{
 "schema_version": "0.2",
 "name": "[[36,2,6]] toric code",
 "code_type": "CSS",
 "n": 36,
 "k": 2,
 "checks": {
  "X": [
   [
    0,
    5,
    30,
    35
   ],
   [
    1,
    2,
    31,
    32
   ],
   [
    3,
    4,
    33,
    34
   ],
   [
    0,
    1,
    6,
    7
   ],
   [
    2,
    3,
    8,
    9
   ],
   [
    4,
    5,
    10,
    11
   ],
   [
    6,
    11,
    12,
    17
   ],
   [
    7,
    8,
    13,
    14
   ],
   [
    9,
    10,
    15,
    16
   ],
   [
    12,
    13,
    18,
    19
   ],
   [
    14,
    15,
    20,
    21
   ],
   [
    16,
    17,
    22,
    23
   ],
   [
    18,
    23,
    24,
    29
   ],
   [
    19,
    20,
    25,
    26
   ],
   [
    21,
    22,
    27,
    28
   ],
   [
    24,
    25,
    30,
    31
   ],
   [
    26,
    27,
    32,
    33
   ],
   [
    28,
    29,
    34,
    35
   ]
  ],
  "Z": [
   [
    0,
    1,
    30,
    31
   ],
   [
    2,
    3,
    32,
    33
   ],
   [
    4,
    5,
    34,
    35
   ],
   [
    0,
    5,
    6,
    11
   ],
   [
    1,
    2,
    7,
    8
   ],
   [
    3,
    4,
    9,
    10
   ],
   [
    6,
    7,
    12,
    13
   ],
   [
    8,
    9,
    14,
    15
   ],
   [
    10,
    11,
    16,
    17
   ],
   [
    12,
    17,
    18,
    23
   ],
   [
    13,
    14,
    19,
    20
   ],
   [
    15,
    16,
    21,
    22
   ],
   [
    18,
    19,
    24,
    25
   ],
   [
    20,
    21,
    26,
    27
   ],
   [
    22,
    23,
    28,
    29
   ],
   [
    24,
    29,
    30,
    35
   ],
   [
    25,
    26,
    31,
    32
   ],
   [
    27,
    28,
    33,
    34
   ]
  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "exact",
   "witness": [
    3,
    9,
    14,
    20,
    26,
    32
   ]
  },
  "Z": {
   "value": 6,
   "confidence": "exact",
   "witness": [
    0,
    7,
    14,
    21,
    28,
    35
   ]
  }
 },
 "provenance": {
  "authors": [
   "Kitaev, A. Yu."
  ],
  "origin": "baseline",
  "construction": "Rotated toric code on an 6x6 torus, distance 6.",
  "date": "1997-07-09",
  "references": [
   "arXiv:quant-ph/9707021"
  ],
  "notes": "Distance is exact by construction. 2D layout added 2026-07-23: the 6x6 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",
 "locality": {
  "coordinates": [
   [
    0.0,
    0.0
   ],
   [
    0.0,
    2.0
   ],
   [
    0.0,
    4.0
   ],
   [
    0.0,
    5.0
   ],
   [
    0.0,
    3.0
   ],
   [
    0.0,
    1.0
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    4.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    1.0
   ],
   [
    4.0,
    0.0
   ],
   [
    4.0,
    2.0
   ],
   [
    4.0,
    4.0
   ],
   [
    4.0,
    5.0
   ],
   [
    4.0,
    3.0
   ],
   [
    4.0,
    1.0
   ],
   [
    5.0,
    0.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    4.0
   ],
   [
    5.0,
    5.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    1.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    4.0
   ],
   [
    3.0,
    5.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    1.0
   ],
   [
    1.0,
    0.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    4.0
   ],
   [
    1.0,
    5.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    1.0
   ]
  ],
  "interaction_radius": 2.8284271247461903,
  "layers": 1
 },
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 6,
    "confidence": "upper_bound",
    "witness": [
     4284,
     4286,
     4297,
     4306,
     4308,
     4314
    ]
   },
   "X": {
    "value": 6,
    "confidence": "upper_bound",
    "witness": [
     14,
     16,
     26,
     41,
     52,
     72
    ]
   }
  },
  "rounds": 6,
  "stim_version": "1.16.0",
  "notes": "uniform plaquette coupling order (X pattern 'kf_x', Z pattern 'kf_x'; kf_* are the Kishony-Fowler diagonal orders of arXiv:2602.09099) on the natural row-major torus indexing; generated by research/circuit_seed_toric.py"
 }
}