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REVIEW 5 major objections 4 minor 91 references

An AI-guided search over quantum error-correcting codes finds constructions that beat a leading reference code at the same physical-qubit budget.

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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2026-08-01 01:15 UTC pith:SSTZMW6X

load-bearing objection The framework is genuinely new, but the headline comparison against the BB codes is under-specified to the point that the claimed advantage is unverified. the 5 major comments →

arxiv 2607.25865 v1 pith:SSTZMW6X submitted 2026-07-28 quant-ph cs.AIcs.MA

OmniQEC: discovering practical quantum error-correcting codes by an AI scientist

Ge Yan , Shanchuan Li , Pengyue Ma , Qixin Zhang , Pingchuan Ma , Jianping Wang , Min-Hsiu Hsieh , Yuxuan Du This is my paper
classification quant-ph cs.AIcs.MA
keywords quantum error correctionqLDPC codeslogical error rateLLM-guided searchcode-circuit-decoder co-designbivariate-bicycle codessyndrome extractionAI scientist
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.

OmniQEC is a system that treats the design of quantum error-correcting codes as a loop in which an LLM-based orchestrator proposes code constructions, a fast screen ranks them by cheap algebraic proxies, and a slower, physically grounded stage compiles the survivors into noisy syndrome-extraction circuits and estimates their logical error rate under decoder simulation. The central claim is that this circuit-level criterion, not the usual code-level figure of merit, is what practical code discovery should optimize. The paper reports that codes discovered this way achieve lower logical error rates than the standard bivariate-bicycle reference codes [[72,12,6]] and [[144,12,12]] when the full implementations are compared at equal total physical-qubit budgets of 98 and 240 qubits, and that the advantage persists across a physical-error-rate sweep. It also reports that the widely used code-level proxy kd^2/n can rank these codes in the opposite order from their true circuit-level performance, which would explain why code-centric searches may miss practical constructions.

Core claim

The paper's central discovery is that physically grounded, circuit-level feedback can be brought into an otherwise algebraic search for qLDPC codes, and that doing so yields codes whose complete implementations—including data qubits, syndrome-measurement ancillas, and the noise introduced by extraction circuits—deliver lower logical error rates than the leading bivariate-bicycle reference at the same or smaller physical-qubit budgets. Concretely, the discovered frontier outperforms the [[72,12,6]] bivariate-bicycle code at 98 total physical qubits and, for the stronger LLM backends, the [[144,12,12]] code at 240 total qubits. The paper further claims that this advantage is not an artifact of

What carries the argument

The load-bearing mechanism is a dual-loop discovery workflow under an LLM-based orchestrator. In the fast loop, generated construction programs are screened in seconds by algebraic validity checks and a code-level figure of merit (k d^2 / n). In the slow loop, selected survivors are compiled into syndrome-extraction circuits under a fixed total physical-qubit budget and evaluated by sampling a detector error model and decoding with belief-propagation-based decoders; the resulting logical error rate is fed back to the orchestrator to steer the next generation of proposals. The circuit-level logical error rate per round per logical qubit is the objective that carries the argument.

Load-bearing premise

The claimed advantage rests on the assumption that the bivariate-bicycle reference codes were compiled and evaluated with implementation quality at least as high as their published hand-optimized circuits; if the generic compilation used here degrades the baseline, the advantage could shrink or disappear.

What would settle it

Re-compile the bivariate-bicycle [[72,12,6]] code using the syndrome-extraction schedule from its original optimized publication, run the same circuit-level noise model and decoder, and compare its logical error rate at 98 total physical qubits with the OmniQEC-discovered code under identical conditions; if the reference matches or beats the discovered code in this setting, the paper's central advantage claim is falsified.

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

If this is right

  • If the central claim is right, practical QEC code search should be conducted at the circuit level, because code-level proxies can actively mis-rank candidates that are superior in implementation.
  • Quantum memories with better error suppression can be built at the same physical-qubit budget as, or a smaller budget than, the leading bivariate-bicycle reference designs.
  • The advantage persisting across a physical-error-rate sweep indicates the discovered codes are not overfit to one noise operating point, so they are plausible candidates for deployment on near-term processors.
  • The dual-loop structure makes the method modular: improvements in circuit synthesis, decoding, or statistical estimation of logical error rates can be inserted without changing the discovery loop.
  • Stronger LLM reasoning backends convert circuit-level feedback into better constructions, so the orchestrator's reflection capability is itself a determinant of discovery performance.

Where Pith is reading between the lines

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

  • I infer that the reported misalignment between kd^2/n and logical error rate generalizes beyond this paper's code families, which would cast doubt on the many existing automated search pipelines that optimize such proxies.
  • A direct extension would be to feed per-gate calibration data (error maps, disabled couplers) into the slow loop, potentially yielding codes tailored to a specific processor rather than to a generic noise model.
  • The backend-dependence observed here suggests that the cost-performance trade-off of the AI scientist is set by the LLM, not the search formulation; a weaker but cheaper model may still find useful codes but with a worse frontier.
  • Because the comparison re-uses a generic compilation for the reference codes, the strongest test of the paper's claim would be a fair re-benchmark against the reference codes' own optimized circuits.

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. OmniQEC is an LLM-orchestrated search system for qLDPC codes. It combines a fast loop that generates and screens candidate construction programs using code-level properties (validity, [[n,k,d]], Φcode) with a slow loop that synthesizes syndrome-extraction circuits, simulates them with Stim, decodes with BP+OSD, and evaluates the per-round, per-logical-qubit logical error rate p_LER under depolarizing noise. The authors report results for three LLM backends (Claude, GPT, DeepSeek) across four code families and 14 total-physical-qubit budgets, and claim that the best discovered codes outperform the BB [[72,12,6]] and [[144,12,12]] reference implementations at complete-implementation budgets of 98 and 240 physical qubits, with the advantage persisting over p∈[0.002,0.01]. Ablations show that removing the slow-loop feedback degrades the top-five candidates, and API costs are reported.

Significance. The workflow is a sensible and potentially valuable contribution: it replaces code-centric search with a circuit-level objective, uses standard tools (Stim, BP+OSD), and the ablation study (Fig. 3d–f) gives clear evidence that slow-loop circuit-level feedback is important. The p-sweeps (Fig. 3a–c) are a good check against overfitting to a single physical error rate. If the headline comparison to the BB codes survives scrutiny, the result would be significant: it would show that LLM-guided, implementation-aware search can find qLDPC codes with lower circuit-level logical error rate at smaller total physical-qubit budgets than two leading reference codes, and would strengthen the case for replacing code-level proxies with implementation-level objectives. However, the current submission does not yet establish that comparison because the fairness of the BB baseline compilation, the per-logical-qubit normalization, and the statistical uncertainty are not adequately addressed.

major comments (5)
  1. [§III.C, Fig. 3 caption] The claim that discovered codes 'outperform' BB depends on the quality of the BB reference circuits. The caption says BB is evaluated 'under the same syndrome-extraction and decoding protocol,' which implies the BB codes were compiled with OmniQEC's generic edge-coloring synthesis (§II.B) rather than the hand-optimized circuits of Bravyi et al. (2024). Different syndrome-extraction schedules can substantially change circuit depth and two-qubit-gate count, and hence LER. Please report the circuit metrics of the OmniQEC-compiled BB circuits versus the published BB circuits, and re-evaluate the discovered codes against the published BB circuits under identical noise/decoder settings. Without this, the headline advantage is not established.
  2. [§III.B, Fig. 2] The comparison does not control for the number of logical qubits. The discovered codes in Fig. 2 mostly have k=1–4 (e.g., [[72,2,11]]), while the BB references have [[72,12,6]] and [[144,12,12]]. Since p_LER is defined per logical qubit, a low-k code can appear better simply because it stores fewer logical qubits; a 98-qubit implementation of a k=2 code is not directly comparable to a 144-qubit implementation of a k=12 code for a fixed memory capacity. Please report the aggregate logical failure probability per round for each complete implementation, or compare at fixed k, or state the physical-qubit overhead per logical qubit.
  3. [Abstract and §III.A] The Abstract says the discovered codes outperform BB 'under complete-implementation budgets of 98 and 240 physical qubits,' while §III.A states the BB codes require N=144 and N=288. If the intended meaning is that the discovered N=98 and N=240 implementations beat BB implementations with N=144 and N=288, this is a resource-efficiency comparison, not an equal-budget comparison, and the text should say so explicitly (the BB points in Fig. 2 at 144 and 288 reinforce this reading). If instead an equal-budget comparison is intended, the §III.A budgets are inconsistent. As written, the headline is ambiguous and should be corrected.
  4. [§III.C, Fig. 3a–c] The central quantitative claims, e.g., '29.23-fold lower at p=0.002' and '1.66-fold lower at p=0.01,' are presented without any statistical uncertainty. LER values estimated from finite Stim samples are binomial counts; without confidence intervals or the number of shots, the differences could be within sampling noise. Please add error bars (e.g., Clopper–Pearson intervals or resampling) and report the shot counts for every data point in Fig. 3 and Fig. 2.
  5. [§II.A, Fig. 1; §III.A] No code, circuits, or data repository is provided, although Fig. 1 advertises a 'ranked package containing reproducible code-construction programs, discovered codes, compiled circuits, and decoding performance.' The manuscript refers to SI A–D but the supplementary material is not included. Without the actual construction programs, Stim circuits, detector error models, and decoder configurations, independent verification of the LER numbers is impossible. These artifacts must be released for the paper's claims to be checkable.
minor comments (4)
  1. [§II.B] Code distance is described as 'estimated or bounded' using BP+LSD and OSD, yet Fig. 2 lists exact-looking parameters [n,k,d]. Please mark which d values are certified and which are estimates; if d is only estimated, the code parameters may be incorrect.
  2. [§III.A] The term 'complete-implementation budget' should be defined once, specifying exactly which qubits are counted (data, ancillas, flags, readout) and why the BB implementations require 2n physical qubits.
  3. [Fig. 3a–c] The code labels are repeated across backends and the individual curves are difficult to distinguish. A table listing each selected code, its total N, k, d, LER values, and error bars would improve readability and reproducibility.
  4. [General] References to 'SI A–D' are made in the text, but no supplementary file is included with the submission. Please provide the supplementary material or remove the pointers.

Circularity Check

0 steps flagged

No significant circularity found: OmniQEC's LER-optimization search is validated against external BB baselines and independent p-sweeps.

full rationale

The paper's derivation chain is a generate-evaluate-refine search: the fast loop ranks candidates by the code-level proxy Phi_code = k d^2 / n, and the slow loop evaluates a subset by circuit-level LER under depolarizing noise at p = 0.005. Reporting the LER of the selected best codes is selection under a stated objective, not circularity; any optimization-based discovery does this. The central comparison is against the external BB [[72,12,6]] and [[144,12,12]] codes from Bravyi et al. [17], and the p-sweeps in Fig. 3a-c are direct re-measurements over p in [0.002, 0.01], not extrapolations. The fitted scaling p_LER ∝ p^Gamma is a fit to measured data, not a fitted parameter renamed as a prediction. No fitted constant is injected back into the search model, and no equation is shown to be equivalent to its own input by construction. Self-citations in the reference list (e.g., [61], [81], [82]) are contextual and are not load-bearing: the actual evaluation pipeline uses external tools (Stim, BP+OSD, BP+LSD, Relay-BP) and external baselines. The abstract's '98 and 240 physical qubits' vs Section III.A's statement that the BB implementations require N=144 and N=288 is a benchmark-definition or fairness concern, not a circularity pattern: it questions whether the BB baseline was recompiled under the same generic syndrome-extraction protocol, but does not make the reported LER advantage equivalent to the paper's inputs by construction. Therefore no enumerated circular step is established, and the appropriate score is 0.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

No new particles or forces are introduced. The work relies on standard CSS code theory, the validity of Stim's noise model as a proxy for hardware, and the BP+OSD decoder as a practical decoder. The main user-set quantities are the noise rate and search scale, which are not derived from first principles.

free parameters (4)
  • Physical error rate p = 0.005 = 0.005
    The search and evaluation objective LER is computed at this single depolarizing rate; the chosen operating point affects which codes are found.
  • Top-candidate selection count (adaptive) = not specified
    The number of candidates promoted from fast to slow loop is selected adaptively; the exact schedule is not given in the main text.
  • Search hyperparameters (T=60, 24 programs/iteration, 20 seeds) = 60/24/20
    These fixed parameters constrain the search and could affect the frontier, though they are not fitted to the result.
  • Code-distance estimate tolerance = not specified
    The code distance d used in the FOM proxy is estimated via BP+LSD/OSD, not certified exactly for all candidates; errors in d could misrank candidates in the fast loop.
axioms (5)
  • standard math CSS check matrices must satisfy H_X H_Z^T = 0 over GF(2)
    Used in code-characterization validity check (Section II.B).
  • domain assumption Circuit-level depolarizing noise with rate p adequately models physical noise on quantum processors
    LER objective is computed with this noise model (Section III.A).
  • domain assumption BP+OSD decoder performance is a reliable proxy for practical decoders in QEC
    All LER evaluations use BP+OSD (Section III.A).
  • ad hoc to paper The four construction families (BB, TB, LP, GLP) cover a useful region of practical qLDPC codes
    Search space restricted to these families; the claim is about these families only.
  • standard math Stim's detector error model and sampling are correct
    Used in circuit evaluation (Section II.B).

pith-pipeline@v1.3.0-alltime-deepseek · 14309 in / 13284 out tokens · 105279 ms · 2026-08-01T01:15:27.143378+00:00 · methodology

0 comments
read the original abstract

Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and $14$ total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with $[\![72,12,6]\!]$ and $[\![144,12,12]\!]$ under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.

Figures

Figures reproduced from arXiv: 2607.25865 by Ge Yan, Jianping Wang, Min-Hsiu Hsieh, Pengyue Ma, Pingchuan Ma, Qixin Zhang, Shanchuan Li, Yuxuan Du.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

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Reference graph

Works this paper leans on

91 extracted references · 15 linked inside Pith

  1. [1]

    Gottesman, An introduction to quantum error correction and fault-tolerant quantum computation, arXiv preprint arXiv:0904.2557 (2009)

    D. Gottesman, An introduction to quantum error correction and fault-tolerant quantum computation, arXiv preprint arXiv:0904.2557 (2009)

    Pith/arXiv arXiv 2009

  2. [2]

    B. M. Terhal, Quantum error correction for quantum memories, Reviews of Modern Physics87, 307 (2015)

    2015

  3. [3]

    Roffe, Quantum error correction: an introductory guide, Contemporary Physics60, 226 (2019)

    J. Roffe, Quantum error correction: an introductory guide, Contemporary Physics60, 226 (2019)

    2019

  4. [4]

    A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics303, 2 (2003)

    2003

  5. [5]

    Dennis, A

    E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics43, 4452 (2002)

    2002

  6. [6]

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Physical Review A—Atomic, Molecular, and Optical Physics86, 032324 (2012)

    2012

  7. [7]

    Bombin and M

    H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Physical review letters97, 180501 (2006)

    2006

  8. [8]

    Lacroix, A

    N. Lacroix, A. Bourassa, F. J. Heras, L. M. Zhang, J. Bausch, A. W. Senior, T. Edlich, N. Shutty, V. Sivak, A. Bengtsson, et al., Scaling and logic in the color code on a superconducting quantum processor, Nature , 1 (2025)

    2025

  9. [9]

    M. B. Hastings and J. Haah, Dynamically generated logical qubits, Quantum5, 564 (2021)

    2021

  10. [10]

    Davydova, N

    M. Davydova, N. Tantivasadakarn, and S. Balasubramanian, Floquet codes without parent subsystem codes, PRX Quantum 4, 020341 (2023)

    2023

  11. [11]

    Gidney, M

    C. Gidney, M. Newman, A. Fowler, and M. Broughton, A fault-tolerant honeycomb memory, Quantum5, 605 (2021)

    2021

  12. [12]

    H. Cao, G. Yan, Y. Du, and F. Pan, Maximum likelihood decoding of quantum error correction codes, arXiv preprint arXiv:2605.17230 (2026)

    Pith/arXiv arXiv 2026

  13. [13]

    Tillich and G

    J.-P. Tillich and G. Z´ emor, Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength, IEEE Transactions on Information Theory60, 1193 (2014)

    2014

  14. [14]

    Panteleev and G

    P. Panteleev and G. Kalachev, Quantum ldpc codes with almost linear minimum distance, IEEE Transactions on Infor- mation Theory68, 213 (2021)

    2021

  15. [15]

    N. P. Breuckmann and J. N. Eberhardt, Balanced product quantum codes, IEEE Transactions on Information Theory67, 6653 (2021)

    2021

  16. [16]

    Panteleev and G

    P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes, inProceedings of the 54th annual ACM SIGACT symposium on theory of computing(2022) pp. 375–388

    2022

  17. [17]

    Bravyi, A

    S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault- tolerant quantum memory, Nature627, 778 (2024)

    2024

  18. [18]

    Goto, High-performance fault-tolerant quantum computing with many-hypercube codes, Science Advances10, eadp6388 (2024)

    H. Goto, High-performance fault-tolerant quantum computing with many-hypercube codes, Science Advances10, eadp6388 (2024)

    2024

  19. [19]

    D. Ruiz, J. Guillaud, A. Leverrier, M. Mirrahimi, and C. Vuillot, Ldpc-cat codes for low-overhead quantum computing in 2d, Nature Communications16, 1040 (2025)

    2025

  20. [20]

    G. Q. AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature614, 676 (2023)

    2023

  21. [21]

    G. Q. AI and Collaborators, Quantum error correction below the surface code threshold, Nature638, 920 (2025)

    2025

  22. [22]

    Bluvsteinet al., Logical quantum processor based on reconfigurable atom arrays, Nature626, 58 (2024)

    D. Bluvsteinet al., Logical quantum processor based on reconfigurable atom arrays, Nature626, 58 (2024)

    2024

  23. [23]

    Q. Xu, J. P. Bonilla Ataides, C. A. Pattison, N. Raveendran, D. Bluvstein, J. Wurtz, B. Vasi´ c, M. D. Lukin, L. Jiang, and H. Zhou, Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays, Nature Physics20, 1084 (2024)

    2024

  24. [24]

    L. Egan, D. M. Debroy, C. Noel, A. Risinger, D. Zhu, D. Biswas, M. Newman, M. Li, K. R. Brown, M. Cetina, and C. Monroe, Fault-tolerant control of an error-corrected qubit, Nature598, 281 (2021)

    2021

  25. [25]

    Ryan-Anderson, J

    C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown,et al., Realization of real-time fault-tolerant quantum error correction, Physical Review X11, 041058 (2021). 10

    2021

  26. [26]

    Bravyi, D

    S. Bravyi, D. Poulin, and B. Terhal, Tradeoffs for reliable quantum information storage in 2d systems, Physical review letters104, 050503 (2010)

    2010

  27. [27]

    Katabarwa, K

    A. Katabarwa, K. Gratsea, A. Caesura, and P. D. Johnson, Early fault-tolerant quantum computing, PRX quantum5, 020101 (2024)

    2024

  28. [28]

    H. Zhou, M. Cain, and M. D. Lukin, Opportunities in full-stack design of low-overhead fault-tolerant quantum computation, Nature Computational Science5, 1110 (2025)

    2025

  29. [29]

    H. P. Nautrup, N. Delfosse, V. Dunjko, H. J. Briegel, and N. Friis, Optimizing quantum error correction codes with reinforcement learning, Quantum3, 215 (2019)

    2019

  30. [30]

    J. Olle, R. Zen, M. Puviani, and F. Marquardt, Simultaneous discovery of quantum error correction codes and encoders with a noise-aware reinforcement learning agent, npj Quantum Information10, 126 (2024)

    2024

  31. [31]

    V. P. Su, C. Cao, H.-Y. Hu, Y. Yanay, C. Tahan, and B. Swingle, Discovery of optimal quantum codes via reinforcement learning, Physical review applied23, 034048 (2025)

    2025

  32. [32]

    B. C. A. Freire, N. Delfosse, and A. Leverrier, Optimizing hypergraph product codes with random walks, simulated annealing and reinforcement learning, in2025 IEEE International Symposium on Information Theory (ISIT)(IEEE,

  33. [33]

    A. Y. He and Z.-W. Liu, Discovering highly efficient low-weight quantum error-correcting codes with reinforcement learning, arXiv preprint arXiv:2502.14372 (2025)

    Pith/arXiv arXiv 2025

  34. [34]

    Y. Du, Y. Zhu, Y.-H. Zhang, M.-H. Hsieh, P. Rebentrost, W. Gao, Y.-D. Wu, J. Eisert, G. Chiribella, D. Tao,et al., Artificial intelligence for representing and characterizing quantum systems, arXiv preprint arXiv:2509.04923 (2025)

    Pith/arXiv arXiv 2025

  35. [35]

    Chengyu, R

    Y. Chengyu, R. Meister, C. Carty, S.-K. Lin, and R. Bondesan, Bayesian optimization for quantum error-correcting code discovery, arXiv preprint arXiv:2601.18562 (2026)

    arXiv 2026

  36. [36]

    Cruz-Benito, A

    J. Cruz-Benito, A. W. Cross, D. Kremer, and I. Faro, Evolutionary discovery of bivariate bicycle codes with llm-guided search, arXiv preprint arXiv:2606.02418 (2026)

    Pith/arXiv arXiv 2026

  37. [37]

    X. He, S. Lu, and B. Zeng, Co-designing quantum codes with transversal diagonal gates via multi-agent systems, in2026 IEEE 19th Dallas Circuits and Systems Conference (DCAS)(IEEE, 2026) pp. 1–6

    2026

  38. [38]

    Liu and F

    Z. Liu and F. Marquardt, Large-language-model discovery of quantum ldpc codes through structured concept evolution, arXiv preprint arXiv:2606.24808 (2026)

    Pith/arXiv arXiv 2026

  39. [39]

    A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Physical Review A54, 1098 (1996)

    1996

  40. [40]

    Steane, Multiple-particle interference and quantum error correction, Proceedings of the Royal Society of London

    A. Steane, Multiple-particle interference and quantum error correction, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences452, 2551 (1996)

    1996

  41. [41]

    Gottesman,Stabilizer codes and quantum error correction(California Institute of Technology, 1997)

    D. Gottesman,Stabilizer codes and quantum error correction(California Institute of Technology, 1997)

    1997

  42. [42]

    Higgott, T

    O. Higgott, T. C. Bohdanowicz, A. Kubica, S. T. Flammia, and E. T. Campbell, Improved decoding of circuit noise and fragile boundaries of tailored surface codes, Physical Review X13, 031007 (2023)

    2023

  43. [43]

    Zhang, D

    K. Zhang, D. Gao, Z. Yang, R. Zhou, F. Liu, Z. Ji, and J. Chen, Optimal compilation of syndrome extraction circuits for general quantum ldpc codes, in2026 Design, Automation & Test in Europe Conference (DATE)(IEEE, 2026) pp. 1–7

    2026

  44. [44]

    Viszlai, S

    J. Viszlai, S. Maurya, S. Tannu, M. Martonosi, and F. T. Chong, Prophunt: Automated optimization of quantum syndrome measurement circuits, inProceedings of the 31st ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2(2026) pp. 1476–1491

    2026

  45. [45]

    Liang, K

    Z. Liang, K. Liu, H. Song, and Y.-A. Chen, Generalized toric codes on twisted tori for quantum error correction, PRX Quantum6, 020357 (2025)

    2025

  46. [46]

    Baspin and A

    N. Baspin and A. Krishna, Connectivity constrains quantum codes, Quantum6, 711 (2022)

    2022

  47. [47]

    Strikis, D

    A. Strikis, D. E. Browne, and M. E. Beverland, High-performance syndrome extraction circuits for quantum codes, arXiv preprint arXiv:2603.05481 (2026)

    arXiv 2026

  48. [48]

    Kishony and A

    G. Kishony and A. Fowler, Surface code off-the-hook: diagonal syndrome-extraction scheduling, arXiv preprint arXiv:2602.09099 (2026)

    arXiv 2026

  49. [49]

    R. Bi, K. Chang, and S. Puri, Untangling qldpc codes with biased noise ancilla, arXiv preprint arXiv:2606.30592 (2026)

    Pith/arXiv arXiv 2026

  50. [50]

    Roffe, D

    J. Roffe, D. R. White, S. Burton, and E. Campbell, Decoding across the quantum low-density parity-check code landscape, Physical Review Research2, 043423 (2020)

    2020

  51. [51]

    D. A. Boiko, R. MacKnight, B. Kline, and G. Gomes, Autonomous chemical research with large language models, Nature 624, 570 (2023)

    2023

  52. [52]

    C. Lu, C. Lu, R. T. Lange, J. Foerster, J. Clune, and D. Ha, The ai scientist: Towards fully automated open-ended scientific discovery, arXiv preprint arXiv:2408.06292 (2024)

    Pith/arXiv arXiv 2024

  53. [53]

    Z. Chen, A. N. Petsch, A. J. Israelski, R. Plumley, L. Shen, C. Wang, C. Peng, Y. Ni, A. Bansil, S. Chowdhury,et al., An agentic artificially intelligent x-ray scientist, Nature Machine Intelligence , 1 (2026)

    2026

  54. [54]

    A. M. Bran, S. Cox, O. Schilter, C. Baldassari, A. D. White, and P. Schwaller, Augmenting large language models with chemistry tools, Nature machine intelligence6, 525 (2024)

    2024

  55. [55]

    S. Arlt, H. Duan, F. Li, S. M. Xie, Y. Wu, and M. Krenn, Meta-designing quantum experiments with language models, Nature Machine Intelligence8, 148 (2026)

    2026

  56. [56]

    Y. Kim, K. Gu, C. Park, C. Park, S. Schmidgall, A. A. Heydari, Y. Yan, Z. Zhang, Y. Zhuang, Y. Liu, M. Malhotra, P. P. Liang, H. W. Park, Y. Yang, X. Xu, Y. Du, S. Patel, T. Althoff, D. McDuff, and X. Liu, Capable language models can outgrow the benefits of collaboration, Nature Machine Intelligence8, 1157 (2026)

    2026

  57. [57]

    Novikov, N

    A. Novikov, N. V˜ u, M. Eisenberger, E. Dupont, P.-S. Huang, A. Z. Wagner, S. Shirobokov, B. Kozlovskii, F. J. Ruiz, A. Mehrabian,et al., Alphaevolve: A coding agent for scientific and algorithmic discovery, arXiv preprint arXiv:2506.13131 (2025). 11

    Pith/arXiv arXiv 2025

  58. [58]

    Gidney, Stim: a fast stabilizer circuit simulator, Quantum5, 497 (2021)

    C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum5, 497 (2021)

    2021

  59. [59]

    S. Yao, J. Zhao, D. Yu, I. Shafran, K. R. Narasimhan, and Y. Cao, React: Synergizing reasoning and acting in language models, inNeurIPS 2022 Foundation Models for Decision Making Workshop(2022)

    2022

  60. [60]

    Shinn, F

    N. Shinn, F. Cassano, A. Gopinath, K. Narasimhan, and S. Yao, Reflexion: Language agents with verbal reinforcement learning, Advances in neural information processing systems36, 8634 (2023)

    2023

  61. [61]

    G. Yan, W. Wu, Y. Chen, K. Pan, X. Lu, Z. Zhou, Y. Wang, R. Wang, and J. Yan, Ai-empowered quantum circuit synthesis and compilation optimization: Overview and prospects, IEEE Transactions on Pattern Analysis and Machine Intelligence (2026)

    2026

  62. [62]

    Panteleev and G

    P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes, arXiv preprint arXiv:2111.03654 (2021)

    Pith/arXiv arXiv 2021

  63. [63]

    L. Voss, S. J. Xian, T. Haug, and K. Bharti, Multivariate bicycle codes, Physical Review A111, L060401 (2025)

    2025

  64. [64]

    Mayer, A

    C. Mayer, A. Ganti, U. Onunkwo, T. Metodi, B. Anker, and J. Skryzalin, Rare event simulation of quantum error-correcting circuits, arXiv preprint arXiv:2509.13678 (2025)

    arXiv 2025

  65. [65]

    Zhang and Y

    G. Zhang and Y. Li, Time-efficient logical operations on quantum low-density parity check codes, Physical Review Letters 134, 070602 (2025)

    2025

  66. [66]

    M. Cain, C. Zhao, H. Zhou, N. Meister, J. Ataides, A. Jaffe, D. Bluvstein, and M. D. Lukin, Correlated decoding of logical algorithms with transversal gates, arXiv preprint arXiv:2403.03272 (2024)

    Pith/arXiv arXiv 2024

  67. [67]

    Horsman, A

    C. Horsman, A. G. Fowler, S. Devitt, R. Van Meter,et al., Surface code quantum computing by lattice surgery, New Journal of physics14, 123011 (2012)

    2012

  68. [68]

    Litinski, A game of surface codes: Large-scale quantum computing with lattice surgery, Quantum3, 128 (2019)

    D. Litinski, A game of surface codes: Large-scale quantum computing with lattice surgery, Quantum3, 128 (2019)

    2019

  69. [69]

    Chamberland and E

    C. Chamberland and E. T. Campbell, Universal quantum computing with twist-free and temporally encoded lattice surgery, PRX Quantum3, 010331 (2022)

    2022

  70. [70]

    Bravyi and A

    S. Bravyi and A. Kitaev, Universal quantum computation with ideal clifford gates and noisy ancillas, Physical Review A—Atomic, Molecular, and Optical Physics71, 022316 (2005)

    2005

  71. [71]

    Bomb ´ ın, Single-shot fault-tolerant quantum error correction, Physical Review X5, 031043 (2015)

    H. Bomb ´ ın, Single-shot fault-tolerant quantum error correction, Physical Review X5, 031043 (2015)

    2015

  72. [72]

    Gidney and A

    C. Gidney and A. G. Fowler, Efficient magic state factories with a catalyzed|ccz⟩to 2|t⟩transformation, Quantum3, 135 (2019)

    2019

  73. [73]

    Romera-Paredes, M

    B. Romera-Paredes, M. Barekatain, A. Novikov, M. Balog, M. P. Kumar, E. Dupont, F. J. Ruiz, J. S. Ellenberg, P. Wang, O. Fawzi,et al., Mathematical discoveries from program search with large language models, Nature625, 468 (2024)

    2024

  74. [74]

    Hillmann, L

    T. Hillmann, L. Berent, A. O. Quintavalle, J. Eisert, R. Wille, and J. Roffe, Localized statistics decoding for quantum low-density parity-check codes, Nature Communications16, 8214 (2025)

    2025

  75. [75]

    Panteleev and G

    P. Panteleev and G. Kalachev, Degenerate quantum ldpc codes with good finite length performance, Quantum5, 585 (2021)

    2021

  76. [76]

    M¨ uller, T

    T. M¨ uller, T. Alexander, M. E. Beverland, M. B¨ uhler, B. R. Johnson, T. Maurer, and D. Vandeth, Improved belief propagation is sufficient for real-time decoding of quantum memory, arXiv preprint arXiv:2506.01779 (2025)

    Pith/arXiv arXiv 2025

  77. [77]

    N. P. Breuckmann and J. N. Eberhardt, Quantum low-density parity-check codes, PRX quantum2, 040101 (2021)

    2021

  78. [78]

    E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature549, 172 (2017)

    2017

  79. [79]

    Ransford, M

    A. Ransford, M. Allman, J. Arkinstall, J. Campora, S. F. Cooper, R. D. Delaney, J. M. Dreiling, B. Estey, C. Figgatt, A. Hall,et al., A 98-qubit trapped-ion quantum computer with all-to-all connectivity, Nature , 1 (2026)

    2026

  80. [80]

    A. W. Senior, T. Edlich, F. J. Heras, L. M. Zhang, O. Higgott, J. S. Spencer, T. Applebaum, S. Blackwell, J. Led- ford, A. ˇZemgulyt˙ e,et al., A scalable and real-time neural decoder for topological quantum codes, arXiv preprint arXiv:2512.07737 (2025)

    arXiv 2025

Showing first 80 references.