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REVIEW 5 major objections 4 minor 89 references

A hybrid neuro-fuzzy system attributes quantum circuit failures to bugs or noise with 89.5% effective accuracy, validated on a 156-qubit superconducting processor.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 21:42 UTC pith:XNHOB7CX

load-bearing objection The problem is real and the study is honest, but the 89.5% accuracy figure comes from features that encode the ground-truth label. the 5 major comments →

arxiv 2602.21253 v2 pith:XNHOB7CX submitted 2026-02-22 quant-ph cs.SE

A Physics-Informed Neuro-Fuzzy Framework for Quantum Error Attribution

Marwa R. Hassan , Naima Kaabouch This is my paper
classification quant-ph cs.SE MSC 81P6868T3762H30 PACS 03.67.-a
keywords quantum error attributionneuro-fuzzy classificationANFISBhattacharyya distanceData Processing InequalityNISQsoftware bug detectionentropy deviation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to solve a practical diagnostic question: when a quantum program on today's noisy processors returns unexpected outputs, is the cause a software bug in the circuit or just hardware noise? It argues that the two leave different statistical and topological fingerprints—noise diffuses and flattens output probability distributions, while software bugs can rotate the state into entirely different regions of Hilbert space. The framework combines seven physics-derived features with a neuro-fuzzy (ANFIS) classifier and a hard 'Bhattacharyya veto' that flags a bug whenever the measured distribution is too far from the ideal for any noise channel to explain. Tested on a 156-qubit superconducting processor across 105 circuits and 17 algorithm families, it reports 89.5% effective accuracy, treating both correct calls and flagged-uncertain calls as safe, with 14.3% of cases sent for human review. If correct, this gives developers a front-end attribution step so error mitigation is not wasted on logically broken circuits.

Core claim

The central claim is that hardware noise and software bugs in quantum executions can be reliably distinguished using distributional features, without full state tomography. The specific discovery is a two-stage decision rule: compute the log-transformed Bhattacharyya distance Dlog_B and entropy deviation Delta-H between measured and ideally expected output distributions; if Dlog_B exceeds 0.20, the deviation is physically impossible for CPTP noise alone (by the data processing inequality) and the circuit is a software bug; otherwise an ANFIS classifier with thresholds 0.35 and 0.70 assigns the case to noise, bug, or an explicit uncertain class. The paper validates this on a 156-qubit Heron r

What carries the argument

The Bhattacharyya veto: a hard threshold on the log-transformed Bhattacharyya distance, Dlog_B = ln(1 + D_B) > 0.20, which corresponds to less than ~82% overlap between measured and ideal output distributions. The paper grounds this threshold in the data processing inequality for completely positive trace-preserving (CPTP) maps, arguing that stochastic noise cannot create topological disjointness between the ideal and measured distributions, so any divergence beyond this bound must come from a unitary (software) error. A second mechanism is entropy deviation Delta-H = |H_measured - H_ideal|, which classifies against the algorithm's expected entropy rather than raw entropy, disambiguating leg

Load-bearing premise

The system needs a trusted ideal-simulation reference for every circuit; in the utility-scale regime where exact simulation is intractable—the very domain the paper targets—it is not shown how that reference is obtained, so entropy deviation and the Bhattacharyya bench both lose their baseline.

What would settle it

Take a circuit known to be bug-free, run it on a noisy processor (or under a characterized CPTP noise model) with enough shots, and compare to the noiseless ideal: if Dlog_B ever exceeds 0.20 while the output distribution still has overlapping support (i.e., no topological disjointness), the veto's physical ceiling is falsified. Equivalently, a simulator with purely depolarizing/amplitude-damping noise that produces Dlog_B > 0.20 from a correct circuit would break the paper's key premise.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Error-mitigation techniques like zero-noise extrapolation and probabilistic error cancellation should be applied only after this attribution step; otherwise they produce high-fidelity estimates of the wrong (buggy) answer.
  • A continuous-integration pipeline could automatically route each circuit to one of three actions: mitigate (noise), debug (bug), or human review (uncertain), with roughly one in seven circuits requiring manual attention.
  • Correct Grover search and other deliberately peaked algorithms can be distinguished from bug-induced collapse by computing deviation from the algorithm's expected entropy, not raw entropy.
  • Phase-only bugs (e.g., |Phi+> vs |Phi->) are provably undetectable from computational-basis measurements alone; this is a fundamental ceiling, not a tunable model deficiency.
  • On this hardware, bugs producing probability shifts below roughly 2% (about a 17-degree rotation) are statistically indistinguishable from calibration drift at 4,096 shots, so the framework's resolution limit is set by the noise floor.

Where Pith is reading between the lines

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

  • The 0.20 veto threshold is calibrated to this device's observed noise ceiling (max Dlog_B = 0.042); porting to a noisier or differently characterizable processor would require re-deriving the threshold, and a device with non-Markovian crosstalk might violate the CPTP assumption the veto rests on.
  • The paper's own multi-basis test (89.25% in simulation vs 78.1% on hardware) suggests the single-basis design is a hardware-constrained optimum; a multi-basis extension would need noise-mitigated basis rotations to recover the simulated advantage.
  • The entropy-deviation trick could generalize beyond Grover to any algorithm whose expected entropy is known from structure—e.g., phase estimation or variational ansatze—potentially fixing the four 'algorithmic generalization' false positives the paper reports.
  • Using temporal stability across calibration cycles could lift the sub-noise-floor resolution limit, since hardware noise drifts while software bugs are deterministic; this is a testable extension the paper mentions but does not implement.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The paper proposes a three-class (software bug / hardware noise / uncertain) attribution framework for quantum circuit outputs. It combines seven hand-crafted features with an ANFIS classifier and a "Bhattacharyya veto" that overrides the classifier when the log-Bhattacharyya distance to an expected distribution exceeds 0.20. The authors report 89.5% effective accuracy on 105 circuits (2–5 qubits) executed on IBM's 156-qubit Heron r2 processor, with 14.3% of circuits flagged as uncertain, and claim this constitutes a deployable pre-mitigation diagnostic layer that works "without a perfect reference." The two most discriminative features, entropy deviation and log-Bhattacharyya distance, are computed against an ideal simulation of the intended circuit, which is the central load-bearing issue for the stated contribution.

Significance. The paper has genuine strengths: real-hardware execution on IBM Heron, an interpretable neuro-fuzzy architecture, an explicit uncertainty/rejection class, and an unusually honest taxonomy of failure modes (Z-basis blind spot, sub-noise-threshold bugs, noise-masked bugs, and algorithmic generalization errors). The effect-size analysis and the Grover boundary discussion are informative. If the central claim were valid, this would be a useful small-circuit diagnostic tool. However, the evaluation is not evidence for the utility-scale, no-reference deployment claim stated in the abstract and contributions: the two strongest features are defined relative to an ideal simulation of the intended bug-free circuit, so ground truth leaks into the features, and the reported accuracy is therefore an upper bound for the known-reference setting only.

major comments (5)
  1. [§3.1.6, §3.1.7, §5.2] Entropy deviation (ΔH) and Dlog_B are computed against an expected distribution “obtained via ideal simulation.” In the validation, the reference is the intended bug-free circuit: the grover_2q_wrong_oracle case has ΔH=1.999 only because the expected distribution is the correct-oracle distribution (§5.2). The labels therefore leak through the two most discriminative features. At utility scale, the paper's own §1.1 states exact simulation is intractable; if the expected distribution is instead an ideal simulation of the circuit as written, bug-induced deviations collapse into the noise signature. The 89.5% figure is thus an upper bound for the known-correct-reference, small-circuit setting, not evidence for the claimed deployment capability “without a perfect reference.”
  2. [§3.4.2, Fig. 2] The veto threshold is not a parameter-free physical constant. The text sets τ_veto=0.20 because the maximum observed Dlog_B on correctly executed circuits is 0.042, then applies this threshold to those same circuits with a “4.8× safety margin.” This is empirical threshold-fitting on the evaluation set, not a derived bound. It cannot support the claim that the veto is a hard physics constraint independent of the data.
  3. [§3.4.2] The DPI-based argument that “CPTP noise cannot create topological disjointness” is not established. The data processing inequality bounds the contraction of a distinguishability measure under a channel; it does not bound the classical Bhattacharyya distance between the measured distribution and a chosen ideal distribution for an arbitrary circuit. A systematic unitary miscalibration is itself a CPTP map and can rotate support away from the ideal. The only paper-specific distinction is magnitude (small-angle hardware errors vs large-angle bugs), which is an assumption, not a consequence of DPI.
  4. [§1.4, §4.2] Contribution 5 claims “Utility-Scale Validation” on a 156-qubit Heron processor, but the circuit suite uses only 2–5 qubits (§4.2). The 156-qubit device is the host platform; the problems are not utility-scale. This matters because the availability of an ideal-simulation reference—the load-bearing premise of Features 6 and 7—is exactly what fails in the 127-qubit utility regime invoked in §1.1. The validation therefore does not test the deployment regime claimed in the abstract.
  5. [§3.3, §3.4.1, §4.3, Table 3] The classification thresholds (τ_bug=0.35, τ_noise=0.70) are described as “tuned on held-out hardware validation data,” and the same sections state that all reported validation results (89.5% effective accuracy, 14.3% uncertainty rate) reflect these tuned thresholds. If the 105-circuit suite was used for tuning, the reported accuracy is optimistic; if a separate split was used, neither its size nor the split procedure is given. The paper should state explicitly which circuits were used for threshold selection and report accuracy on an untouched test set.
minor comments (4)
  1. [§4.4, Abstract] The abstract reports “89.5% effective accuracy” without noting that UNCERTAIN predictions are counted as safe. The table gives strict accuracy of 75.2%; the abstract should at least mention that the headline number includes abstentions.
  2. [Table 4] The percentages in Table 4 sum to 99% (18+18+36+27) due to rounding; add a rounding note or adjust the fractions.
  3. [§3.4.2, Fig. 11] The “combined noise floor” in Fig. 11 is presented as shot noise plus gate error, but the 2.24% value is not derived in the text. Clarify how the gate-error contribution is combined with the 1.56% shot-noise term.
  4. [§4.3] The 2,000 training samples are generated from ibm_fez calibration data using templates “distinct from the validation suite,” but no measure of template distance or overlap is given. A brief statement on how training and validation circuit families were kept separate would strengthen the generalization claim.

Circularity Check

3 steps flagged

Validation encodes ground truth via ideal-simulation references and tunes both ANFIS and veto thresholds on the evaluated circuits, so the headline accuracy is partly a fit.

specific steps
  1. fitted input called prediction [§3.3 (Classification Thresholds), §4.3, §5.1]
    "After training, classification thresholds were tuned on held-out hardware validation data to minimize errors while maintaining acceptable uncertainty rates. The final thresholds—τbug = 0.35 and τnoise = 0.70—require approximately 65–70% classifier confidence before committing to a definitive attribution. Predictions in the intermediate range are flagged as UNCERTAIN for manual review. All reported validation results (89.5% effective accuracy, 14.3% uncertainty rate) reflect these tuned thresholds."

    The evaluation set is used to select the decision thresholds (0.35/0.70), and the same set is then used to report 'validation' accuracy. Any accuracy number obtained this way is a post-fit resubstitution estimate, not an independent prediction: the classifier's operating points were chosen to make the 105-circuit confusion matrix look good. Thus the headline 89.5% effective accuracy is partly forced by the fitting procedure and cannot be read as out-of-sample evidence for the deployment claim.

  2. fitted input called prediction [§3.4.2 (Bhattacharyya Veto), Fig. 2]
    "This threshold was derived empirically: across all correctly-executed circuits on IBM hardware, the maximum observed Dlog_B was 0.042. Setting τveto = 0.20 provides a 4.8× safety margin, ensuring no correctly-executed circuit triggers a false bug classification."

    The 'physical' veto threshold is set to 4.8× the maximum Dlog_B observed among the correct validation circuits, and then the veto is validated on those same circuits. The claim that no correctly-executed circuit triggers a false bug classification is therefore true by construction, not a consequence of the Data Processing Inequality. DPI (ref [76]) only bounds contraction of distinguishability between two states; it does not fix a numerical cutoff of 0.20 for the classical log-Bhattacharyya distance to an ideal output. The threshold is a fitted constant renamed as a physics constraint.

  3. self definitional [§1.1, §3.1.6, §3.1.7, §5.2]
    "Expected entropy is computed via ideal simulation. ... The expected entropy for a correctly-implemented Grover search is low—the algorithm should produce a peaked distribution—so the small measured-to-expected entropy difference indicates correct operation despite noise. ... In this utility era ... the ability to blindly distinguish between hardware noise and software logic errors without a perfect reference becomes a key requirement."

    Features 6 and 7 are, by definition, distances from the ideal simulation of the intended bug-free circuit. A buggy circuit is 'buggy' because its output differs from that reference (e.g., grover_2q_wrong_oracle has ΔH = 1.999 only because the reference is the correct oracle). The paper claims the framework meets the deployment need 'without a perfect reference,' but at utility scale the intended circuit cannot be classically simulated; if the reference is instead the ideal simulation of the circuit as written, bug-induced deviations match the reference and the two strongest features collapse to the noise signature. Thus the validation encodes the ground-truth label in the inputs, and the deployment claim is not derived from the construction.

full rationale

The paper is not circular in the sense of deriving a theorem from itself; the ANFIS is trained on separate simulated data and the 105-circuit hardware suite is a genuine experiment. However, the central validation and the physical veto contain substantial fit-on-evaluation circularity: the 0.35/0.70 ANFIS thresholds and the 0.20 veto are tuned on the same 105 circuits used to report the 89.5% effective accuracy, so the headline number is partly a resubstitution statistic rather than an independent estimate. More fundamentally, the two dominant features (entropy deviation and log-Bhattacharyya distance) are defined as divergence from an ideal simulation of the known-correct circuit, so the ground-truth label is embedded in the feature construction; the paper's own deployment goal—attribution 'without a perfect reference'—is therefore not supported by the validation. No load-bearing self-citation chain is present, and the error analysis is transparent about blind spots, so this is partial circularity rather than a fully definitional result.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

No new physical entities are postulated. The 'Bhattacharyya Veto' is a decision rule and the 'attribution gap' is a framing concept; neither adds degrees of freedom to the physics. The free parameters that matter are the fitted thresholds (veto 0.20; ANFIS 0.35/0.70), both calibrated on the very data they are then evaluated on, and the axioms that matter are the empirically fitted 'noise cannot exceed Dlog_B=0.042' bound and the availability of the bug-free reference circuit.

free parameters (5)
  • τ_veto (Bhattacharyya veto threshold) = 0.20 in log-Bhattacharyya units (BC ≈ 0.819)
    Derived empirically from the maximum Dlog_B = 0.042 observed across correctly-executed circuits in the 105-circuit validation set, with a 4.8× margin (§3.4.2). Applied to those same circuits; presented as a physics constraint rather than a fit.
  • τ_bug / τ_noise (ANFIS classification thresholds) = 0.35 / 0.70
    Tuned on the held-out hardware validation data to keep uncertainty < 15%; the headline 89.5% effective accuracy is reported on that same set (§3.3).
  • Number of fuzzy rules = 16
    Selected from 'preliminary experiments showing diminishing returns' (§4.3).
  • Uncertainty-penalty hyperparameters = λ=0.3, τ_margin=0.20
    Hand-chosen for the loss (§3.3); minor influence on the central claim.
  • Veto margin factor = 4.8×
    Ratio 0.20/0.042; this is the actual rule separating 'physics constraint' from observed-data fit (§3.4.2).
axioms (5)
  • ad hoc to paper CPTP hardware noise cannot produce output distributions with Dlog_B > 0.20 relative to the ideal (no topological disjointness).
    Invoked to justify the veto (§3.4.2, §1.4). The DPI [76] bounds contraction of distinguishability between two states through a channel; it yields no constant bound between the measured and ideal output distributions. Amplitude damping (their own T1 model, §2.1.1) maps |1⟩→|0⟩, moving population outside the ideal support - D_B can be arbitrarily large under CPTP noise alone.
  • domain assumption The expected/ideal distribution used for entropy deviation and Bhattacharyya distance is available in the deployment setting (computed via ideal simulation of the intended circuit).
    §3.1.6 defines the features against 'ideal simulation'; §5.2 shows the reference is the intended bug-free circuit (wrong-oracle Grover has ∆H=1.999). §1.1 argues classical simulation is intractable at utility scale - the setting the paper motivates. For 2-5 qubit validation circuits the reference is trivially available, which is why the evaluation works.
  • domain assumption The Qiskit Aer noise model built from ibm_fez calibration data is faithful enough that training transfers to hardware.
    Training is on NoiseModel.from_backend() simulation (§4.3). The synthetic/held-out gap (87.75% vs 75.2% strict) suggests imperfect transfer (§6.7 vs §5.1).
  • domain assumption The 105 validation circuits are independent samples for the Wilson CI.
    §4.4/§5.1 treat the 105 circuits as independent; multiple circuits share algorithm families (14 Bell, 11 GHZ, etc., §4.2), so the effective sample size is smaller.
  • standard math Z-basis projective measurement discards phase information, making phase-only errors invisible (Helstrom bound P_err=0.5).
    §5.4.1, §6.2.1. This is correct, textbook quantum mechanics; not an ad hoc assumption.

reviewed 2026-08-02 · how reviews work

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Cite this review

Pith. "Pith review of A Physics-Informed Neuro-Fuzzy Framework for Quantum Error Attribution." pith.science (2026). https://pith.science/paper/XNHOB7CX

@misc{pith2026260221253,
  author       = {Pith},
  title        = {Pith review of: A Physics-Informed Neuro-Fuzzy Framework for Quantum Error Attribution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XNHOB7CX}},
  note         = {Machine review of arXiv:2602.21253}
}
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read the original abstract

As quantum processors scale beyond 100 qubits, distinguishing software bugs from stochastic hardware noise becomes a critical diagnostic challenge. We present a neuro-fuzzy framework that addresses this attribution problem by combining Adaptive Neuro-Fuzzy Inference Systems (ANFIS) with physics-grounded feature engineering. We introduce the Bhattacharyya Veto, a hard physical constraint grounded in the Data Processing Inequality that prevents the classifier from attributing topologically impossible output distributions to noise. Validated on IBM's 156-qubit Heron r2 processor (ibm_fez) across 105 circuits spanning 17 algorithm families, the framework achieves 89.5% effective accuracy (+/- 5.9% CI). The system implements a safe failure mode, flagging 14.3% of ambiguous cases for manual review rather than forcing low-confidence predictions. We resolve key ambiguities -- such as distinguishing correct Grover amplification from bug-induced collapse -- and identify fundamental limits of single-basis diagnostics, including a Z-basis blind spot where phase-flip errors remain statistically invisible. This work establishes a robust, interpretable diagnostic layer that prevents error mitigation techniques from being applied to logically flawed circuits.

Figures

Figures reproduced from arXiv: 2602.21253 by Marwa R. Hassan, Naima Kaabouch.

Figure 1
Figure 1. Figure 1: ANFIS Architecture: The 5-Layer Neuro-Fuzzy Stack [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Classification Decision Logic: Veto check followed by ANFIS thresholds [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Classification outcomes for the 105-circuit validation suite on IBM Heron. The framework [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Decision logic mapped onto the feature space. The horizontal band above [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Resolution of the Grover boundary problem. (a) Actual Grover circuits from the validation [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Feature space visualization of log-transformed Bhattacharyya distance ( [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of ANFIS output P(noise) by ground truth class. Correctly-functioning circuits cluster near P(noise) = 1.0, while buggy circuits concentrate near 0. The yellow-shaded uncertainty zone (0.35–0.70) captures ambiguous cases flagged for manual review [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Breakdown of the 11 misclassified circuits by root cause. Information-theoretic limits [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Feature discriminability analysis using Cohen’s [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The Z-basis blind spot illustrated with Bell states. Both [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Resolution limit imposed by hardware noise. Rotation errors producing probability shifts [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

89 extracted references · 19 canonical work pages · 1 internal anchor

  1. [1]

    Senior, Francisco J

    Johannes Bausch, Andrew W. Senior, Francisco J. H. Heras, et al. Learning high-accuracy error decoding for quantum processors.Nature, 635(8040):834–840, November 2024.doi:10.1038/s41586-024-08148-8. 30

    doi:10.1038/s41586-024-08148-8 2024

  2. [2]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, et al. A quantum engineer’s guide to superconducting qubits.Applied Physics Reviews, 6(2):021318, June 2019.doi:10.1063/1.5089550

    doi:10.1063/1.5089550 2019

  3. [3]

    Bishop, Easwar Magesan, et al

    Sarah Sheldon, Lev S. Bishop, Easwar Magesan, et al. Characterizing errors on qubit operations via iterative randomized benchmarking.Physical Review A, 93(1):012301, January 2016.doi:10.1103/PhysRevA.93.012301

    doi:10.1103/physreva.93.012301 2016

  4. [4]

    Statistical assertions for validating patterns and finding bugs in quantum programs

    Yipeng Huang and Margaret Martonosi. Statistical assertions for validating patterns and finding bugs in quantum programs. InProceedings of the 46th International Symposium on Computer Architecture, ISCA ’19, pages 541–553, New York, NY, USA, June 2019. Association for Computing Machinery.doi:10.1145/3307650.3322213

    arXiv 2019

  5. [5]

    Quantum Computing in the NISQ era and beyond.Quantum, 2:79, August 2018.doi:10.22331/ q-2018-08-06-79

    John Preskill. Quantum Computing in the NISQ era and beyond.Quantum, 2:79, August 2018.doi:10.22331/ q-2018-08-06-79

    2018

  6. [6]

    Testing and Debugging Quantum Programs: The Road to 2030.ACM Trans

    Neilson Carlos Leite Ramalho, Higor Amario de Souza, and Marcos Lordello Chaim. Testing and Debugging Quantum Programs: The Road to 2030.ACM Trans. Softw. Eng. Methodol., 34(5):155:1–155:46, May 2025. doi:10.1145/3715106

    doi:10.1145/3715106 2030

  7. [7]

    Quantum Software Engineering: Roadmap and Challenges Ahead.ACM Trans

    Juan Manuel Murillo, Jose Garcia-Alonso, Enrique Moguel, et al. Quantum Software Engineering: Roadmap and Challenges Ahead.ACM Trans. Softw. Eng. Methodol., 34(5):154:1–154:48, May 2025.doi:10.1145/3712002

    doi:10.1145/3712002 2025

  8. [8]

    Mitigating Noise in Quantum Software Testing Using Machine Learning.IEEE Transactions on Software Engineering, 50(11):2947–2961, November 2024

    Asmar Muqeet, Tao Yue, Shaukat Ali, and Paolo Arcaini. Mitigating Noise in Quantum Software Testing Using Machine Learning.IEEE Transactions on Software Engineering, 50(11):2947–2961, November 2024. doi:10.1109/TSE.2024.3462974

    arXiv 2024

  9. [9]

    Junjie Luo, Pengzhan Zhao, Zhongtao Miao, et al. A Comprehensive Study of Bug Fixes in Quantum Programs: 29th IEEE International Conference on Software Analysis, Evolution and Reengineering, SANER 2022.Proceedings - 2022 IEEE International Conference on Software Analysis, Evolution and Reengineering, SANER 2022, pages 1239–1246, 2022.doi:10.1109/SANER5343...

    arXiv 2022

  10. [10]

    Bugs in Quantum computing platforms: An empirical study.Proceedings of the ACM on Programming Languages, 6(OOPSLA1):1–27, April 2022.doi:10.1145/3527330

    Matteo Paltenghi and Michael Pradel. Bugs in Quantum computing platforms: An empirical study.Proceedings of the ACM on Programming Languages, 6(OOPSLA1):1–27, April 2022.doi:10.1145/3527330

    doi:10.1145/3527330 2022

  11. [11]

    Identifying Bug Patterns in Quantum Programs

    Pengzhan Zhao, Jianjun Zhao, and Lei Ma. Identifying Bug Patterns in Quantum Programs, March 2021. arXiv:2103.09069,doi:10.48550/arXiv.2103.09069

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2103.09069 2021

  12. [12]

    Bug Characteristics in Quantum Software Ecosystem, September 2023.arXiv:4564656,doi:10.2139/ssrn.4564656

    Mohamed Raed El Aoun, Heng Li, Foutse Khomh, and Lionel Tidjon. Bug Characteristics in Quantum Software Ecosystem, September 2023.arXiv:4564656,doi:10.2139/ssrn.4564656

    work page doi:10.2139/ssrn.4564656 2023

  13. [13]

    Evidence for the utility of quantum computing before fault tolerance.Nature, 618(7965):500–505, June 2023.doi:10.1038/s41586-023-06096-3

    Youngseok Kim, Andrew Eddins, Sajant Anand, et al. Evidence for the utility of quantum computing before fault tolerance.Nature, 618(7965):500–505, June 2023.doi:10.1038/s41586-023-06096-3

    doi:10.1038/s41586-023-06096-3 2023

  14. [14]

    A Tool For Debugging Quantum Circuits

    Sara Ayman Metwalli and Rodney Van Meter. A Tool For Debugging Quantum Circuits. In2022 IEEE International Conference on Quantum Computing and Engineering (QCE), pages 624–634, September 2022. doi:10.1109/QCE53715.2022.00085

    arXiv 2022

  15. [15]

    Testing and Debugging Quantum Circuits.IEEE Transactions on Quantum Engineering, 5:1–15, 2024.doi:10.1109/TQE.2024.3374879

    Sara Ayman Metwalli and Rodney Van Meter. Testing and Debugging Quantum Circuits.IEEE Transactions on Quantum Engineering, 5:1–15, 2024.doi:10.1109/TQE.2024.3374879

    arXiv 2024

  16. [16]

    Byrd, and Huiyang Zhou

    Ji Liu, Gregory T. Byrd, and Huiyang Zhou. Quantum Circuits for Dynamic Runtime Assertions in Quantum Computation. InProceedings of the Twenty-Fifth International Conference on Architectural Support for Pro- gramming Languages and Operating Systems, ASPLOS ’20, pages 1017–1030, New York, NY, USA, March 2020. Association for Computing Machinery.doi:10.1145...

    arXiv 2020

  17. [17]

    Andriy Miranskyy, Lei Zhang, and Javad Doliskani. Is your quantum program bug-free? InProceedings of the ACM/IEEE 42nd International Conference on Software Engineering: New Ideas and Emerging Results, ICSE-NIER ’20, pages 29–32, New York, NY, USA, September 2020. Association for Computing Machinery. doi:10.1145/3377816.3381731

    arXiv 2020

  18. [18]

    Gambetta

    Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. Error Mitigation for Short-Depth Quantum Circuits. Physical Review Letters, 119(18):180509, November 2017.doi:10.1103/PhysRevLett.119.180509

    doi:10.1103/physrevlett.119.180509 2017

  19. [19]

    Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, Andrea Mari, and William J. Zeng. Digital zero noise extrapolation for quantum error mitigation. In2020 IEEE International Conference on Quantum Computing and Engineering (QCE), pages 306–316, October 2020.doi:10.1109/QCE49297.2020.00045

    arXiv 2020

  20. [20]

    Minev, Abhinav Kandala, and Kristan Temme

    Ewout van den Berg, Zlatko K. Minev, Abhinav Kandala, and Kristan Temme. Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors.Nature Physics, 19(8):1116–1121, August 2023. doi:10.1038/s41567-023-02042-2

    doi:10.1038/s41567-023-02042-2 2023

  21. [21]

    Gupta, Ewout van den Berg, Maika Takita, Diego Ristè, Kristan Temme, and Abhinav Kandala

    Riddhi S. Gupta, Ewout van den Berg, Maika Takita, Diego Ristè, Kristan Temme, and Abhinav Kandala. Probabilistic error cancellation for dynamic quantum circuits.Physical Review A, 109(6):062617, June 2024. doi:10.1103/PhysRevA.109.062617. 31

    doi:10.1103/physreva.109.062617 2024

  22. [22]

    Wang, Iskandar Sitdikov, Ciro Salcedo, Alireza Seif, and Zlatko K

    Haoran Liao, Derek S. Wang, Iskandar Sitdikov, Ciro Salcedo, Alireza Seif, and Zlatko K. Minev. Machine learning for practical quantum error mitigation.Nature Machine Intelligence, 6(12):1478–1486, December 2024. doi:10.1038/s42256-024-00927-2

    doi:10.1038/s42256-024-00927-2 2024

  23. [23]

    Unifying and benchmarking state-of-the-art quantum er- ror mitigation techniques.Quantum, 7:1034, June 2023.arXiv:2107.13470, doi:10.22331/q-2023-06-06-1034

    Daniel Bultrini, Max Hunter Gordon, Piotr Czarnik, et al. Unifying and benchmarking state-of-the-art quantum er- ror mitigation techniques.Quantum, 7:1034, June 2023.arXiv:2107.13470, doi:10.22331/q-2023-06-06-1034

    Pith/arXiv arXiv 2023

  24. [24]

    Jyh-shing R. Jang. ANFIS: Adaptive-network-based fuzzy inference system.IEEE Transactions on Systems, Man, & Cybernetics, 23(3):665–685, 1993.doi:10.1109/21.256541

    work page doi:10.1109/21.256541 1993

  25. [25]

    On a measure of divergence between two statistical populations defined by their probability distributions.Bulletin of the Calcutta Mathematical Society, 35(3):99–109, 1943

    Anil Kumar Bhattacharyya. On a measure of divergence between two statistical populations defined by their probability distributions.Bulletin of the Calcutta Mathematical Society, 35(3):99–109, 1943

    1943

  26. [26]

    Fuchs and J

    C.A. Fuchs and J. van de Graaf. Cryptographic distinguishability measures for quantum-mechanical states.IEEE Transactions on Information Theory, 45(4):1216–1227, May 1999.doi:10.1109/18.761271

    doi:10.1109/18.761271 1999

  27. [27]

    Phonon engineering of atomic-scale defects in superconducting quantum circuits.Science Advances, 10(37):eado6240.doi:10.1126/ sciadv.ado6240

    Mo Chen, John Clai Owens, Harald Putterman, Max Schäfer, and Oskar Painter. Phonon engineering of atomic-scale defects in superconducting quantum circuits.Science Advances, 10(37):eado6240.doi:10.1126/ sciadv.ado6240

  28. [28]

    A comparative analysis and noise robustness evaluation in quantum neural networks.Scientific Reports, 15(1):33654, September 2025

    Tasnim Ahmed, Muhammad Kashif, Alberto Marchisio, and Muhammad Shafique. A comparative analysis and noise robustness evaluation in quantum neural networks.Scientific Reports, 15(1):33654, September 2025. doi:10.1038/s41598-025-17769-6

    work page doi:10.1038/s41598-025-17769-6 2025

  29. [29]

    Burnett, Andreas Bengtsson, Marco Scigliuzzo, et al

    Jonathan J. Burnett, Andreas Bengtsson, Marco Scigliuzzo, et al. Decoherence benchmarking of superconducting qubits.npj Quantum Information, 5(1):54, June 2019.doi:10.1038/s41534-019-0168-5

    doi:10.1038/s41534-019-0168-5 2019

  30. [30]

    Carroll, S

    M. Carroll, S. Rosenblatt, P. Jurcevic, I. Lauer, and A. Kandala. Dynamics of superconducting qubit relaxation times.npj Quantum Information, 8(1):132, November 2022.doi:10.1038/s41534-022-00643-y

    work page doi:10.1038/s41534-022-00643-y 2022

  31. [31]

    Simulating noisy quantum circuits with matrix product density operators.Physical Review Research, 3(2):023005, April 2021.doi:10.1103/PhysRevResearch.3.023005

    Song Cheng, Chenfeng Cao, Chao Zhang, et al. Simulating noisy quantum circuits with matrix product density operators.Physical Review Research, 3(2):023005, April 2021.doi:10.1103/PhysRevResearch.3.023005

    doi:10.1103/physrevresearch.3.023005 2021

  32. [32]

    Iverson and John Preskill

    Joseph K. Iverson and John Preskill. Coherence in logical quantum channels.New Journal of Physics, 22(7):073066, July 2020.arXiv:1912.04319,doi:10.1088/1367-2630/ab8e5c

    Pith/arXiv arXiv 2020

  33. [33]

    da Silva, Erik Nielsen, Timothy Proctor, Kenneth Rudinger, Mohan Sarovar, and Kevin Young

    Robin Blume-Kohout, Marcus P. da Silva, Erik Nielsen, Timothy Proctor, Kenneth Rudinger, Mohan Sarovar, and Kevin Young. A Taxonomy of Small Markovian Errors.PRX Quantum, 3(2):020335, May 2022. doi: 10.1103/PRXQuantum.3.020335

    doi:10.1103/prxquantum.3.020335 2022

  34. [34]

    Hogle, Ravi K

    Kenneth Rudinger, Craig W. Hogle, Ravi K. Naik, et al. Experimental Characterization of Crosstalk Errors with Simultaneous Gate Set Tomography.PRX Quantum, 2(4):040338, November 2021.doi:10.1103/PRXQuantum.2. 040338

    doi:10.1103/prxquantum.2 2021

  35. [35]

    AbuGhanem

    M. AbuGhanem. IBM Quantum Computers: Evolution, Performance, and Future Directions.The Journal of Supercomputing, 81(5):687, April 2025.arXiv:2410.00916,doi:10.1007/s11227-025-07047-7

    Pith/arXiv arXiv 2025

  36. [36]

    Muskit: A mutation analysis tool for quantum software testing

    Eñaut Mendiluze, Shaukat Ali, Paolo Arcaini, and Tao Yue. Muskit: A mutation analysis tool for quantum software testing. InProceedings of the 36th IEEE/ACM International Conference on Automated Software Engineering, ASE ’21, pages 1266–1270, Melbourne, Australia, June 2022. IEEE Press.doi:10.1109/ASE51524.2021.9678563

    arXiv 2022

  37. [37]

    QMutPy: A mutation testing tool for Quantum algorithms and applications in Qiskit

    Daniel Fortunato, José Campos, and Rui Abreu. QMutPy: A mutation testing tool for Quantum algorithms and applications in Qiskit. InProceedings of the 31st ACM SIGSOFT International Symposium on Software Testing and Analysis, ISSTA 2022, pages 797–800, New York, NY, USA, July 2022. Association for Computing Machinery.doi:10.1145/3533767.3543296

    arXiv 2022

  38. [38]

    Ilaria Gianani, Alessio Belenchia, Stefano Gherardini, et al. Diagnostics of quantum-gate coherences deteriorated by unitary errors via end-point-measurement statistics.Quantum Science and Technology, 8(4):045018, August 2023.doi:10.1088/2058-9565/acedca

    work page doi:10.1088/2058-9565/acedca 2023

  39. [39]

    Fidelity decay and error accumulation in random quantum circuits.SciPost Physics, 19(1):013, July 2025.doi:10.21468/SciPostPhys.19.1.013

    Nadir Samos, Rafał Bistroń, Marcin Rudziński, et al. Fidelity decay and error accumulation in random quantum circuits.SciPost Physics, 19(1):013, July 2025.doi:10.21468/SciPostPhys.19.1.013

    work page doi:10.21468/scipostphys.19.1.013 2025

  40. [40]

    Calibration of Drive Nonlinearity for Arbitrary- Angle Single-Qubit Gates Using Error Amplification.Physical Review Applied, 20(2):024036, August 2023

    Stefania Lazăr, Quentin Ficheux, Johannes Herrmann, et al. Calibration of Drive Nonlinearity for Arbitrary- Angle Single-Qubit Gates Using Error Amplification.Physical Review Applied, 20(2):024036, August 2023. doi:10.1103/PhysRevApplied.20.024036

    work page doi:10.1103/physrevapplied.20.024036 2023

  41. [41]

    Efficient implementation of multicontrolled quantum gates.Physical Review Applied, 24(4):044030, October 2025.doi:10.1103/8blx-nfcr

    Ben Zindorf and Sougato Bose. Efficient implementation of multicontrolled quantum gates.Physical Review Applied, 24(4):044030, October 2025.doi:10.1103/8blx-nfcr

    work page doi:10.1103/8blx-nfcr 2025

  42. [42]

    Neural-network quantum state tomography.Nature Physics, 14(5):447–450, May 2018.doi:10.1038/s41567-018-0048-5

    Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, et al. Neural-network quantum state tomography.Nature Physics, 14(5):447–450, May 2018.doi:10.1038/s41567-018-0048-5. 32

    doi:10.1038/s41567-018-0048-5 2018

  43. [43]

    Quantum State Tomography with Conditional Generative Adversarial Networks.Physical Review Letters, 127(14):140502, September 2021

    Shahnawaz Ahmed, Carlos Sánchez Muñoz, Franco Nori, and Anton Frisk Kockum. Quantum State Tomography with Conditional Generative Adversarial Networks.Physical Review Letters, 127(14):140502, September 2021. doi:10.1103/PhysRevLett.127.140502

    work page doi:10.1103/physrevlett.127.140502 2021

  44. [44]

    Efficient quantum state tomography with convolutional neural networks.npj Quantum Information, 8(1):115, September 2022.doi:10.1038/s41534-022-00621-4

    Tobias Schmale, Moritz Reh, and Martin Gärttner. Efficient quantum state tomography with convolutional neural networks.npj Quantum Information, 8(1):115, September 2022.doi:10.1038/s41534-022-00621-4

    doi:10.1038/s41534-022-00621-4 2022

  45. [45]

    From Ideal to Noisy: Adapting Property-Based Testing for Real-World Noisy Quantum Computers

    Gabriel Pontolillo, Asmar Muqeet, Shaukat Ali, and Mohammad Reza Mousavi. From Ideal to Noisy: Adapting Property-Based Testing for Real-World Noisy Quantum Computers. In2025 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 01, pages 405–416, August 2025.doi:10.1109/QCE65121. 2025.00053

    arXiv 2025

  46. [46]

    Quantum supremacy using a programmable superconducting processor.Nature, 574(7779):505–510, October 2019.doi:10.1038/s41586-019-1666-5

    Frank Arute, Kunal Arya, Ryan Babbush, et al. Quantum supremacy using a programmable superconducting processor.Nature, 574(7779):505–510, October 2019.doi:10.1038/s41586-019-1666-5

    doi:10.1038/s41586-019-1666-5 2019

  47. [47]

    Smith, Michael J

    Robert S. Smith, Michael J. Curtis, and William J. Zeng. A Practical Quantum Instruction Set Architecture, February 2017.arXiv:1608.03355,doi:10.48550/arXiv.1608.03355

    Pith/arXiv arXiv doi:10.48550/arxiv.1608.03355 2017

  48. [48]

    AssertsQ: A Quantum Assertion Tool for Quantum Software Debugging:

    Javier Veganzones, Danel Alamo, Alfredo Cuzzocrea, and Pablo Bringas. AssertsQ: A Quantum Assertion Tool for Quantum Software Debugging:. InProceedings of the 1st International Conference on Quantum Software, pages 49– 60, Bilbao, Spain, 2025. SCITEPRESS - Science and Technology Publications.doi:10.5220/0013553300004525

    work page doi:10.5220/0013553300004525 2025

  49. [49]

    Distinguishing Quantum Software Bugs from Hardware Noise: A Statistical Approach

    Ahmik Virani, Devraj, Anirudh Suresh, Lei Zhang, and M V Panduranga Rao. Distinguishing Quantum Software Bugs from Hardware Noise: A Statistical Approach. In2025 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 01, pages 837–848, August 2025.doi:10.1109/QCE65121.2025.00096

    arXiv 2025

  50. [50]

    Fuzzy identification of systems and its applications to modeling and control.IEEE Transactions on Systems, Man, and Cybernetics, SMC-15(1):116–132, January 1985

    Tomohiro Takagi and Michio Sugeno. Fuzzy identification of systems and its applications to modeling and control.IEEE Transactions on Systems, Man, and Cybernetics, SMC-15(1):116–132, January 1985. doi: 10.1109/TSMC.1985.6313399

    arXiv 1985

  51. [51]

    C. Chow. On optimum recognition error and reject tradeoff.IEEE Transactions on Information Theory, 16(1):41–46, January 1970.doi:10.1109/TIT.1970.1054406

    arXiv 1970

  52. [52]

    Bartlett and Marten H

    Peter L. Bartlett and Marten H. Wegkamp. Classification with a Reject Option using a Hinge Loss.J. Mach. Learn. Res., 9:1823–1840, June 2008

    2008

  53. [53]

    Selective Classification for Deep Neural Networks, June 2017.arXiv: 1705.08500,doi:10.48550/arXiv.1705.08500

    Yonatan Geifman and Ran El-Yaniv. Selective Classification for Deep Neural Networks, June 2017.arXiv: 1705.08500,doi:10.48550/arXiv.1705.08500

    Pith/arXiv arXiv doi:10.48550/arxiv.1705.08500 2017

  54. [54]

    SelectiveNet: A Deep Neural Network with an Integrated Reject Option

    Yonatan Geifman and Ran El-Yaniv. SelectiveNet: A Deep Neural Network with an Integrated Reject Option. InProceedings of the 36th International Conference on Machine Learning, pages 2151–2159. PMLR, May 2019

    2019

  55. [55]

    Leveson.Engineering a Safer World: Systems Thinking Applied to Safety

    Nancy G. Leveson.Engineering a Safer World: Systems Thinking Applied to Safety. Engineering Systems. MIT Press, Cambridge, MA, USA, December 2016

    2016

  56. [56]

    A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems

    David J Hand and Robert J Till. A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems

  57. [57]

    C. E. Shannon. A mathematical theory of communication.The Bell System Technical Journal, 27(3):379–423, July 1948.doi:10.1002/j.1538-7305.1948.tb01338.x

    arXiv 1948

  58. [58]

    Helstrom

    Carl W. Helstrom. Quantum detection and estimation theory.Journal of Statistical Physics, 1(2):231–252, 1969. doi:10.1007/BF01007479

    doi:10.1007/bf01007479 1969

  59. [59]

    Noise effects on purity and quantum entanglement in terms of physical imple- mentability.npj Quantum Information, 9(1):11, February 2023.doi:10.1038/s41534-023-00680-1

    Yuchen Guo and Shuo Yang. Noise effects on purity and quantum entanglement in terms of physical imple- mentability.npj Quantum Information, 9(1):11, February 2023.doi:10.1038/s41534-023-00680-1

    work page doi:10.1038/s41534-023-00680-1 2023

  60. [60]

    Error-Divisible Two-Qubit Gates.Physical Review Applied, 19(2):024043, February 2023.doi:10.1103/PhysRevApplied.19.024043

    David Rodríguez Pérez, Paul Varosy, Ziqian Li, et al. Error-Divisible Two-Qubit Gates.Physical Review Applied, 19(2):024043, February 2023.doi:10.1103/PhysRevApplied.19.024043

    doi:10.1103/physrevapplied.19.024043 2023

  61. [61]

    J. Eisert. Entangling Power and Quantum Circuit Complexity.Physical Review Letters, 127(2):020501, July 2021.doi:10.1103/PhysRevLett.127.020501

    work page doi:10.1103/physrevlett.127.020501 2021

  62. [62]

    Evered, Dolev Bluvstein, Marcin Kalinowski, et al

    Simon J. Evered, Dolev Bluvstein, Marcin Kalinowski, et al. High-fidelity parallel entangling gates on a neutral-atom quantum computer.Nature, 622(7982):268–272, October 2023.doi:10.1038/s41586-023-06481-y

    doi:10.1038/s41586-023-06481-y 2023

  63. [63]

    Bussandri, Tristán M

    Diego G. Bussandri, Tristán M. Osán, Diego G. Bussandri, and Tristán M. Osán. Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences.Entropy, 25(6), June 2023.doi:10.3390/e25060912

    work page doi:10.3390/e25060912 2023

  64. [64]

    Riofrio, Oliver Mitevski, Caitlin Jones, et al

    Carlos A. Riofrio, Oliver Mitevski, Caitlin Jones, et al. A Characterization of Quantum Generative Models.ACM Transactions on Quantum Computing, 5(2):12:1–12:34, June 2024.doi:10.1145/3655027

    doi:10.1145/3655027 2024

  65. [65]

    Observation of entanglement transition of pseudo-random mixed states

    Tong Liu, Shang Liu, Hekang Li, et al. Observation of entanglement transition of pseudo-random mixed states. Nature Communications, 14(1):1971, April 2023.doi:10.1038/s41467-023-37511-y. 33

    work page doi:10.1038/s41467-023-37511-y 1971

  66. [66]

    Entropic property of randomized QAOA circuits.Laser Physics Letters, 21(1):015204, December 2023.doi:10.1088/1612-202X/ad12ad

    A Yu Chernyavskiy, B I Bantysh, and Yu I Bogdanov. Entropic property of randomized QAOA circuits.Laser Physics Letters, 21(1):015204, December 2023.doi:10.1088/1612-202X/ad12ad

    work page doi:10.1088/1612-202x/ad12ad 2023

  67. [67]

    Isakov, Vadim N

    Sergio Boixo, Sergei V. Isakov, Vadim N. Smelyanskiy, et al. Characterizing quantum supremacy in near-term devices.Nature Physics, 14(6):595–600, June 2018.doi:10.1038/s41567-018-0124-x

    doi:10.1038/s41567-018-0124-x 2018

  68. [68]

    Resource-Efficient Context-Aware Dynamical Decoupling Embedding for Arbitrary Large-Scale Quantum Algorithms.PRX Quantum, 6(1):010332, February 2025

    Paul Coote, Roman Dimov, Smarak Maity, et al. Resource-Efficient Context-Aware Dynamical Decoupling Embedding for Arbitrary Large-Scale Quantum Algorithms.PRX Quantum, 6(1):010332, February 2025. doi:10.1103/PRXQuantum.6.010332

    work page doi:10.1103/prxquantum.6.010332 2025

  69. [69]

    Yulun Wang and Predrag S. Krstic. Prospect of using Grover’s search in the noisy-intermediate-scale quantum- computer era.Physical Review A, 102(4):042609, October 2020.doi:10.1103/PhysRevA.102.042609

    work page doi:10.1103/physreva.102.042609 2020

  70. [70]

    Error per single-qubit gate below $10^{-4}$ in a superconducting qubit

    Zhiyuan Li, Pei Liu, Peng Zhao, et al. Error per single-qubit gate below $10^{-4}$ in a superconducting qubit. npj Quantum Information, 9(1):111, November 2023.arXiv:2302.08690,doi:10.1038/s41534-023-00781-x

    Pith/arXiv arXiv 2023

  71. [71]

    High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler.Physical Review X, 13(3):031035, September 2023.doi:10.1103/PhysRevX.13.031035

    Leon Ding, Max Hays, Youngkyu Sung, et al. High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler.Physical Review X, 13(3):031035, September 2023.doi:10.1103/PhysRevX.13.031035

    doi:10.1103/physrevx.13.031035 2023

  72. [72]

    SupermarQ: A Scalable Quantum Benchmark Suite, April 2022.arXiv:2202.11045,doi:10.48550/arXiv.2202.11045

    Teague Tomesh, Pranav Gokhale, Victory Omole, et al. SupermarQ: A Scalable Quantum Benchmark Suite, April 2022.arXiv:2202.11045,doi:10.48550/arXiv.2202.11045

    Pith/arXiv arXiv doi:10.48550/arxiv.2202.11045 2022

  73. [73]

    Nielsen and Isaac L

    Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th An- niversary Edition. https://www.cambridge.org/highereducation/books/quantum-computation-and-quantum- information/01E10196D0A682A6AEFFEA52D53BE9AE, December 2010.doi:10.1017/CBO9780511976667

    doi:10.1017/cbo9780511976667 2010

  74. [74]

    E. H. Mamdani and S. Assilian. An experiment in linguistic synthesis with a fuzzy logic controller.International Journal of Man-Machine Studies, 7(1):1–13, January 1975.doi:10.1016/S0020-7373(75)80002-2

    doi:10.1016/s0020-7373(75)80002-2 1975

  75. [75]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A Method for Stochastic Optimization, January 2017.arXiv: 1412.6980,doi:10.48550/arXiv.1412.6980

    Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980 2017

  76. [76]

    Wilde.Quantum Information Theory

    Mark M. Wilde.Quantum Information Theory. Cambridge University Press, Cambridge, 2 edition, 2017. doi:10.1017/9781316809976

    doi:10.1017/9781316809976 2017

  77. [77]

    IBM Quantum delivers on 2022 100x100 performance challenge | IBM Quantum Computing Blog

    Jay Gambetta and Ryan Mandelbaum. IBM Quantum delivers on 2022 100x100 performance challenge | IBM Quantum Computing Blog. https://www.ibm.com/quantum/blog/qdc-2024, 2024

    2022

  78. [78]

    Edwin B. Wilson. Probable Inference, the Law of Succession, and Statistical Inference.Journal of the American Statistical Association, 22(158):209–212, June 1927.doi:10.1080/01621459.1927.10502953

    arXiv 1927

  79. [79]

    Routledge, New York, 2 edition, May 2013

    Jacob Cohen.Statistical Power Analysis for the Behavioral Sciences. Routledge, New York, 2 edition, May 2013. doi:10.4324/9780203771587

    doi:10.4324/9780203771587 2013

  80. [80]

    Papert.Perceptrons: An Introduction to Computational Geometry

    Marvin Minsky and Seymour A. Papert.Perceptrons: An Introduction to Computational Geometry

Showing first 80 references.

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