n
144
Paper: arXiv:2610.06623, "Large Language Model-Guided Discovery of Weight-Five Bivariate Bicycle Codes" (match W5PBB-144-4-8-aefa6773).
Target: the general-stabilizer board's unrestricted x weight-6 (and looser) cells. Same PBB construction family as the companion submissions in this batch (block-1 z-part [C | D] added to a CSS bivariate-bicycle stabilizer matrix: H = (A B | C D; 0 0 | B^T A^T)).
Source: a weight-5-targeted LLM-guided evolutionary search (OpenEvolve, "pbb-large" campaign) over 4-tuples (A, B, C, D), screened by k, isotropy, the combined non-CSS gate (evaluation/noncss_gate.py), and a BP-OSD distance estimate. The underlying code was first found as one of the isomorphic components of a disconnected parent presentation at (ell=18, m=12), n=432, k=12 (evaluation/connectivity.py:stabilizer_components + components_isomorphic); the parent's exact MILP distance (results/weight5_pbb_large_v1_deep_milp_verify.jsonl) transfers to each component. A standalone, explicit presentation of one component at its native (ell=18, m=4) was then independently constructed and certified (results/weight5_pbb_component_certifications.jsonl, match W5PBB-144-4-8-aefa6773): re-run through the same non-CSS screens (commutation verified; not CSS-equivalent under any tested Clifford class) and confirmed connected.
(ell, m) = (18, 4), A = 1 + x^3y, B = 1 + xy^2 + x^2, perturbation C = 1 + x^3y, D = xy^2 (0-indexed exponent pairs: A=[[0,0],[3,1]], B=[[0,0],[1,2],[2,0]], C=[[0,0],[3,1]], D=[[1,2]]). n = 2·18·4 = 144, k = 4, max check weight 5.
optimal at weight 8 on the (18,12) parent (parent_exact_distance_source, results/weight5_pbb_large_v1_deep_milp_verify.jsonl) -- exact, transferred to this component by the isomorphism/homogeneity argument.
check matrix directly from the (18,4) component's own generators via evaluation/pbb_code.py:build_pbb_code, then ran this repo's own cli/qldpc.py submit --dry-run (RIS search, 20,000 trials, gf2_fast accelerator at 1,000,000 trials). Independently found d<=8, matching the source's exact claim.
Final claim here: witness-backed upper_bound; the source repository's own evidence tier is exact.
Not applicable -- this submission mined an existing, already-vetted and now-published campaign result.
Model: jointly attributed to Claude Opus 5 and GPT-5.6 Sol (both aliases recovered against the parent's lineage log, 14 observations), matches provenance.model. This submission's rebuild, independent re-verification, and packaging in *this* repository was done separately, using only this repository's own tooling.
from evaluation.pbb_code import build_pbb_code
code = build_pbb_code(ell=18, m=4,
A_terms=[(0,0),(3,1)],
B_terms=[(0,0),(1,2),(2,0)],
C_terms=[(0,0),(3,1)],
D_terms=[(1,2)])
# code.matrix is the (144, 288) symplectic stabilizer matrix [X-part | Z-part]
Source: github.com/qiskit-community/qcode-discovery @ d6abdbd, evaluation/pbb_code.py, results/weight5_pbb_component_certifications.jsonl.