← back to the board
[[25,1,5]] d =
n
25
k
1
d
5
kd²/n
1.0
w
4
g
1
r
1.4142
layers
1

Share this result

Distance

d_X 5 · witness weight 5 (claimed exact)
witness operator (support, 5 qubits)
[2, 3, 5, 6, 9]
d_Z 5 · witness weight 5 (claimed exact)
witness operator (support, 5 qubits)
[0, 5, 10, 16, 21]
certificate exact, d = 5 · scipy/HiGHS MILP
X: min over 1 Z-logical cosets = 5, all proven; Z: min over 1 X-logical cosets = 5, 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 (25)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 5.
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//5, q%5) on the 5x5 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 12 · Z-checks 12
H_X (12 checks, sparse supports)
[0, 1, 5, 6] [2, 3, 7, 8] [4, 9] [5, 10] [6, 7, 11, 12] [8, 9, 13, 14] [10, 11, 15, 16] [12, 13, 17, 18] [14, 19] [15, 20] [16, 17, 21, 22] [18, 19, 23, 24]
H_Z (12 checks, sparse supports)
[0, 1] [2, 3] [1, 2, 6, 7] [3, 4, 8, 9] [5, 6, 10, 11] [7, 8, 12, 13] [11, 12, 16, 17] [13, 14, 18, 19] [15, 16, 20, 21] [17, 18, 22, 23] [21, 22] [23, 24]
raw submission JSON