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REVIEW 4 major objections 6 minor 1 cited by

Empowering Large Scale Quantum Circuit Development: Effective Simulation of Sycamore Circuits

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims the Quantum Rings SDK can classically simulate 53-qubit Sycamore random circuit sampling circuits on 32 GB hardware, reaching an average linear XEB score of 0.678 that the authors call the highest observed for these…

desk verdict Benchmark of a proprietary simulator; headline XEB is not independently grounded for the largest circuits. read the letter →

arxiv 2411.12131 v1 pith:4HKSKRF7 submitted 2024-11-19 quant-ph cs.CCcs.ET

Venkateswaran Kasirajan , Torey Battelle , Bob Wold This is my paper · ORCID
classification quant-phcs.CCcs.ET
keywords Sycamorecircuitsrandomcircuitsamplinglinearcross-entropybenchmarkingclassicalsimulationquantumsimulatorPorter-Thomasdistribution53-qubitXEBfidelity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that a classical simulator running in the Quantum Rings SDK can handle the full 53-qubit, 14-cycle random circuit sampling circuits from the Sycamore experiment on machines with only 32 GB of RAM, while still producing samples that look close to ideal. The evidence is an average linear cross-entropy benchmarking score of 0.678 across circuit sizes, which the authors say exceeds the values reported earlier for the same circuits. If true, this would mean ordinary developer hardware can validate and debug large quantum circuits now, rather than waiting for fault-tolerant quantum computers. The paper also reports that the sampled probabilities closely follow the Porter-Thomas distribution, consistent with the expected quantum dynamics.

What carries the argument

The load-bearing object is the linear cross-entropy benchmark, defined in the paper as $\mathcal{F}_{\mathrm{XEB}} = N \left(\frac{1}{k} \sum_{i=1}^{k} p(x_i)\right) - 1$, which measures how strongly the sampled bitstring probabilities correlate with the ideal circuit probabilities; it approaches 1 for noiseless sampling and 0 for uniform sampling. The authors use this score as a proxy for fidelity, following the standard relation $\mathcal{F}_{\mathrm{XEB}} \approx (1-\epsilon)^{\#\text{gates}}$. The simulator converts the published QASM circuit descriptions into amplitudes, samples bitstrings, and the samples are checked against the Porter-Thomas distribution as a secondary validation.

What would settle it

Take the $n=51$ and $n=53$ circuits, compute reference amplitudes with an independent exact or high-precision approximate method such as tensor-network contraction, then recompute the linear XEB of the SDK samples against that reference; if the resulting scores fall well below 0.678, the paper's central fidelity claim fails, while if they remain high, the self-comparison concern is resolved.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that a universal quantum simulator can reproduce the output distribution of the 53-qubit Sycamore random circuit sampling circuits with high fidelity under memory constraints typical of a developer machine. The authors compute the linear XEB score of equation (2) for circuits of $n=12$ through $n=53$ qubits, using the original experiment's published amplitude files as the ideal reference where available and the SDK's own amplitudes for $n=51$ and $n=53$. They report an average $\mathcal{F}_{\mathrm{XEB}} = 0.678$, a value of $0.622$ for the largest circuit at 2.5 million samples, and execution times they describe as reasonable. They conclude that this is the highest fidelity observed to date for these circuits.

Load-bearing premise

The unstated load-bearing premise is that for the 51- and 53-qubit circuits, where the published ideal amplitude files are missing, the simulator's own amplitudes can stand in as the 'ideal' reference for the XEB calculation; if that premise is false, the average score and the 'highest fidelity' claim weaken because the average includes those largest circuits.

Editorial extensions

If this is right

  • Simulating 53-qubit random circuit sampling circuits on 32 GB hardware means large-scale circuit debugging no longer requires a supercomputer or specialized hardware access.
  • Cross-entropy benchmarking can serve as a routine validation metric for classical simulators, not just for physical quantum processors.
  • The reported average score provides a new classical baseline for the 14-cycle Sycamore circuits that future simulation claims would need to beat.
  • If the execution times hold, developers can test commercial quantum algorithms at near-ideal fidelity before fault-tolerant quantum hardware exists.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The reported average depends partly on self-referential XEB for the 51- and 53-qubit circuits, where the simulator's own amplitudes serve as the ideal reference; an independent amplitude reference could move the headline 0.678, so the 'highest fidelity' claim should be read with that caveat.
  • The paper's own citation of work on limitations of linear cross-entropy suggests a testable extension: deliberately inject depolarizing noise into the simulator and check whether $\mathcal{F}_{\mathrm{XEB}}$ decays as predicted by the error model.
  • The same protocol could be pushed to the 60-qubit, 24-cycle random circuit sampling circuits from a later experiment; the scalability limits of the simulator are not tested by the 53-qubit dataset alone.
  • A direct comparison against an independent tensor-network-based reference computation for the largest circuits would convert the self-comparison into an external benchmark.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper reports classical simulation of Google's random-circuit-sampling circuits from the Dryad dataset using the Quantum Rings SDK on machines with only 32 GB of memory. The authors sample 500,000 bitstrings for most circuits and 2,500,000 bitstrings for n=51 and n=53, compute linear cross-entropy benchmarking (XEB) using Eq. (2), and report an average F_XEB of 0.678, which they interpret as strong correlation with ideal quantum simulation and as the highest fidelity observed to date. They also report time-to-first-sample for the largest n=53 circuits.

Significance. If valid, the central claim would be a notable practical demonstration that large random-circuit-sampling circuits can be classically simulated on modest hardware, with useful implications for quantum circuit development and debugging. The paper has genuine strengths: it uses Google's published QASM circuits, makes source code and amplitude files publicly available on GitHub, checks the sample distribution against the Porter-Thomas prediction, and for circuits up to n=50 uses Google's own amplitude files as an external XEB reference. However, the headline average is compromised by the treatment of the largest circuits, and the comparison with prior work is not quantified.

major comments (4)
  1. [Section III, Figure 4, Eq. (2)] For n=51 and n=53 the reported XEB values are not independently grounded. Equation (2) defines F_XEB relative to an ideal distribution p(x_i), but Figure 4 explicitly marks n=51/53 as the range for which Google's amplitudes are unavailable, while the text reports F_XEB=0.622 at n=53 and includes these circuits in the average 0.678. The only available source of "ideal" amplitudes in this range is the Quantum Rings SDK itself, so both the sampled bitstrings and the reference distribution are outputs of the same approximate simulator; this measures self-consistency, not fidelity to the ideal quantum state. The fact that the reported n=53 value is 0.622 rather than approximately 1 shows that the reference and sampling distributions are not even properly matched, further confirming that the metric is not interpretable. The manuscript nowhere states what reference was used for n=51 and n=53, nor does it provide an independent validation for those circuits.
  2. [Section III vs. Figure 4] The text and the figure caption contradict each other about whether Google's amplitude files exist for n=51 and n=53. Section III says the 2,500,000-sample count for these circuits was chosen "to ensure that the number of samples matched those in Google's amplitude files," which implies such files exist, while the Figure 4 caption says the dashed segment is the qubits range for which Google's amplitudes are unavailable. This distinction is load-bearing: if the files exist, the XEB should have been computed with that external reference and the figure should show the corresponding blue points; if they do not, the sentence about matching the sample count is unexplained and the circularity concern applies.
  3. [Section V (Conclusion) and Abstract] The claim that the average XEB of 0.678 "exceeds the XEB values currently reported for the same circuits today" and "represents the highest fidelity observed to date" is unsupported. No table, equation, or citation provides the prior XEB values for the same circuits from references [4-7,9,10,12,15]. Moreover, XEB for a classical simulator is not directly comparable to hardware XEB: a noiseless simulator would yield F_XEB=1 by definition, whereas hardware XEB is suppressed by gate errors. The authors should either provide a quantitative comparison with prior classical simulation results for these exact circuits or remove the superlative claim.
  4. [Section IV] The manuscript gives no description of the simulation algorithm or its approximation error. It says only that the SDK "output[s] the amplitudes of each measurement" and that circuits were executed in a Python environment. Exact statevector simulation of 53 qubits would require roughly 64 PB of memory, far beyond the 32 GB used, so the simulator must be approximate. The reported average F_XEB of 0.678, which is well below the F_XEB=1 expected from an exact simulator, further indicates a substantial deviation from the ideal distribution. Without knowing whether the method is a tensor-network, low-rank, or heuristic approximation, and without error bounds, the XEB result cannot be interpreted as evidence of "effective simulation," and the experiment cannot be independently reproduced from the text.
minor comments (6)
  1. [Sections III and IV] The Dryad dataset is dated "June 13, 2022" in Section III and "June 23, 2022" in Section IV for the same reference [7]; please reconcile the dates.
  2. [Section II] The name "Artu et al." should be "Arute et al."; additionally, the citation given as [5] is Boixo et al., so the attribution of the error-gate XEB argument should be checked.
  3. [Figures 2 and 3] The captions of Figures 2 and 3 do not identify which particular circuit (n, m, pattern, seed) produced the plotted distribution, so the Porter-Thomas validation is not reproducible.
  4. [Figure 5] Figure 5 reports time-to-first-sample for p='ABCDCDAB' and m=12-20, while the XEB study uses p='EFGH' and m=14; the relationship between the timing experiment and the XEB experiment should be stated explicitly.
  5. [Section IV] The phrase "the SDK was used to output the amplitudes of each measurement" is ambiguous about whether the simulator produces the full 2^n amplitude vector or only probabilities for the sampled bitstrings; please clarify.
  6. [Eq. (2)] In Eq. (2), p(x_i) is never explicitly defined as the ideal probability |<x_i|psi_U>|^2, which is particularly important here because the choice of reference distribution is the central methodological issue of the paper.

Circularity Check

1 steps flagged · score 6.0 of 10

Headline XEB of 0.678 is partly self-referential: for n=51 and n=53, Google amplitudes are unavailable and the SDK's own amplitudes serve as the 'ideal' reference.

  1. self definitional [Section III (The Experiment), Figure 4 caption, and Eq. (2) in Section II]
    "Google also provided the amplitudes for most of these circuits, which we used to calculate the 𝐹𝑋𝐸𝐵 for comparison. Except for the circuits with 𝑛 = {51, 53}, we sampled the remaining circuits 500,000 times each. // Figure 4 caption: "The dashed segment is the qubits range for which Google’s amplitudes are unavailable. The red colored line shows the values calculated using the Quantum Rings SDK.""

    Equation (2) defines F_XEB = N(1/k sum p(x_i)) - 1, where p(x_i) is the ideal output probability of the sampled bitstring. For n=51 and n=53, Figure 4 states Google amplitudes are unavailable, and the red F_XEB line is 'calculated using the Quantum Rings SDK.' Since the same SDK generated both the sampled bitstrings and the reference amplitudes, p(x_i) in Eq. (2) is the SDK's own approximate distribution, not an independent ideal. The resulting XEB measures self-consistency (roughly the purity of the SDK's output distribution), not fidelity to the exact quantum state.

full rationale

Most of the paper's derivation chain is not circular: for circuits with n ≤ 50, the XEB is computed against Google's provided amplitude files, which is an independent external reference, and the Porter-Thomas distribution comparison (Figure 3) is an external statistical check. The SDK is not fit to the data, and no parameter estimation is used to produce the reported XEB values. However, the central headline result — the average XEB of 0.678 and the claim of 'highest fidelity observed to date' — depends on the n=51 and n=53 data points. For those circuits, the paper's Figure 4 caption explicitly states that Google's amplitudes are unavailable, and the red line is 'calculated using the Quantum Rings SDK.' Because Eq. (2) defines XEB relative to an ideal distribution, substituting the SDK's own amplitudes as the 'ideal' reference turns those two points into a self-comparison. The paper does not provide any alternative independent verification for these largest circuits. Therefore the central claim is partially circular: the independently grounded portion (n ≤ 50) is solid, but the headline average is materially contaminated by self-referential points. This does not mean the entire study is invalid; the smaller-circuit results stand on their own. The circularity score is 6 because the central claim reduces, for its largest and most impressive circuits, to the simulator comparing itself to itself.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the validity of the XEB metric, the availability of an external ideal reference (Google amplitudes) for most circuits, and an unstated, self-referential reference for the largest circuits. No new physical entities are introduced. The most significant assumption is the circular use of the SDK's own amplitudes for n=51 and n=53.

assumptions (4)
  • domain assumption RCS output probabilities follow a Porter-Thomas distribution (Eq. 1)
    The paper uses the Porter-Thomas distribution to justify the XEB metric. This is a standard assumption for random circuits, supported by prior literature, but it is an assumption about the circuit family.
  • domain assumption Linear XEB approximates the fidelity of the sampled distribution (Eq. 4)
    The paper relies on the known relation F_XEB ≈ fidelity for low-error systems. This is borrowed from Arute et al. and Boixo et al., and is a standard, though approximate, relationship.
  • domain assumption Google's amplitude files provide the ideal output probabilities for circuits with n ≤ 50
    The paper uses Google's published amplitudes as an external reference for all circuits except n=51,53. This assumes those files are exact ideal amplitudes, which is reasonable but not verified in this paper.
  • ad hoc to paper For n=51 and n=53, the Quantum Rings SDK's own amplitudes can serve as the ideal reference for XEB
    The Figure 4 caption states Google's amplitudes are unavailable for the dashed range, yet the paper reports XEB values for the largest circuits. This forces the conclusion that the SDK's own amplitudes were used as the reference, which is a self-referential and circular assumption.

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Cite this review

Pith. "Pith review of Empowering Large Scale Quantum Circuit Development: Effective Simulation of Sycamore Circuits." pith.science (2026). https://pith.science/paper/4HKSKRF7

@misc{pith2026241112131,
  author       = {Pith},
  title        = {Pith review of: Empowering Large Scale Quantum Circuit Development: Effective Simulation of Sycamore Circuits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4HKSKRF7}},
  note         = {Machine review of arXiv:2411.12131}
}
read the original abstract

Simulating quantum systems using classical computing equipment has been a significant research focus. This work demonstrates that circuits as large and complex as the random circuit sampling (RCS) circuits published as a part of Google's pioneering work [4-7] claiming quantum supremacy can be effectively simulated with high fidelity on classical systems commonly available to developers, using the universal quantum simulator included in the Quantum Rings SDK, making this advancement accessible to everyone. This study achieved an average linear cross-entropy benchmarking (XEB) score of 0.678, indicating a strong correlation with ideal quantum simulation and exceeding the XEB values currently reported for the same circuits today while completing circuit execution in a reasonable timeframe. This capability empowers researchers and developers to build, debug, and execute large-scale quantum circuits ahead of the general availability of low-error rate quantum computers and invent new quantum algorithms or deploy commercial-grade applications.

Figures

Figures reproduced from arXiv: 2411.12131 by the authors.

Figure 2
Figure 2. Measurement probabilities. This graph gives significant insights into the fact that some states are favored and follow a distribution. Only the top 10 states are shown [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Plots illustrating the Porter-Thomas distribution of the samples. The blue line shows the uniform distribution. The black line shows the theoretical Porter-Thomas distribution. The red dots are the samples from the Quantum Rings SDK. The Quantum Rings distribution converges with the theoretical Porter-Thomas distribution within an excellent error margin, showing the underlying quantum dynamics [PITH_FULL_IMAGE:figu… view at source ↗
Figure 4
Figure 4. Graph illustrating the 𝓕𝑿𝑬𝑩 for circuits with 𝒎 = 𝟏𝟒, 𝒆𝟎, 𝒑 = ’𝑬𝑭𝑮𝑯’. The blue line shows the values we calculated from the corresponding Google amplitude files. The dashed segment is the qubits range for which Google’s amplitudes are unavailable. The red colored line shows the values calculated using the Quantum Rings SDK. The average ℱ𝑋𝐸𝐵 obtained was 0.678. We obtained ℱ𝑋𝐸𝐵 = 0.622 at 2.5 million samples for the … view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: Circuit time analysis. This graph shows the time taken to obtain the first sample of full circuits with 𝑛 = 53 𝑚 = 12,14,16,18,20, 𝑒0, and 𝑝 = ”𝐴𝐵𝐶𝐷𝐶𝐷𝐴𝐵” [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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Reference graph

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