{
 "schema_version": "0.4",
 "name": "[[12,3,3]] weight-4 non-CSS stabilizer code",
 "code_type": "stabilizer",
 "n": 12,
 "k": 3,
 "checks": {
  "S": [
   {
    "X": [
     0,
     2,
     4
    ],
    "Z": [
     0,
     1
    ]
   },
   {
    "X": [
     0,
     8,
     9,
     11
    ],
    "Z": [
     0,
     9
    ]
   },
   {
    "X": [
     1,
     7
    ],
    "Z": [
     4,
     6
    ]
   },
   {
    "X": [
     0,
     1,
     7,
     11
    ],
    "Z": [
     1,
     7,
     11
    ]
   },
   {
    "X": [
     3,
     9
    ],
    "Z": [
     2,
     3,
     4,
     9
    ]
   },
   {
    "X": [
     6,
     7
    ],
    "Z": [
     5,
     7,
     10
    ]
   },
   {
    "X": [
     4,
     5,
     6
    ],
    "Z": [
     3,
     6
    ]
   },
   {
    "X": [
     5,
     10,
     11
    ],
    "Z": [
     8,
     10,
     11
    ]
   },
   {
    "X": [
     3,
     8,
     9
    ],
    "Z": [
     5,
     8
    ]
   }
  ]
 },
 "distance": {
  "d": 3,
  "P": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     0,
     1
    ],
    "Z": [
     0,
     2
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@MicheldeMessieres"
  ],
  "construction": "Non-CSS stabilizer code with 9 independent generators of weight <= 4 on 12 qubits, found by a SAT search (kissat) over all such generator sets in which every pair of generators commutes and the 36 single-qubit Paulis have distinct nonzero syndromes (so every Pauli of weight 1 or 2 is detected and d >= 3). Generators: YZXIXIIIIIII, YIIIIIIIXYIX, IXIIZIZXIIII, XYIIIIIYIIIY, IIZYZIIIIYII, IIIIIZXYIIZI, IIIZXXYIIIII, IIIIIXIIZIYY, IIIXIZIIYXII. k = 12 - 9 = 3. Not CSS under any single-qubit Clifford.",
  "origin": "submission",
  "date": "2026-10-13",
  "model": "Claude Opus 5.5 (Claude Code)",
  "references": [
   "arXiv:2601.19848",
   "arXiv:2501.17447",
   "arXiv:2601.15446 (literature check; see the note)"
  ],
  "novelty": "unknown",
  "notes": "Distance: an exhaustive enumeration of every Pauli operator of weight 1 and 2 finds no nontrivial logical and no stabilizer element, and weight-3 logicals exist (36 of them, among them the stored witness), so d = 3 exactly for these generators; filed as an upper bound because the board's Pauli-weight certifier is not available yet. Not CSS under any single-qubit Clifford: checked by the verifier on the generators and, by two separate tests, on the whole stabilizer group. Same kd^2/n (2.25) as the published weight-4 [[8,2,3]] code of Cross and Vandeth (arXiv:2501.17447; on the board as the literature baseline codes/8-2-3.json), with one more logical qubit. Wei, Han, He, Li and Liu (arXiv:2601.19848, Table 2) list the lowest generator weight of a [[12,3,3]] stabilizer code as 4-5; these generators have weight 4. Literature novelty is not claimed.",
  "search_budget": {
   "cpu_hours": 0.01
  }
 },
 "family": "other"
}