{
 "schema_version": "0.2",
 "name": "[[7,1,3]] color code",
 "code_type": "CSS",
 "n": 7,
 "k": 1,
 "checks": {
  "X": [
   [
    3,
    4,
    5,
    6
   ],
   [
    1,
    2,
    5,
    6
   ],
   [
    0,
    2,
    4,
    6
   ]
  ],
  "Z": [
   [
    3,
    4,
    5,
    6
   ],
   [
    1,
    2,
    5,
    6
   ],
   [
    0,
    2,
    4,
    6
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "exact",
   "witness": [
    1,
    3,
    5
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "exact",
   "witness": [
    2,
    4,
    5
   ]
  }
 },
 "provenance": {
  "authors": [
   "Steane, Andrew M."
  ],
  "origin": "baseline",
  "construction": "Steane code: the distance-3 2D color code.",
  "date": "1996-01-29",
  "references": [
   "arXiv:quant-ph/9601029"
  ],
  "notes": "Distance is exact by construction. 2D layout added 2026-07-23: compact unit-spaced triangular patch (qubit 6, shared by all three faces, at the centre); single layer, measured interaction radius 2.0."
 },
 "family": "topological",
 "locality": {
  "coordinates": [
   [
    1.5,
    0.8660254037844386
   ],
   [
    -0.5,
    0.8660254037844386
   ],
   [
    0.5,
    0.8660254037844386
   ],
   [
    -0.5,
    -0.8660254037844386
   ],
   [
    1.0,
    0.0
   ],
   [
    -1.0,
    0.0
   ],
   [
    0.0,
    0.0
   ]
  ],
  "interaction_radius": 2.0,
  "layers": 1
 },
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     269,
     270
    ]
   },
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     47,
     78
    ]
   }
  },
  "rounds": 3,
  "stim_version": "1.16.0",
  "notes": "Generic sequential two-block extraction: one ancilla per check, X checks then Z checks each round with joint reset and measurement layers; CX layers are a proper edge coloring of each Tanner graph (4 X + 4 Z CX layers per round, coloring candidate 0); generated by qldpc submit (research/circuit_autogen.py, seed 0), the first of up to 6 candidates whose RIS screen at 2 rounds found nothing below d; witnesses from RIS on ker(H_dem) at twice the gate's trial budget, validated in GF(2)",
  "logicals": {
   "X": [
    [
     0,
     1,
     2,
     3,
     4,
     5,
     6
    ]
   ],
   "Z": [
    [
     0,
     1,
     2,
     3,
     4,
     5,
     6
    ]
   ]
  },
  "gates": [
   {
    "gate": "H",
    "name": "logical Hadamard",
    "logical_action": {
     "X0": [
      "Z0"
     ],
     "Z0": [
      "X0"
     ]
    }
   }
  ],
  "contributed_by": {
   "by": [
    "@MathysRennela"
   ],
   "date": "2026-09-23"
  }
 }
}