{
 "schema_version": "0.2",
 "name": "[[16,2,4]] toric code",
 "code_type": "CSS",
 "n": 16,
 "k": 2,
 "checks": {
  "X": [
   [
    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
   ]
  ],
  "Z": [
   [
    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
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "exact",
   "witness": [
    0,
    4,
    8,
    12
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "exact",
   "witness": [
    2,
    7,
    8,
    13
   ]
  }
 },
 "provenance": {
  "authors": [
   "Kitaev, A. Yu."
  ],
  "origin": "baseline",
  "construction": "Rotated toric code on an 4x4 torus, distance 4.",
  "date": "1997-07-09",
  "references": [
   "arXiv:quant-ph/9707021"
  ],
  "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",
 "locality": {
  "coordinates": [
   [
    0.0,
    0.0
   ],
   [
    0.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    0.0,
    1.0
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    1.0
   ],
   [
    1.0,
    0.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    1.0
   ]
  ],
  "interaction_radius": 2.8284271247461903,
  "layers": 1
 },
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 4,
    "confidence": "upper_bound",
    "witness": [
     1165,
     1166,
     1176,
     1177
    ]
   },
   "X": {
    "value": 4,
    "confidence": "upper_bound",
    "witness": [
     820,
     822,
     975,
     977
    ]
   }
  },
  "rounds": 4,
  "stim_version": "1.16.0",
  "notes": "Kishony-Fowler diagonal coupling order (arXiv:2602.09099; X pattern 'kf_x', Z pattern 'kf_x') on the natural row-major torus indexing -- axis-aligned zigzags halve one basis on a torus; generated by research/circuit_seed_toric.py",
  "ler": {
   "X": {
    "p": 0.001,
    "shots": 60000,
    "failures": 413,
    "seed": 7,
    "decoder": "bposd-cs-10",
    "ler_per_round": 0.001729789,
    "ci95": [
     0.001570536,
     0.001905161
    ]
   },
   "Z": {
    "p": 0.001,
    "shots": 60000,
    "failures": 408,
    "seed": 7,
    "decoder": "bposd-cs-10",
    "ler_per_round": 0.001708739,
    "ci95": [
     0.001550513,
     0.001883083
    ]
   }
  }
 }
}