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[[81,1,9]] d =
n
81
k
1
d
9
kd²/n
1.0
w
4
g
1
r
1.4142
layers
1

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Distance

d_X 9 · witness weight 9 (claimed exact)
witness operator (support, 9 qubits)
[0, 1, 11, 21, 31, 41, 44, 51, 52]
d_Z 9 · witness weight 9 (claimed exact)
witness operator (support, 9 qubits)
[0, 9, 18, 27, 36, 45, 54, 64, 73]
certificate exact, d = 9 · scipy/HiGHS MILP
X: min over 1 Z-logical cosets = 9, all proven; Z: min over 1 X-logical cosets = 9, 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 = 1.414
X checkZ checkqubit site (81)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 surface code, distance 9.
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: qubit q at (q//9, q%9) on the 9x9 planar grid; single layer, measured interaction radius 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 40 · Z-checks 40
H_X (40 checks, sparse supports)
[0, 1, 9, 10] [2, 3, 11, 12] [4, 5, 13, 14] [6, 7, 15, 16] [8, 17] [9, 18] [10, 11, 19, 20] [12, 13, 21, 22] [14, 15, 23, 24] [16, 17, 25, 26] [18, 19, 27, 28] [20, 21, 29, 30] [22, 23, 31, 32] [24, 25, 33, 34] [26, 35] [27, 36] [28, 29, 37, 38] [30, 31, 39, 40] [32, 33, 41, 42] [34, 35, 43, 44] [36, 37, 45, 46] [38, 39, 47, 48] [40, 41, 49, 50] [42, 43, 51, 52] [44, 53] [45, 54] [46, 47, 55, 56] [48, 49, 57, 58] [50, 51, 59, 60] [52, 53, 61, 62] [54, 55, 63, 64] [56, 57, 65, 66] [58, 59, 67, 68] [60, 61, 69, 70] [62, 71] [63, 72] [64, 65, 73, 74] [66, 67, 75, 76] [68, 69, 77, 78] [70, 71, 79, 80]
H_Z (40 checks, sparse supports)
[0, 1] [2, 3] [4, 5] [6, 7] [1, 2, 10, 11] [3, 4, 12, 13] [5, 6, 14, 15] [7, 8, 16, 17] [9, 10, 18, 19] [11, 12, 20, 21] [13, 14, 22, 23] [15, 16, 24, 25] [19, 20, 28, 29] [21, 22, 30, 31] [23, 24, 32, 33] [25, 26, 34, 35] [27, 28, 36, 37] [29, 30, 38, 39] [31, 32, 40, 41] [33, 34, 42, 43] [37, 38, 46, 47] [39, 40, 48, 49] [41, 42, 50, 51] [43, 44, 52, 53] [45, 46, 54, 55] [47, 48, 56, 57] [49, 50, 58, 59] [51, 52, 60, 61] [55, 56, 64, 65] [57, 58, 66, 67] [59, 60, 68, 69] [61, 62, 70, 71] [63, 64, 72, 73] [65, 66, 74, 75] [67, 68, 76, 77] [69, 70, 78, 79] [73, 74] [75, 76] [77, 78] [79, 80]
raw submission JSON