[[80,33,8]] · QEC Challenge

[[80,33,8]] d ≤stabilizer

kd²/n

26.4

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Distance

a general stabilizer code has no X and Z sides: d is the minimum Pauli weight of a nontrivial logical operator (a Y factor counts one qubit), and the witness is one Pauli operator that commutes with every generator and is not a product of them

d 8 · witness Pauli weight 8 (claimed upper_bound)

witness operator (Pauli string, 8 qubits)

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIXXIIIIIIIIIIIIXXIIXXIIIIIIIIIIIIIIIIIIII X: [32, 33, 40, 41, 54, 55, 58, 59] Z: []

certificate none yet · distance stands as a self-certified upper bound (d ≤); the Pauli-weight certifier is not built yet, so stabilizer entries cannot earn d= for now

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth S 4 (shortest cycle of the generator Tanner graph; longer is friendlier to belief propagation)

check weights S 10–16 (mean 15.106)

qubit degrees S 6–11 (mean 8.875)

trapping sets S (1,6)×1 (2,6)×4 (3,6)×6 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,6): 1 (1,7): 7 (1,8): 20 (1,9): 29 (1,10): 19 (1,11): 4 (2,6): 4 (2,7): 10 (2,8): 38 (2,9): 62 (2,10): 119 (2,11): 188 (2,12): 272 (2,13): 332 (2,14): 423 (2,15): 449 (2,16): 336 (2,17): 208 (2,18): 74 (2,19): 17 (3,6): 6 (3,7): 23 (3,8): 70 (3,9): 185 (3,10): 435 (3,11): 1001 (3,12): 1784 (3,13): 3037 (3,14): 4625 (3,15): 6420 (3,16): 8026 (3,17): 9066 (3,18): 9363 (3,19): 8822 (3,20): 7434 (3,21): 5787 (3,22): 3726 (3,23): 1947 (3,24): 900 (3,25): 316 (3,26): 91 (3,27): 4 (3,28): 1

Construction & provenance

authors @hirobumii

provenance submitted through the challenge

novelty novelty not audited

construction A literal rank47 subgroup of the source-directed exact mixed80/k32 parent. Replace thirteen pure weight10 rows by twelve pair products along the recorded tree. Complete source-directed component cosets through7 and all511 nonzero coupled annihilator directions prove exact general-Pauli distance8. Displayed vector(80,33,8,16,11,47,710).

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

builds on https://arxiv.org/abs/quant-ph/9705052

date 2026-10-18

notes Displayed presentation: maximum check weight 16, maximum qubit degree 11, 47 checks and total incidence 710.

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

[[80,33,8]] - general stabilizer subgroup code

Direction & hypothesis

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

What was searched

A literal rank47 subgroup of the mixed80/k32 parent. Replace thirteen pure weight10 rows by twelve pair products along the recorded tree. Displayed vector(80,33,8,16,11,47,710).

The displayed presentation has maximum check weight 16, maximum qubit degree 11, 47 checks and total incidence 710.

Evidence trail

The JSON contains weight-8 logical witnesses. Distance confidence: P: upper_bound.

Tools

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

Reproduction

Read codes/80-33-8.json. For each checks.S row, set A[q]=1 for q in X and B[q]=1 for q in Z, using 80 columns in each half. Form S=(A|B); a column present in both halves carries Y. Preserve row and qubit order.

Parent row parity support: [0,2,3,4,5,6,8,13,15,16,17,18,19].

Tree edges for row products: [[0,19],[0,2],[2,5],[6,19],[6,13],[13,15],[8,15],[8,18],[3,6],[3,16],[16,17],[4,17]].

Coefficient annihilator: ["18014673458692613","268435458","281511500749832","2322194339397648","1073741856","17592186044480","14254138133856384","36028797018964224","1125899940397056"].

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

Construction references:

https://arxiv.org/abs/quant-ph/9705052

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

Stabilizer generators

generators 47 (max weight 16; 19 mixed X/Z) (one binary symplectic matrix S = (A | B); generator i is X on A_i and Z on B_i, Y where both)

generators (47, Pauli strings on 80 qubits)

IIIIXIIIIIXIIIIIIIIIIIXIIIIIXIIIIIIXIIIIIIIIIXIIIIIIIIIXIXIIIIIIIIIIXIIIIIIIXIII IIIIIIIZIIZIIIIIIIIIZIIIIIIIIIZIIIIIIIIZIIIIIIIZIIIIIZIIIZIIIIIIIIIIIIIZZIIIIIII IIZIIIIIIIZIIIIIIIIIIIIZIZIIIIIIIIIZIIIIIIIIIZIIIIZIIIIIZIIIIIIIIIIIZIIIIIZIIIII IIIIIZIIIIIIZIIIIIIIZIIIIZIIIIIIIIIIIIIZIIIIZIIIIIIZIIIIIIIIZIIIIIIIIIZIIIZIIIII IIZIIIIIZIIIIIIIIZIIIIIIIZIIIIIIIIIIZIIIIIIIIIIZIZIIIIIIIIIIIIZIIZIIIIIIIIIZIIII IIIIZIIIIZIIIIIIIIIIIIIZIIIIIZIIIIIIZIIIIIIIZIIIIIIIIIZIIIZIIIIIIIIIZIIIIIIZIIII IIIZIIIIIIIZIIIIIIIIIIZIZIIIIIIIIIZIIIIIIIIIZIIIIIIZIIIIIZIIIIIIIIIIIZIIIIIZIIII IYIIIIIIIIIYIIIIIIZIXIIIIIZXIIIIIIIIIXIZIIIIZIXIIIZXIIIIIIIXIZIIIIYIIIIIYIIIIIII ZIIIIIXIZXIIIIIIIIIIIZIXIIIYIIIIIYIIIIIIIXIIIIIZYIIIIIIIIIYIIIIIIIIIXIZIZXIIIIII IIIIYIIIIIIXIZIIIIIIXZIIZIXIIIIIIIIIIIYIIIIIXZIIIIZIXIIIIIIIIYIIIIIIIIIYIXIZIIII ZIIIIXIIIYIIIIIIIZIXIIIIIIIIYIIIIIZXIIIIXZIIIIIIIIIIIIYIIZIXIIIIIIIYIIIIIIXIIIIZ XIIIIIZIIIIIIIZXIXIZIIIIIIIIIYIIIIIIIIIYIZIIIIIXIIIIIIYIIIIIYIIIZIXIIIIIIIIIIIZX IIIIIIIIXIIXIIIIIXIIIIXIIIXIIIXIXXIIIIIIXIXIIIIIIXIIXIIIIXIXIIIIIXIIIXIIIIIIIIII IIIIIIIYXZIIIIIIIIIZIIXIIIYIIIIIXIZIIIIIYIIIIIIIIXIIZIIIIIZXIIIIIIIIIYIIXIZIIIII IIIIIXIXIIXXIIIIIXIIXIIIXIIIIIXIIXXIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIXIIIIIXXIXIIIII IIIIIIXZIZIIXIIIIIIYIIIIIIZIXIIIIIYIIIIIZXIIIIIIIIIIYIIIIIZIXIIIIIIIIYIIIIZIIIIX IIIIIIIIXIIIIXIIIIXIIIXIIIXIIXIIXIIXIIIIIIIIIIIIIXIIIXIIIIIXIXIIIIIIXXIIXIIIIIXI IIIIIIIYIIIIIXIZIIYIIIIIIIIIZXIIIIIXIIZIYIIIIIIIIIIIIXIZIIIIIYIIIZIIXIIIIIIIIIXZ IIIIIIYIIIXZIIIIXIIIIZIIIIIIIIIYXIIIIIZIIIIXIIZIIIIIZXIIYIIIIIIIXIIIIIZIIYIIIIII IIIIIXXIIIXIIIIXIIIIIIIIIIIIIIIIXXIIIIIIIIXXIIIIIIIIIXIXXIIIIIIXXIIIIIXIIXIIXIII IIIIIYIIIIIIIZIXYIIIIIIIIIIIIIZXIXIIZIIIIIYIIIIIIIIIIZIXIIIIIIIYIIIZIIXIIIIIXZII IIIXIZIIIIIIIYIIZXIIIIIIIIIXIIZIIIIIYIIIIIYIIIIIXIIIIZIIIIIIIIXZIIIYIIIIIIIXIZII IIIXIIXIIXIIIXIIIXIIIIXIXIIXIIIIIIIIIIIIIIXIIIXIXIIIIIXIIIIIIIXXIIIXIXIIIIIIIIII IIXXIIIIIIIIIIIIIXXIIIIIIIIXXIIIXIIIXIIIIIIIIIIIXIXIIIIIIIIXIIXIIXIXIIIIIIIXIIIX IIIIIIIIXIIIIXIIIIXIIIIXXIIIXIIIXIIIIIXIIIXIIXIIXIXIIIIIXIIXIIIIIIIIIIIIIIIXIIIX IIIIIZZIIIIIIIIIIZIIIZIIZIIIIIIZZIIIIIZIIIZIIIZIIIIIZIZIIIIIIIIIIIIIIIZZZZIIIIII ZXIIIIIIIIZIIIIXIIIYIIIIIXIZIIIIIIIIIIYIXIIIIZIIIIXZIIIIIIIIYIIIIXIZIIIIIYIIIIII XXIIIIIIIIIIIIIIXIIXIIIIIXIIIIXIIIXIIIXIIIIIIIIIXIXIIIIIIXIIXIIIIXIXIIIIIXIIIXII XXIIIIIIIIIIIIXXIIIIIIIIIIIIXIXIIIXIIIXIXIIIIIXIXIIIIIIXIXIIIXIIIIIIIIIIIIIIIXXI IYIIIIIIIIIIIIXZXIIIIZIIIIIIYIIIIIIIZIXIIIIIIIYIIIZIIIIXIIIIZXIIIIIYIIIIIIIIZIXI IZIIIIZIIIIIIIIIIIIIIZIZIIZIZIIIIIIIIIIIIIIIIIZZZIZIIIIIIIIIZIIZIIIZIZIIIZIIZIII IIIIIIIIIIIIIXIXIIIXIIIXXXIIIIIIIIIIIIXXXIIIXIIIIIIIIIIIIIIIXIIXIXIIIIIXIXIIIIXI IYIIIIIIIIIIZXIIIIZIIIIXYIIIIIIIIZIIIIIXIZIIXIIIIIXZIIIIIIIIIIIYIZIIIIIXIIIIIIYI IZIXIIIIIIIIYIIIIIZXIIIIZIIIIXIIIYIIIIIIIZIXIIIIIIIYIIIIIIXIIIIZXZIIIIIIIIIIIIYI IIXXIIIIIIIIXXIIIIIIIIIIIIIIIXIXIXIIIXIIIIIXIXIIIIIXXIIIIIXIIIXIIIIIIIIIIIIIIXXI IIYIIIIIIIIIYIIIXIIIIIZIIIXIIIIZIIIIIXIZIIIXIZIIIYIIIIIIIIIIIIIYZIXIIIIIIIXIIIIZ IIXXIIIIIIIIXIIXXIIIIXIIIIIIIIIIIIIIIIIIIIIXIIXIXXIIIIIIIIIIIXIXIIXIIXIIIIXIXIII IIIXIIIXIXIIIIIXIIIIIIIIIIXIIIIXXIIIIXIIIIIIIIIIXIIIXIIIIIXIIXIIIIIIIXIXIIIIXIIX IIZIIIIZIIIIZIZIIIIIIIIIIIIZIIIZIIIIIZIZIIIIIZZIIIIIIIIIIIIIIIZZZIIIZIIIZIIIIIIZ IIIIIIZZZIIIIIZIIIZIIIZIIIIIIIIIIIIZIZIIIZIIIIZIIZIIIZIIIIIZIIZIIIIIIIIIZIIZIIII IIIZIIZIZIZIIIIIIIIIIIIIIIIZIIIZIZIZIIIIIZZIIIIIIIIIIIIIIIZZIIIIZIIIZIIIIIIZZIII IIIZZIIIIIIIIIIIZIZIIIIIIZIIIIIZIIIIIIIIIIZZIIIIIIIIIZIZIZZIIIIIZIIIIIZIIZIIZIII IZIIZIIIZIZIIIIIIIIIIIIIIZIIIZIIIZIZIIIIZIIZIIIIIIIIIIIIZZIIIIIIIIZIIIZIIZIIIIZI IIXIIIIZIIIIIIYIIIIIXIZIIIIYIIIIIIIIXZIIIIIIIIZXIYIIIIIIIIIIXIZIIIIIYIIIZIIIIXII ZIXIIIIIIIIIIIYIIIIIYIIIIIIXIZIIIIIIXZIIIIIIIIIYIXIZIIIIIIIIXZIIIIZIXIIIIIIIIYII ZIIIZIIIIIIIIIIIIIIIZIIZIIIIIZIZIIZIIZIIIZIIIIIZIIIZIIIZZIIIIZIIIIZIIIIZIIIIIIII IIIIZXIIIIIXIIZIIIIIIIIYIIIIIXIZIIYIIIIIIZIIXIIIIIIIIIXZYIIIIIIIIIIIIXIZIIIIIYII

symplectic rows (A | B) (47, sparse supports)

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

Code ID 80-33-8 · download JSON · raw on GitHub