[[47,1,11]] · QEC Challenge

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Distance

X/Z asymmetry 1 · d_X ≤ 11, d_Z ≤ 11 · w_X = 16, w_Z = 16 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 11 · witness weight 11 (claimed upper_bound)

witness operator (support, 11 qubits)

[0, 4, 9, 15, 19, 25, 26, 38, 39, 45, 46]

d_Z 11 · witness weight 11 (claimed upper_bound)

witness operator (support, 11 qubits)

[0, 4, 9, 15, 19, 25, 26, 38, 39, 45, 46]

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 12–16 (mean 13.217) · H_Z 12–16 (mean 13.217)

qubit degrees H_X 1–15 (mean 6.468) · H_Z 1–15 (mean 6.468)

trapping sets H_X (1,1)×23 (2,9)×135 (3,8)×1101 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 23 (1,10): 8 (1,11): 8 (1,14): 7 (1,15): 1 (2,9): 135 (2,10): 164 (2,13): 172 (2,14): 79 (2,17): 6 (2,18): 1 (3,8): 1101 (3,9): 1629 (3,10): 400 (3,11): 523 (3,12): 2227 (3,13): 1544 (3,14): 372 (3,15): 296 (3,16): 222 (3,17): 75 (3,18): 22 (3,19): 2 (3,20): 1

trapping sets H_Z (1,1)×23 (2,9)×135 (3,8)×1101 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 23 (1,10): 8 (1,11): 8 (1,14): 7 (1,15): 1 (2,9): 135 (2,10): 164 (2,13): 172 (2,14): 79 (2,17): 6 (2,18): 1 (3,8): 1101 (3,9): 1629 (3,10): 400 (3,11): 523 (3,12): 2227 (3,13): 1544 (3,14): 372 (3,15): 296 (3,16): 222 (3,17): 75 (3,18): 22 (3,19): 2 (3,20): 1

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction contributed via qldpc submit

model Beam 1.0 (claimed, not verified)

date 2026-11-09

family other (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight > 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 23 (max weight 16) · Z-checks 23 (max weight 16)

H_X (23 checks, sparse supports)

[0, 20, 22, 23, 25, 26, 28, 31, 36, 38, 40, 42] [1, 20, 23, 24, 25, 28, 29, 30, 33, 34, 36, 37, 38, 40, 42, 43] [2, 20, 23, 24, 28, 30, 32, 33, 36, 37, 38, 39, 41, 42, 45, 46] [3, 20, 22, 24, 30, 32, 37, 38, 40, 41, 44, 45] [4, 22, 24, 25, 26, 28, 29, 32, 36, 38, 41, 44] [5, 20, 22, 23, 25, 29, 31, 32, 33, 34, 36, 37, 39, 40, 42, 44] [6, 20, 24, 26, 28, 29, 30, 33, 36, 39, 40, 42, 43, 44, 45, 46] [7, 20, 24, 25, 26, 28, 32, 34, 37, 39, 41, 45] [8, 23, 24, 25, 28, 32, 33, 34, 36, 37, 44, 46] [9, 20, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 40, 44, 45, 46] [10, 20, 23, 24, 26, 28, 29, 30, 31, 34, 37, 40, 41, 43, 44, 45] [11, 22, 24, 25, 28, 30, 32, 34, 36, 37, 38, 39, 40, 41, 43, 46] [12, 20, 29, 31, 32, 33, 36, 37, 38, 41, 44, 46] [13, 20, 22, 23, 24, 31, 36, 39, 40, 43, 44, 45] [14, 20, 24, 25, 26, 28, 29, 30, 31, 32, 42, 43] [15, 24, 31, 32, 33, 34, 37, 39, 40, 41, 43, 44] [16, 22, 23, 25, 28, 32, 38, 40, 43, 44, 45, 46] [17, 22, 26, 29, 30, 33, 36, 37, 38, 40, 42, 44] [18, 20, 23, 28, 29, 34, 36, 39, 40, 41, 42, 45] [19, 20, 24, 25, 26, 30, 37, 38, 39, 40, 42, 46] [21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 41, 42] [27, 28, 29, 30, 31, 32, 33, 34, 43, 44, 45, 46] [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]

H_Z (23 checks, sparse supports)

[0, 20, 22, 23, 25, 26, 28, 31, 36, 38, 40, 42] [1, 20, 23, 24, 25, 28, 29, 30, 33, 34, 36, 37, 38, 40, 42, 43] [2, 20, 23, 24, 28, 30, 32, 33, 36, 37, 38, 39, 41, 42, 45, 46] [3, 20, 22, 24, 30, 32, 37, 38, 40, 41, 44, 45] [4, 22, 24, 25, 26, 28, 29, 32, 36, 38, 41, 44] [5, 20, 22, 23, 25, 29, 31, 32, 33, 34, 36, 37, 39, 40, 42, 44] [6, 20, 24, 26, 28, 29, 30, 33, 36, 39, 40, 42, 43, 44, 45, 46] [7, 20, 24, 25, 26, 28, 32, 34, 37, 39, 41, 45] [8, 23, 24, 25, 28, 32, 33, 34, 36, 37, 44, 46] [9, 20, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 40, 44, 45, 46] [10, 20, 23, 24, 26, 28, 29, 30, 31, 34, 37, 40, 41, 43, 44, 45] [11, 22, 24, 25, 28, 30, 32, 34, 36, 37, 38, 39, 40, 41, 43, 46] [12, 20, 29, 31, 32, 33, 36, 37, 38, 41, 44, 46] [13, 20, 22, 23, 24, 31, 36, 39, 40, 43, 44, 45] [14, 20, 24, 25, 26, 28, 29, 30, 31, 32, 42, 43] [15, 24, 31, 32, 33, 34, 37, 39, 40, 41, 43, 44] [16, 22, 23, 25, 28, 32, 38, 40, 43, 44, 45, 46] [17, 22, 26, 29, 30, 33, 36, 37, 38, 40, 42, 44] [18, 20, 23, 28, 29, 34, 36, 39, 40, 41, 42, 45] [19, 20, 24, 25, 26, 30, 37, 38, 39, 40, 42, 46] [21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 41, 42] [27, 28, 29, 30, 31, 32, 33, 34, 43, 44, 45, 46] [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]

Code ID 47-1-11-b · download JSON · raw on GitHub