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"confidence": "upper_bound", "witness": [ 37, 46, 49, 62, 70, 73, 84, 107, 119, 126, 130, 141, 142, 162, 243, 264, 273, 275, 285, 296, 308, 319, 321, 322 ] } }, "provenance": { "authors": [ "Zijian Liang", "Ke Liu", "Hao Song", "Yu-An Chen" ], "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+x^-1y^3, g(x,y)=1+y+x^3y^-1 on the abelian quotient group Z^2/L with twist basis a_1=[0, 30], a_2=[6, 6] (n=2|det[a_1,a_2]|=2*180). Reconstructed from the published polynomials and twist; CSS form H_X=[f|g], H_Z=[gbar|fbar].", "references": [ "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. LAYOUT added 2026-09-01: a two-layer planar layout on a unit-spacing triangular lattice with measured interaction radius 6.9282 (min site spacing 1.0, at most 2 qubits per site), placing the code in the local-2d-bilayer class with kd^2/n = 19.2 (previous weight-6 bilayer cell best 7.14, codes/84-6-10.json; previous best 2D-local code at any weight 12.46, codes/578-18-20.json). Layout credit and method are recorded in locality.contributed_by; the CODE, its distance claims (an upper bound per the paper), and its authorship are unchanged from the literature baseline.", "origin": "baseline", "novelty": "known_parameters" }, "family": "bivariate-bicycle", "locality": { "coordinates": [ [ 6.0, 5.196152422706632 ], [ 5.5, 4.330127018922193 ], [ 6.0, 5.196152422706632 ], [ 4.0, 3.4641016151377544 ], [ 9.0, 5.196152422706632 ], [ 5.0, 6.928203230275509 ], [ 7.5, 2.598076211353316 ], [ 7.0, 3.4641016151377544 ], [ 7.5, 6.06217782649107 ], [ 6.5, 7.794228634059947 ], [ 8.5, 2.598076211353316 ], [ 5.5, 4.330127018922193 ], [ 7.5, 6.06217782649107 ], [ 6.0, 6.928203230275509 ], [ 10.0, 6.928203230275509 ], [ 11.0, 5.196152422706632 ], [ 6.5, 2.598076211353316 ], [ 7.5, 4.330127018922193 ], [ 9.5, 6.06217782649107 ], [ 8.0, 8.660254037844386 ], [ 7.0, 12.12435565298214 ], [ 10.0, 0.0 ], [ 8.5, 4.330127018922193 ], [ 7.5, 4.330127018922193 ], [ 7.0, 6.928203230275509 ], [ 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Search driven by Claude Fable 5.1." } } }