Distance
X/Z asymmetry 1 · d_X = 7, d_Z = 7 · w_X = 4, w_Z = 4 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 7 · witness weight 7 (claimed exact)
witness operator (support, 7 qubits)
[38, 39, 40, 41, 42, 43, 44]
d_Z 7 · witness weight 7 (claimed exact)
witness operator (support, 7 qubits)
[0, 7, 14, 21, 28, 36, 43]
certificate exact, d = 7 · scipy/HiGHS MILP
X: min over 1 Z-logical cosets = 7, all proven; Z: min over 1 X-logical cosets = 7, all proven
Diagnostics
computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–4 (mean 3.5) · H_Z 2–4 (mean 3.5)
qubit degrees H_X 1–2 (mean 1.714) · H_Z 1–2 (mean 1.714)
trapping sets H_X (1,1)×14 (2,0)×6 (3,1)×70 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 14
(1,2): 35
(2,0): 6
(2,1): 26
(2,2): 82
(3,1): 70
(3,2): 197
(3,3): 12
(3,4): 48
trapping sets H_Z (1,1)×14 (2,0)×6 (3,1)×70 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 14
(1,2): 35
(2,0): 6
(2,1): 26
(2,2): 82
(3,1): 70
(3,2): 197
(3,3): 12
(3,4): 48
witness diameter X 6.0828 · Z 6.0828 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)
Circuit tier
syndrome-extraction memory circuits committed under
circuits/49-1-7/ · canonical noise recipe, 7 rounds, stim 1.16.0
d_circ ≤ 7 (min over bases; penalty-only, clamped to ≤ d)
d_circ^X 7 · fault-set witness of 7 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 7)
[42, 44, 59, 79, 98, 257, 681]
d_circ^Z 7 · fault-set witness of 7 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 7)
[4586, 4590, 4658, 5025, 5319, 5430, 5431]
no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see
Construction & provenance
authors Kitaev, A. Yu.
provenance literature baseline
construction Rotated surface code, distance 7.
model classical construction (no AI model)
date 1997-07-09
notes Distance is exact by construction. 2D layout added 2026-07-23: qubit q at (q//7, q%7) on the 7x7 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)
Parity checks
X-checks 24 (max weight 4) · Z-checks 24 (max weight 4)
H_X (24 checks, sparse supports)
[0, 1, 7, 8]
[2, 3, 9, 10]
[4, 5, 11, 12]
[6, 13]
[7, 14]
[8, 9, 15, 16]
[10, 11, 17, 18]
[12, 13, 19, 20]
[14, 15, 21, 22]
[16, 17, 23, 24]
[18, 19, 25, 26]
[20, 27]
[21, 28]
[22, 23, 29, 30]
[24, 25, 31, 32]
[26, 27, 33, 34]
[28, 29, 35, 36]
[30, 31, 37, 38]
[32, 33, 39, 40]
[34, 41]
[35, 42]
[36, 37, 43, 44]
[38, 39, 45, 46]
[40, 41, 47, 48]
H_Z (24 checks, sparse supports)
[0, 1]
[2, 3]
[4, 5]
[1, 2, 8, 9]
[3, 4, 10, 11]
[5, 6, 12, 13]
[7, 8, 14, 15]
[9, 10, 16, 17]
[11, 12, 18, 19]
[15, 16, 22, 23]
[17, 18, 24, 25]
[19, 20, 26, 27]
[21, 22, 28, 29]
[23, 24, 30, 31]
[25, 26, 32, 33]
[29, 30, 36, 37]
[31, 32, 38, 39]
[33, 34, 40, 41]
[35, 36, 42, 43]
[37, 38, 44, 45]
[39, 40, 46, 47]
[43, 44]
[45, 46]
[47, 48]