Construction & provenance
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-1 on the abelian quotient group Z2/L with twist basis a_1=[0, 7], a_2=[5, 1] (n=2|det[a_1,a_2]|=2*35). Reconstructed from the published polynomials and twist; CSS form H_X=[f|g], H_Z=[gbar|fbar].
model classical construction (no AI model)
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.
family bivariate bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)
Parity checks
X-checks 35 · Z-checks 35
H_X (35 checks, sparse supports)
[0, 1, 4, 35, 37, 56]
[1, 3, 7, 36, 39, 61]
[2, 4, 8, 36, 37, 40]
[3, 6, 11, 38, 42, 65]
[4, 7, 12, 38, 39, 43]
[5, 8, 13, 39, 40, 44]
[6, 10, 16, 41, 46, 68]
[7, 11, 17, 41, 42, 47]
[8, 12, 18, 42, 43, 48]
[9, 13, 19, 43, 44, 49]
[0, 10, 15, 45, 51, 55]
[11, 16, 22, 45, 46, 52]
[12, 17, 23, 46, 47, 53]
[13, 18, 24, 47, 48, 54]
[14, 19, 25, 48, 49, 55]
[1, 15, 21, 35, 50, 60]
[0, 2, 16, 50, 51, 57]
[17, 22, 27, 51, 52, 58]
[18, 23, 28, 52, 53, 59]
[19, 24, 29, 53, 54, 60]
[20, 21, 25, 50, 54, 55]
[3, 21, 26, 36, 56, 64]
[2, 5, 22, 35, 57, 62]
[23, 27, 31, 57, 58, 63]
[24, 28, 32, 58, 59, 64]
[25, 26, 29, 56, 59, 60]
[6, 26, 30, 38, 61, 67]
[5, 9, 27, 37, 62, 66]
[28, 31, 34, 62, 63, 67]
[29, 30, 32, 61, 63, 64]
[10, 30, 33, 41, 65, 69]
[9, 14, 31, 40, 66, 69]
[32, 33, 34, 65, 66, 67]
[15, 20, 33, 45, 49, 68]
[14, 20, 34, 44, 68, 69]
H_Z (35 checks, sparse supports)
[0, 15, 22, 35, 45, 51]
[1, 2, 21, 35, 36, 50]
[0, 2, 27, 37, 51, 57]
[3, 4, 26, 36, 38, 56]
[1, 4, 5, 35, 37, 39]
[2, 5, 31, 40, 57, 62]
[6, 7, 30, 38, 41, 61]
[3, 7, 8, 36, 39, 42]
[4, 8, 9, 37, 40, 43]
[5, 9, 34, 44, 62, 66]
[10, 11, 33, 41, 45, 65]
[6, 11, 12, 38, 42, 46]
[7, 12, 13, 39, 43, 47]
[8, 13, 14, 40, 44, 48]
[9, 14, 33, 49, 66, 69]
[15, 16, 20, 45, 50, 68]
[10, 16, 17, 41, 46, 51]
[11, 17, 18, 42, 47, 52]
[12, 18, 19, 43, 48, 53]
[13, 19, 20, 44, 49, 54]
[10, 14, 20, 55, 68, 69]
[0, 21, 25, 50, 55, 56]
[16, 22, 23, 46, 52, 57]
[17, 23, 24, 47, 53, 58]
[18, 24, 25, 48, 54, 59]
[15, 19, 25, 49, 55, 60]
[1, 26, 29, 56, 60, 61]
[22, 27, 28, 52, 58, 62]
[23, 28, 29, 53, 59, 63]
[21, 24, 29, 54, 60, 64]
[3, 30, 32, 61, 64, 65]
[27, 31, 32, 58, 63, 66]
[26, 28, 32, 59, 64, 67]
[6, 33, 34, 65, 67, 68]
[30, 31, 34, 63, 67, 69]