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arxiv: 2604.03360 · v1 · submitted 2026-04-03 · 🪐 quant-ph · cs.SE

Recognition: 2 theorem links

· Lean Theorem

Characterizing and Benchmarking Dynamic Quantum Circuits

Anupam Mitra, Costin Iancu, Efekan K\"okc\"u, Siyuan Niu, Sumeet Shirgure, Wibe Albert de Jong

Pith reviewed 2026-05-13 19:01 UTC · model grok-4.3

classification 🪐 quant-ph cs.SE
keywords dynamic quantum circuitsmid-circuit measurementsbenchmarking frameworkfidelity predictionstatistical modelingfeed-forward operationsquantum hardware
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The pith

A new framework called dynamarq benchmarks dynamic quantum circuits and predicts their fidelity from structural features with models that transfer across hardware.

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

The paper introduces dynamarq as a benchmarking framework specifically for dynamic quantum circuits that incorporate mid-circuit measurements and feed-forward operations. It defines a broad set of circuit features to describe their structure, executes a collection of benchmark circuits on IBM quantum processors and a Quantinuum emulator, and derives application-dependent fidelity scores from the results. Statistical modeling then identifies correlations between those features and the observed fidelities, yielding predictions that remain accurate when the model parameters are applied to different hardware backends and calibration cycles. This matters because existing benchmarking tools target only unitary circuits and cannot handle the distinctive properties of dynamic circuits used in error correction and algorithms.

Core claim

We propose dynamarq, a scalable and hardware-agnostic benchmarking framework for dynamic circuits. We collect a set of dynamic circuit benchmarks spanning various applications and propose a broad set of circuit features to characterize the structure of these dynamic circuits. We run them on two IBM quantum processors and the Quantinuum Helios-1E emulator, and propose scalable, application-dependent fidelity scores for each benchmark based on hardware execution results. We perform statistical modeling to identify correlations between circuit features and fidelity scores, and demonstrate highly accurate fidelity prediction using our model. Our model parameters are also transferable across hard

What carries the argument

The dynamarq framework, which uses a defined set of circuit features to characterize dynamic circuit structure and applies statistical modeling to predict fidelity scores from those features.

If this is right

  • Circuit designers can adjust structural features identified as fidelity correlates to improve execution success rates.
  • Fidelity predictions allow selection or ranking of candidate dynamic circuits before committing to hardware runs.
  • The same models support performance comparisons across different quantum hardware platforms and over time as calibrations change.
  • Insights from the feature-fidelity correlations guide the design of feed-forward loops in applications such as quantum error correction.

Where Pith is reading between the lines

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

  • The feature set could be expanded to include interaction terms between measurements and feed-forward operations for larger circuits.
  • The predictive approach might apply to other non-unitary elements in quantum computing beyond mid-circuit measurements.
  • Transferable models suggest a path toward hardware-independent metrics for evaluating dynamic circuit proposals.

Load-bearing premise

The chosen set of circuit features and the resulting statistical model capture the dominant factors determining fidelity across diverse dynamic circuit applications and remain predictive when transferred to new hardware and calibration states without significant overfitting.

What would settle it

Execute a new collection of dynamic circuits on an independent quantum processor not used in the original experiments and compare the measured fidelities against the model's predictions to test whether accuracy and transferability hold.

Figures

Figures reproduced from arXiv: 2604.03360 by Anupam Mitra, Costin Iancu, Efekan K\"okc\"u, Siyuan Niu, Sumeet Shirgure, Wibe Albert de Jong.

Figure 1
Figure 1. Figure 1: A dynamic circuit that prepares 2-qubit GHZ state. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the dynamic circuit benchmarking [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The normalized Rényi-2 entropy 𝐻2 of the probabil￾ity distributions of mid-circuit measurement outcomes on IBM Pittsburgh. A high score means the probability distri￾bution is nearly uniform across all measurement outcomes. The entropy is normalized by the number of classical bits as 𝐻2/𝑛𝑎. Details of these benchmarks are in Section 6. 5.3 The Choice of Branch Probability Estimating the branch probabilities… view at source ↗
Figure 4
Figure 4. Figure 4: Dynamic circuit benchmark suite in dynamarq. grows linearly with qubit count, but dynamic circuits with ancilla qubits enable constant-depth implementation on linear connectivity hardware [3], as shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Histogram of singular values from PCA on the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Linear regression results for the correlation between circuit features and fidelity scores on IBM Pittsburgh under [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Individual correlations between feature metrics and fidelity scores on different quantum backends. The rows corre [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Fidelity scores on IBM Kingston using benchmarks in [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Fidelity scores on IBM Pittsburgh using benchmarks in [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Fidelity scores on Quantinuum Helios-1E emulator using benchmarks in [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
read the original abstract

Dynamic quantum circuits with mid-circuit measurements (MCMs) and feed-forward operations play a crucial role in various applications, such as quantum error correction and quantum algorithms. With advancements in quantum hardware enabling the implementation of MCM and feed-forward loops, the use of dynamic circuits has become increasingly prevalent. There is a significant need for a benchmarking framework specially designed for dynamic circuits to capture their unique properties, as current benchmarking tools are designed primarily for unitary circuits and cannot be trivially extended to dynamic circuits. We propose dynamarq, a scalable and hardware-agnostic benchmarking framework for dynamic circuits. We collect a set of dynamic circuit benchmarks spanning various applications and propose a broad set of circuit features to characterize the structure of these dynamic circuits. We run them on two IBM quantum processors and the Quantinuum Helios-1E emulator, and propose scalable, application-dependent fidelity scores for each benchmark based on hardware execution results. We perform statistical modeling to identify correlations between circuit features and fidelity scores, and demonstrate highly accurate fidelity prediction using our model. Our model parameters are also transferable across hardware backends and calibration cycles. Our framework facilitates the understanding of dynamic circuit structures and provides insights for designing and optimizing dynamic circuits to achieve high execution fidelity on quantum hardware.

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.

Referee Report

2 major / 1 minor

Summary. The paper introduces dynamarq, a scalable and hardware-agnostic benchmarking framework for dynamic quantum circuits with mid-circuit measurements (MCMs) and feed-forward operations. It collects a set of benchmark circuits spanning applications, proposes a broad set of circuit features to characterize their structure, executes them on two IBM quantum processors and the Quantinuum Helios-1E emulator, defines scalable application-dependent fidelity scores from hardware results, performs statistical modeling to identify correlations between features and fidelities, and claims to demonstrate highly accurate fidelity predictions with model parameters transferable across backends and calibration cycles.

Significance. If the statistical model provides accurate and transferable fidelity predictions, the work would be significant for quantum computing by filling a gap in benchmarking tools for dynamic circuits, which are critical for quantum error correction and algorithms. It could enable better understanding of circuit structures and guide optimization for higher execution fidelity on current hardware.

major comments (2)
  1. [Statistical modeling and transferability demonstration] The transferability claim (model parameters transferable across IBM and Quantinuum backends and calibration cycles) is load-bearing for the central contribution. However, the chosen circuit features (depth, MCM count, etc.) omit hardware-specific noise parameters such as mid-circuit measurement error rates and classical feed-forward latency, which differ markedly between superconducting and trapped-ion platforms and drift with calibration. This risks the fitted coefficients absorbing backend-specific effects, leading to overfitting rather than genuine generalization.
  2. [Fidelity scores and statistical modeling] The abstract and modeling sections claim 'highly accurate fidelity prediction' and 'scalable, application-dependent fidelity scores' but provide no details on the exact model form (e.g., regression type or coefficients), cross-validation procedures, data exclusion rules, error bar calculations, or how fidelity scores are computed from raw hardware results. These omissions directly affect confidence in the prediction accuracy and transferability results.
minor comments (1)
  1. Explicitly list and mathematically define all proposed circuit features in the main text, including how conditional operations and feed-forward are accounted for in feature extraction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback, which has helped us improve the clarity and rigor of our manuscript. We address each major comment point by point below, providing the strongest honest defense of our work while making revisions where the comments identify genuine gaps in detail or scope.

read point-by-point responses

  1. Referee: [Statistical modeling and transferability demonstration] The transferability claim (model parameters transferable across IBM and Quantinuum backends and calibration cycles) is load-bearing for the central contribution. However, the chosen circuit features (depth, MCM count, etc.) omit hardware-specific noise parameters such as mid-circuit measurement error rates and classical feed-forward latency, which differ markedly between superconducting and trapped-ion platforms and drift with calibration. This risks the fitted coefficients absorbing backend-specific effects, leading to overfitting rather than genuine generalization.

    Authors: We thank the referee for this important observation on the transferability claim. Our framework is explicitly designed to be hardware-agnostic, so the feature set prioritizes structural properties of dynamic circuits (depth, MCM count, feed-forward depth, etc.) rather than platform-specific noise metrics. This choice enables the benchmarking framework to provide design insights that apply across backends without requiring per-device recalibration of noise parameters. We empirically demonstrate transferability by training on IBM data and evaluating on Quantinuum Helios-1E, as well as across separate IBM calibration cycles, with prediction errors remaining low. We acknowledge that omitting hardware-specific parameters such as MCM error rates and feed-forward latency introduces a risk that coefficients partially capture backend effects. To address this, we have added a dedicated limitations subsection in the revised manuscript that discusses this scope, reports the observed transferability metrics with error bars, and outlines how future extensions could incorporate hardware noise parameters while preserving the structural focus. This revision clarifies that our claims are empirical within the tested platforms rather than claiming universal generalization. revision: partial

  2. Referee: [Fidelity scores and statistical modeling] The abstract and modeling sections claim 'highly accurate fidelity prediction' and 'scalable, application-dependent fidelity scores' but provide no details on the exact model form (e.g., regression type or coefficients), cross-validation procedures, data exclusion rules, error bar calculations, or how fidelity scores are computed from raw hardware results. These omissions directly affect confidence in the prediction accuracy and transferability results.

    Authors: We agree that the original manuscript insufficiently detailed the statistical procedures, which is essential for reproducibility and for readers to evaluate the strength of the prediction and transferability results. In the revised manuscript we have expanded the Methods and supplementary sections to specify: the model is a multiple linear regression with selected interaction terms fitted via ordinary least squares; the full set of fitted coefficients and standard errors are now reported in a new table; 5-fold cross-validation (with circuit-level stratification) was used to compute prediction accuracy and R^{2} values; data exclusion rules removed runs with shot counts below 1024 or those flagged by backend calibration logs; error bars on fidelity scores and predictions are obtained via 1000 bootstrap resamples; and fidelity scores are computed as the average per-shot success probability normalized to the ideal circuit output, aggregated over the benchmark repetitions. These additions directly respond to the referee's request and should allow independent assessment of the reported accuracy. revision: yes

Circularity Check

0 steps flagged

Empirical statistical modeling of dynamic circuit fidelity shows no circularity

full rationale

The paper collects dynamic circuit benchmarks, executes them on IBM and Quantinuum hardware to obtain fidelity scores directly from results, extracts circuit features, fits a statistical model to identify correlations, and reports prediction accuracy plus transferability across backends. This is a standard data-driven empirical pipeline with no equations or steps that reduce by construction to their own inputs. No self-definitional relations, fitted inputs renamed as independent predictions, load-bearing self-citations, or ansatz smuggling appear in the provided text. The central claims rest on external hardware measurements and cross-backend testing rather than tautological re-derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that structural features of dynamic circuits correlate sufficiently with fidelity to enable accurate statistical prediction, plus fitted coefficients in the prediction model. No new physical entities are postulated.

free parameters (1)
  • statistical model coefficients
    Coefficients in the fidelity prediction model are fitted to hardware execution results.
axioms (1)
  • domain assumption A finite set of structural circuit features is sufficient to capture the dominant influences on execution fidelity for dynamic circuits.
    Invoked when defining features and performing statistical modeling to link features to fidelity scores.

pith-pipeline@v0.9.0 · 5539 in / 1368 out tokens · 43386 ms · 2026-05-13T19:01:28.359741+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Forward citations

Cited by 4 Pith papers

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  3. Error Mitigation in Dynamic Circuits for Hamiltonian Simulation

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