{
 "schema_version": "0.2",
 "name": "[[90,4,9]] weight-5 mixed-monomial BB code (LLM-guided evolutionary search)",
 "code_type": "CSS",
 "n": 90,
 "k": 4,
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 "distance": {
  "d": 9,
  "X": {
   "value": 9,
   "confidence": "exact",
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 "provenance": {
  "authors": [
   "@cbjuan"
  ],
  "construction": "Bivariate bicycle code over F_2[x,y]/(x^5-1, y^9-1), weight-5 mixed-monomial polynomials A = 1 + x^2 y^8 + x^3 y^7, B = 1 + x^2 y^6, found by an LLM-guided evolutionary search (OpenEvolve, weight-5 mixed-monomial campaign) over CSS BB polynomial pairs. This connected (ell=5, m=9) presentation is BLISS-isomorphic to one of 2 identical connected components of a disconnected parent BB code (ell=10, m=9, k=8, n=180, A = 1 + x^4 y^8 + x^6 y^7, B = 1 + x^4 y^6) whose exact distance d=9 was established by MILP in the source repository; the component presentation used here was independently re-verified exact (d_X=d_Z=9, no lighter logical on either side) with this repository's own verify/certify.py (scipy/HiGHS MILP, tlim=600s, 70s wall time).",
  "references": [
   "an internal weight-5 bivariate-bicycle evolutionary campaign in github.com/qiskit-community/qcode-discovery (branch weight5-campaigns, not part of a public branch at the time of this submission -- this submission's own distance/CSS claims are independently re-derived and re-verified using only this repository's tools and do not rely on that source being externally checkable)"
  ],
  "date": "2026-09-07",
  "notes": "Independently corroborated with this repo's own tools before submission: research/kit/surrogate.py distance_rand at 5,000 and 50,000 trials both returned d=9; research/kit/distance.py decoder_distance (BP+OSD, 200,000 injected-error trials) returned d_heuristic=9, verdict=corroborated; research/kit/distance.py exact_distance (scipy/HiGHS MILP) proved d_X=d_Z=9 exact. Per the source campaign's own per-candidate model-attribution log, this code was independently discovered by both GPT 5.6 Sol (first, chronologically, within the ensemble run) and Claude Opus 5 (rediscovered later, independently, in the same run) -- this is recorded as joint/dual attribution, not resolved to a single model. This submission's re-verification and packaging was done separately by Claude Sonnet 5.",
  "model": [
   "GPT 5.6 Sol",
   "Claude Opus 5"
  ]
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
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    "value": 9,
    "confidence": "upper_bound",
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   "Z": {
    "value": 9,
    "confidence": "upper_bound",
    "witness": [
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  },
  "rounds": 9,
  "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/measure layers; CX layers are a proper edge coloring of each Tanner graph (5 X + 5 Z CX layers per round, schedule seed 0; hook-aware orders: every CNOT order suffix needs >= d-1 further data errors to complete a logical, with the exact completion cost, layered by min-conflicts search). Pairs of hooks on different ancillas of the same type are also constrained: an assignment pair is admitted only if every such hook pair needs >= d faults in total (2 + flags + completion cost). 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 second-to-last CX slot and measured every round, slot assignments filtered by an exact hook-cost criterion over single, same-ancilla and cross-ancilla hook pairs; screened by RIS and a seeded BP+OSD search"
  }
 }
}