[[119,31,6]] · QEC Challenge

[[119,31,6]] d ≤

119

kd²/n

9.37815

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 6, d_Z ≤ 6 · w_X = 9, w_Z = 9 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 6 · witness weight 6 (claimed upper_bound)

witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-02

witness operator (support, 6 qubits)

[24, 40, 42, 46, 72, 84]

d_Z 6 · witness weight 6 (claimed upper_bound)

witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-02

witness operator (support, 6 qubits)

[19, 33, 58, 107, 111, 115]

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 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 9 · H_Z 9

qubit degrees H_X 1–5 (mean 3.328) · H_Z 1–5 (mean 3.328)

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

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

(1,1): 3 (1,2): 17 (1,3): 47 (1,4): 42 (1,5): 10 (2,1): 1 (2,2): 18 (2,3): 100 (2,4): 304 (2,5): 555 (2,6): 429 (2,7): 158 (2,8): 19 (3,1): 1 (3,2): 31 (3,3): 253 (3,4): 1159 (3,5): 3552 (3,6): 7145 (3,7): 8900 (3,8): 6861 (3,9): 3482 (3,10): 1192 (3,11): 286 (3,12): 52 (3,13): 2

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

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

(1,1): 3 (1,2): 16 (1,3): 49 (1,4): 41 (1,5): 10 (2,1): 2 (2,2): 12 (2,3): 103 (2,4): 324 (2,5): 542 (2,6): 429 (2,7): 147 (2,8): 25 (3,1): 3 (3,2): 23 (3,3): 242 (3,4): 1196 (3,5): 3696 (3,6): 7151 (3,7): 8785 (3,8): 6765 (3,9): 3435 (3,10): 1208 (3,11): 318 (3,12): 57 (3,13): 5

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction priced calculus E-PUNCTURE transform of codes/120-24-10.json

model Beam 1.0 (claimed, not verified)

date 2026-11-02

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

[[119,31,6]] — priced calculus E-PUNCTURE transform of codes/120-24-10.json

Direction & hypothesis

Weight-9 unrestricted CSS cell. Transform a connected CSS parent (codes/120-24-10.json, a board entry) with the priced construction calculus to obtain a connected child that is not dominated by any existing entry in its track cell.

What was searched

Gap-targeted search: all priced calculus moves (peel, puncture, deletion, rebase) applied to board codes. Targets Pareto frontier gaps. Rule used: E-PUNCTURE. Parent: codes/120-24-10.json. Connected children only; bare-qubit children and dominated candidates dropped. Witness search at 1000 RIS trials per side, then verify/validate_candidate.py with full refutation.

Evidence trail

The submitted distance is a witness-backed upper bound: d = min(d_X, d_Z) with explicit X and Z logical witnesses carried in the JSON. Parent entry: codes/120-24-10.json.

Tools

Model: Beam 1.0. Harness: research/kit (coordination, submit, prescreen), code-calculus consumer.

Reproduction

Rebuild H_X/H_Z from codes/120-24-10.json by applying the E-PUNCTURE move of the priced calculus; re-run the witness search at the stated budget.

Parity checks

X-checks 44 (max weight 9) · Z-checks 44 (max weight 9)

H_X (44 checks, sparse supports)

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

H_Z (44 checks, sparse supports)

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

Code ID 119-31-6 · download JSON · raw on GitHub