{
 "schema_version": "0.2",
 "name": "[[62,10,6]] twisted-torus BB code (arXiv:2503.03827)",
 "code_type": "CSS",
 "n": 62,
 "k": 10,
 "checks": {
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 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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    36,
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  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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    26,
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    54,
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  }
 },
 "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+x^-1y, g(x,y)=1+y+x^-1y^-1 on the abelian quotient group Z^2/L with twist basis a_1=[0, 31], a_2=[1, 13] (n=2|det[a_1,a_2]|=2*31). 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 (2 layers, capacity 1 per site per layer); measured interaction radius 3.605551 (bilayer); same code, same check matrices.",
  "origin": "baseline",
  "novelty": "known_parameters"
 },
 "family": "bivariate-bicycle",
 "locality": {
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  "interaction_radius": 3.605551275463989,
  "layers": 2
 },
 "circuit": {
  "d_circ": {
   "X": {
    "value": 6,
    "confidence": "upper_bound",
    "witness": [
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     112,
     325,
     331,
     387,
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   },
   "Z": {
    "value": 6,
    "confidence": "upper_bound",
    "witness": [
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     1030,
     1544,
     1549,
     1792
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   }
  },
  "rounds": 6,
  "stim_version": "1.16.0",
  "notes": "Flag-qubit sequential two-block extraction: one ancilla and one flag qubit per check, X checks then Z checks each round with joint reset/measure layers. Each check's 6 CNOTs occupy 6 slot layers (a proper edge coloring of its Tanner graph); the flag (|0> for X checks, |+> for Z checks) is coupled to the ancilla after the check's CNOT 1 and again after CNOT 5, and measured every round as a single-record detector, so an ancilla hook in that window also fires the flag. 8 X + 8 Z CX layers per round, schedule seed 0. Hook-aware orders: every proper suffix S_j of a check's CNOT order needs >= d-1 further data errors if unflagged and >= d-2 if flagged, and every same-ancilla pair of hooks needs >= d-2 (or d-3 when exactly one is flagged) further errors to complete a logical; layered by min-conflicts search. Screened by RIS on ker(H_dem) and an observable-constrained seeded BP+OSD search; witnesses validated in GF(2).",
  "contributed_by": {
   "by": [
    "@vprusso"
   ],
   "date": "2026-09-19",
   "method": "generic CSS memory schedule with one flag qubit per check: CX layers from a bipartite edge coloring, the flag coupled to the ancilla after the first and the fifth CNOT and measured every round, CNOT orders filtered by a single- and pair-hook cost criterion; screened by RIS on ker(H_dem) and an observable-constrained seeded BP+OSD search"
  }
 }
}