[[80,9,8]] · QEC Challenge

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[[80,9,8]] d =

kd²/n

7.2

0.0092

5.2915

layers

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Distance

d_X 9 · witness weight 9 (claimed upper_bound)

witness operator (support, 9 qubits)

[26, 32, 37, 52, 59, 64, 68, 73, 79]

d_Z 8 · witness weight 8 (claimed upper_bound)

witness operator (support, 8 qubits)

[3, 7, 17, 23, 27, 37, 46, 64]

certificate exact, d = 8 · scipy/HiGHS MILP

X: no logical < 9 exists; Z: no logical < 8 exists

Verified 2D layout

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

X checkZ checkqubit site (41)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

Construction & provenance

authors Lin, Hsiang-Ku and Pryadko, Leonid P.

provenance literature baseline

construction Two-block group algebra (2BGA) code over (C_10 x C_2) rtimes C_2: a={1, s r⁵, r⁵, s r⁶}, b={1, s², r, s² r³} (Lin & Pryadko, arXiv:2306.16400, Table 1).

model classical construction (no AI model)

reference arXiv:2306.16400

date 2023

notes Literature baseline (arXiv:2306.16400, Lin & Pryadko, 28 Jun 2023). Two-block group algebra code reconstructed from the published group presentation; distance d=9 taken from the paper's Table 1 and certified by an explicit non-stabilizer witness on each side (regenerated via the research kit's RIS search). Literature novelty confirmed by manual cross-check: arXiv:2306.16400 Table 1 explicitly reports the [[80,9,9]] parameters with W=6 (reconstructed checks have weight 8). The verifier's 'literature novelty UNVERIFIED' label is by-design (validate_candidate.py performs no literature lookup) and is intentionally not overridden. 2D-local layout added 2026-07-27: simulated annealing over qubit-to-site assignments on a unit-spaced triangular grid (2 layers, capacity 1 per site per layer); measured interaction radius 5.291503 (bilayer); same code, same check matrices.

family 2BGA coset (a tag, not a ranking)

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

weight class weight ≤ 8 (computed)

How this code was found

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

Parity checks

X-checks 40 · Z-checks 40

H_X (40 checks, sparse supports)

[0, 20, 23, 27, 40, 42, 70, 76] [1, 21, 22, 26, 41, 43, 47, 53] [2, 21, 22, 25, 40, 42, 68, 78] [3, 20, 23, 24, 41, 43, 45, 55] [4, 17, 21, 24, 40, 44, 46, 74] [5, 16, 20, 25, 45, 47, 51, 57] [6, 19, 23, 26, 42, 44, 46, 72] [7, 18, 22, 27, 45, 47, 49, 59] [8, 15, 19, 28, 44, 48, 50, 78] [9, 14, 18, 29, 49, 51, 55, 61] [10, 13, 17, 30, 46, 48, 50, 76] [11, 12, 16, 31, 49, 51, 53, 63] [9, 12, 13, 32, 42, 48, 52, 54] [8, 12, 13, 33, 53, 55, 59, 65] [11, 14, 15, 34, 40, 50, 52, 54] [10, 14, 15, 35, 53, 55, 57, 67] [7, 11, 16, 36, 46, 52, 56, 58] [6, 10, 17, 37, 57, 59, 63, 69] [5, 9, 18, 38, 44, 54, 56, 58] [4, 8, 19, 39, 57, 59, 61, 71] [0, 1, 5, 20, 50, 56, 60, 62] [0, 1, 4, 21, 61, 63, 67, 73] [2, 3, 7, 22, 48, 58, 60, 62] [2, 3, 6, 23, 61, 63, 65, 75] [3, 4, 24, 39, 54, 60, 64, 66] [2, 5, 25, 38, 65, 67, 71, 77] [1, 6, 26, 37, 52, 62, 64, 66] [0, 7, 27, 36, 65, 67, 69, 79] [8, 28, 33, 37, 58, 64, 68, 70] [9, 29, 32, 36, 41, 69, 71, 75] [10, 30, 35, 39, 56, 66, 68, 70] [11, 31, 34, 38, 43, 69, 71, 73] [12, 31, 32, 35, 62, 68, 72, 74] [13, 30, 33, 34, 45, 73, 75, 79] [14, 29, 33, 34, 60, 70, 72, 74] [15, 28, 32, 35, 47, 73, 75, 77] [16, 25, 29, 36, 66, 72, 76, 78] [17, 24, 28, 37, 43, 49, 77, 79] [18, 27, 31, 38, 64, 74, 76, 78] [19, 26, 30, 39, 41, 51, 77, 79]

H_Z (40 checks, sparse supports)

[0, 2, 4, 14, 40, 60, 61, 67] [1, 3, 29, 39, 41, 60, 61, 66] [0, 2, 6, 12, 42, 62, 63, 65] [1, 3, 31, 37, 43, 62, 63, 64] [4, 6, 8, 18, 44, 59, 61, 64] [3, 5, 7, 33, 45, 58, 60, 65] [4, 6, 10, 16, 46, 57, 63, 66] [1, 5, 7, 35, 47, 56, 62, 67] [8, 10, 12, 22, 48, 53, 59, 68] [7, 9, 11, 37, 49, 52, 58, 69] [8, 10, 14, 20, 50, 55, 57, 70] [5, 9, 11, 39, 51, 54, 56, 71] [12, 14, 16, 26, 51, 52, 53, 72] [1, 11, 13, 15, 50, 52, 53, 73] [12, 14, 18, 24, 49, 54, 55, 74] [3, 9, 13, 15, 48, 54, 55, 75] [16, 18, 20, 30, 45, 51, 56, 76] [5, 15, 17, 19, 44, 50, 57, 77] [16, 18, 22, 28, 47, 49, 58, 78] [7, 13, 17, 19, 46, 48, 59, 79] [20, 22, 24, 34, 40, 43, 45, 60] [9, 19, 21, 23, 41, 42, 44, 61] [20, 22, 26, 32, 41, 42, 47, 62] [11, 17, 21, 23, 40, 43, 46, 63] [24, 26, 28, 38, 43, 44, 64, 77] [13, 23, 25, 27, 42, 45, 65, 76] [24, 26, 30, 36, 41, 46, 66, 79] [15, 21, 25, 27, 40, 47, 67, 78] [2, 28, 30, 32, 48, 68, 75, 77] [17, 27, 29, 31, 49, 69, 74, 76] [0, 28, 30, 34, 50, 70, 73, 79] [19, 25, 29, 31, 51, 71, 72, 78] [6, 32, 34, 36, 52, 69, 72, 75] [21, 31, 33, 35, 53, 68, 73, 74] [4, 32, 34, 38, 54, 71, 73, 74] [23, 29, 33, 35, 55, 70, 72, 75] [0, 10, 36, 38, 56, 67, 69, 76] [25, 35, 37, 39, 57, 66, 68, 77] [2, 8, 36, 38, 58, 65, 71, 78] [27, 33, 37, 39, 59, 64, 70, 79]

raw submission JSON