witness diameter X 5.3852 · Z 5.3852 (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)
Verified 2D layout
as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
layout contributed by @dorakingx · Simulated annealing over site assignments on an integer grid with the repo's own research/local2d/fold_layout.search_layout (max-diameter objective, several bounding boxes and seeds); single layer at radius 4 tried first, then two layers at 7. Radius and per-site occupancy re-measured with the verifier's rule. · 2026-10-02
X checkZ checkqubit site (21)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 110 nearest-neighbor SWAPs per round in total, at most 5 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)
construction Generalized-bicycle CSS code: circulant matrices A,B over F2[x]/(x21-1), a=(0,1,3), b=(0,2,13), Hx=[A|B], Hz=[B^T|A^T]
modelClaude Sonnet 5 (claimed, not verified)
date 2026-09-19
notes Shares [[42,6,6]] parameters with codes/42-6-6.json (@mathysrennela, 2D-local bilayer via simulated annealing over an integer grid). Confirmed NOT equivalent: this code has uniform check weight 6 and uniform qubit degree 6 throughout (expected for its algebraic circulant construction), while the existing entry has a mixed weight-3/4/5/6 and degree-3/4/5/6 distribution (expected for a geometrically-annealed layout). Row-weight and degree histograms are permutation invariants, so this rules out equivalence under any qubit/check relabeling.
family generalized bicycle (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
[[n,k,d]] — one-line description of the construction
Direction & hypothesis
targeting the weight-6/GB family since weight-4 GB codes proved degenerate
What was searched
l from 9-22, 3-term polynomials a,b over Z_l, ~6,000 candidates screened
Evidence trail
exhaustive weight<=4 exclusion proved d>=5 before submission; the CLI's own 20,000-trial RIS search then found d<=6, giving the final witness-backed upper bound d=6
Dead ends
weight-4/2-term GB codes were all degenerate — every high-rate candidate had a real weight<=4 logical, proven by exhaustive search, not heuristic
Tools
Tools
Model: Claude Sonnet 5 (search construction, GF(2) rank/certification code, and the codes//notes/ write-up assembled interactively with the model).
Search & certification ran in the model's own sandboxed environment (pure Python 3 + numpy, no GPU needed — the construction and the exhaustive weight<=4 exhaustive check are cheap: the full l=9..22 sweep runs in under a minute).
Local execution (cloning the repo, running ./qldpc submit, and the final RIS distance search) was run under WSL (Ubuntu) on:
CPU: AMD Ryzen 5 7520U with Radeon Graphics (2.80 GHz)
RAM: 8 GB
GPU: AMD Radeon 610M (not used — no GPU-accelerated steps in this pipeline)
OS: Windows 11, WSL2/Ubuntu, 64-bit x64
No specialized hardware (GPU, cluster, HPC) was required for either the search or the verifier's distance witness search (20,000 RIS trials, a few seconds on this machine).
Reproduction
l=21, a=(0,1,3), b=(0,2,13), pointing at gb_search_toolkit.py