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[[36,2,6]] d =
n
36
k
2
d
6
kd²/n
2.0
w
4
g
0.125
r
2.8284
layers
1

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Distance

d_X 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[3, 9, 14, 20, 26, 32]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 7, 14, 21, 28, 35]
certificate exact, d = 6 · scipy/HiGHS MILP
X: min over 2 Z-logical cosets = 6, all proven; Z: min over 2 X-logical cosets = 6, all proven

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 2.828
X checkZ checkqubit site (36)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 Kitaev, A. Yu.
provenance literature baseline
construction Rotated toric code on an 6x6 torus, distance 6.
model classical construction (no AI model)
reference arXiv:quant-ph/9707021
date 1997-07-09
notes Distance is exact by construction. 2D layout added 2026-07-23: the 6x6 torus folded into the plane (ring fold i -> 2i / 2(L-i)-1 per axis), making the wrap-around checks geometrically local; single layer, measured interaction radius 2*sqrt(2).
family topological (a tag, not a ranking)
locality 2D-local single (computed from the layout)
weight class weight ≤ 4 (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 18 · Z-checks 18
H_X (18 checks, sparse supports)
[0, 5, 30, 35] [1, 2, 31, 32] [3, 4, 33, 34] [0, 1, 6, 7] [2, 3, 8, 9] [4, 5, 10, 11] [6, 11, 12, 17] [7, 8, 13, 14] [9, 10, 15, 16] [12, 13, 18, 19] [14, 15, 20, 21] [16, 17, 22, 23] [18, 23, 24, 29] [19, 20, 25, 26] [21, 22, 27, 28] [24, 25, 30, 31] [26, 27, 32, 33] [28, 29, 34, 35]
H_Z (18 checks, sparse supports)
[0, 1, 30, 31] [2, 3, 32, 33] [4, 5, 34, 35] [0, 5, 6, 11] [1, 2, 7, 8] [3, 4, 9, 10] [6, 7, 12, 13] [8, 9, 14, 15] [10, 11, 16, 17] [12, 17, 18, 23] [13, 14, 19, 20] [15, 16, 21, 22] [18, 19, 24, 25] [20, 21, 26, 27] [22, 23, 28, 29] [24, 29, 30, 35] [25, 26, 31, 32] [27, 28, 33, 34]
raw submission JSON