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REVIEW 3 major objections 2 minor 2 cited by

Parity-Aware Byte-Pair Encoding: Improving Cross-lingual Fairness in Tokenization

T0 review · 3 major / 2 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Two papers share one file: a BPE fairness promise and a quantum-gadget proof.

desk verdict The abstract describes a plausible and potentially useful tokenizer variant, but the supplied full text is a different paper, so none of the empirical claims can be assessed. read the letter →

arxiv 2508.04796 v3 pith:PCFNSK4H submitted 2025-08-06 cs.CL cs.AIcs.LG

Negar Foroutan , Clara Meister , Debjit Paul , Joel Niklaus , Sina Ahmadi , Antoine Bosselut , Rico Sennrich This is my paper
classification cs.CLcs.AIcs.LG
keywords parity-awareBPEcross-lingualtokenizationfairnessGinicoefficientbyte-pairencodingautomorphismgadgetshomologicalproductcodesfault-tolerantquantumgateseffectivedistancepreservation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper's stated aim is a tokenizer variant, Parity-aware BPE, that replaces the standard BPE merge objective with a fair-max rule: at each merge, maximize the compression gain of the currently worst-compressed language. The abstract claims this reduces cross-lingual tokenization inequality, measured by the Gini coefficient of per-language token costs, by up to 89% relative to classical BPE, with negligible global compression loss and no measured downstream LM degradation. The supplied full text, however, is a different manuscript: it develops a framework for automorphism gadgets in homological product quantum codes, showing that symmetries of classical input codes lift to logical operations on the product code, and it proves effective-distance preservation for those gadgets under free physical permutations. A sympathetic reader can only treat the BPE results as an unbacked abstract claim in this file; the body's actual contribution is the automorphism-gadget framework.

What carries the argument

The central object is the automorphism gadget: a logical operation on a homological product code inherited from a permutation symmetry of an input code, implemented physically as a qubit permutation plus a subsystem circuit, or purely as a permutation when the input symmetry is a Tanner graph automorphism. The argument rides on the tensor-product structure of the product parity-check matrices: an input automorphism satisfying $H\sigma = WH$ lifts to a gadget of the form $(\sigma \otimes 1) \oplus (W \otimes 1)$, and the logical action becomes a direct product $V = v^{-T} \otimes 1$ on the canonical logical basis.

What would settle it

For the body: implement an automorphism gadget in a homological product code with physical permutations realized as SWAP gates under circuit-level noise; if fewer than distance $d$ faults can produce a logical error, the effective-distance claim fails. For the abstract: rerun Parity-aware BPE on held-out languages absent from the training corpus; if the Gini reduction collapses or downstream LM accuracy drops, the 89% claim was corpus-bound.

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Extended reading notes

Core claim

For homological product codes, including the hypergraph product as a base case, automorphisms of the input classical or quantum codes lift to logical operations on the product code: the group of inherited automorphism gadgets is the direct product of the input automorphism groups. When the input symmetry is a Tanner graph automorphism, the lifted gadget is a pure permutation of physical qubits; more general code automorphisms yield gadgets built from qubit permutations plus a subsystem circuit. The paper proves that in hypergraph product and quantum-by-classical homological product codes these gadgets preserve the effective fault distance, assuming physical permutations do not spread errors,

Load-bearing premise

The claims rest on two load-bearing premises: in the body, physical qubit permutations spread no errors and the input automorphism gadgets already preserve effective fault distance; in the abstract, the chosen corpus and language sample represent real token usage for each language.

Editorial extensions

If this is right

  • If a homological product code is built from classical input codes with nontrivial automorphism groups, the product code inherits their automorphisms as logical gadgets, with the gadget group being the direct product of the input groups.
  • When the input symmetry is a Tanner graph automorphism, the lifted gadget is a pure qubit permutation, so the logical gate can be performed by relabeling or physically moving qubits rather than by a compiled circuit.
  • In hypergraph product and quantum-by-classical homological product codes, the gadgets are distance-preserving under the noise-free-permutation assumption, so they do not lower the code's fault tolerance.
  • Automorphism gadgets can reroute transversal CZ and CCZ gates to different logical qubits, increasing the addressability of those gates without magic-state distillation.
  • If the abstract's BPE claim is reproduced with its missing evaluation, it would give a drop-in tokenizer variant that equalizes per-language token costs at negligible global compression cost.

Reading between the lines

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

  • The file-level mismatch is itself a finding: as this document stands, the 89% Gini reduction is an unsupported abstract statement, since no corpus, language set, or token-cost measurement protocol is present to check it.
  • The body's symmetry-based design heuristic—choose seed codes with large Tanner graph automorphism groups, such as cycle codes or group-algebra codes—suggests a natural extension to lifted and balanced product codes, which the paper only sketches.
  • A direct testable extension of the fair-max idea would apply it to other frequency-based tokenizers such as WordPiece and Unigram, asking whether the same Gini reduction appears; the paper does not do this.
  • The effective-distance guarantee probably degrades when physical permutations are implemented as noisy SWAP gates rather than assumed noise-free motion; an architecture-level noise simulation would reveal the practical threshold.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The manuscript under review (arXiv:2508.04796, cs.CL) introduces Parity-aware Byte-Pair Encoding (BPE), a tokenizer training variant whose merge rule maximizes compression gain for the currently worst-compressed language. The abstract claims that this fair-max rule reduces tokenization inequality, measured by the Gini coefficient of per-language token costs, by up to 89% relative to Classical BPE, with negligible impact on global compression and no evidence of systematic downstream LM degradation. The supplied full text, however, is not the BPE paper: it is arXiv:2508.04794, a quantum error-correction paper on automorphism gadgets in homological product codes. The BPE manuscript's experimental section, datasets, baselines, error bars, and downstream evaluation are therefore absent from the review material, and the empirical claims cannot be checked.

Significance. If the reported results are correct and reproducible, Parity-aware BPE is a simple, drop-in tokenizer modification with potentially large cross-lingual fairness gains at small compression cost. That is a practically meaningful contribution to multilingual NLP. However, the significance assessment is conditional on evidence that is not present in the supplied material. The manuscript, as provided, contains no experimental details whatsoever. Moreover, the headline metric—the Gini coefficient of per-language token costs—is the direct objective of the fair-max merge rule, so the reported inequality reduction is partly built into the optimization target rather than constituting independent evidence. The lack of a downstream evaluation with reported variance further weakens the claim of 'no systematic degradation.' No code, proofs, or reproducibility artifacts are supplied.

major comments (3)
  1. [Full text (arXiv ID mismatch)] The supplied full text is arXiv:2508.04794, a quantum error-correction paper, not the cs.CL BPE paper described by the title and abstract. Consequently, the experimental design, corpora, language sample, baselines, hyperparameters, error bars, and downstream LM evaluation are all absent. The abstract's numerical claims ('up to 89%', 'negligible impact', 'no evidence of systematic degradation') are therefore unverifiable in this review. This is load-bearing because the paper's contribution is entirely empirical.
  2. [Abstract (evaluation metric)] The headline reduction is measured by the Gini coefficient of per-language token costs, which is exactly the quantity that the fair-max merge rule is designed to improve. Unless the evaluation is performed on held-out languages or held-out corpora that were not used to train the tokenizer, the reported 89% reduction largely reflects in-sample optimization of the objective. The abstract gives no indication of train/test separation or whether per-language costs are computed on the training corpus. Without such details, the result is circular relative to the algorithm's own objective.
  3. [Abstract (downstream null claim)] The claim of 'no evidence of systematic degradation in downstream LM performance' is a null result, but no downstream task, metric, number of languages, or statistical power is reported. A bare null summary cannot distinguish 'no measured degradation' from 'degradation too small to see' or 'degradation on the long tail not analyzed'. The manuscript needs a controlled comparison with per-language results, variances, and a pre-specified equivalence threshold before this claim can be accepted.
minor comments (2)
  1. [Abstract] The abstract should state the number of languages, the composition of the multilingual corpus, the tokenizer vocabulary size, and the baseline BPE configuration. These quantities are essential for interpreting 'up to 89%'.
  2. [Abstract] 'Up to 89%' is a maximum; reporting the median, mean, and range of Gini reduction across languages or seeds, along with confidence intervals, would be more informative.

Circularity Check

1 steps flagged · score 5.0 of 10

Partial circularity: the headline Gini reduction is the algorithm's own design objective; the 89% magnitude and null downstream claims cannot be checked because the supplied full text is an unrelated quantum-error-correction paper.

  1. self definitional [Abstract (only supplied text; full text arXiv:2508.04794 is a different quant-ph paper)]
    "At every merge step, Parity-aware BPE applies a fair-max rule that maximizes the compression gain of the currently worst-compressed language... We find empirically that Parity-aware BPE reduces tokenization inequality -- operationalized by the Gini coefficient of per-language token costs -- by up to 89% relative to Classical BPE."

    The fair-max rule is defined to improve the per-language token cost of the currently worst-compressed language, while the evaluation metric is the Gini coefficient computed over the same per-language token costs. The qualitative direction of the headline claim—that inequality, as measured by that Gini, decreases—is the algorithm's stated objective rather than an independent empirical prediction. The empirical residue is the magnitude (89%) and the claimed mild global-compression trade-off, which are not verifiable from the supplied text. The otherwise independent downstream-LM null result is only asserted and unsupported by the available full text, which is an unrelated paper.

full rationale

The abstract's central fairness claim exhibits partial self-definitional circularity: the algorithm explicitly maximizes the worst-compressed language's compression gain, and the paper's chosen inequality metric is the Gini coefficient of per-language token costs. Improving the worst language is the main lever for reducing that Gini, so reporting 'reduces tokenization inequality' as a finding partly restates the design goal. The quantitative magnitude (up to 89%) and the claimed negligible global-compression impact are not forced by the definition and would constitute genuine empirical content, but the supplied full text is arXiv:2508.04794, a quantum error-correction paper, not the BPE paper, so no experimental section, corpus, baselines, or variance information is available to evaluate those numbers. This is an evidence gap rather than circularity by itself. I do not flag the unrelated full text's internal mathematics as circular; its proofs are built from stated definitions and external references. However, the BPE paper's headline metric is too tightly aligned with its objective to count as an independent confirmation, yielding a score of 5 rather than 0.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

No free parameters or invented entities are identifiable from the abstract alone; the fair-max rule as described has no explicit fitted constant. A full-text check would be needed to rule out smoothing terms, per-language weights, or a compression-parity trade-off parameter. The two domain assumptions listed are the load-bearing premises of the fairness claim and its evaluation.

assumptions (2)
  • domain assumption Frequency-based tokenization objectives disproportionately favor languages overrepresented in the training corpus
    Stated as the motivating phenomenon in the abstract; it is not demonstrated there and is the premise the entire fairness argument rests on.
  • domain assumption The Gini coefficient of per-language token costs is a valid operationalization of tokenization inequality
    The abstract explicitly defines inequality this way; the headline 89% reduction inherits this measurement choice, including implicit corpus and language-sample assumptions.

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Cite this review

Pith. "Pith review of Parity-Aware Byte-Pair Encoding: Improving Cross-lingual Fairness in Tokenization." pith.science (2026). https://pith.science/paper/PCFNSK4H

@misc{pith2026250804796,
  author       = {Pith},
  title        = {Pith review of: Parity-Aware Byte-Pair Encoding: Improving Cross-lingual Fairness in Tokenization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PCFNSK4H}},
  note         = {Machine review of arXiv:2508.04796}
}
abstract

Tokenization is the first -- and often least scrutinized -- step of most NLP pipelines. Standard algorithms for learning tokenizers rely on frequency-based objectives, which favor languages dominant in the training data and consequently leave lower-resource languages with tokenizations that are disproportionately longer, morphologically implausible, or even riddled with $<UNK>$ placeholders. This phenomenon ultimately amplifies computational and financial inequalities between users from different language backgrounds. To remedy this, we introduce Parity-aware Byte Pair Encoding (BPE), a variant of the widely-used BPE algorithm. At every merge step, Parity-aware BPE applies a fair-max rule that maximizes the compression gain of the currently worst-compressed language, trading a small amount of global compression for cross-lingual parity. We find empirically that Parity-aware BPE reduces tokenization inequality -- operationalized by the Gini coefficient of per-language token costs -- by up to 89% relative to Classical BPE. This comes with negligible impact on global compression rate and no evidence of systematic degradation in downstream LM performance.

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Forward citations

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Reference graph

Works this paper leans on

38 extracted references · 3 canonical work pages · cited by 2 Pith papers

  1. [4]

    [BDSB24] Simon Burton, Elijah Durso-Sabina, and Natalie C. Brown. Genons, double covers and fault- tolerant clifford gates. arXiv preprint arXiv:2406.09951 ,

    arXiv

  2. [6]

    Improved qldpc surgery: Logical measurements and bridging codes

    [CHRY24] Andrew Cross, Zhiyang He, Patrick Rall, and Theodore Yoder. Improved qldpc surgery: Logical measurements and bridging codes. arXiv preprint arXiv:2407.18393 ,

    arXiv

  3. [7]

    Locally testable codes with constant rate, distance, and locality

    [DEL+22] Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, and Shahar Mozes. Locally testable codes with constant rate, distance, and locality. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing , STOC 2022, page 357–374, New York, NY, USA,

    work page 2022

  4. [10]

    On the addressability problem on CSS codes.arXiv preprint arXiv:2502.13889,

    [GJ25] J´ erˆ ome Guyot and Samuel Jaques. On the addressability problem on CSS codes.arXiv preprint arXiv:2502.13889,

    arXiv

  5. [11]

    Kiani, and Alexander Zlokapa

    [GKZ24] David Gamarnik, Bobak T. Kiani, and Alexander Zlokapa. Slow mixing of quantum gibbs samplers. arXiv preprint arXiv:2411.04300 ,

    arXiv

  6. [12]

    Quantum ldpc codes with transversal non-clifford gates via products of algebraic codes

    60 [GL24] Louis Golowich and Ting-Chun Lin. Quantum ldpc codes with transversal non-clifford gates via products of algebraic codes. arXiv preprint arXiv:2410.14662 ,

    arXiv

  7. [13]

    Stabilizer codes and quantum error correction

    [Got97] Daniel Gottesman. Stabilizer codes and quantum error correction. arXiv preprint arXiv:quant- ph/9705052,

    arXiv

  8. [16]

    Investigations on automorphism groups of quantum stabilizer codes.arXiv preprint arXiv:2109.12735,

    [Hao21] Hanson Hao. Investigations on automorphism groups of quantum stabilizer codes.arXiv preprint arXiv:2109.12735,

    arXiv

Show all 38 references
  1. [19]

    Classifying logical gates in quantum codes via cohomology operations and symmetry

    [HKZ24] Po-Shen Hsin, Ryohei Kobayashi, and Guanyu Zhu. Classifying logical gates in quantum codes via cohomology operations and symmetry. arXiv preprint arXiv:2411.15848 ,

    arXiv

  2. [21]

    Quantum state isomorphism.arXiv preprint arXiv:1709.09622,

    [LG17] Joshua Lockhart and Carlos E Gonz´ alez Guill´ en. Quantum state isomorphism.arXiv preprint arXiv:1709.09622,

    arXiv

  3. [22]

    Gullans, Victor V

    [LGAB24] Ali Lavasani, Michael J. Gullans, Victor V. Albert, and Maissam Barkeshli. On stability of k-local quantum phases of matter. arXiv preprint arXiv:2405.19412 ,

    arXiv

  4. [23]

    Malcolm, Andrew N

    [MGF+25] Alexander J. Malcolm, Andrew N. Glaudell, Patricio Fuentes, Daryus Chandra, Alexis Schotte, Colby DeLisle, Rafael Haenel, Amir Ebrahimi, Joschka Roffe, Armanda O. Quintavalle, Ste- fanie J. Beale, Nicholas R. Lee-Hone, and Stephanie Simmons. Computing efficiently in q...

  5. [25]

    Construction and decoding of quantum margulis codes

    [PCV25] Michele Pacenti, Dimitris Chytas, and Bane Vasic. Construction and decoding of quantum margulis codes. arXiv preprint arXiv:2503.03936 ,

    arXiv

  6. [26]

    Asymptotically good quantum and locally testable classical LDPC codes

    [PK22] Pavel Panteleev and Gleb Kalachev. Asymptotically good quantum and locally testable classical LDPC codes. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022, page 375–388, New York, NY, USA,

    2022

  7. [29]

    The physics of (good) ldpc codes i

    [RK23] Tibor Rakovszky and Vedika Khemani. The physics of (good) ldpc codes i. gauging and dualities. arXiv preprint arXiv:2310.16032 ,

    arXiv

  8. [30]

    The physics of (good) ldpc codes ii

    [RK24] Tibor Rakovszky and Vedika Khemani. The physics of (good) ldpc codes ii. product construc- tions. arXiv preprint arXiv:2402.16831 ,

    arXiv

  9. [31]

    Ldpc stabilizer codes as gapped quantum phases: stability under graph-local perturbations

    [RKL+24] Wojciech De Roeck, Vedika Khemani, Yaodong Li, Nicholas O’Dea, and Tibor Rakovszky. Ldpc stabilizer codes as gapped quantum phases: stability under graph-local perturbations. arXiv preprint arXiv:2411.02384,

  10. [32]

    [SJOY25] Esha Swaroop, Tomas Jochym-O’Connor, and Theodore J. Yoder. Universal adapters between quantum ldpc codes. arXiv preprint arXiv:2410.03628 ,

  11. [33]

    Fault-tolerant logical clifford gates from code automorphisms

    [SKW+25] Hasan Sayginel, Stergios Koutsioumpas, Mark Webster, Abhishek Rajput, and Dan E Browne. Fault-tolerant logical clifford gates from code automorphisms. arXiv preprint arXiv:2409.18175,

    arXiv

  12. [35]

    Effective distance of higher dimensional HGPs and weight-reduced quantum LDPC codes

    [TS24] Shi Jie Samuel Tan and Lev Stambler. Effective distance of higher dimensional HGPs and weight-reduced quantum LDPC codes. arXiv preprint arXiv:2409.02193 ,

  13. [36]

    Pablo Bonilla Ataides, Mikhail D

    [XZZ+24] Qian Xu, Hengyun Zhou, Guo Zheng, Dolev Bluvstein, J. Pablo Bonilla Ataides, Mikhail D. Lukin, and Liang Jiang. Fast and parallelizable logical computation with homological product codes. arXiv preprint arXiv:2407.18490 ,

    arXiv

  14. [37]

    Low-density parity-check codes as stable phases of quantum matter

    [YL24] Chao Yin and Andrew Lucas. Low-density parity-check codes as stable phases of quantum matter. arXiv preprint arXiv:2411.01002 ,

    arXiv

  15. [1954]

    Nguyen and Christopher A

    [NP24] Quynh T. Nguyen and Christopher A. Pattison. Quantum fault tolerance with constant-space and logarithmic-time overheads. arXiv preprint arXiv:2411.03632 ,

    arXiv

  16. [1968]

    Graph isomorphisms in quasi- polynomial time

    [HBD17] Harald Andr´ es Helfgott, Jitendra Bajpai, and Daniele Dona. Graph isomorphisms in quasi- polynomial time. arXiv preprint arXiv:1710.04574 ,

    arXiv

  17. [1996]

    Polylog-time- and constant-space- overhead fault-tolerant quantum computation with quantum low-density parity-check codes

    [TKY24] Shiro Tamiya, Masato Koashi, and Hayata Yamasaki. Polylog-time- and constant-space- overhead fault-tolerant quantum computation with quantum low-density parity-check codes. arXiv preprint arXiv:2411.03683 ,

    arXiv

  18. [1997]

    Breuckmann, and Vedika Khemani

    62 [PRBK24] Benedikt Placke, Tibor Rakovszky, Nikolas P. Breuckmann, and Vedika Khemani. Topological quantum spin glass order and its realization in qldpc codes. arXiv preprint arXiv:2412.13248 ,

    arXiv

  19. [1998]

    Automorphism ensemble decoding of quantum ldpc codes

    [KSWB25] Stergios Koutsioumpas, Hasan Sayginel, Mark Webster, and Dan E Browne. Automorphism ensemble decoding of quantum ldpc codes. arXiv preprint arXiv:2503.01738 ,

    arXiv

  20. [2008]

    The classification of reversible bit operations

    58 [AGS15] Scott Aaronson, Daniel Grier, and Luke Schaeffer. The classification of reversible bit operations. arXiv preprint arXiv:1504.05155 ,

    arXiv

  21. [2013]

    [GR24] Anqi Gong and Joseph M. Renes. Computation with quantum reed-muller codes and their mapping onto 2d atom arrays. arXiv preprint arXiv:2410.23263 ,

    arXiv

  22. [2014]

    Leveraging automorphisms of quantum codes for fault- tolerant quantum computation

    [GR13] Markus Grassl and Martin Roetteler. Leveraging automorphisms of quantum codes for fault- tolerant quantum computation. In 2013 IEEE International Symposium on Information Theory, page 534–538. IEEE,

    2013

  23. [2015]

    Reed-muller codes: Theory and algorithms

    [ASY20] Emmanuel Abbe, Amir Shpilka, and Min Ye. Reed-muller codes: Theory and algorithms. arXiv preprint arXiv:2002.03317,

    2002 arXiv

  24. [2017]

    Williamson, and Theodore J

    [HCWY25] Zhiyang He, Alexander Cowtan, Dominic J. Williamson, and Theodore J. Yoder. Extractors: Qldpc architectures for efficient pauli-based computation. arXiv preprint arXiv:2503.10390 ,

  25. [2019]

    Gul- lans, J

    59 [CFD+24] Nathan Constantinides, Ali Fahimniya, Dhruv Devulapalli, Dolev Bluvstein, Michael J. Gul- lans, J. V. Porto, Andrew M. Childs, and Alexey V. Gorshkov. Optimal routing protocols for reconfigurable atom arrays. arXiv preprint arXiv:2411.05061 ,

    arXiv

  26. [2020]

    Cross, and Benjamin J

    [ZSP+24] Guanyu Zhu, Shehryar Sikander, Elia Portnoy, Andrew W. Cross, and Benjamin J. Brown. Non-clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum ldpc codes via higher symmetries. arXiv preprint arXiv:2310.16982,

  27. [2021]

    No-go theorems for logical gates on product quantum codes

    [FZLL25] Xiaozhen Fu, Han Zheng, Zimu Li, and Zi-Wen Liu. No-go theorems for logical gates on product quantum codes. arXiv preprint arXiv:2507.16797 ,

  28. [2023]

    Reichardt, David Aasen, Rui Chao, Alex Chernoguzov, Wim van Dam, John P

    [RAC+24] Ben W. Reichardt, David Aasen, Rui Chao, Alex Chernoguzov, Wim van Dam, John P. Gae- bler, Dan Gresh, Dominic Lucchetti, Michael Mills, Steven A. Moses, Brian Neyenhuis, Adam Paetznick, Andres Paz, Peter E. Siegfried, Marcus P. da Silva, Krysta M. Svore, Zhenghan Wang...

    arXiv

  29. [2024]

    Breuckmann, Margarita Davydova, Jens N

    [BDET24] Nikolas P. Breuckmann, Margarita Davydova, Jens N. Eberhardt, and Nathanan Tanti- vasadakarn. Cups and gates i: Cohomology invariants and logical quantum operations. arXiv preprint arXiv:2410.16250,

    arXiv

  30. [2025]

    Quantum ldpc codes of almost linear distance via homological products

    [GG24] Louis Golowich and Venkatesan Guruswami. Quantum ldpc codes of almost linear distance via homological products. arXiv preprint arXiv:2411.03646 ,

    arXiv

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Reviewed August 5, 2026 · model on record in the stance chip above.