← back to the board
[[16,2,4]] d =
n
16
k
2
d
4
kd²/n
2.0
w
4
g
0.125
r
2.8284
layers
1

Share this result

Distance

d_X 4 · witness weight 4 (claimed exact)
witness operator (support, 4 qubits)
[0, 4, 8, 12]
d_Z 4 · witness weight 4 (claimed exact)
witness operator (support, 4 qubits)
[2, 7, 8, 13]
certificate exact, d = 4 · scipy/HiGHS MILP
X: min over 2 Z-logical cosets = 4, all proven; Z: min over 2 X-logical cosets = 4, 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 (16)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 4x4 torus, distance 4.
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 4x4 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 8 · Z-checks 8
H_X (8 checks, sparse supports)
[0, 3, 12, 15] [1, 2, 13, 14] [0, 1, 4, 5] [2, 3, 6, 7] [4, 7, 8, 11] [5, 6, 9, 10] [8, 9, 12, 13] [10, 11, 14, 15]
H_Z (8 checks, sparse supports)
[0, 1, 12, 13] [2, 3, 14, 15] [0, 3, 4, 7] [1, 2, 5, 6] [4, 5, 8, 9] [6, 7, 10, 11] [8, 11, 12, 15] [9, 10, 13, 14]
raw submission JSON