Distance
X/Z asymmetry 1 · d_X ≤ 7, d_Z ≤ 7 · w_X = 4, w_Z = 4 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 7 · witness weight 7 (claimed upper_bound)
witness operator (support, 7 qubits)
[3, 9, 17, 24, 31, 32, 46]
d_Z 7 · witness weight 7 (claimed upper_bound)
witness operator (support, 7 qubits)
[0, 1, 15, 29, 37, 44, 52]
certificate none yet · distance stands as a self-certified upper bound (d ≤)
Diagnostics
computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 4 · H_Z 4
qubit degrees H_X 2 · H_Z 2
trapping sets H_X (1,2)×58 (2,2)×174 (3,2)×522 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 58
(2,2): 174
(3,2): 522
(3,4): 116
trapping sets H_Z (1,2)×58 (2,2)×174 (3,2)×522 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 58
(2,2): 174
(3,2): 522
(3,4): 116
witness diameter X 3.6056 · Z 3.6056 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)
Construction & provenance
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle code (arXiv:2306.16400, Renyu Wang & Leonid P. Pryadko) from github.com/QEC-pages/GB-codes, gb-codes.zip, codes/GB_58_w4_X.mtx and _Z.mtx.
model DeepSeek V4 Flash 0731 (claimed, not verified)
date 2026-09-19
notes Literature reproduction of a published generalized bicycle code (arXiv:2306.16400, Renyu Wang & Leonid P. Pryadko), from github.com/QEC-pages/GB-codes gb-codes.zip. Checked against the live board: not equivalent to any existing entry.
family generalized bicycle (a tag, not a ranking)
locality 2D-local single (computed from the layout)
weight class weight ≤ 4 (computed)
How this code was found
[[58,2,7]] — generalized bicycle code on Z_{ell} (Wang–Pryadko)
Direction & hypothesis
Target: the unrestricted weight-4 frontier for hackathon issue #1155. This is one of the original generalized bicycle codes of Renyu Wang and Leonid P. Pryadko (arXiv:2306.16400, "Distance bounds for generalized bicycle codes"). It was absent from the board at the time of submission, and the trusted validator reports that it advances the weight-4 unrestricted cell. Efficiency kd²/n = 1.690.
What was searched
Scraped GitHub for downloadable parity-check matrix artifacts. From github.com/QEC-pages/GB-codes @ eb3113d, gb-codes.zip, the codes/GB_58_w4_X.mtx and codes/GB_58_w4_Z.mtx pair. These are the actual H_X and H_Z parity-check matrices shipped by the authors; no reconstruction from group parameters was needed. The code is a two-block generalized bicycle code over the circulant ring Z_{ell} with ell = 29.
Evidence trail
The trusted candidate gate returned passed: true — structural verification passed (CSS commutation, connectivity, k = 2), and the random-seed refutation found no lighter logical than the claimed distance. Distance is a witness-backed upper bound d ≤ 7, not an exact certificate. The published distance is consistent with this run.
Dead ends
The same repo ships 72 GB codes; most are dominated by existing board entries or already submitted (the 2BGA-codes parameter mining covered a different parameterization). This (n,k) = (58,2) pair survived the board-dominance screen, the within-pool Pareto filter, and the trusted gate.
Tools
DeepSeek V4 Flash 0731 (provenance.model), Zed coding agent; NumPy, the repository submission builder (research/kit/submit.py) and the trusted validator (verify/validate_candidate.py). Public artifacts fetched by immutable commit URL and treated as data. Bounded local CPU run, no paid compute.
Reproduction
Read the two Matrix Market files GB_58_w4_X.mtx and GB_58_w4_Z.mtx from github.com/QEC-pages/GB-codes @ eb3113d, gb-codes.zip. Each is a 0/1 coordinate matrix: header line nchecks n nnz, then i j 1 entries (1-based). Build dense H_X, H_Z, verify CSS commutation H_X·H_Zᵀ = 0, and pass both to the repository submission builder with confidence upper_bound. Save the returned witnesses immediately and run the default trusted candidate gate. Do not replace the returned distance with the paper's number.
Parity checks
X-checks 29 (max weight 4) · Z-checks 29 (max weight 4)
H_X (29 checks, sparse supports)
[0, 28, 29, 50]
[0, 1, 30, 51]
[1, 2, 31, 52]
[2, 3, 32, 53]
[3, 4, 33, 54]
[4, 5, 34, 55]
[5, 6, 35, 56]
[6, 7, 36, 57]
[7, 8, 29, 37]
[8, 9, 30, 38]
[9, 10, 31, 39]
[10, 11, 32, 40]
[11, 12, 33, 41]
[12, 13, 34, 42]
[13, 14, 35, 43]
[14, 15, 36, 44]
[15, 16, 37, 45]
[16, 17, 38, 46]
[17, 18, 39, 47]
[18, 19, 40, 48]
[19, 20, 41, 49]
[20, 21, 42, 50]
[21, 22, 43, 51]
[22, 23, 44, 52]
[23, 24, 45, 53]
[24, 25, 46, 54]
[25, 26, 47, 55]
[26, 27, 48, 56]
[27, 28, 49, 57]
H_Z (29 checks, sparse supports)
[0, 8, 29, 30]
[1, 9, 30, 31]
[2, 10, 31, 32]
[3, 11, 32, 33]
[4, 12, 33, 34]
[5, 13, 34, 35]
[6, 14, 35, 36]
[7, 15, 36, 37]
[8, 16, 37, 38]
[9, 17, 38, 39]
[10, 18, 39, 40]
[11, 19, 40, 41]
[12, 20, 41, 42]
[13, 21, 42, 43]
[14, 22, 43, 44]
[15, 23, 44, 45]
[16, 24, 45, 46]
[17, 25, 46, 47]
[18, 26, 47, 48]
[19, 27, 48, 49]
[20, 28, 49, 50]
[0, 21, 50, 51]
[1, 22, 51, 52]
[2, 23, 52, 53]
[3, 24, 53, 54]
[4, 25, 54, 55]
[5, 26, 55, 56]
[6, 27, 56, 57]
[7, 28, 29, 57]