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[[64,2,8]] d =
n
64
k
2
d
8
kd²/n
2.0
w
4
g
0.125
r
2.8284
layers
1

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Distance

d_X 8 · witness weight 8 (claimed exact)
witness operator (support, 8 qubits)
[0, 8, 17, 26, 35, 43, 50, 57]
d_Z 8 · witness weight 8 (claimed exact)
witness operator (support, 8 qubits)
[6, 7, 56, 57, 58, 59, 60, 61]
certificate exact, d = 8 · scipy/HiGHS MILP
X: min over 2 Z-logical cosets = 8, all proven; Z: min over 2 X-logical cosets = 8, 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 (64)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 8x8 torus, distance 8.
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 8x8 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 32 · Z-checks 32
H_X (32 checks, sparse supports)
[0, 7, 56, 63] [1, 2, 57, 58] [3, 4, 59, 60] [5, 6, 61, 62] [0, 1, 8, 9] [2, 3, 10, 11] [4, 5, 12, 13] [6, 7, 14, 15] [8, 15, 16, 23] [9, 10, 17, 18] [11, 12, 19, 20] [13, 14, 21, 22] [16, 17, 24, 25] [18, 19, 26, 27] [20, 21, 28, 29] [22, 23, 30, 31] [24, 31, 32, 39] [25, 26, 33, 34] [27, 28, 35, 36] [29, 30, 37, 38] [32, 33, 40, 41] [34, 35, 42, 43] [36, 37, 44, 45] [38, 39, 46, 47] [40, 47, 48, 55] [41, 42, 49, 50] [43, 44, 51, 52] [45, 46, 53, 54] [48, 49, 56, 57] [50, 51, 58, 59] [52, 53, 60, 61] [54, 55, 62, 63]
H_Z (32 checks, sparse supports)
[0, 1, 56, 57] [2, 3, 58, 59] [4, 5, 60, 61] [6, 7, 62, 63] [0, 7, 8, 15] [1, 2, 9, 10] [3, 4, 11, 12] [5, 6, 13, 14] [8, 9, 16, 17] [10, 11, 18, 19] [12, 13, 20, 21] [14, 15, 22, 23] [16, 23, 24, 31] [17, 18, 25, 26] [19, 20, 27, 28] [21, 22, 29, 30] [24, 25, 32, 33] [26, 27, 34, 35] [28, 29, 36, 37] [30, 31, 38, 39] [32, 39, 40, 47] [33, 34, 41, 42] [35, 36, 43, 44] [37, 38, 45, 46] [40, 41, 48, 49] [42, 43, 50, 51] [44, 45, 52, 53] [46, 47, 54, 55] [48, 55, 56, 63] [49, 50, 57, 58] [51, 52, 59, 60] [53, 54, 61, 62]
raw submission JSON