[[80,34,5]] · QEC Challenge

[[80,34,5]] d ≤

kd²/n

10.625

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 5, d_Z ≤ 5 · w_X = 11, w_Z = 11 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 5 · witness weight 5 (claimed upper_bound)

witness operator (support, 5 qubits)

[7, 16, 18, 24, 42]

d_Z 5 · witness weight 5 (claimed upper_bound)

witness operator (support, 5 qubits)

[5, 7, 11, 21, 26]

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 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 9–11 (mean 10.087) · H_Z 9–11 (mean 10.087)

qubit degrees H_X 1–5 (mean 2.9) · H_Z 1–5 (mean 2.9)

trapping sets H_X (1,1)×4 (2,1)×11 (3,1)×51 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,1): 4 (1,2): 26 (1,3): 25 (1,4): 24 (1,5): 1 (2,1): 11 (2,2): 76 (2,3): 190 (2,4): 305 (2,5): 246 (2,6): 142 (2,7): 12 (3,1): 51 (3,2): 328 (3,3): 1242 (3,4): 2766 (3,5): 4112 (3,6): 4223 (3,7): 2846 (3,8): 1372 (3,9): 340 (3,10): 91 (3,11): 7

trapping sets H_Z (1,1)×4 (2,1)×11 (3,1)×51 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

Construction & provenance

authors @hirobumii

provenance submitted through the challenge

novelty novelty not audited

construction CSS-preserving physical CNOT image of a rank23-per-sector tilted subgroup of the public [[80,24,8]] source; directed CNOT edges [[0, 14], [15, 48], [19, 2], [25, 56], [33, 78], [40, 1], [43, 66], [50, 23], [70, 35], [79, 41], [5, 39], [19, 60], [54, 44], [29, 66]].

model GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration) (claimed, not verified)

date 2026-10-18

notes Displayed presentation: maximum check weight 11, maximum qubit degree 8, 46 checks and total incidence 464.

family other (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[80,34,5]] - CSS sparse stabilizer code

Direction & hypothesis

Study the dimension–distance tradeoff obtained by selecting stabilizer subgroups and changing sparse presentations.

What was searched

CSS-preserving physical CNOT image of a rank23-per-sector tilted subgroup of the public [[80,24,8]] source; directed CNOT edges [[0, 14], [15, 48], [19, 2], [25, 56], [33, 78], [40, 1], [43, 66], [50, 23], [70, 35], [79, 41], [5, 39], [19, 60], [54, 44], [29, 66]].

The displayed presentation has maximum check weight 11, maximum qubit degree 8, 46 checks and total incidence 464.

Evidence trail

The JSON contains weight-5 logical witnesses. Distance confidence: X: upper_bound, Z: upper_bound.

Tools

Recorded workflow configuration: GPT-6 Astra + GPT-6.1 Sol. Official tooling: verify/qldpc_verify.py.

Reproduction

Read codes/80-34-5.json. Allocate zero binary matrices H_X and H_Z with 80 columns. For each row list in checks.X or checks.Z, set the listed zero-based columns to 1, preserving row order. This reconstructs the displayed presentation exactly.

Ordered CNOT pairs (control,target), zero-based: [[0,14],[15,48],[19,2],[25,56],[33,78],[40,1],[43,66],[50,23],[70,35],[79,41],[5,39],[19,60],[54,44],[29,66]].

Public source: 80-24-8, contributed by @FarLab.

Local validation: the official verify/validate_candidate.py passed, including independent-seed distance refutation.

Parity checks

X-checks 23 (max weight 11) · Z-checks 23 (max weight 11)

H_X (23 checks, sparse supports)

[0, 1, 14, 15, 16, 30, 34, 40, 57, 67, 77] [1, 14, 17, 31, 35, 41, 49, 56, 66, 76] [4, 11, 20, 26, 38, 44, 52, 61, 71, 73] [5, 10, 21, 27, 35, 45, 53, 60, 70, 72] [3, 9, 22, 25, 39, 44, 49, 56, 57, 64, 74] [2, 6, 12, 19, 28, 34, 52, 69, 79] [6, 10, 16, 31, 32, 43, 53, 56, 64, 66, 73] [7, 11, 17, 30, 33, 42, 52, 57, 65, 72, 78] [4, 8, 18, 29, 34, 41, 55, 58, 75] [2, 14, 20, 27, 36, 47, 49, 60, 68, 77] [3, 15, 21, 26, 37, 46, 61, 69, 76] [1, 13, 24, 39, 44, 50, 63, 71, 78] [0, 18, 24, 39, 41, 51, 61, 64, 72] [3, 13, 17, 27, 36, 42, 48, 62, 67, 75] [5, 11, 23, 29, 34, 39, 54, 56, 66, 69, 77] [6, 8, 20, 30, 33, 35, 47, 53, 59, 70] [1, 7, 8, 22, 26, 32, 40, 49, 59, 69, 72] [6, 9, 23, 27, 33, 41, 48, 58, 68, 73, 78] [4, 11, 21, 23, 25, 43, 50, 66, 70, 75] [3, 12, 18, 30, 36, 44, 53, 63, 65, 76] [13, 19, 31, 37, 45, 52, 60, 62, 64, 77] [1, 14, 16, 28, 38, 46, 55, 61, 67, 78] [8, 15, 19, 24, 25, 40, 45, 50, 73, 75]

H_Z (23 checks, sparse supports)

[1, 12, 18, 24, 40, 41, 51, 63, 65, 78, 79] [0, 13, 19, 25, 32, 40, 50, 62, 64, 79] [5, 8, 22, 28, 37, 45, 55, 59, 69, 74] [4, 9, 23, 29, 36, 44, 50, 58, 68, 75] [5, 11, 17, 24, 25, 32, 42, 54, 56, 71, 72] [14, 20, 37, 43, 47, 51, 61, 66, 77] [2, 8, 17, 19, 25, 36, 47, 49, 62, 65, 75] [3, 9, 15, 16, 24, 37, 46, 48, 63, 64, 74] [0, 10, 27, 38, 45, 51, 60, 67, 73] [6, 12, 21, 29, 32, 43, 53, 58, 69, 79] [7, 13, 20, 28, 42, 52, 59, 68, 78] [5, 15, 22, 30, 35, 40, 54, 57, 76] [0, 9, 17, 28, 34, 41, 54, 57, 67] [3, 10, 18, 31, 33, 42, 53, 58, 64, 76] [12, 19, 20, 25, 39, 44, 51, 54, 60, 70, 74] [6, 23, 26, 36, 47, 48, 50, 63, 69, 73] [1, 9, 20, 26, 32, 40, 46, 49, 59, 71, 73] [0, 8, 15, 21, 27, 33, 47, 48, 58, 70, 72] [2, 10, 19, 23, 35, 45, 56, 68, 70, 74] [5, 13, 16, 30, 36, 42, 53, 63, 67, 77] [4, 12, 17, 29, 31, 37, 52, 62, 66, 76] [7, 15, 18, 28, 38, 40, 55, 61, 65, 79] [1, 4, 8, 10, 35, 56, 57, 66, 73, 78]

Code ID 80-34-5 · download JSON · raw on GitHub