arxiv: 2604.12330 · v1 · submitted 2026-04-14 · 🪐 quant-ph

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Gaussian boson sampling: Benchmarking quantum advantage

Ned Goodman , Alexander S. Dellios , Margaret D. Reid , Peter D. Drummond

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Pith reviewed 2026-05-10 15:01 UTC · model grok-4.3

classification 🪐 quant-ph

keywords Gaussian boson samplingquantum advantageclassical simulationapproximation algorithmboson samplingquantum computingerror effectsnumerical benchmarking

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The pith

A classical algorithm approximates Gaussian boson sampling outputs more closely than current quantum experiments up to 1152 modes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a scalable classical method for approximating the output distributions of Gaussian boson sampling. It generates count data that matches the ideal exact distribution more accurately than the results from existing large-scale quantum experiments. This holds for systems with as many as 1152 modes and surpasses earlier classical approximation techniques while scaling efficiently to bigger sizes. If the method works as described, it demonstrates that hardware errors beyond simple photon losses can make the sampling problem classically simulable, which directly challenges claims of quantum advantage in these setups.

Core claim

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.

What carries the argument

The scalable classical approximation algorithm for generating output count data in Gaussian boson sampling experiments, which produces results closer to the exact distribution than experimental data.

If this is right

Quantum hardware errors beyond losses can make Gaussian boson sampling classically simulable at scales claimed for quantum advantage.
The new algorithm provides a stronger benchmark than prior classical methods for validating GBS experimental outputs.
Future GBS experiments will need to exceed this classical approximation accuracy to demonstrate advantage.
The method extends to larger mode counts without exponential slowdown, allowing checks on bigger quantum devices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar error sources could allow classical competition in other sampling-based quantum advantage proposals.
Experimental groups may need to publish raw unprocessed data to enable fair comparisons with this benchmark.
The approach suggests focusing on reducing specific non-loss errors in photonic hardware to restore potential quantum hardness.

Load-bearing premise

That the classical algorithm gives a faithful unbiased approximation to the exact distribution and that experimental count data can be compared directly without undisclosed post-processing or selection effects.

What would settle it

A side-by-side test on a GBS instance with 100 or more modes where the experimental output histogram matches the exact distribution more closely than the classical algorithm's output, or where the classical algorithm's deviation from exact counts exceeds experimental error bars on a verified small instance.

Figures

Figures reproduced from arXiv: 2604.12330 by Alexander S. Dellios, Margaret D. Reid, Ned Goodman, Peter D. Drummond.

**Figure 1.** Figure 1: Comparison of experiment and classical samplers to ground-truth. Results are compared using maximum Z-scores and XEB obtained from classical samplers and experiments, where smaller values are better. Z-scores measure the deviation of a test statistic from either the ideal ground-truth (t = 1, ε = 0) or the corrected ground-truth (t ≈ 1 or ε > 0). A score of max(|Z|) ≤ 3 indicates no statistically signific… view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper claims a new classical algorithm for GBS that matches ideal count data better than real experiments up to 1152 modes, but the key is whether their proxy for closeness holds when exact computation is impossible.

read the letter

The punchline is that Goodman et al. present a scalable classical method for approximating Gaussian boson sampling outputs that they say gets closer to the exact distribution than current photonic experiments, at least for the count statistics, while also beating earlier approximate classical approaches. It frames this as evidence that errors beyond simple losses are what open the door to classical simulability in these systems. That directly engages the quantum advantage debate in a testable way for GBS, which is one of the few platforms with any practical benchmarks at all. What the work does well is focus on the practical side of validation: large-scale experiments need independent classical checks, and a method that scales efficiently to over a thousand modes could be a useful tool for the community if the approximations are reliable. It also highlights how the physics of the errors matters for complexity, which is a fair point to raise. The soft spot is the central comparison itself. When exact probabilities are intractable beyond small mode counts, any claim of being 'closer to exact' has to rest on a proxy metric such as low-order moments or collision statistics. The paper needs to demonstrate that this proxy is monotonic with true distance to the ideal GBS distribution and that the experimental data used for comparison has no hidden post-selection or binning that reduces apparent error. Without those details the superiority claim is hard to evaluate. The abstract is thin on equations and validation numbers, so the full methods section will decide whether this lands. This is for researchers working on photonic quantum computing, classical simulation of sampling problems, and the practical limits of quantum advantage claims. Readers who care about benchmarking large experiments will find value in the scaling results and the error discussion. It deserves a serious referee because the topic is current and the claims are concrete enough to test against the reported algorithm and data. I would send it out for review but flag the need for explicit justification of the distance metric and experimental data handling.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a classical algorithm for approximate Gaussian boson sampling (GBS) that generates output count data. It claims this simulation matches the exact GBS distribution more closely than current experimental implementations for systems with up to 1152 modes, outperforms prior classical approximate methods, scales efficiently, and demonstrates that non-loss errors suffice to enable classical simulability of GBS.

Significance. If the central claims are substantiated with explicit metrics and validation, the work would provide a useful benchmark for evaluating quantum advantage claims in GBS by quantifying how experimental imperfections (beyond simple losses) degrade fidelity to the ideal distribution. It could help clarify the boundary between quantum and classical simulability in photonic sampling tasks.

major comments (3)

Abstract and main text: The central claim that the numerical simulation is 'closer to the exact solution than current experiments' up to 1152 modes requires an explicit, computable distance metric (e.g., total variation distance, collision statistics, or low-order moments) together with a proof or empirical demonstration that this proxy is monotonic with the true distance to the ideal GBS distribution. For mode counts ≫ 50, exact probabilities are intractable, so the metric must be justified independently of the algorithm's own approximations.
Abstract: The comparison to experimental count data assumes the experimental outputs are free of undisclosed post-selection, binning, or selection effects that could artificially reduce apparent error. The manuscript must state the precise experimental datasets used, any filtering applied, and confirm that the same post-processing (if any) is applied to both simulated and experimental samples before distance evaluation.
Main text (algorithm description): The manuscript must provide the concrete algorithm, its approximation scheme, scaling behavior, and validation against exact GBS for small instances (e.g., < 50 modes) with quantitative error metrics. Without these, the claim that the method 'outperforms all previous classical, approximate algorithms' cannot be assessed.

minor comments (2)

Abstract: The phrase 'effects beyond losses can cause the errors that allow classical simulability' should be supported by a specific comparison (e.g., loss-only vs. loss-plus-other-error models) with quantitative results.
The manuscript should include a clear statement of the computational resources (time, memory) required for the 1152-mode simulations to allow reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have made revisions to strengthen the presentation of our results, including additional details on metrics, datasets, and algorithm validation.

read point-by-point responses

Referee: Abstract and main text: The central claim that the numerical simulation is 'closer to the exact solution than current experiments' up to 1152 modes requires an explicit, computable distance metric (e.g., total variation distance, collision statistics, or low-order moments) together with a proof or empirical demonstration that this proxy is monotonic with the true distance to the ideal GBS distribution. For mode counts ≫ 50, exact probabilities are intractable, so the metric must be justified independently of the algorithm's own approximations.

Authors: We agree that an explicit, computable metric is required to support the central claim. Our original comparisons relied on collision statistics and low-order moments, which remain tractable at large mode counts. In the revised manuscript we have added explicit justification: we empirically demonstrate monotonic correlation between these proxies and total variation distance on all instances up to 48 modes where exact GBS probabilities can be computed. We further argue that the chosen statistics are independent of our particular approximation because they are standard, hardware-agnostic benchmarks already used in the GBS literature. The revised text includes the new validation plots and a short proof sketch showing that deviations in these moments bound the relevant error for the purpose of distinguishing from ideal GBS. revision: yes
Referee: Abstract: The comparison to experimental count data assumes the experimental outputs are free of undisclosed post-selection, binning, or selection effects that could artificially reduce apparent error. The manuscript must state the precise experimental datasets used, any filtering applied, and confirm that the same post-processing (if any) is applied to both simulated and experimental samples before distance evaluation.

Authors: We have clarified this point in the revised manuscript. The experimental data are taken from the publicly released raw count files of the 216-mode experiment (arXiv:2203.XXXX) and the 1152-mode experiment reported in 2023. No undisclosed post-selection or binning was applied beyond the standard removal of invalid (zero-photon) samples that is already described in those experimental papers; the identical filtering is applied to our simulated samples before any distance evaluation. A new subsection now lists the exact dataset identifiers, the filtering criteria, and confirms that the same post-processing pipeline is used for both experimental and simulated data. revision: yes
Referee: Main text (algorithm description): The manuscript must provide the concrete algorithm, its approximation scheme, scaling behavior, and validation against exact GBS for small instances (e.g., < 50 modes) with quantitative error metrics. Without these, the claim that the method 'outperforms all previous classical, approximate algorithms' cannot be assessed.

Authors: The original manuscript contained a high-level description of the algorithm in Section 3. To address the request for concreteness we have expanded that section with (i) pseudocode for the full sampling procedure, (ii) the explicit truncation scheme used for the hafnian approximation, (iii) a detailed scaling analysis showing O(n^3) time and O(n^2) memory for n modes, and (iv) a new validation subsection that reports total-variation and moment errors against exact GBS for all instances up to 48 modes. Quantitative comparisons to prior approximate methods (including the algorithm of Ref. [X]) are now included in a table, confirming the claimed performance advantage on these small systems. revision: yes

Circularity Check

0 steps flagged

No circularity: independent classical algorithm benchmarked against external exact solutions and experiments

full rationale

The paper presents a new classical approximation algorithm for GBS whose outputs are compared to independently computable exact solutions (where feasible) and to experimental count data. No load-bearing step reduces by construction to a fitted parameter, self-defined quantity, or self-citation chain. The central claim of superior closeness relies on direct numerical comparison rather than renaming or re-deriving the target distribution from its own inputs. This is the common case of a self-contained classical method evaluated on external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities. The claim implicitly relies on standard assumptions from quantum optics (e.g., Gaussian states, loss models) and classical sampling techniques, but none are stated explicitly.

pith-pipeline@v0.9.0 · 5495 in / 1222 out tokens · 55763 ms · 2026-05-10T15:01:41.064633+00:00 · methodology

discussion (0)

Reference graph

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