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References

Every paper and tool the challenge cites. Submissions reference an entry by its arXiv id or DOI; verified codes that cite each one are listed beneath it. The machine-readable source is refs.bib.

albert2026zoo
Albert, Victor V. and Faist, Philippe. Handbook of Error-Correcting Codes. 2026. arXiv:2606.11484
aydin2026breaking
Aydin, Arda and Tamo, Itzhak and Barg, Alexander. Breaking the bicycle frame: Coset-based quantum LDPC codes. 2026. arXiv:2606.17268
cited by 8[[240,13,15]][[240,16,20]][[168,16,15]][[180,18,14]][[336,20,21]][[336,20,20]][[168,20,14]][[180,20,14]]
bhardwaj2026mitten
Bhardwaj, Aditya and Ma, Muzhou and Meister, Nadine and King, Robbie and Bluvstein, Dolev and Preskill, John and Cain, Madelyn and Xu, Qian and Huang, Hsin-Yuan. High-rate qLDPC processors. 2026. arXiv:2607.28795
cited by 12[[120,24,8]][[170,34,8]][[180,36,8]][[190,38,8]][[195,39,8]][[200,40,12]][[220,44,10]][[230,46,8]][[300,60,14]][[500,100,16]][[540,108,18]][[630,126,20]]
bravyi2010tradeoffs
Bravyi, Sergey and Poulin, David and Terhal, Barbara. Tradeoffs for reliable quantum information storage in 2D systems. Physical Review Letters 104(5):050503. 2010. arXiv:0909.5200 · doi
bravyi2024high
Bravyi, Sergey and Cross, Andrew W. and Gambetta, Jay M. and Maslov, Dmitri and Rall, Patrick and Yoder, Theodore J. High-threshold and low-overhead fault-tolerant quantum memory. Nature 627:778-782. 2024. arXiv:2308.07915 · doi
cited by 7[[120,8,12]][[90,8,10]][[108,8,10]][[288,12,18]][[144,12,12]][[72,12,6]][[482,146,42]]
breuckmann2021quantum
Breuckmann, Nikolas P. and Eberhardt, Jens Niklas. Quantum Low-Density Parity-Check Codes. PRX Quantum 2(4):040101. 2021. arXiv:2103.06309 · doi
calderbank1996good
Calderbank, A. Robert and Shor, Peter W. Good quantum error-correcting codes exist. Physical Review A 54(2):1098-1105. 1996. arXiv:quant-ph/9512032 · doi
cruzbenito2026evolutionary
Cruz-Benito, Juan and Cross, Andrew W. and Kremer, David and Faro, Ismael. Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search. 2026. arXiv:2606.02418
cited by 3[[288,46,8]][[288,48,8]][[288,50,8]]
gottesman1997stabilizer
Gottesman, Daniel. Stabilizer Codes and Quantum Error Correction. 1997. arXiv:quant-ph/9705052
grassl2007codetables
Grassl, Markus. Bounds on the minimum distance of linear codes and quantum codes. 2007.
gu2026nearest
Gu, Boren and Noszko, Tamas and Steffan, Vincent and Eberhardt, Jens Niklas and Roffe, Joschka and Eisert, Jens and Koutsioumpas, Stergios. Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid. 2026. arXiv:2606.19482
cited by 1[[294,12,14]]
he2025reinforcement
He, Austin Yubo and Liu, Zi-Wen. Discovering highly efficient low-weight quantum error-correcting codes with reinforcement learning. 2025. arXiv:2502.14372
hong2026zszlp
Hong, Yifan. Quantum LDPC codes with design rate 1/5 and good performance below 1000 physical qubits. 2026. arXiv:2607.27644
cited by 13[[60,12,6]][[100,20,8]][[150,30,10]][[160,32,10]][[210,42,12]][[240,48,12]][[270,54,10]][[320,64,14]][[390,78,16]][[525,105,18]][[550,110,18]][[625,125,20]][[700,140,22]]
kapshikar2023hardness
Kapshikar, Upendra and Kundu, Srijita. On the Hardness of the Minimum Distance Problem of Quantum Codes. IEEE Transactions on Information Theory 69(10). 2023. arXiv:2203.04262 · doi
kasai2026orthogonality
Kasai, Kenta. Breaking the Orthogonality Barrier in Quantum LDPC Codes. 2026. arXiv:2601.08824
cited by 1[[684,8,85]]
kitaev2003fault
Kitaev, A. Yu. Fault-tolerant quantum computation by anyons. Annals of Physics 303(1):2-30. 2003. arXiv:quant-ph/9707021 · doi
cited by 6[[81,1,9]][[49,1,7]][[25,1,5]][[64,2,8]][[36,2,6]][[16,2,4]]
liang2025planar
Liang, Zijian and Eberhardt, Jens Niklas and Chen, Yu-An. Planar quantum low-density parity-check codes with open boundaries. 2025. arXiv:2504.08887 · doi
cited by 27[[299,5,13]][[231,5,11]][[153,5,9]][[120,5,8]][[91,5,7]][[66,5,5]][[45,5,4]][[336,6,14]][[264,6,12]][[240,6,11]][[180,6,10]][[160,6,9]][[128,6,8]][[112,6,7]][[72,6,6]][[88,6,6]][[50,6,4]][[392,8,15]][[288,8,12]][[200,8,9]][[128,8,6]][[384,12,17]][[294,12,14]][[192,12,8]][[198,12,7]][[216,15,11]][[263,16,12]]
liang2025selfdual
Liang, Zijian and Chen, Yu-An. Self-dual bivariate bicycle codes with transversal Clifford gates. 2025. arXiv:2510.05211
liang2025twisted
Liang, Zijian and Liu, Ke and Song, Hao and Chen, Yu-An. Generalized toric codes on twisted tori for quantum error correction. 2025. arXiv:2503.03827
cited by 39[[354,4,28]][[318,4,26]][[276,4,24]][[246,4,22]][[204,4,20]][[174,4,18]][[114,4,14]][[96,4,12]][[78,4,10]][[48,4,8]][[30,4,6]][[18,4,4]][[12,4,2]][[350,6,26]][[308,6,24]][[266,6,22]][[224,6,20]][[182,6,18]][[154,6,16]][[140,6,14]][[98,6,12]][[84,6,10]][[70,6,8]][[14,6,2]][[330,8,24]][[312,8,22]][[270,8,20]][[234,8,18]][[192,8,16]][[162,8,14]][[60,8,6]][[248,10,18]][[186,10,14]][[62,10,6]][[360,12,24]][[252,12,16]][[340,16,18]][[292,18,8]][[146,18,4]]
lin2023twoblock
Lin, Hsiang-Ku and Pryadko, Leonid P. Quantum two-block group algebra codes. 2023. arXiv:2306.16400
lin2024quantum
Lin, Hsiang-Ku and Pryadko, Leonid P. Quantum two-block group algebra codes. Physical Review A 109(2):022407. 2024. arXiv:2306.16400 · doi
cited by 29[[144,6,18]][[132,6,17]][[136,6,17]][[120,6,16]][[126,6,16]][[54,6,9]][[40,6,5]][[24,6,4]][[140,8,16]][[144,8,16]][[128,8,15]][[80,8,8]][[32,8,4]][[80,9,8]][[140,10,10]][[128,12,16]][[240,13,15]][[310,14,21]][[288,16,16]][[126,18,14]][[336,20,21]][[336,20,20]][[168,20,14]][[210,24,20]][[258,32,22]][[254,44,24]][[254,44,21]][[390,82,30]][[482,146,42]]
liu2026concept
Liu, Zidu and Marquardt, Florian. Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution. 2026. arXiv:2606.24808
cited by 1[[336,20,20]]
nixon2026vine
Nixon, Georgia M. and McLauchlan, Campbell K. and van Rest, Charles C. L. Vine Codes: Low-Overhead Quantum LDPC Codes on a Planar Square Grid. 2026. arXiv:2606.20263
okada2026highgirth
Okada, Koki and Kasai, Kenta. High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures. 2026. arXiv:2604.20838
cited by 1[[684,8,85]]
panteleev2021degenerate
Panteleev, Pavel and Kalachev, Gleb. Degenerate quantum LDPC codes with good finite length performance. Quantum 5:585. 2021. arXiv:1904.02703 · doi
cited by 12[[126,18,14]][[210,24,20]][[126,28,8]][[258,32,22]][[254,44,24]][[254,44,21]][[254,58,21]][[390,68,28]][[390,82,32]][[390,82,31]][[390,82,30]][[390,82,27]]
panteleev2022asymptotically
Panteleev, Pavel and Kalachev, Gleb. Asymptotically good quantum and locally testable classical LDPC codes. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pp. 375-388. 2022. arXiv:2111.03654 · doi
perlin2023qldpc
Perlin, Michael A. qLDPC. 2023. github.com
pryadko2023qdistrnd
Pryadko, Leonid P. and Shabashov, Vadim A. and Kozin, Valerii K. QDistRnd: A GAP package for computing the distance of quantum error-correcting codes. Journal of Open Source Software 7(71):4120. 2022. doi
roffe2020decoding
Roffe, Joschka and White, David R. and Burton, Simon and Campbell, Earl. Decoding across the quantum low-density parity-check code landscape. Physical Review Research 2(4):043423. 2020. arXiv:2005.07016 · doi
shor1995scheme
Shor, Peter W. Scheme for reducing decoherence in quantum computer memory. Physical Review A 52(4):R2493-R2496. 1995. doi
steane1996error
Steane, Andrew M. Error correcting codes in quantum theory. Physical Review Letters 77(5):793-797. 1996. arXiv:quant-ph/9601029 · doi
cited by 3[[7,1,3]][[16,6,4]][[15,7,3]]
steffan2025tile
Steffan, Vincent and Choe, Shin Ho and Breuckmann, Nikolas P. and Pereira, Francisco Revson Fernandes and Eberhardt, Jens Niklas. Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary. 2025. arXiv:2504.09171
cited by 1[[294,12,14]]
tillich2014quantum
Tillich, Jean-Pierre and Zemor, Gilles. Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength. IEEE Transactions on Information Theory 60(2):1193-1202. 2014. arXiv:0903.0566 · doi
cited by 11[[51,12,3]][[80,16,4]][[87,22,3]][[102,33,3]][[148,44,4]][[117,44,3]][[170,52,3]][[201,78,3]][[232,104,3]][[281,121,4]][[241,121,3]]
wang2022distance
Wang, Renren and Pryadko, Leonid P. Distance bounds for generalized bicycle codes. Symmetry 14(7):1348. 2022. arXiv:2203.17216 · doi
cited by 8[[56,2,8]][[40,6,5]][[24,6,4]][[42,8,3]][[254,58,21]][[390,68,28]][[390,82,31]][[390,82,27]]
yan2026omniqec
Yan, Ge and Li, Shanchuan and Ma, Pengyue and Zhang, Qixin and Ma, Pingchuan and Wang, Jianping and Hsieh, Min-Hsiu and Du, Yuxuan. OmniQEC: Discovering Practical Quantum Error-Correcting Codes by an AI Scientist. 2026. arXiv:2607.25865