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REVIEW 4 major objections 6 minor 55 references

Encoding a quantum circuit's structure and its backend's physics lets a learned denoiser catch faults that earlier filtering almost entirely misses.

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2026-08-01 03:16 UTC pith:ARXB4Q6G

load-bearing objection A real new architecture and a careful evaluation, but the denoised vectors aren't actually normalized despite the claim, so the headline metrics may not mean what they appear to. the 4 major comments →

arxiv 2607.23211 v1 pith:ARXB4Q6G submitted 2026-07-25 cs.SE

Backend-Aware Graph Learning for Denoising Outcome Distributions in Quantum Program Testing

Ning Ma , Jun Dai , Heng Li This is my paper
classification cs.SE
keywords quantum program testingnoise mitigationgraph transformerbackend-aware machine learningoutcome distribution denoisingoracle-based testingHellinger distancefault detection
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.

Quantum program testing on noisy hardware is unreliable because device noise shifts measured distributions and can flip pass/fail verdicts. This paper tries to establish that a graph transformer which encodes the transpiled circuit's gate structure, timing, and backend calibration, and then conditions that encoding on observed shot statistics, can undo enough of the noise to make oracle-based tests trustworthy. Across 23 simulated device noise models and six circuit families, the denoiser moves output distributions closer to the noise-free ideal than the strongest prior learned filter on every device. In fault-injection testing it detects over 80 percent of bug-induced failures while keeping precision near 94 percent, where the prior approach detects under 10 percent. A single model shared across all backends preserves most of this benefit, so per-device retraining is not strictly necessary.

Core claim

The central claim is that noise mitigation for quantum program testing is best done as structure-aware distribution reconstruction rather than summary-based reweighting. Q-BRIDGE converts the transpiled circuit into a directed acyclic graph whose node features carry gate type, per-qubit calibration (T1, T2, gate error, readout error), timing, and gate parameters, and whose edge features carry idle-time decoherence survival factors computed from scheduling gaps. A graph transformer with edge-biased attention encodes this graph, and a feature-wise linear modulation (FiLM) head combines the graph embedding with per-outcome observation features—empirical probability, its complement, log odds, an

What carries the argument

The load-bearing mechanism is a graph transformer with edge-biased attention combined with a state-wise FiLM (feature-wise linear modulation) conditioning head. The encoder treats each gate as a node and each dependency as an edge, with edge attributes encoding how much a qubit's state decays during the idle gap between gates via exp(-Δt/T1) and exp(-Δt/T2) survival factors. The FiLM head modulates the graph embedding separately for every computational basis state using that state's observed count statistics, allowing the model to decide per-outcome whether to amplify or suppress probability mass. This lets the model reconstruct a full output distribution instead of predicting a single expec

Load-bearing premise

The headline results rest on the assumption that the 23 vendor-supplied simulated device noise models faithfully capture what real quantum hardware does—including calibration drift and crosstalk—so the measured Hellinger improvements and test metrics may not transfer to actual devices.

What would settle it

Run the same six circuit families and the same fault-injected mutants on real quantum hardware backends, apply the trained denoiser, and compare denoised distributions to the ideal simulator distributions over several days. If the Hellinger reduction over the unfiltered output shrinks toward zero, or recall of bug-induced failures drops toward the prior baseline, the central claim is refuted; if calibration drift changes results from day to day, the model's backend conditioning is incomplete.

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

If this is right

  • Distribution-level denoising can be framed as supervised graph-to-distribution regression trained on paired noisy and ideal executions, and this framing transfers across devices.
  • A shared backend-conditioned model recovers most of the accuracy of per-device models, lowering the cost of deploying noise mitigation to many backends.
  • Oracle-based test verdicts become substantially more reliable: far fewer correct programs are rejected, while most bug-induced failures are still caught.
  • On larger circuits (8–15 qubits) the same approach still beats the prior learned filter, though absolute error grows, suggesting scalability but with diminishing returns.
  • Residual error concentrates on backends with highly heterogeneous readout errors and two-qubit gate errors, so calibration quality, not just circuit structure, bounds what any learned denoiser can recover.

Where Pith is reading between the lines

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

  • Editorial extension: because the experiments use vendor-supplied simulated noise models rather than live hardware, the most direct testable prediction is that the same gains will appear on real devices; if calibration drift is severe, the general model's backend embedding may need to be refreshed continuously.
  • Editorial extension: the per-state observation features (empirical probability, complement, log odds, shot count) are essentially sufficient statistics of a multinomial observation, so the method may extend naturally to other output alphabets, including continuous or hybrid observables, by swapping the embedding layer.
  • Editorial extension: the failure-mode analysis suggests a cheap diagnostic—backends whose readout-error heterogeneity or two-qubit gate-error heterogeneity is high will be the ones where learned denoising helps least, so a testing team could use those indicators to decide when mitigation is worth running.
  • Editorial extension: one could test the general model on a backend never seen in training by initializing its embedding and fine-tuning only that vector, turning cross-backend generalization into a few-shot adaptation problem.

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

4 major / 6 minor

Summary. Q-BRIDGE is a graph-transformer-based denoiser for quantum program testing. The method encodes the transpiled circuit as a DAG with node/edge features derived from gate types, calibration data, and scheduling, and uses a FiLM-style head to condition on per-state observation statistics extracted from noisy executions. A general model also conditions on a learned backend embedding. The model is trained by per-state MSE to match ideal-simulator distributions. Experiments cover 23 Qiskit Aer fake IBM noise models and 6 circuit families, with two deployment scenarios (backend-wise and general). The paper reports lower Hellinger distance than the QOIN baseline on all backends/families and improved precision/recall under UOF/WODF oracles.

Significance. If the empirical claims are sustained, Q-BRIDGE would be a useful contribution to noise-aware quantum software testing: it incorporates circuit structure and backend information more explicitly than prior summary-based methods, and it addresses the practical scenario of distribution-level denoising rather than single-observable mitigation. The paper has clear strengths: a public replication package, held-out CFUT inputs, five random seeds, consistent baselines under the same pretrain/fine-tune protocol, and explicit ablation and scalability studies. However, two load-bearing issues currently prevent acceptance: the inference procedure does not appear to output a normalized probability vector despite the paper's claims, and all 'backends' are vendor-supplied simulator noise models rather than real quantum hardware. Both issues affect the interpretation of the headline numbers.

major comments (4)
  1. [§III.A and §III.E] There is a direct internal inconsistency in the definition of the denoised distribution. Section III.A writes \hat p_t ∝ clip(\tilde p_t,0,1), which implies renormalization, and Section II.C claims the model 'enforce[s] a valid probability simplex at inference.' However, Section III.E describes only clipping to [0,1] with no division by the sum. Since the training objective in Section III.D is a per-state MSE with no sum-to-one constraint, the model has no incentive to emit a normalized vector. Hellinger distance and the UOF/WODF oracles in Section IV.F/V all assume a valid probability distribution; computing them on an unnormalized vector can produce meaningless or even negative values inside the Hellinger square root. This is load-bearing for every quantitative claim in Tables III–V. Please clarify the actual inference code: if it normalizes, correct the text; if it does not, re-run th
  2. [§IV.B.2, §VII, Abstract] All 23 'IBM noise backends' are Qiskit Aer device noise models (Fake* backends), not real hardware executions. Section VII correctly acknowledges that real-device transfer is future work, but the abstract and headline phrasing ('23 IBM noise backends') overstates the evidence. The paper's broader claim that considering 'physical characteristics of specific quantum backends' is a practical route to reliable testing is not yet supported for actual devices, since calibration drift, crosstalk, and simulator-model mismatch are explicitly named as open threats. At a minimum, revise the abstract and conclusions to say 'simulated IBM noise models', and temper the practical-route language. A real-hardware validation on even one or two backends would substantially strengthen the claim.
  3. [§III.C.2.d and RQ2] The general model conditions on a learned backend embedding table E indexed by the 23 training backends. There is no described mechanism to compute an embedding for an unseen backend at inference time. Thus RQ2 demonstrates parameter sharing across the 23 seen backends, not generalization to new devices. The phrase 'cross-backend generalization' should be qualified accordingly, and the paper should state what happens when the model is applied to a backend not in the embedding table (e.g., zero vector, nearest neighbor, or retraining required).
  4. [§V.C and Table V] The testing evaluation uses the same ideal simulator as the training target and as the oracle reference for ground-truth labeling. This is an acceptable denoising benchmark because QOIN is evaluated under the same protocol, but the phrase 'detecting bug-induced failures' should be qualified. The protocol measures whether denoising makes noisy outputs consistent with a known ideal reference distribution; it does not evaluate a situation where no ideal reference is available. Please state this explicitly in the RQ3 discussion so readers do not over-interpret the precision/recall numbers as evidence of fault detection without an ideal oracle.
minor comments (6)
  1. [Abstract] Use 'simulated IBM noise models' or 'Qiskit Aer fake backends' instead of 'IBM noise backends' to avoid implying real-hardware evaluation.
  2. [§III.A] The notation '\hat p_t ≜ p_ideal_t' is confusing: it suggests the output is defined as the target. Use a target variable such as y_t = p_ideal_t.
  3. [§III.B.1] The observation feature includes log(ODR_t), but ODR_t is undefined if POS_t is clipped to ε or 1-ε. The clipping choice ε=1e-6 is not analyzed; a sentence on sensitivity would help.
  4. [§VI] The ablation study is only summarized in words and relegated to the replication package. Since the paper claims each architectural component contributes positively, include at least a compact table (e.g., Hellinger values with/without edge bias, FiLM, backend embedding) in the main text.
  5. [§IV.F] The WODF threshold is set to 0.01 following prior work, but no sensitivity analysis is reported. Given the large effect on precision/recall in Table V, a brief threshold sweep would strengthen the results.
  6. [Throughout] Minor typographical issues: 'QISKIT' is inconsistently capitalized; 'we hypothesis' should be 'we hypothesize'; Table III uses many decimal places for standard deviations that are occasionally exactly zero, which may indicate rounding artifacts.

Circularity Check

0 steps flagged

No significant circularity: held-out evaluation against an external baseline; the only self-citation is motivational background.

full rationale

The paper's central claim is an empirical, head-to-head comparison: a graph-transformer denoiser trained (supervised) to map noisy observations plus circuit/backend features to ideal-simulator distributions, then evaluated on held-out inputs from six CFUTs against QOIN, an external baseline whose data the authors regenerate from the released code [23]. Training a regressor to predict the ideal distribution and later measuring Hellinger distance to that same ideal on a disjoint test set is ordinary supervised generalization, not circularity-by-construction: the inference features contain no ideal target, and Section IV-D1 states that test inputs are strictly disjoint from training/validation inputs and exercise disjoint path combinations. The only self-citation is [21] (Ning Ma and Heng Li, two of the present authors), used in the Introduction/Related Work to motivate graph transformers for quantum programs alongside external reference [38]; it is background motivation, not the load-bearing evidence for Q-BRIDGE's reported improvements. Section VII explicitly limits the claims to simulated IBM noise models and defers real-hardware transfer, which is an external-validity limitation rather than a circular step. One non-circular correctness concern remains: Section II.C claims a 'valid probability simplex at inference' is enforced, but Section III.E describes only clipping outputs to [0,1] without normalization, so the Hellinger and oracle metrics may be computed on non-normalized vectors; this threatens the validity of the empirical claims but does not make the derivation circular.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

Central claim rests on supervised pairs from an ideal simulator and Qiskit Aer noise models, plus modeling choices for graph features; no new physical entities are introduced. The main free parameters are learned or selected hyperparameters and the WODF threshold; none are fitted to the reported test results in a way that would force the conclusion.

free parameters (3)
  • model_hyperparameters = d=256, H=8, L=4, FFN=512, dropout=0.1, lr=5e-4/1e-3, epochs 500/1000 pretrain, 5-20 finetune
    Selected via a small pilot sweep (Section IV-G); not derived from theory and may overfit the benchmark.
  • WODF_threshold = 0.01
    Chosen following QOIN [23] (Section V-C1b); directly controls the FP/FN trade-off in the testing evaluation.
  • backend_embedding_z_b = learned vector per backend (dim db)
    In the general model, backend identity embedding is learned from pooled data (Section III-C2d); it is identifier conditioning, not a physical parameter.
axioms (5)
  • domain assumption The ideal QASM simulator output distribution is the correct denoising target and ground-truth oracle for test verdicts.
    Used in Section III-A and IV-B1 for training targets and in Section V-C for ground-truth labels; if simulator idealization is wrong, the fitted denoiser learns the wrong target.
  • domain assumption Qiskit Aer Fake-backend noise models faithfully represent real IBM device noise (including calibration, T1/T2, readout error) for the conclusions to transfer.
    All noisy executions are Aer noise models (Section IV-B2); authors acknowledge real-hardware transfer is future work (Section VII).
  • domain assumption UOF and WODF oracles are valid operationalizations of quantum program correctness.
    Adopted from prior work [41,42] and used to label mutants and verdicts (Section V-C); WODF threshold 0.01 may create false positives under sampling noise, acknowledged in Section VII.
  • domain assumption The hand-designed graph node/edge features (gate type, timing, decoherence survival factors, calibration) capture sufficient circuit structure for denoising.
    Model capacity and performance depend on this feature choice (Section III-B2); no formal guarantee, ablation deferred.
  • standard math Standard transformer and stochastic-gradient training machinery behaves as assumed.
    Uses multi-head attention, LayerNorm, AdamW; no formal verification is provided.

pith-pipeline@v1.3.0-alltime-deepseek · 18989 in / 13371 out tokens · 125517 ms · 2026-08-01T03:16:39.904154+00:00 · methodology

0 comments
read the original abstract

Testing quantum programs on NISQ (Noisy Intermediate-Scale Quantum) backends is challenging because the noise disturbs outcome distributions and can affect pass/fail decisions. We present Q-BRIDGE, a graph learning-based approach that converts noisy observations into denoised distributions suitable for oracle-based verification. Q-BRIDGE uses a graph transformer architecture to encode a transpiled quantum circuit, capturing the characteristics of its gates and their connectivity; the physical backend information is encoded together with the logical structure of the circuit. An additional conditioning layer, based on FiLM (Feature-Wise Linear Modulation), takes the encoding as input and integrates noisy observations to produce denoised outcomes. We evaluate Q-BRIDGE on 23 IBM noise backends and 6 circuit families representative of practical workloads. In the first setting, we train a separate Q-BRIDGE model for each backend; in the second setting, we train a single general model shared across all backends. Across both settings, Q-BRIDGE outperforms the state-of-the-art baseline in noise mitigation by a large margin. In testing scenarios with noisy executions, Q-BRIDGE achieves 93.97%-94.90% precision and 82.50%-83.51% recall in detecting bug-induced test failures, significantly outperforming the state-of-the-art baseline. These results indicate that considering the graph structure of the transpiled circuits and the physical characteristics of specific quantum backends is a practical route to more reliable noise-aware quantum program testing.

Figures

Figures reproduced from arXiv: 2607.23211 by Heng Li, Jun Dai, Ning Ma.

Figure 1
Figure 1. Figure 1: Model architecture overview. Left: Graph Transformer [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: End-to-end workflow used in our study: pretrain [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Reference graph

Works this paper leans on

55 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Shaukat Ali and Tao Yue. 2023. Quantum software test- ing: A brief introduction. In2023 IEEE/ACM 45th Inter- national Conference on Software Engineering: Compan- ion Proceedings (ICSE-Companion). IEEE, 332–333

    2023

  2. [2]

    Thomas Ayral, Franc ¸ois-Marie Le R´egent, Zain Saleem, Yuri Alexeev, and Martin Suchara. 2021. Quantum divide and compute: exploring the effect of different noise sources.SN Computer Science2, 3 (2021), 132

    2021

  3. [3]

    Tianyi Bao, Xinyu Ye, Hang Ruan, Chang Liu, Wenjie Wu, and Junchi Yan. 2025. Beyond Circuit Connec- tions: A Non-Message Passing Graph Transformer Ap- proach for Quantum Error Mitigation. InThe Thirteenth International Conference on Learning Representations. https://openreview.net/forum?id=XnVttczoA V

    2025

  4. [4]

    Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jennifer Wortman Vaughan. 2010. A theory of learning from different domains.Machine learning79, 1 (2010), 151–175

    2010

  5. [5]

    Avner Bensoussan, Elena Chachkarova, Karine Even- Mendoza, Sophie Fortz, and Vasileios Klimis. 2025. Toward Live Noise Fingerprinting in Quantum Software Engineering. arXiv:2512.18667 [quant-ph] https://arxiv. org/abs/2512.18667

    Pith/arXiv arXiv 2025

  6. [6]

    Lawrence D Brown, T Tony Cai, and Anirban DasGupta

  7. [7]

    Benjamin, Suguru Endo, William J

    Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien. 2023. Quantum error mitigation. Rev. Mod. Phys.95 (Dec 2023), 045005. Issue 4. doi:10 .1103/RevModPhys.95.045005

    2023

  8. [8]

    Rich Caruana. 1997. Multitask Learning.Machine Learning28 (1997), 41–75. https://api.semanticscho lar.org/CorpusID:45998148

    1997

  9. [9]

    Coles, and Lukasz Cincio

    Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. 2021. Error mitigation with Clifford quantum-circuit data.Quantum5 (Nov. 2021), 592. doi:10.22331/q-2021-11-26-592

    doi:10.22331/q-2021-11-26-592 2021

  10. [10]

    Daniel Fortunato, Jos ´e Campos, and Rui Abreu. 2022. 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(Virtual, South Korea)(ISSTA 2022). Association for Computing Machinery, New York, NY , USA, 797–800. doi:10.1145/3533767.3543296

    arXiv 2022

  11. [11]

    Constantin Gonzalez. 2021. Cloud based qc with amazon braket.Digitale Welt5, 2 (2021), 14–17

    2021

  12. [12]

    Yipeng Huang and Margaret Martonosi. 2019. Statistical assertions for validating patterns and finding bugs in quantum programs. InProceedings of the 46th Interna- tional Symposium on Computer Architecture(Phoenix, Arizona)(ISCA ’19). Association for Computing Ma- chinery, New York, NY , USA, 541–553. doi:10.1145/33 07650.3322213

    arXiv 2019

  13. [13]

    Akshaya Jayashankar and Prabha Mandayam. 2022. Quantum Error Correction: Noise-adapted Techniques and Applications. arXiv:2208.00365 [quant-ph] https: //arxiv.org/abs/2208.00365

    Pith/arXiv arXiv 2022

  14. [14]

    2013.Decoherence and the appearance of a classical world in quantum theory

    Erich Joos, H Dieter Zeh, Claus Kiefer, Domenico JW Giulini, Joachim Kupsch, and Ion-Olimpiu Stamatescu. 2013.Decoherence and the appearance of a classical world in quantum theory. Springer Science & Business Media

    2013

  15. [15]

    Stephen P. Jordan. [n. d.]. Quantum Algorithm Zoo. ht tps://quantumalgorithmzoo.org

  16. [16]

    Vasileios Klimis, Avner Bensoussan, Elena Chachkarova, Karine Even-Mendoza, Sophie Fortz, and Connor Leni- han. 2025. Shaking Up Quantum Simulators with Fuzzing and Rigour. 9, OOPSLA2, Article 322 (Oct. 2025), 29 pages. doi:10.1145/3763100

    work page doi:10.1145/3763100 2025

  17. [17]

    Jonathan Wei Zhong Lau, Kian Hwee Lim, Harshank Shrotriya, and Leong Chuan Kwek. 2022. NISQ com- puting: where are we and where do we go?AAPPS bulletin32, 1 (2022), 27

    2022

  18. [18]

    Gushu Li, Yufei Ding, and Yuan Xie. 2019. Tackling the qubit mapping problem for NISQ-era quantum de- vices. InProceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems. 1001–1014

    2019

  19. [19]

    Gushu Li, Li Zhou, Nengkun Yu, Yufei Ding, Mingsheng Ying, and Yuan Xie. 2020. Projection-based runtime assertions for testing and debugging Quantum programs. Proc. ACM Program. Lang.4, OOPSLA, Article 150 (Nov. 2020), 29 pages. doi:10.1145/3428218

    doi:10.1145/3428218 2020

  20. [20]

    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. 2023. Ma- chine Learning for Practical Quantum Error Mitigation. InNeurIPS 2023 AI for Science Workshop. https: //openreview.net/forum?id=xYbECDx0JF

    2023

  21. [21]

    Ning Ma and Heng Li. 2024. Understanding and Estimating the Execution Time of Quantum Programs. arXiv:2411.15631 [cs.SE] https://arxiv.org/abs/2411.1 5631

    arXiv 2024

  22. [22]

    E ˜naut Mendiluze, Shaukat Ali, Paolo Arcaini, and Tao Yue. 2021. Muskit: A Mutation Analysis Tool for Quantum Software Testing. In2021 36th IEEE/ACM International Conference on Automated Software Engi- neering (ASE). 1266–1270. doi:10.1109/ASE51524.202 1.9678563

    work page doi:10.1109/ase51524.202 2021

  23. [23]

    Asmar Muqeet, Tao Yue, Shaukat Ali, and Paolo Arcaini

  24. [24]

    Quantum Software Engineering: Roadmap and Challenges Ahead

    Juan Manuel Murillo, Jos ´e Garc ´ıa-Alonso, Enrique Moguel, Johanna Barzen, Frank Leymann, Shaukat Ali, Tao Yue, Paolo Arcaini, Ricardo P ´erez-Castillo, Ignacio Garc´ıa Rodr ´ıguez de Guzm ´an, Mario Piattini, Antonio Ruiz-Cort´es, Antonio Brogi, Jianjun Zhao, Andriy V . Miranskyy, and Manuel Wimmer. 2024. Challenges of 11 Quantum Software Engineering f...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2404.06825 2024

  25. [25]

    Mikhail S Nikulin et al. 2001. Hellinger distance. Encyclopedia of mathematics78 (2001)

    2001

  26. [26]

    Matteo Paltenghi and Michael Pradel. 2023. MorphQ: Metamorphic Testing of the Qiskit Quantum Comput- ing Platform . In2023 IEEE/ACM 45th International Conference on Software Engineering (ICSE). IEEE Com- puter Society, Los Alamitos, CA, USA, 2413–2424. doi:10.1109/ICSE48619.2023.00202

    arXiv 2023

  27. [27]

    Tirthak Patel and Devesh Tiwari. 2021. Qraft: reverse your Quantum circuit and know the correct program output. InProceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems(Virtual, USA)(AS- PLOS ’21). Association for Computing Machinery, New York, NY , USA, 443–455. doi:10.1145/3445814.3446 743

    arXiv 2021

  28. [28]

    John Preskill. 2018. Quantum computing in the NISQ era and beyond.Quantum2 (2018), 79

    2018

  29. [29]

    Quantum Computing UK. [n. d.]. Quantum Code Repos- itory. https://quantumcomputinguk.org/code-repository. Accessed 2025-09-06

    2025

  30. [30]

    Neilson Carlos Leite Ramalho, Higor Amario de Souza, and Marcos Lordello Chaim. 2024. Testing and Debugging Quantum Programs: The Road to 2030. arXiv:2405.09178 [cs.SE] https://arxiv.org/abs/2405 .09178

    Pith/arXiv arXiv 2024

  31. [31]

    Karpuzcu

    Salonik Resch and Ulya R. Karpuzcu. 2021. Benchmark- ing Quantum Computers and the Impact of Quantum Noise.ACM Comput. Surv.54, 7, Article 142 (July 2021), 35 pages. doi:10.1145/3464420

    doi:10.1145/3464420 2021

  32. [32]

    Matthias Steffen, David P DiVincenzo, Jerry M Chow, Thomas N Theis, and Mark B Ketchen. 2011. Quan- tum computing: An IBM perspective.IBM Journal of Research and Development55, 5 (2011), 13–1

    2011

  33. [33]

    Yehui Tang, Junchi Yan, and Hancock Edwin. 2022. From quantum graph computing to quantum graph learn- ing: A survey.arXiv preprint arXiv:2202.09506(2022)

    Pith/arXiv arXiv 2022

  34. [34]

    Gambetta

    Kristan Temme, Sergey Bravyi, and Jay M. Gambetta

  35. [35]

    Barbara M Terhal. 2015. Quantum error correction for quantum memories.Reviews of Modern Physics87, 2 (2015), 307–346

    2015

  36. [36]

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is all you need. Advances in neural information processing systems30 (2017)

    2017

  37. [37]

    Petar Velickovic, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, Yoshua Bengio, et al. 2017. Graph attention networks.stat1050, 20 (2017), 10– 48550

    2017

  38. [38]

    doi:10.1103/PhysRevLett.119.180509

    doi:10.1103/physrevlett.119.180509

  39. [39]

    Jiyuan Wang, Ming Gao, Yu Jiang, Jianguang Lou, Yue Gao, Dongmei Zhang, and Jiaguang Sun. 2018. QuanFuzz: Fuzz Testing of Quantum Program. arXiv:1810.10310 [cs.SE] https://arxiv.org/abs/1810.10310

    Pith/arXiv arXiv 2018

  40. [40]

    Jiyuan Wang, Qian Zhang, Guoqing Harry Xu, and Miryung Kim. 2021. QDiff: Differential Testing of Quan- tum Software Stacks. In2021 36th IEEE/ACM Interna- tional Conference on Automated Software Engineering (ASE). 692–704. doi:10.1109/ASE51524.2021.9678792

    arXiv 2021

  41. [42]

    Hanrui Wang, Pengyu Liu, Jinglei Cheng, Zhiding Liang, Jiaqi Gu, Zirui Li, Yongshan Ding, Weiwen Jiang, Yiyu Shi, Xuehai Qian, et al. 2022. Quest: Graph transformer for quantum circuit reliability estimation.arXiv preprint arXiv:2210.16724(2022)

    Pith/arXiv arXiv 2022

  42. [43]

    Dennis Willsch, M Willsch, Fengping Jin, Hans De Raedt, and Kristel Michielsen. 2018. Testing quantum fault tolerance on small systems.Physical Review A98, 5 (2018), 052348

    2018

  43. [44]

    Jiaming Ye, Shangzhou Xia, Fuyuan Zhang, Paolo Ar- caini, Lei Ma, Jianjun Zhao, and Fuyuki Ishikawa

  44. [45]

    Shuo Yu, Ciyuan Peng, Yingbo Wang, Ahsan Shehzad, Feng Xia, and Edwin R Hancock. 2023. Quantum graph learning: Frontiers and outlook.arXiv preprint arXiv:2302.00892(2023)

    Pith/arXiv arXiv 2023

  45. [46]

    Seongjun Yun, Minbyul Jeong, Raehyun Kim, Jaewoo Kang, and Hyunwoo J Kim. 2019. Graph transformer networks.Advances in neural information processing systems32 (2019)

    2019

  46. [47]

    Pengzhan Zhao, Jianjun Zhao, and Lei Ma. 2021. Iden- tifying Bug Patterns in Quantum Programs. In2021 IEEE/ACM 2nd International Workshop on Quantum Software Engineering (Q-SE). 16–21. doi:10.1109/Q-S E52541.2021.00011

    arXiv 2021

  47. [48]

    Xinyi Wang, Paolo Arcaini, Tao Yue, and Shaukat Ali

  48. [56]

    Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, et al. 2020. Quantum computational advantage using photons.Science370, 6523 (2020), 1460–1463. 12

    2020

  49. [188]

    doi:10.1109/QRS54544.2021.00029

    arXiv 2021

  50. [2001]

    Statistical science16, 2 (2001), 101–133

    Interval estimation for a binomial proportion. Statistical science16, 2 (2001), 101–133

    2001

  51. [2017]

    Error Mitigation for Short-Depth Quantum Cir- cuits.Phys. Rev. Lett.119 (Nov 2017), 180509. Issue

    2017

  52. [2021]

    In2021 IEEE 21st International Conference on Software Quality, Reliability and Security (QRS)

    Application of Combinatorial Testing to Quantum Programs. In2021 IEEE 21st International Conference on Software Quality, Reliability and Security (QRS). 179–

  53. [2022]

    InProceedings of the ACM/IEEE 44th Interna- tional Conference on Software Engineering: Compan- ion Proceedings(Pittsburgh, Pennsylvania)(ICSE ’22)

    QuSBT: search-based testing of quantum pro- grams. InProceedings of the ACM/IEEE 44th Interna- tional Conference on Software Engineering: Compan- ion Proceedings(Pittsburgh, Pennsylvania)(ICSE ’22). Association for Computing Machinery, New York, NY , USA, 173–177. doi:10.1145/3510454.3516839

    arXiv

  54. [2023]

    In2023 38th IEEE/ACM International Conference on Automated Software Engi- neering (ASE)

    QuraTest: Integrating Quantum Specific Features in Quantum Program Testing. In2023 38th IEEE/ACM International Conference on Automated Software Engi- neering (ASE). 1149–1161. doi:10.1109/ASE56229.202 3.00196

    work page doi:10.1109/ase56229.202

  55. [2024]

    doi:10.1109/TS E.2024.3462974

    Mitigating Noise in Quantum Software Testing Using Machine Learning.IEEE Transactions on Software Engineering50, 11 (2024), 2947–2961. doi:10.1109/TS E.2024.3462974

    arXiv 2024