[[102,33,3]] · QEC Challenge

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[[102,33,3]] d =

102

kd²/n

2.912

X/Z

0.0035

5.3852

layers

swaps

263

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Distance

X/Z asymmetry 1 · d_X = 3, d_Z = 3 · w_X = 11, 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 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[54, 56, 58]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[41, 59, 77]

certificate exact, d = 3 · scipy/HiGHS MILP

X: no logical < 3 exists; Z: no logical < 3 exists

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 9–11 (mean 9.833) · H_Z 4–8 (mean 5.8)

qubit degrees H_X 1–4 (mean 2.314) · H_Z 1–8 (mean 2.559)

trapping sets H_X (1,1)×24 (2,1)×168 (3,0)×210 (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): 36 (1,3): 28 (1,4): 14 (2,1): 168 (2,2): 228 (2,3): 172 (2,4): 136 (2,5): 108 (2,6): 32 (3,0): 210 (3,1): 684 (3,2): 1020 (3,3): 1432 (3,4): 2110 (3,5): 2264 (3,6): 1498 (3,7): 660 (3,8): 128

trapping sets H_Z (1,1)×30 (2,1)×105 (3,0)×60 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 30 (1,2): 45 (1,3): 15 (1,8): 12 (2,1): 105 (2,2): 75 (2,7): 64 (2,8): 210 (2,9): 96 (3,0): 60 (3,1): 120 (3,2): 60 (3,3): 30 (3,6): 224 (3,7): 1216 (3,8): 2412 (3,9): 1856 (3,10): 640 (3,11): 72 (3,14): 240 (3,15): 240

witness diameter X 3.6056 · Z 5.0 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair

X checkZ checkqubit site (51)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release

routing cost 263 nearest-neighbor SWAPs per round in total, at most 8 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction Hypergraph product of classical codes ham15 and sham6

model Tencent Hy3 (claimed, not verified)

builds on arXiv:0903.0566

date 2026-07-17

family hypergraph product (a tag, not a ranking)

locality 2D-local bilayer (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 24 (max weight 11) · Z-checks 45 (max weight 8)

H_X (24 checks, sparse supports)

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

H_Z (45 checks, sparse supports)

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

Code ID 102-33-3 · download JSON · raw on GitHub