{
 "schema_version": "0.2",
 "name": "[[81,1,9]] surface code",
 "code_type": "CSS",
 "n": 81,
 "k": 1,
 "checks": {
  "X": [
   [
    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
   ]
  ],
  "Z": [
   [
    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
   ]
  ]
 },
 "distance": {
  "d": 9,
  "X": {
   "value": 9,
   "confidence": "exact",
   "witness": [
    0,
    1,
    11,
    21,
    31,
    41,
    44,
    51,
    52
   ]
  },
  "Z": {
   "value": 9,
   "confidence": "exact",
   "witness": [
    0,
    9,
    18,
    27,
    36,
    45,
    54,
    64,
    73
   ]
  }
 },
 "provenance": {
  "authors": [
   "Kitaev, A. Yu."
  ],
  "origin": "baseline",
  "construction": "Rotated surface code, distance 9.",
  "date": "1997-07-09",
  "references": [
   "arXiv:quant-ph/9707021"
  ],
  "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",
 "locality": {
  "coordinates": [
   [
    0.0,
    0.0
   ],
   [
    0.0,
    1.0
   ],
   [
    0.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    0.0,
    4.0
   ],
   [
    0.0,
    5.0
   ],
   [
    0.0,
    6.0
   ],
   [
    0.0,
    7.0
   ],
   [
    0.0,
    8.0
   ],
   [
    1.0,
    0.0
   ],
   [
    1.0,
    1.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    4.0
   ],
   [
    1.0,
    5.0
   ],
   [
    1.0,
    6.0
   ],
   [
    1.0,
    7.0
   ],
   [
    1.0,
    8.0
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    4.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    6.0
   ],
   [
    2.0,
    7.0
   ],
   [
    2.0,
    8.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    4.0
   ],
   [
    3.0,
    5.0
   ],
   [
    3.0,
    6.0
   ],
   [
    3.0,
    7.0
   ],
   [
    3.0,
    8.0
   ],
   [
    4.0,
    0.0
   ],
   [
    4.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    4.0,
    4.0
   ],
   [
    4.0,
    5.0
   ],
   [
    4.0,
    6.0
   ],
   [
    4.0,
    7.0
   ],
   [
    4.0,
    8.0
   ],
   [
    5.0,
    0.0
   ],
   [
    5.0,
    1.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    4.0
   ],
   [
    5.0,
    5.0
   ],
   [
    5.0,
    6.0
   ],
   [
    5.0,
    7.0
   ],
   [
    5.0,
    8.0
   ],
   [
    6.0,
    0.0
   ],
   [
    6.0,
    1.0
   ],
   [
    6.0,
    2.0
   ],
   [
    6.0,
    3.0
   ],
   [
    6.0,
    4.0
   ],
   [
    6.0,
    5.0
   ],
   [
    6.0,
    6.0
   ],
   [
    6.0,
    7.0
   ],
   [
    6.0,
    8.0
   ],
   [
    7.0,
    0.0
   ],
   [
    7.0,
    1.0
   ],
   [
    7.0,
    2.0
   ],
   [
    7.0,
    3.0
   ],
   [
    7.0,
    4.0
   ],
   [
    7.0,
    5.0
   ],
   [
    7.0,
    6.0
   ],
   [
    7.0,
    7.0
   ],
   [
    7.0,
    8.0
   ],
   [
    8.0,
    0.0
   ],
   [
    8.0,
    1.0
   ],
   [
    8.0,
    2.0
   ],
   [
    8.0,
    3.0
   ],
   [
    8.0,
    4.0
   ],
   [
    8.0,
    5.0
   ],
   [
    8.0,
    6.0
   ],
   [
    8.0,
    7.0
   ],
   [
    8.0,
    8.0
   ]
  ],
  "interaction_radius": 1.4142135623730951,
  "layers": 1
 },
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 9,
    "confidence": "upper_bound",
    "witness": [
     12666,
     12667,
     12670,
     12671,
     12675,
     12676,
     12679,
     12680,
     12681
    ]
   },
   "X": {
    "value": 9,
    "confidence": "upper_bound",
    "witness": [
     5,
     6,
     31,
     98,
     100,
     119,
     140,
     166,
     466
    ]
   }
  },
  "rounds": 9,
  "stim_version": "1.16.0",
  "notes": "standard geometric zigzag schedule (X pattern 'n', Z pattern 'z') derived from the 2D layout; generated by research/circuit_seed.py"
 }
}
