{
 "schema_version": "0.2",
 "name": "[[56,2,8]] generalized bicycle code",
 "code_type": "CSS",
 "n": 56,
 "k": 2,
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 "distance": {
  "d": 8,
  "X": {
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   "confidence": "upper_bound",
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 },
 "provenance": {
  "authors": [
   "Wang, Renren",
   "Pryadko, Leonid P."
  ],
  "origin": "baseline",
  "construction": "Generalized bicycle code, circulant size 28, a(x) = 1 + x^1 + x^2 + x^4, b(x) = 1 + x^19.",
  "date": "2022-03-31",
  "references": [
   "arXiv:2203.17216"
  ],
  "notes": "Distance d=8 from arXiv:2203.17216; witness here is a decoder-found logical operator of that weight (upper bound).\n\nLayout certification: a verifier-accepted honest bilayer layout (stacked 4x7 grid, 2 qubits per site, layers=2, measured interaction radius ~6.708) was found by @mathysrennela (Aug 2026). It earns the code the local-2d-bilayer class and makes the site's geometric efficiency g = 4kd^2/(n rho^2 r^4) computable. Code authorship unchanged; layout credit to @mathysrennela."
 },
 "family": "generalized-bicycle",
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  "layers": 2
 },
 "circuit": {
  "d_circ": {
   "X": {
    "value": 7,
    "confidence": "upper_bound",
    "witness": [
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   "Z": {
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    "confidence": "upper_bound",
    "witness": [
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  "rounds": 8,
  "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 CX layers per round; X-check term slots [6, 3, 4, 2, 5, 1], Z-check term slots [0, 3, 4, 2, 1, 5] over terms A_0..A_3, B_0..B_1; terms recovered from H by commuting permutation decomposition; generated by research/circuit_seed_twoblock.py; X memory: an exact SAT search (kissat, weight cap 7, all observables) found this weight-7 undetected logical fault set in the final round that the seeded and RIS searches had missed, so d_circ.X <= 7"
 }
}