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"verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 13504069, 1681214693 ] } }, "Z": { "value": 28, "confidence": "upper_bound", "witness": [ 5, 18, 20, 41, 54, 66, 69, 79, 109, 114, 119, 129, 131, 145, 157, 178, 194, 201, 203, 237, 239, 263, 278, 300, 333, 352, 357, 364 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-25", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 13504069, 1681214693 ] } }, "d": 28 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Periodic bivariate-bicycle code on Z_62 x Z_3 (n = 2*l*m = 372): x = S_62 tensor I_3, y = I_62 tensor S_3 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^16y^0 + x^41y^1 + x^58y^2, B = x^0y^0 + x^15y^2 + x^32y^1 + x^44y^1; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(62, 3, [[0, 0], [16, 0], [41, 1], [58, 2]], [[0, 0], [15, 2], [32, 1], [44, 1]])). gcd(62, 3) = 1, so Z_62 x Z_3 is cyclic of order 186 and the code is the cyclic generalized-bicycle code over Z_186 with a(z) = z^0 + z^78 + z^103 + z^182, b(z) = z^0 + z^77 + z^94 + z^106 (CRT relabeling x^a y^b -> z^t, t = a mod 62, t = b mod 3).", "date": "2026-09-25", "notes": "Found by the third LER-objective search (coprime bivariate-bicycle codes (gcd(l, m) = 1) at 100 <= n <= 420, weight 6 and 8, k >= 8): circuit-level logical error rate at 3 rounds under the board's depolarizing recipe, interleaved schedule, decoded with CUDA-Q QEC nv-qldpc-decoder (BP+OSD-CS order 10). At p = 0.002, 100000 shots per basis: Z memory 70 failures, X memory 55 failures, against 12 copies of the distance-7 rotated surface code (1164 physical qubits, same builder and decoder) with 119 and 110 failures. Decoder-based d_circ estimate at 3 rounds: 75. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. Details in the accompanying note.", "origin": "submission", "novelty": "unknown", "model": "Claude Fable 5.1 (Claude Code)" } }