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[[118,14,8]] d ≤
n
118
k
14
d
8
kd²/n
7.593
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 8, d_Z ≤ 8 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[32, 33, 56, 57, 76, 77, 88, 89]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[10, 11, 14, 15, 22, 23, 70, 71]
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 5–8 (mean 6.607) · H_Z 5–8 (mean 6.459)
qubit degrees H_X 2–6 (mean 3.415) · H_Z 2–6 (mean 3.339)
trapping sets H_X (1,2)×16 (2,2)×24 (3,2)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 16 (1,3): 56 (1,4): 34 (1,5): 5 (1,6): 7 (2,2): 24 (2,3): 72 (2,4): 272 (2,5): 304 (2,6): 213 (2,7): 115 (2,8): 72 (2,9): 4 (2,10): 8 (3,2): 24 (3,3): 132 (3,4): 808 (3,5): 1824 (3,6): 2732 (3,7): 3514 (3,8): 2630 (3,9): 1916 (3,10): 918 (3,11): 292 (3,12): 216 (3,13): 24 (3,14): 41
trapping sets H_Z (1,2)×20 (2,2)×30 (3,2)×30 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 20 (1,3): 60 (1,4): 25 (1,5): 4 (1,6): 9 (2,2): 30 (2,3): 84 (2,4): 294 (2,5): 252 (2,6): 141 (2,7): 164 (2,8): 44 (2,9): 12 (2,10): 15 (3,2): 30 (3,3): 180 (3,4): 868 (3,5): 2012 (3,6): 2237 (3,7): 2804 (3,8): 2653 (3,9): 1620 (3,10): 786 (3,11): 552 (3,12): 185 (3,13): 84 (3,14): 36 (3,15): 4 (3,16): 1

Circuit tier

syndrome-extraction memory circuits committed under circuits/118-14-8/ · canonical noise recipe, 8 rounds, stim 1.16.0
d_circ ≤ 4 (min over bases; penalty-only, clamped to ≤ d)
d_circ^X 4 · fault-set witness of 4 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 4)
[24602, 24623, 24859, 24878]
d_circ^Z 4 · fault-set witness of 4 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 4)
[11120, 11122, 14809, 14811]
no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction One amplification of [[25,7,4]] base by flagged [[4,2,2]] amplifier (arXiv:2609.37231).
model Beam 1.0 (claimed, not verified)
date 2026-10-18
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

[[118,14,8]] — amplification of [[25,7,4]] by the flagged [[4,2,2]] amplifier

Direction & hypothesis

Target: unrestricted / any-weight (w=8) cell. One amplification step of [[25,7,4]] base by flagged [[4,2,2]] (arXiv:2609.37231).

Evidence trail

d=8 upper bound (4*2). CLI RIS search passed.

Tools

Model: Beam 1.0. Base code: codes/25-7-4.json.

Reproduction

Base: codes/25-7-4.json. Amplifier: flagged [[4,2,2]]. Central three-term tensor product. Result n=118, k=14, d=8, w=8.

Parity checks

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