{
 "schema_version": "0.2",
 "name": "[[14,6,2]] twisted-torus BB code (arXiv:2503.03827)",
 "code_type": "CSS",
 "n": 14,
 "k": 6,
 "checks": {
  "X": [
   [
    0,
    1,
    2,
    7,
    8,
    9
   ],
   [
    1,
    3,
    4,
    8,
    10,
    11
   ],
   [
    2,
    4,
    5,
    9,
    11,
    12
   ],
   [
    2,
    3,
    6,
    9,
    10,
    13
   ],
   [
    0,
    4,
    6,
    7,
    11,
    13
   ],
   [
    0,
    3,
    5,
    7,
    10,
    12
   ],
   [
    1,
    5,
    6,
    8,
    12,
    13
   ]
  ],
  "Z": [
   [
    0,
    4,
    5,
    7,
    11,
    12
   ],
   [
    0,
    1,
    6,
    7,
    8,
    13
   ],
   [
    0,
    2,
    3,
    7,
    9,
    10
   ],
   [
    1,
    3,
    5,
    8,
    10,
    12
   ],
   [
    1,
    2,
    4,
    8,
    9,
    11
   ],
   [
    2,
    5,
    6,
    9,
    12,
    13
   ],
   [
    3,
    4,
    6,
    10,
    11,
    13
   ]
  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    2,
    9
   ]
  },
  "Z": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    3,
    10
   ]
  }
 },
 "provenance": {
  "authors": [
   "Zijian Liang",
   "Ke Liu",
   "Hao Song",
   "Yu-An Chen"
  ],
  "construction": "Twisted-torus bivariate-bicycle code from Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025). Stabilizers f(x,y)=1+x+y, g(x,y)=1+y+x on the abelian quotient group Z^2/L with twist basis a_1=[0, 7], a_2=[1, 2] (n=2|det[a_1,a_2]|=2*7). Reconstructed from the published polynomials and twist; CSS form H_X=[f|g], H_Z=[gbar|fbar].",
  "references": [
   "arXiv:2503.03827"
  ],
  "date": "2025",
  "notes": "Reconstructed baseline from Liang, Liu, Song, Chen, Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025), arXiv:2503.03827. The [[n,k,d]] parameter set and stabilizer polynomials are published in that paper; this entry reproduces them. Distance is an upper bound per the paper (probabilistic for d>20); the witness is the surrogate logical of that weight. Seeded to fill a board coverage gap at this block size, not a discovery. 2D-local layout added 2026-07-27: simulated annealing over qubit-to-site assignments on a unit-spaced triangular grid (1 layer, capacity 1 per site per layer); measured interaction radius 3.605551 (single-layer); same code, same check matrices.",
  "origin": "baseline",
  "novelty": "known_parameters"
 },
 "family": "bivariate-bicycle",
 "locality": {
  "coordinates": [
   [
    -1.0,
    0.0
   ],
   [
    1.5,
    0.8660254037844386
   ],
   [
    1.0,
    0.0
   ],
   [
    0.5,
    2.598076211353316
   ],
   [
    1.5,
    -0.8660254037844386
   ],
   [
    1.5,
    2.598076211353316
   ],
   [
    -0.5,
    0.8660254037844386
   ],
   [
    -1.5,
    0.8660254037844386
   ],
   [
    0.5,
    -0.8660254037844386
   ],
   [
    0.5,
    0.8660254037844386
   ],
   [
    -1.0,
    1.7320508075688772
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    1.7320508075688772
   ],
   [
    1.0,
    1.7320508075688772
   ]
  ],
  "interaction_radius": 3.605551275463989,
  "layers": 1
 },
 "circuit": {
  "d_circ": {
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     801,
     802
    ]
   },
   "Z": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     774,
     775
    ]
   }
  },
  "rounds": 2,
  "stim_version": "1.16.0",
  "notes": "Interleaved two-block extraction (Bravyi et al. arXiv:2308.07915 Table 5 style): joint reset and measurement layers, 7 data CX layers per round; X-check term slots [6, 1, 5, 2, 3, 4], Z-check term slots [1, 5, 0, 3, 4, 2] over terms A_0..A_2, B_0..B_2; terms recovered from H alone by a commuting permutation decomposition. Order screened by RIS among the 1248 slot assignments satisfying the overlap-parity criterion (first one tried); the claim then survived 2 seeds x 1000 RIS trials per basis and an observable-constrained seeded BP+OSD search over symmetric seeds, whose lightest undetected logical fault set is weight 2 in both bases.",
  "ler": {
   "X": {
    "p": 0.001,
    "shots": 40000,
    "failures": 2358,
    "seed": 7,
    "decoder": "bposd-cs-10",
    "ler_per_round": 0.030399106,
    "ci95": [
     0.029194261,
     0.031652262
    ]
   },
   "Z": {
    "p": 0.001,
    "shots": 40000,
    "failures": 2527,
    "seed": 7,
    "decoder": "bposd-cs-10",
    "ler_per_round": 0.032653769,
    "ci95": [
     0.031402421,
     0.033953477
    ]
   }
  }
 }
}