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Featuremetric benchmarking: Quantum computer benchmarks based on circuit features

T0 review · 3 major / 7 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Featuremetric benchmarking claims that quantum computer performance on circuits can be modeled from a small set of circuit features, and shows that Gaussian process regression can reconstruct volumetric benchmark plots from a fraction of…

desk verdict A practical, honest methods paper that generalizes volumetric benchmarking to arbitrary circuit features and shows GPs can reconstruct capability plots from sparse data, though the abstract oversells out-of-distribution prediction. read the letter →

arxiv 2504.12575 v1 pith:CLJ2HMWE submitted 2025-04-17 quant-ph cs.LG

Timothy Proctor , Anh Tran , Xingxin Liu , Aditya Dhumuntarao , Stefan Seritan , Alaina Green , Norbert M Linke This is my paper · ORCID
classification quant-phcs.LG
keywords featuremetricbenchmarkingvolumetriccircuitfeaturesGaussianprocessregressioncapabilitylearningmirrorcircuitstwo-qubitgatedensityfidelity
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 introduces featuremetric benchmarking, a framework for measuring how well a quantum computer executes circuits as a function of chosen circuit features, such as width, depth, and two-qubit gate density, rather than only the two features used in volumetric benchmarking. It argues that this generalization yields richer and more faithful performance models, because no two features fully determine circuit error. The paper demonstrates the approach on cloud-access quantum computers of up to 27 qubits and shows that Gaussian process regression can reconstruct entire volumetric benchmarking plots from as little as 20 percent of the data. If the framework works as claimed, a modest batch of feature-parameterized circuits could produce predictive capability models for a quantum computer.

What carries the argument

The central object is the feature vector $\vec{f}=(f_1,\dots,f_\chi)$, a small set of computable circuit properties, together with the sampling distribution $P_{\vec{v}}$ over circuits whose expected feature value equals $\vec{v}$. Performance is summarized by a capability function $s(c)$, for example the success probability of mirror circuits or the process fidelity of random Clifford circuits. The paper's analytic engine is Gaussian process regression, both ordinary and monotonic, which interpolates the mean capability $\bar{s}(\vec{v})$ across feature space; the monotonic version enforces the expected decay of fidelity with increasing depth, width, and two-qubit density. Quasirandom Sobol sampling of feature vectors makes the experiment fill a $\chi$-dimensional feature space efficiently.

What would settle it

Run two structurally different circuit families that cover the same feature values on one device, train the Gaussian process on one family, and evaluate it on the other; if the mean absolute prediction error is no better than predicting the global average performance, the feature set is not predictive and the framework's central assumption fails.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that the performance of a quantum computer on a circuit family is well approximated by a low-dimensional function of that circuit's features, so learning that function from measured circuits yields a predictive capability model. Concretely, it claims that with three features, namely width, depth, and two-qubit gate density, faithful performance models can be learned, and that Gaussian process regression can reproduce a volumetric benchmarking plot with high accuracy using as little as 20 percent of the data. The paper also establishes a formal framework: a featuremetric benchmark is defined by a feature vector, a rule for sampling circuits at each feature value, and a capability function such as success probability or process fidelity, with estimates obtained by running the sampled circuits.

Load-bearing premise

The framework assumes that a small set of circuit features explains most of the variation in how accurately a quantum computer runs circuits, so that interpolating between measured circuits predicts untested ones.

Editorial extensions

If this is right

  • Volumetric benchmarking plots can be generated from substantially fewer circuits than an exhaustive grid requires, cutting experimental cost while preserving accuracy for interpolation.
  • Adding two-qubit gate density as a third feature markedly improves predictive accuracy; at one operating point the mean success probability changed from roughly 51 percent to 7 percent as the density varied.
  • Capability models can predict performance at feature values that were never run, enabling continuous volumetric plots rather than discrete grids.
  • The same analysis pipeline applies to any capability function and any circuit family, including algorithm-derived families with pseudo-features such as QAOA layer count.

Reading between the lines

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

  • A natural extension the authors leave implicit is active learning: because Gaussian processes supply uncertainty estimates, a benchmark could choose the next feature vector where model uncertainty is highest, reducing circuit counts further.
  • The framework invites learned features: instead of hand-picking width, depth, and density, one could use representation learning to find feature directions that minimize residual variance, making models more transferable across devices.
  • If the feature-predictivity assumption holds across hardware, featuremetric models could serve as compact, interpretable summaries for comparing devices, with residual variance as a measure of how idiosyncratic circuit behavior is.
  • A critical test not in the paper is to train on one circuit family and predict another with the same feature values; success would show genuine feature sufficiency, while failure would bound the framework's scope.
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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

3 major / 7 minor

Summary. Featuremetric benchmarking is proposed as a framework that generalizes volumetric benchmarking by characterizing a quantum computer's circuit-level performance as a function of a small set of circuit features (e.g., width, depth, two-qubit gate density), rather than only width and depth. The framework is formalized through definitions of circuit features, pseudo-features, feature vectors, and circuit-sampling distributions, and it is demonstrated in three cloud-executed experiments: a two-feature randomized-mirror-circuit benchmark on ibmq montreal, a three-feature randomized-mirror-circuit benchmark on ibmq algiers, and a three-feature random-Clifford process-fidelity benchmark on IonQ Forte1 with quasirandom (Sobol) feature-vector selection. For data analysis, the authors use standard and monotonic Gaussian process (GP) regression to learn the mean capability s̄(v) as a function of the feature vector, validating on held-out grid points from random train/test splits. They report mean absolute errors of roughly 3-5% when training on about half the data, demonstrate that a GP trained on 20-50% of the montreal data approximately reproduces the full volumetric benchmarking plot, and show that adding two-qubit gate density as a feature substantially improves predictive accuracy.

Significance. The framework is a natural, clearly formalized generalization of a widely used benchmarking methodology, and the demonstrated dependence on two-qubit gate density (Fig. 3 shows 51% vs. 7% mean success at (w,d)=(14,64) as ξ2Q goes from 0 to 1/4) gives concrete evidence that going beyond width and depth is valuable. The GP analysis is methodologically appropriate for low-dimensional interpolation, the held-out validation is sound, and the data-efficiency result for the two-feature volumetric case (Figs. 6 and 7) is a useful and honest quantitative contribution. The three real experimental datasets on IBM Q and IonQ systems of up to 27 qubits are a genuine strength, as is the authors' explicit Section VI statement of the extrapolation limitation. The paper's main weaknesses are the gap between the abstract-level 'faithful models' claim and the interpolation-only validation, the selected-extreme statistics used for the Fig. 5 monotonicity conclusion, and the lack of released data and code. With the claims scoped to interpolation, this will be a solid contribution to the quantum-benchmarking literature.

major comments (3)
  1. [Abstract; Section I; Section V B; Fig. 6; Section VI] The abstract's claim that featuremetric benchmarking 'enables richer and more faithful models of quantum computer performance' is not supported for circuits outside the training distribution. The validation in Section V B trains the GP on random subsets of the measurement grid and tests on the remaining grid points, which is in-distribution interpolation, and the caption of Fig. 6 explicitly limits the 20%-data model's accuracy to 'interpolation as opposed to extrapolation.' Section VI itself concedes that 'it is unlikely that our current feature sets are rich enough for our GP models to accurately predict the performance of circuits that are not drawn from the same distribution as the training data' (with the manuscript's two typos in this sentence corrected). Because a capability model is of interest precisely for predicting untested circuits, the abstract and Section I should be scoped to interpolation within the explored feature ranges, or the authors should add an explicit out-of-distribution test (e.g., training on interior Sobol points and testing on boundary or previously unobserved feature vectors) to substantiate the stronger claim.
  2. [Section IV C; Fig. 5; Fig. 7; Appendix C] The statement that the Forte1 data is 'not statistically consistent with monotonicity' rests on a single value δ_v = (−4 ± 1)% that is described as 'four σ inconsistent with being non-negative,' with the argument that among 248 events one would not expect a 4-sigma event by chance. This significance claim is computed on the most extreme of the 248 δ values, and each δ is itself a minimum over many pairwise comparisons, so the quoted z-score is a selected-extreme statistic and the informal multiple-events argument does not account for that selection or for correlations among feature vectors. A bootstrap or permutation analysis of the maximum deviation is needed to support the quantitative claim; the qualitative conclusion that the three-feature data is much closer to monotonic than any two-feature projection is well supported by the histograms and will likely survive such an analysis. In addition, the monotonic GP of Fig. 7 (with sharpness parameter ν = 10^{-6}, Appendix C) is applied to this same dataset despite the manuscript's own finding that it is not statistically consistent with monotonicity; the paper should justify this modeling choice and discuss whether the hard monotonicity constraint distorts predictions where the observed response is locally non-monotonic.
  3. [Sections IV-V; Appendix C] Neither the processed benchmark data nor the analysis code is made available. The central quantitative claims — the data-efficiency of GP-based reconstruction of volumetric plots (Figs. 6 and 8), the mean-absolute-error curves (Fig. 7), and the monotonic-versus-regular GP comparison — cannot be reproduced or independently verified from the manuscript alone, and the monotonic GP with expectation propagation (Appendix C) involves numerical choices not fully specified in the text. A data availability statement and a release of the datasets and code (or a clearly identified repository) should be provided.
minor comments (7)
  1. [Appendix B] The symbol η² is used for the signal variance in Eq. (B2) and again for the observation-noise variance in Eq. (B3), and the noise variance later appears as σ² I in Eq. (B6); please use distinct symbols for the signal and noise variances throughout the appendix.
  2. [Fig. 5] The axis label 'Monoticity Score' and the legend text 'Monoticity in Process Fidelity Decay' contain a typo ('Monoticity' → 'Monotonicity'), and the caption should include the caveat, stated in the main text, that the three-feature data is not statistically consistent with monotonicity.
  3. [Section V A] The GP observation model (Eq. B3) is homoscedastic, but the per-feature-vector means carry different bootstrap standard errors (e.g., Fig. 3); please state whether heteroscedastic noise was modeled or explain why it was neglected.
  4. [Section IV B] In the sentence quoting success probabilities at (w,d) = (14,64), the notation 'χ2Q' should be 'ξ2Q' to match the convention used elsewhere in the paper.
  5. [Section III A] Reference [26] is cited informally as 'Tomesh et al.'; please use the numbered citation style of the rest of the manuscript.
  6. [Section VI] In the concession paragraph, 'although it unlikely that our current feature sets are rich enough for our GP models to accurate predict' should read 'although it is unlikely that ... to accurately predict'; the typo matters here because this sentence carries the principal scope limitation of the paper.
  7. [Section V B] The sentence 'We train a GP on two randomly-selected subsets ... and then predicted the mean success probabilities' mixes tenses; 'predicted' should be 'predict.'

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: GP predictions are validated on held-out data, and the paper explicitly limits its claims to interpolation.

full rationale

The paper's derivation chain is self-contained. The central predictive claim—that Gaussian process regression can reproduce a volumetric benchmarking plot with less data—is tested by random train/test splits in Section V B and Figures 6–9, so the predictions are not fitted to the held-out test points. The monotonicity prior is an explicitly stated modeling assumption, not a hidden input: Section V A says 'for many features vi we expect s̄(v) to monotonically increase or decrease as vi increases' and 'We can incorporate this assumption into our model using a monotonic GP.' The load-bearing premise that a small feature set explains most performance variation is presented as an open hypothesis, not as a derived consequence: Section III A says 'it is plausible that a small, fixed set of features will be sufficient to predict s(c) in many systems.' The paper itself narrows the scope of the claim: the Figure 6 caption says the GP is 'very accurate at interpolation as opposed to extrapolation,' and Section VI concedes 'it unlikely that our current feature sets are rich enough for our GP models to accurate predict the performance of circuits that are not drawn from the same distribution as the training data.' These are scope limitations on the abstract's 'faithful models' claim, not circular steps. Self-citations (capability learning Refs. [52,59,60], mirror circuits [22,50,51], SR-DFE [66], and monotonic GP [79,80]) supply tools and prior formalism, but none of these citations is the source of the held-out prediction result; the GP mathematics is standard and is independently described in Appendices B and C. Therefore no circularity is found.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claim rests on the stability assumption, the assumed predictability of circuit features, the monotonicity prior for GP regression, and the reliability of the SR-DFE estimator. The GP hyperparameters are fitted to data, which is standard for machine learning but means the models are not parameter-free.

free parameters (3)
  • GP hyperparameters (signal variance, length-scales, noise variance) = not reported
    Optimized by maximizing the log marginal likelihood (Appendix B, Eq. B6) on each training set. The prediction accuracy central to the paper's claims depends on these fitted values.
  • Monotonic GP sharpness parameter ν = 1e-6
    Fixed constant in the probit likelihood (Appendix C) that controls how strictly monotonicity is enforced; chosen by convention, not from the data.
  • Sobol feature bounds (width, depth, density ranges) = width 2-20, depth 2-128, density 0-0.5
    Experimenter-chosen bounds in Section IV C that define the explored feature space; the model's interpolation range is limited by these choices.
assumptions (4)
  • domain assumption The quantum computer is stable during benchmarking; slow drift and time-varying errors are ignored.
    Section II A states this assumption directly. If drift is significant, s(c) is not a single well-defined number and the GP model fits a moving target.
  • domain assumption A small, fixed set of circuit features can explain most of the variation in circuit performance.
    Section III A and III E motivate the framework from this plausibility. The paper's demonstrations use only width, depth, and two-qubit gate density.
  • domain assumption Performance is expected to be monotonic in each feature (e.g., error increases with depth), justifying the monotonic GP prior.
    Section V A and Figure 5 test this; the 3D data is close to but not fully monotonic, and the 2D projections are clearly non-monotonic.
  • domain assumption SR-DFE reliably estimates process fidelity for Clifford circuits on the IonQ system.
    Appendix A relies on the SR-DFE procedure from Ref. [66] to produce the process fidelity estimates used in the Forte1 benchmark. The accuracy of the models depends on these estimates being unbiased.

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Cite this review

Pith. "Pith review of Featuremetric benchmarking: Quantum computer benchmarks based on circuit features." pith.science (2026). https://pith.science/paper/CLJ2HMWE

@misc{pith2026250412575,
  author       = {Pith},
  title        = {Pith review of: Featuremetric benchmarking: Quantum computer benchmarks based on circuit features},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CLJ2HMWE}},
  note         = {Machine review of arXiv:2504.12575}
}
read the original abstract

Benchmarks that concisely summarize the performance of many-qubit quantum computers are essential for measuring progress towards the goal of useful quantum computation. In this work, we present a benchmarking framework that is based on quantifying how a quantum computer's performance on quantum circuits varies as a function of features of those circuits, such as circuit depth, width, two-qubit gate density, problem input size, or algorithmic depth. Our featuremetric benchmarking framework generalizes volumetric benchmarking -- a widely-used methodology that quantifies performance versus circuit width and depth -- and we show that it enables richer and more faithful models of quantum computer performance. We demonstrate featuremetric benchmarking with example benchmarks run on IBM Q and IonQ systems of up to 27 qubits, and we show how to produce performance summaries from the data using Gaussian process regression. Our data analysis methods are also of interest in the special case of volumetric benchmarking, as they enable the creation of intuitive two-dimensional capability regions using data from few circuits.

Figures

Figures reproduced from arXiv: 2504.12575 by the authors.

Figure 1
Figure 1. Volumetric benchmarking of ibmq montreal. (a) The results of a volumetric benchmark run on a 27-qubit IBM quan￾tum computer (ibmq montreal). This plot shows the mean success probability of randomized mirror circuits versus circuit shape (circuit width w and benchmark depth [50] d). (b) Histograms of the success probabilities of the 20 circuits of each shape that were run, for a selection of circuit shapes. Each circ… view at source ↗
Figure 2
Figure 2. Randomized mirror circuits. A diagram of the random￾ized mirror circuits used in two of our example featuremetric bench￾marks, both of which we ran on IBM Q systems. These particu￾lar randomized mirror circuits contain only Clifford gates (Ci , with i = 0, 1, . . . , 23, denote the 24 single-qubit Clifford gates). They have a variable width, depth, and mean density of two-qubit gates. However, this requirement turns… view at source ↗
Figure 3
Figure 3. A simple featuremetric benchmark summarized in volumetric benchmarking plots (ibmq algiers). An example of a simple featuremetric benchmark, with three features, in which the data can be summarized with three volumetric benchmarking plots, which we ran on ibmq algiers. This featuremetric benchmark consists of varying three circuit features: circuit width (w), circuit depth (d), and two-qubit gate density (ξ2Q), and … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: A three-dimensional featuremetric benchmark (Forte1). The results of a three-dimensional featuremetric benchmark run on 20 qubits of IonQ’s Forte1 cloud-access system. In this benchmark, we measured the process fidelities F of random circuits versus three circuit featu…
Figure 5
Figure 5. Figure 5: Quantifying the monotonicity of the circuit fidelity de￾cay (Forte1). We quantify the monotonicity of the decay in cir￾cuit fidelities with increasing feature values using a simple metric δ⃗v given by the minimum of F⃗v ′ − F⃗v over all ⃗v ′ that are strictly smaller t…
Figure 6
Figure 6. Figure 6: Learning a volumetric model from fewer data (ibmq montreal). The standard approach to creating a volumetric benchmarking plot (a.k.a. capability region) requires running many circuits—K ≫ 1 at each width and depth in a grid of circuit shapes. In this work, we show how …
Figure 7
Figure 7. Figure 7: Model prediction error. The prediction error of our fea￾turemetric models for each of our three datasets, on the test data, versus the amount of training data. We created these models using regular (orange points) and monontonic (blue diamonds) GP regres￾sion. Predicti…
Figure 8
Figure 8. Figure 8: Continuous volumetric benchmarking plots. Capability models enable the prediction of a circuit’s performance with arbitrary values for its features, i.e., the capability model M can take any value for the feature vector and makes a prediction M(⃗v) for the perfor￾mance…
Figure 9
Figure 9. Figure 9: Model predictions on test data. The prediction error of our featuremetric models for each of our three datasets, on the test data, when using 50% of the data to train each GP (this is for a single instance with one particular random division of the data into test and t…

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.