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

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

authors Zijian Liang and Ke Liu and Hao Song and Yu-An Chen

provenance literature baseline

construction Twisted-torus bivariate-bicycle code from Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025). Stabilizers f(x,y)=1+x+xy, g(x,y)=1+y+xy on the abelian quotient group Z²/L with twist basis a_1=[0, 3], a_2=[3, 0] (n=2|det[a_1,a_2]|=2*9). Reconstructed from the published polynomials and twist; CSS form H_X=[f|g], H_Z=[gbar|fbar].

model classical construction (no AI model)

reference arXiv:2503.03827

date 2025

notes Reconstructed baseline from Liang, Liu, Song, Chen, Generalized toric codes on twisted tori for quantum error correction (PRX Quantum 6, 020357, 2025), arXiv:2503.03827. The [[n,k,d]] parameter set and stabilizer polynomials are published in that paper; this entry reproduces them. Distance is an upper bound per the paper (probabilistic for d>20); the witness is the surrogate logical of that weight. Seeded to fill a board coverage gap at this block size, not a discovery. 2D-local layout added 2026-07-27: simulated annealing over qubit-to-site assignments on a unit-spaced triangular grid (1 layer, capacity 1 per site per layer); measured interaction radius 3.464102 (single-layer); same code, same check matrices.

family bivariate bicycle (a tag, not a ranking)

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

weight class weight ≤ 6 (computed)

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

X-checks 9 · Z-checks 9