulty of the later. However, like those in the original version, noises in GBS will also result in the deviation of output patterns and the reduction of classical simulation complexity. We extend the pattern recognition validation, together with the correlation approach as a comparison, on GBS using photon number resolving detectors, with noises of both photon loss and distinguishability, to quantificationally evaluate noise levels. As for the classical simulation with noises to be used during validations, it is actually a simulation of mixed states where we employ an existing photon-pair strategy to realize polynomial speedup locally. Furthermore, we use an output-binning strategy to realize validation speedup. Our simulation indicates that the pattern recognition protocol is useful for noise evaluations of GBS even when noises are sufficiently low.
Abstract Gaussian boson sampling (GBS) is a variety of boson sampling overcoming the stable single-photon preparation difficulty of the later. However, like those in the original version, noises in GBS will also result in the deviation of output distributions and the reduction of classical simulation complexity. We extend the pattern recognition validation, together with the correlation validation as a comparison, on GBS using photon number resolving detectors, with noises of both photon loss and distinguishability, to quantificationally evaluate noise levels. As for the classical simulation with noises to be used during validations, it is actually a simulation of mixed states where noises have been proved to be possibly utilized to realize computation speedup. Furthermore, we use an output-binning strategy to realize validation speedup. Our work indicates that the pattern recognition protocol is useful for noise evaluations of GBS even when noises are sufficiently low.
Gaussian boson sampling (GBS), a computational problem conjectured to be hard to simulate on a classical machine, has been at the forefront of recent years' experimental and theoretical efforts to demonstrate quantum advantage. The classical intractability of the sampling task makes validating these experiments a challenging and essential undertaking. In this paper, we propose binned-detector probability distributions as a suitable quantity to statistically validate GBS experiments employing photon-number-resolving detectors. We show how to compute such distributions by leveraging their connection with their respective characteristic function. The latter may be efficiently and analytically computed for squeezed input states as well as for relevant classical hypothesis like squashed states. Our scheme encompasses other validation methods based on marginal distributions and correlation functions. Additionally, it can accommodate various sources of noise, such as losses and partial distinguishability, a feature that have received limited attention within the GBS framework so far. We also illustrate how binned-detector probability distributions behave when Haar-averaged over all possible interferometric networks, extending known results for Fock boson sampling.
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), a computational problem conjectured to be hard to simulate on a classical machine, has been at the forefront of recent years’ experimental and theoretical efforts to demonstrate quantum advantage. The classical intractability of the sampling task makes validating these experiments a challenging and essential undertaking. In this paper, we propose binned-detector probability distributions as a suitable quantity to statistically validate GBS experiments employing photon-number-resolving detectors. We develop the theoretical framework to compute such distributions by leveraging their connection with their respective characteristic function. The latter may be efficiently and analytically computed for squeezed input states as well as for relevant classical hypothesis like squashed states. Our theoretical framework encompasses other validation methods based onmarginal distributions and correlation functions. Additionally, it can analytically accommodate various sources of noise, such as losses and partial distinguishability, a feature that has received limited attention within the GBS framework so far. We also derive how binned-detector probability distributions behave when Haar averaged over all possible interferometric networks, extending known results for Fock boson sampling.
As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS-in the form of an inequality between the input squeezing parameter, the overall transmission rate, and the quality of photon detectors. Our result serves as a nonclassicality test that must be passed by any quantum computational supremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.
Gaussian boson sampling (GBS) seeks quantum advantage by sampling photon-number patterns generated with squeezed inputs and passive linear optics. Many proposed GBS applications instead target function computation by applying functions to mode-resolved photon-number outcomes---a natural form of experimental postprocessing that produces classical outputs. Sampling hardness alone, however, does not determine the complexity of these tasks. By analyzing the irreducible decomposition of fixed-photon-number operator spaces, we prove that the expectation value of every such function in the average case over passive linear-optical networks can be classically evaluated for inputs with finite squeezing strength. We also provide a classical algorithm that estimates this value to inverse-polynomial additive error. The result provides new theoretical tools for analyzing linear-optical quantum systems, helps clarify the origin of current GBS hardness evidence, and inspires new applications of GBS with genuine quantum advantages.