← back to the board
[[88,6,6]] d =
n
88
k
6
d
6
kd²/n
2.455
w
6
g
0.0303
r
3.0
layers
2

Share this result

Distance

d_X 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[2, 42, 50, 58, 76, 86]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[1, 17, 19, 27, 37, 87]
certificate exact, d = 6 · scipy/HiGHS cutoff IP
X: no logical < 6 exists; Z: no logical < 6 exists

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 3
X checkZ checkqubit site (53)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

Construction & provenance

authors Liang, Zijian and Eberhardt, Jens Niklas and Chen, Yu-An
provenance literature baseline
construction Liang-Eberhardt-Chen k=6 family f=1+x+x-1y-2, g=1+y+xy-1; (6,8) open-boundary lattice.
model classical construction (no AI model)
reference arXiv:2504.08887
date 2025-04-11
notes Reference baseline (Liang, Eberhardt, Chen). Bilayer grid layout added 2026-07-23, recovered from the check structure by template matching: the 18+24 weight-6 bulk checks are translated copies of (f, g), which pins 84 of 88 qubits on the two-layer grid; the 4 notch-boundary qubits were placed by exhaustive local search. Measured interaction radius sqrt(10). Layout shear-optimized 2026-07-23: linear map [[1.000000,-0.318933],[0.000000,0.968940]] applied to the template-solved grid with the 4 notch-boundary qubits re-placed in the sheared lattice, reducing the interaction radius sqrt(10) -> 3.0; same code, same check matrices.
family bivariate bicycle (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 6 (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 42 · Z-checks 43
H_X (42 checks, sparse supports)
[0, 10, 18, 49, 50, 56] [1, 11, 19, 50, 51, 57] [2, 12, 20, 51, 52, 58] [3, 13, 21, 52, 53, 59] [4, 14, 22, 53, 54, 60] [5, 15, 23, 54, 55, 61] [8, 18, 26, 57, 58, 64] [9, 19, 27, 58, 59, 65] [10, 20, 28, 59, 60, 66] [11, 21, 29, 60, 61, 67] [12, 22, 30, 61, 62, 68] [13, 23, 31, 62, 63, 69] [16, 26, 34, 65, 66, 72] [17, 27, 35, 66, 67, 73] [18, 28, 36, 67, 68, 74] [19, 29, 37, 68, 69, 75] [20, 30, 38, 69, 70, 76] [21, 31, 39, 70, 71, 77] [2, 40] [3, 41] [4, 42] [5, 43] [6, 44] [7, 45] [32, 81, 82] [33, 82, 83] [34, 83, 84] [35, 84, 85] [36, 85, 86] [37, 86, 87] [10, 40, 41, 42, 48] [11, 41, 42, 43, 49] [12, 42, 43, 44, 50] [13, 43, 44, 45, 51] [14, 44, 45, 46, 52] [15, 45, 46, 47, 53] [24, 34, 73, 74, 80] [25, 35, 74, 75, 81] [26, 36, 75, 76, 82] [27, 37, 76, 77, 83] [28, 38, 77, 78, 84] [29, 39, 78, 79, 85]
H_Z (43 checks, sparse supports)
[2, 8, 9, 40, 48, 58] [3, 9, 10, 41, 49, 59] [4, 10, 11, 42, 50, 60] [5, 11, 12, 43, 51, 61] [6, 12, 13, 44, 52, 62] [7, 13, 14, 45, 53, 63] [10, 16, 17, 48, 56, 66] [11, 17, 18, 49, 57, 67] [12, 18, 19, 50, 58, 68] [13, 19, 20, 51, 59, 69] [14, 20, 21, 52, 60, 70] [15, 21, 22, 53, 61, 71] [18, 24, 25, 56, 64, 74] [19, 25, 26, 57, 65, 75] [20, 26, 27, 58, 66, 76] [21, 27, 28, 59, 67, 77] [22, 28, 29, 60, 68, 78] [23, 29, 30, 61, 69, 79] [26, 32, 33, 64, 72, 82] [27, 33, 34, 65, 73, 83] [28, 34, 35, 66, 74, 84] [29, 35, 36, 67, 75, 85] [30, 36, 37, 68, 76, 86] [31, 37, 38, 69, 77, 87] [0, 56] [8, 64] [16, 72] [24, 80] [1, 57, 64] [9, 65, 72] [17, 73, 80] [1, 8, 57] [9, 16, 65] [17, 24, 73] [25, 32, 81] [15, 47, 55] [23, 55, 63] [31, 63, 71] [39, 71, 79] [14, 15, 46, 54] [22, 23, 54, 62] [30, 31, 62, 70] [38, 39, 70, 78]
raw submission JSON