[[141,89,2]] · QEC Challenge

← back to the board

[[141,89,2]] d ≤

141

kd²/n

2.52482

X/Z

1.5

Share this result

Distance

X/Z asymmetry 1.5 · d_X ≤ 2, d_Z ≤ 3 · w_X = 12, w_Z = 12 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 2 · witness weight 2 (claimed upper_bound)

witness operator (support, 2 qubits)

[24, 55]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[73, 88, 103]

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 12 · H_Z 12

qubit degrees H_X 1–3 (mean 2.213) · H_Z 1–3 (mean 2.213)

trapping sets H_X (1,1)×24 (2,0)×18 (3,0)×95 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 24 (1,2): 63 (1,3): 54 (2,0): 18 (2,1): 155 (2,2): 455 (2,3): 629 (2,4): 349 (3,0): 95 (3,1): 923 (3,2): 3751 (3,3): 7456 (3,4): 8170 (3,5): 4279 (3,6): 1010 (3,7): 370

trapping sets H_Z (1,1)×19 (2,0)×17 (3,0)×87 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 19 (1,2): 73 (1,3): 49 (2,0): 17 (2,1): 166 (2,2): 480 (2,3): 643 (2,4): 298 (3,0): 87 (3,1): 986 (3,2): 3931 (3,3): 7825 (3,4): 7835 (3,5): 3657 (3,6): 982 (3,7): 292

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction code-calculus v0.2rc E-PUNCTURE

model Beam 1.0 (claimed, not verified)

date 2026-11-13

notes Generated by the priced construction calculus. Distance is reported only with witness-backed upper bounds; lower interval bounds are kept in the separate local ledger.

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

[[141,89,2]] greedy 1 from 143-79-2

Direction & hypothesis

Unrestricted-weight CSS parents with 99 <= n <= 400, searched with the priced construction calculus (code-calculus v0.2rc) greedy multi-step composition. The rule used on this step is E-PUNCTURE.

What was searched

Greedy multi-step composition of C-DELETE-CHECK / E-PEEL / E-PUNCTURE with sector-targeted planning, sector swap, bounded support search, and Pareto ranking. This candidate is step 1 of a chain from codes/143-79-2.json (target sector X).

Evidence trail

Staged deep-verify (2k -> 20k -> 200k -> 2M trials, multi-seed) kept the screened distance unchanged; the witness-backed upper bound is d_X <= 2, d_Z <= 2. No downgrade at any depth.

Dead ends

Parents whose display carries a dependent generator produce no derivable child; candidates whose deep-verified slug collides with an existing board entry are skipped.

Tools

Model: Beam 1.0. Harness: code-calculus v0.2rc greedy gated campaign with the verifier's staged deep-verify used before submission.

Reproduction

Start from codes/143-79-2.json, apply E-PUNCTURE on the target sector, and repeat greedily with Pareto ranking and staged deep-verify.

Parity checks

X-checks 26 (max weight 12) · Z-checks 26 (max weight 12)

H_X (26 checks, sparse supports)

[3, 20, 24, 34, 48, 58, 72, 84, 98, 113, 118, 129] [4, 21, 25, 35, 45, 59, 69, 81, 99, 114, 119, 130] [5, 18, 22, 36, 46, 60, 70, 82, 100, 115, 120, 131] [6, 19, 23, 37, 47, 57, 71, 83, 97, 116, 117, 132] [7, 17, 29, 39, 49, 63, 73, 85, 103, 110, 123, 134] [9, 15, 27, 40, 51, 61, 75, 87, 101, 112, 121, 136] [0, 12, 32, 41, 56, 66, 80, 92, 94, 105, 126, 137] [1, 13, 33, 42, 53, 67, 77, 89, 95, 106, 127, 138] [2, 11, 31, 44, 55, 65, 79, 91, 93, 108, 125, 140] [1, 14, 32, 36, 45, 60, 69, 84, 96, 110, 125, 130] [2, 16, 30, 34, 47, 58, 71, 82, 94, 112, 127, 132] [0, 17, 31, 35, 48, 59, 72, 83, 95, 109, 128, 129] [5, 19, 29, 40, 50, 61, 74, 85, 97, 115, 122, 135] [6, 20, 26, 38, 51, 62, 75, 86, 98, 116, 123, 136] [3, 21, 27, 39, 52, 63, 76, 87, 99, 113, 124, 133] [7, 10, 24, 43, 53, 68, 77, 92, 104, 106, 117, 138] [8, 11, 25, 44, 54, 65, 78, 89, 101, 107, 118, 139] [9, 12, 22, 41, 55, 66, 79, 90, 102, 108, 119, 140] [2, 11, 26, 43, 47, 57, 70, 81, 96, 108, 122, 137] [0, 12, 27, 44, 48, 58, 71, 82, 93, 105, 123, 138] [1, 13, 28, 41, 45, 59, 72, 83, 94, 106, 124, 139] [3, 16, 31, 40, 52, 62, 75, 86, 97, 109, 127, 134] [4, 17, 32, 38, 49, 63, 76, 87, 98, 110, 128, 135] [5, 14, 33, 39, 50, 64, 73, 88, 99, 111, 125, 136] [9, 19, 22, 36, 55, 65, 78, 89, 104, 116, 118, 129] [7, 21, 24, 34, 53, 67, 80, 91, 102, 114, 120, 131]

H_Z (26 checks, sparse supports)

[1, 10, 25, 41, 56, 58, 77, 84, 94, 105, 119, 139] [2, 12, 23, 43, 54, 60, 79, 82, 96, 107, 117, 137] [0, 13, 24, 44, 55, 57, 80, 83, 93, 108, 118, 138] [4, 14, 29, 38, 48, 62, 69, 88, 98, 109, 123, 135] [5, 15, 26, 39, 45, 63, 70, 85, 99, 110, 124, 136] [3, 17, 28, 40, 47, 61, 72, 87, 97, 112, 122, 134] [7, 18, 33, 34, 52, 66, 73, 92, 102, 113, 127, 131] [8, 19, 30, 35, 49, 67, 74, 89, 103, 114, 128, 132] [9, 20, 31, 36, 50, 68, 75, 90, 104, 115, 125, 129] [1, 11, 22, 37, 53, 68, 79, 89, 96, 106, 117, 131] [2, 13, 24, 35, 55, 66, 77, 91, 94, 108, 119, 129] [0, 10, 25, 36, 56, 67, 78, 92, 95, 105, 120, 130] [4, 15, 26, 40, 49, 60, 75, 81, 100, 110, 121, 135] [5, 16, 27, 38, 50, 57, 76, 82, 97, 111, 122, 136] [6, 17, 28, 39, 51, 58, 73, 83, 98, 112, 123, 133] [7, 19, 30, 44, 45, 64, 71, 85, 104, 114, 125, 139] [8, 20, 31, 41, 46, 61, 72, 86, 101, 115, 126, 140] [9, 21, 32, 42, 47, 62, 69, 87, 102, 116, 127, 137] [9, 11, 23, 34, 48, 65, 71, 91, 101, 108, 118, 129] [7, 13, 25, 36, 46, 67, 69, 89, 103, 106, 120, 131] [8, 10, 22, 37, 47, 68, 70, 90, 104, 107, 117, 132] [2, 15, 27, 38, 52, 61, 75, 87, 93, 112, 122, 133] [0, 16, 28, 39, 49, 62, 76, 88, 94, 109, 123, 134] [6, 19, 31, 41, 56, 57, 79, 83, 97, 116, 126, 137] [3, 20, 32, 42, 53, 58, 80, 84, 98, 113, 127, 138] [4, 21, 33, 43, 54, 59, 77, 81, 99, 114, 128, 139]

Code ID 141-89-2 · download JSON · raw on GitHub