Gaussian boson sampling: Benchmarking quantum advantage
Ned Goodman, Alexander S. Dellios, Margaret D. Reid, Peter D. Drummond
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.
AI Impact Assessments
(3 models)Scientific Impact Assessment: "Gaussian Boson Sampling: Benchmarking Quantum Advantage"
1. Core Contribution
This paper introduces a classical approximate sampling algorithm for Gaussian Boson Sampling (GBS) based on the positive-P phase-space representation. The key idea is conceptually elegant: positive-P samples live in a 4M-dimensional phase space, but classical (efficiently simulable) states correspond to the 2M-dimensional subspace where α = β*. The authors project positive-P samples onto this physical subspace, then apply iterative whitening-coloring transformations to restore correct low-order statistics. The central claim is that this classical sampler produces output count distributions closer to the theoretical ground truth than the actual GBS quantum experiments (Jiuzhang 2, 3, and Borealis) across multiple benchmarks, scaling up to 1152 modes.
The paper also proves a theorem showing that linear losses alone do not remove quantum features from the output state (negative covariance eigenvalues are preserved under non-degenerate linear transformations), implying that the experimental deviations enabling classical simulability stem from other noise sources—decoherence, parameter errors, and thermal noise—rather than photon loss alone.
2. Methodological Rigor
The methodology is grounded in well-established quantum optics formalism (positive-P representation, Glauber-Sudarshan P-distribution). The projection-plus-whitening approach is physically motivated rather than purely heuristic: by choosing compact distributions (Eq. 12) that minimize the distance to the classical subspace, they reduce projection error.
The comparison framework is reasonably thorough, employing multiple metrics: grouped count distributions (GCDs), marginal distributions up to 20th order, and cross-entropy benchmarking (XEB). Converting to Z-scores provides a standardized comparison across different observables. The authors appropriately note that no single metric has complexity-theoretic hardness guarantees, and that only the collection might resist spoofing.
However, there are methodological concerns. The whitening-coloring transformation (Eq. 10-11) is designed to match low-order moments, which means the method is essentially constructing classical samples that reproduce the correct first and second moments by design. The claim of being "closer to ground truth" is therefore somewhat circular for moment-based metrics. The real question—how well the full distribution is approximated—cannot be answered without total variation distance, which the authors acknowledge is intractable. The authors also introduce a "corrected ground truth" with thermal noise parameters (ε) and transmission corrections (t), fitting these to experimental data. While physically motivated, this adds free parameters that could improve apparent agreement.
The proof that losses preserve quantum features (Sylvester's law of inertia argument) is clean and correct, though it requires non-degenerate transmission matrices—a reasonable assumption for real experiments.
3. Potential Impact
This work has significant implications for the quantum advantage debate in photonic quantum computing:
Challenging quantum advantage claims: By demonstrating that a polynomial-time classical algorithm can outperform experiments on verifiable benchmarks, it undermines standing claims of quantum advantage for GBS. This is consequential for the field's credibility and funding landscape.
Diagnostic value: The results identify that errors beyond photon loss (thermal decoherence, parameter imprecisions) are the primary enablers of classical simulation, providing actionable guidance for experimentalists designing next-generation GBS systems.
Scalability advantage: Unlike the MPS approach (which requires exponential memory scaling) or exact methods (exponential time), this positive-P sampler scales quadratically in memory and polynomially in time. The 1152-mode simulation on modest hardware (50 CPU cores, 4GB RAM each, ~26 minutes) versus MPS requiring 144 GPUs demonstrates practical scalability.
Broader relevance: While GBS-specific, the insight that experimental noise in quantum systems can be exploited by phase-space projection methods may generalize to other quantum advantage architectures, though the authors' claim of broader applicability to other QC architectures is speculative.
4. Timeliness & Relevance
This paper is extremely timely. Multiple groups (USTC, Xanadu) maintain active quantum advantage claims based on GBS, and the quantum computing community is engaged in ongoing debate about the validity of these claims. The paper arrives alongside other classical simulation challenges (squashed states, greedy samplers, MPS methods) but claims superiority over all of them in the quantum advantage regime.
The work also responds to Jiuzhang 4 (3050 photons, referenced as Ref [10] from 2025), acknowledging it as future work but claiming their quadratic scaling should handle it with moderate additional resources. This forward-looking scalability is important given the experimental trajectory.
5. Strengths & Limitations
Strengths:
Limitations:
Notable gap: The paper does not address Jiuzhang 4 (the largest current experiment), which weakens the claim of universal applicability despite the authors' assertion about scalability.
Overall Assessment
This is an important and timely contribution to the quantum advantage debate. The efficient classical simulability of current GBS experiments—demonstrated more convincingly than by previous classical algorithms—is a significant result. However, the fundamental question of whether improved experiments could escape classical simulation remains open, as the method's success depends on experimental noise levels that future experiments may reduce. The work is more impactful as a diagnostic tool and benchmark challenge than as a definitive refutation of GBS quantum advantage.
Generated Apr 15, 2026
Comparison History (39)
Paper 1 addresses the fundamental question of quantum advantage by introducing a scalable classical algorithm that challenges large-scale Gaussian boson sampling experiments, directly impacting the validity claims of pioneering quantum computing demonstrations. This has broad implications across quantum computing, computational complexity, and experimental physics. Paper 2 presents an incremental improvement in fault-tolerant syndrome extraction for CSS codes, which is valuable but more narrowly focused. Paper 1's challenge to quantum advantage claims is more timely and consequential for the field's direction.
Paper 2 addresses a fundamental and highly debated topic in quantum computing: verifying claims of quantum advantage. By introducing a classical algorithm that outperforms current Gaussian boson sampling experiments, it fundamentally challenges existing milestones and sets a new standard for benchmarking quantum systems. This broad, paradigm-shifting impact on the entire field of quantum computing outweighs Paper 1's narrower, albeit important, technological contribution to quantum networking and interconnects.
Paper 2 introduces a broadly applicable, unified quantum-algorithmic framework (generalized parameter-shift reformulation) for computing arbitrary n-th order nonlinear spectroscopy, with demonstrated execution on real hardware and clear extensions across condensed matter, AMO, and chemical physics. It targets a major bottleneck (exponential classical cost) and opens new near-term quantum-simulation capabilities with direct experimental relevance. Paper 1 is timely and rigorous but primarily impacts benchmarking and de-risking claimed quantum advantage in a narrower subfield; it is more corrective/diagnostic than enabling new application domains.
Paper 2 likely has higher scientific impact: it introduces a broadly relevant mechanism for stable non-ergodic dynamics—exponentially many symmetry-protected zero modes—linking thermalization breakdown, localization transitions, and robustness to perturbations. This advances fundamental many-body physics with cross-cutting implications for quantum information, transport, and engineered quantum matter, and is experimentally testable in accessible platforms. Paper 1 is timely for quantum-advantage verification and provides a strong classical benchmark, but its impact is narrower (GBS-specific) and partly incremental as an improved simulation/critique rather than a new general physical principle.
Paper 1 addresses a fundamental question about quantum advantage claims by introducing a scalable classical algorithm that outperforms current GBS experiments up to 1152 modes. This directly challenges major experimental claims of quantum supremacy, which has broad implications for the entire quantum computing field. Paper 2 presents a useful but more incremental contribution combining error correction with error mitigation for the pre-fault-tolerant regime. While practically relevant, Paper 1's impact is larger because it reshapes understanding of quantum advantage benchmarks and affects how the community evaluates quantum supremacy claims.
Paper 1 addresses a central question in quantum computing—whether current quantum advantage claims are valid—by introducing a scalable classical algorithm that outperforms existing GBS experiments up to 1152 modes. This directly challenges major experimental milestones and has broad implications for the entire quantum computing field's benchmarking standards. Paper 2 makes a solid theoretical contribution to energy-constrained purification, but its impact is more niche. Paper 1's relevance to the high-profile quantum advantage debate, combined with its immediate practical implications for experimental validation, gives it greater potential impact.
Paper 2 directly challenges claims of quantum advantage in Gaussian boson sampling experiments, a high-profile topic in quantum computing. By introducing a scalable classical algorithm that outperforms current GBS experiments up to 1152 modes, it has broad implications for the entire quantum advantage narrative. This addresses a fundamental question about the boundary between classical and quantum computation, affecting multiple research groups and future experimental designs. Paper 1, while useful for practical quantum error correction optimization, addresses a more specialized problem with narrower immediate impact.
Paper 1 addresses a fundamental question in quantum computing—whether current large-scale quantum advantage experiments actually achieve what they claim. By introducing a scalable classical algorithm that outperforms GBS experiments up to 1152 modes, it directly challenges landmark quantum supremacy claims, which has enormous implications for the entire quantum computing field. Paper 2, while technically sound, presents incremental optimization improvements for NOON-state phase estimation using existing simulation tools, with impact limited to quantum metrology. Paper 1's breadth of impact, timeliness, and relevance to the high-profile quantum advantage debate far exceed Paper 2's contributions.
Paper 1 challenges major quantum advantage claims (Gaussian boson sampling experiments up to 1152 modes) by introducing a scalable classical algorithm that outperforms current quantum experiments. This directly impacts the foundational question of quantum computational supremacy, a central issue in quantum computing. Its implications affect billions in quantum computing investment and research direction. Paper 2 addresses the important but more niche problem of post-selection in measurement-induced phase transitions using ML, which is valuable but has narrower immediate impact on the broader quantum computing and physics communities.
Paper 2 directly addresses the highly debated and impactful topic of quantum advantage, offering a classical algorithm that outperforms current large-scale Gaussian boson sampling experiments. This broadly impacts the quantum computing community by providing a critical benchmark that challenges existing claims of quantum supremacy. Paper 1, while rigorously exploring unitary k-designs, is more theoretical and niche in scope, giving Paper 2 a broader and more immediate scientific impact.
Paper 2 likely has higher impact due to timeliness and direct relevance to ongoing claims of quantum advantage. It proposes a scalable classical approximation algorithm that challenges/benchmarks large Gaussian boson sampling experiments up to 1152 modes, with immediate implications for experimental validation, error modeling, and complexity claims. This has clear real-world applications for quantum computing verification and could influence standards across platforms. Paper 1 is a broad, valuable synthesis of the kicked rotor and newer directions, but as a chapter-style overview it is less likely to shift the field compared to a concrete algorithmic advance affecting active debates.
Paper 2 likely has higher impact because it directly addresses a central, timely issue in quantum computing: validating and benchmarking claimed quantum advantage. By providing a scalable classical approximate algorithm that matches/approaches experimental GBS data up to very large mode numbers, it can immediately influence how experiments are interpreted, how future advantage claims are designed, and what error mechanisms matter. Its applications span photonic QC, complexity theory, verification, and experimental methodology. Paper 1 is novel and valuable for nonequilibrium many-body physics, but its near-term cross-field and practical impact is narrower and more exploratory.
Paper 2 likely has higher impact: it directly affects claims of quantum advantage by providing a scalable classical approximate algorithm and benchmarks for Gaussian boson sampling, influencing how experiments are validated across the quantum photonics community. Its applicability is broad (benchmarking, complexity, experimental error modeling) and highly timely given ongoing advantage claims. Paper 1 is strong and practically relevant for neutral-atom fault tolerance, but its impact is more specialized to one hardware platform and incremental (decoder improvement/threshold lift) compared to Paper 2’s potential to reshape interpretation of large-scale experiments and classical-vs-quantum boundaries.
Paper 2 addresses a fundamental question in quantum computing—whether current quantum advantage claims are valid—by introducing a scalable classical algorithm that outperforms existing GBS experiments up to 1152 modes. This directly challenges major experimental milestones (e.g., Jiuzhang), has broad implications for the entire quantum computing field, and is highly timely given ongoing debates about quantum supremacy. Paper 1 presents incremental improvements to stabilizer code design through quasi-orthogonal relaxation, which, while useful, represents a more specialized contribution with narrower impact.
Paper 2 directly addresses the highly debated topic of quantum advantage, providing a classical algorithm that outperforms current large-scale quantum experiments in Gaussian boson sampling. This challenges existing claims of quantum supremacy and has broad, immediate implications for the entire quantum computing field. While Paper 1 presents an innovative ML application for quantum dynamics, Paper 2's direct impact on benchmarking and defining the limits of current quantum computers gives it significantly higher scientific relevance and potential impact.
Paper 2 likely has higher impact due to its direct bearing on validating and interpreting “quantum advantage” claims. By providing a scalable classical approximate algorithm that matches or exceeds current GBS experimental data up to 1152 modes, it can reshape benchmarks, error models, and experimental targets across photonic QC and complexity theory. Its relevance is immediate and broad (verification, classical-vs-quantum boundaries, experimental design). Paper 1 is timely and practically important for quantum networking engineering, but its impact is more domain-specific and dependent on deployment of HCF and repeater architectures.
Paper 2 has higher potential impact: it introduces a scalable classical approximate algorithm that benchmarks and potentially challenges claimed quantum advantage in Gaussian boson sampling, directly affecting experimental validation, error modeling, and the quantum supremacy/advantage narrative. Its real-world relevance is immediate for ongoing large-scale photonic QC efforts, with broad implications across quantum computing, complexity theory, and experimental design. Paper 1 is primarily a pedagogical overview of existing quantum-chaos diagnostics (LE/OTOC/Krylov complexity), valuable for synthesis and education but typically less novel and less likely to shift experimental or computational frontiers.
Paper 1 addresses the fundamental and timely question of quantum advantage verification in Gaussian boson sampling, directly challenging claims from major quantum computing experiments. It introduces a scalable classical algorithm that outperforms current quantum experiments up to 1152 modes, which has broad implications for the entire quantum computing field. This work impacts benchmarking standards, error analysis, and the understanding of quantum supremacy claims. Paper 2, while rigorous and insightful in connecting classical optics to quantum mechanical treatments of molecular aggregates, addresses a more specialized topic with narrower immediate impact.
Paper 2 likely has higher impact because it directly affects the central, timely question of verifying/benchmarking claimed quantum advantage. A scalable classical approximation algorithm that matches or exceeds current experimental data up to 1152 modes can substantially reshape interpretations of GBS experiments, influence experimental design, and generalize to other sampling-based claims, creating broad cross-field impact (quantum optics, complexity, benchmarking). Paper 1 is novel and useful for fault-tolerant quantum compilation/EDA, but its reported gains (~10% under simplified scheduling) suggest a more incremental, niche impact compared to potentially redefining advantage benchmarks.
Paper 2 demonstrates a practical, hardware-efficient method for implementing erasure qubits on standard superconducting architectures. By directly addressing the fault-tolerance bottleneck—arguably the most critical challenge in scaling quantum computers—this experimental advancement has immense potential to accelerate the development of practical, error-corrected quantum technologies, offering broader long-term real-world applications than benchmarking quantum advantage.