X/Z asymmetry 1 · d_X = 4, d_Z = 4 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 4 · witness weight 4 (claimed upper_bound)

d_Z 4 · witness weight 4 (claimed upper_bound)

certificate exact, d = 4 · scipy/HiGHS MILP

X: no logical < 4 exists; Z: no logical < 4 exists

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 8 · H_Z 8

qubit degrees H_X 2–6 (mean 4.0) · H_Z 2–6 (mean 4.0)

trapping sets H_X (1,2)×16 (2,2)×16 (3,2)×96 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

trapping sets H_Z (1,2)×16 (2,2)×16 (3,2)×96 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

witness diameter X 3.6056 · Z 3.6056 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

syndrome-extraction memory circuits committed under circuits/32-8-4/ · canonical noise recipe, 4 rounds, stim 1.16.0

d_circ ≤ 4 (min over bases; penalty-only, clamped to ≤ d)

d_circ^X 4 · fault-set witness of 4 mechanisms (claimed upper_bound)

d_circ^Z 4 · fault-set witness of 4 mechanisms (claimed upper_bound)

ler/round (X) 0.0166 95% CI [0.0153, 0.018] · 632/10⁴ shots · decoder bposd-cs-10 at p=0.001

ler/round (Z) 0.0155 95% CI [0.0142, 0.0168] · 590/10⁴ shots · decoder bposd-cs-10 at p=0.001

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair

routing cost 82 nearest-neighbor SWAPs per round in total, at most 4 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

authors Lin, Hsiang-Ku and Pryadko, Leonid P.

provenance literature baseline

construction Two-block group algebra (2BGA) code over C_8 x C_2: a={1, r²}, b={1, s r⁵, s r⁴, r², s r⁷, s r⁶} (Lin & Pryadko, arXiv:2306.16400, Table 1).

model classical construction (no AI model)

reference arXiv:2306.16400

date 2023

notes Literature baseline (arXiv:2306.16400, Lin & Pryadko, 28 Jun 2023). Two-block group algebra code reconstructed from the published group presentation; distance d=4 taken from the paper's Table 1 and certified by an explicit non-stabilizer witness on each side (regenerated via the research kit's RIS search). Literature novelty confirmed by manual cross-check: arXiv:2306.16400 Table 1 explicitly reports the [[32,8,4]] parameters with W=8. The verifier's 'literature novelty UNVERIFIED' label is by-design (validate_candidate.py performs no literature lookup) and is intentionally not overridden. Layout certification: a verifier-accepted honest bilayer layout (stacked 4x4 grid, 2 qubits per site, layers=2, measured interaction radius ~4.243) 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 2BGA coset (a tag, not a ranking)

locality 2D-local bilayer (computed from the layout)

weight class weight ≤ 8 (computed)

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

X-checks 16 (max weight 8) · Z-checks 16 (max weight 8)

Code ID 32-8-4 · download JSON · raw on GitHub