[[184,70,2]] · QEC Challenge

[[184,70,2]] d ≤

184

kd²/n

1.52174

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 2, d_Z ≤ 2 · w_X = 6, w_Z = 6 (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)

[88, 114]

d_Z 2 · witness weight 2 (claimed upper_bound)

witness operator (support, 2 qubits)

[28, 59]

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 12 · H_Z 12 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 6 · H_Z 6

qubit degrees H_X 1–2 (mean 1.859) · H_Z 1–2 (mean 1.859)

trapping sets H_X (1,1)×26 (2,0)×4 (3,0)×18 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 26 (1,2): 158 (2,0): 4 (2,1): 122 (2,2): 729 (3,0): 18 (3,1): 575 (3,2): 3371 (3,3): 231 (3,4): 895

trapping sets H_Z (1,1)×26 (2,0)×4 (3,0)×18 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 26 (1,2): 158 (2,0): 4 (2,1): 122 (2,2): 729 (3,0): 18 (3,1): 574 (3,2): 3374 (3,3): 228 (3,4): 896

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 ≤ 6 (computed)

How this code was found

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

[[184,70,2]] greedy 0 from 185-67-2

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 0 of a chain from codes/185-67-2.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/185-67-2.json, apply E-PUNCTURE on the target sector, and repeat greedily with Pareto ranking and staged deep-verify.

Parity checks

X-checks 57 (max weight 6) · Z-checks 57 (max weight 6)

H_X (57 checks, sparse supports)

[0, 30, 61, 92, 123, 154] [1, 32, 63, 94, 125, 156] [2, 33, 64, 95, 126, 157] [3, 34, 65, 96, 127, 158] [4, 35, 66, 97, 128, 159] [5, 36, 67, 98, 129, 160] [6, 37, 68, 99, 130, 161] [7, 38, 69, 100, 131, 162] [8, 39, 70, 101, 132, 163] [9, 40, 71, 102, 133, 164] [10, 41, 72, 103, 134, 165] [11, 42, 73, 104, 135, 166] [12, 43, 74, 105, 136, 167] [13, 44, 75, 106, 137, 168] [14, 45, 76, 107, 138, 169] [15, 46, 77, 108, 139, 170] [16, 47, 78, 109, 140, 171] [17, 48, 79, 110, 141, 172] [18, 49, 80, 111, 142, 173] [19, 50, 81, 112, 143, 174] [20, 51, 82, 113, 144, 175] [21, 52, 83, 114, 145, 176] [22, 53, 84, 115, 146, 177] [23, 54, 85, 116, 147, 178] [24, 55, 86, 117, 148, 179] [25, 56, 87, 118, 149, 180] [26, 57, 88, 119, 150, 181] [27, 58, 89, 120, 151, 182] [28, 59, 90, 121, 152, 183] [0, 29, 89, 115, 142, 167] [1, 31, 60, 117, 144, 169] [2, 32, 61, 118, 145, 170] [3, 33, 62, 119, 146, 171] [4, 34, 63, 120, 147, 172] [5, 35, 64, 121, 148, 173] [6, 36, 65, 91, 149, 174] [7, 37, 66, 92, 150, 175] [8, 38, 67, 93, 151, 176] [9, 39, 68, 94, 152, 177] [10, 40, 69, 95, 122, 178] [11, 41, 70, 96, 123, 179] [12, 42, 71, 97, 124, 180] [13, 43, 72, 98, 125, 181] [14, 44, 73, 99, 126, 182] [15, 45, 74, 100, 127, 183] [16, 46, 75, 101, 128, 153] [17, 47, 76, 102, 129, 154] [18, 48, 77, 103, 130, 155] [19, 49, 78, 104, 131, 156] [20, 50, 79, 105, 132, 157] [21, 51, 80, 106, 133, 158] [22, 52, 81, 107, 134, 159] [23, 53, 82, 108, 135, 160] [24, 54, 83, 109, 136, 161] [25, 55, 84, 110, 137, 162] [26, 56, 85, 111, 138, 163] [27, 57, 86, 112, 139, 164]

H_Z (57 checks, sparse supports)

[0, 35, 66, 92, 142, 173] [1, 37, 68, 94, 144, 175] [2, 38, 69, 95, 145, 176] [3, 39, 70, 96, 146, 177] [4, 40, 71, 97, 147, 178] [5, 41, 72, 98, 148, 179] [6, 42, 73, 99, 149, 180] [7, 43, 74, 100, 150, 181] [8, 44, 75, 101, 151, 182] [9, 45, 76, 102, 152, 183] [10, 46, 77, 103, 122, 153] [11, 47, 78, 104, 123, 154] [12, 48, 79, 105, 124, 155] [13, 49, 80, 106, 125, 156] [14, 50, 81, 107, 126, 157] [15, 51, 82, 108, 127, 158] [16, 52, 83, 109, 128, 159] [17, 53, 84, 110, 129, 160] [18, 54, 85, 111, 130, 161] [19, 55, 86, 112, 131, 162] [20, 56, 87, 113, 132, 163] [21, 57, 88, 114, 133, 164] [22, 58, 89, 115, 134, 165] [23, 59, 90, 116, 135, 166] [24, 29, 60, 117, 136, 167] [25, 30, 61, 118, 137, 168] [26, 31, 62, 119, 138, 169] [27, 32, 63, 120, 139, 170] [28, 33, 64, 121, 140, 171] [0, 30, 90, 115, 152, 177] [1, 32, 61, 117, 123, 179] [2, 33, 62, 118, 124, 180] [3, 34, 63, 119, 125, 181] [4, 35, 64, 120, 126, 182] [5, 36, 65, 121, 127, 183] [6, 37, 66, 91, 128, 153] [7, 38, 67, 92, 129, 154] [8, 39, 68, 93, 130, 155] [9, 40, 69, 94, 131, 156] [10, 41, 70, 95, 132, 157] [11, 42, 71, 96, 133, 158] [12, 43, 72, 97, 134, 159] [13, 44, 73, 98, 135, 160] [14, 45, 74, 99, 136, 161] [15, 46, 75, 100, 137, 162] [16, 47, 76, 101, 138, 163] [17, 48, 77, 102, 139, 164] [18, 49, 78, 103, 140, 165] [19, 50, 79, 104, 141, 166] [20, 51, 80, 105, 142, 167] [21, 52, 81, 106, 143, 168] [22, 53, 82, 107, 144, 169] [23, 54, 83, 108, 145, 170] [24, 55, 84, 109, 146, 171] [25, 56, 85, 110, 147, 172] [26, 57, 86, 111, 148, 173] [27, 58, 87, 112, 149, 174]

Code ID 184-70-2 · download JSON · raw on GitHub