[[128,52,2]] · QEC Challenge

[[128,52,2]] d ≤

128

kd²/n

1.625

X/Z

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Distance

X/Z asymmetry 1 · d_X ≤ 2, d_Z ≤ 2 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 2 · witness weight 2 (claimed upper_bound)

witness operator (support, 2 qubits)

[124, 125]

d_Z 2 · witness weight 2 (claimed upper_bound)

witness operator (support, 2 qubits)

[17, 33]

certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 6 · H_Z 6

qubit degrees H_X 1–3 (mean 1.688) · H_Z 1–3 (mean 1.875)

trapping sets H_X (1,1)×56 (2,0)×32 (3,0)×128 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,1): 56 (1,2): 56 (1,3): 16 (2,0): 32 (2,1): 160 (2,2): 244 (2,3): 72 (2,4): 4 (3,0): 128 (3,1): 704 (3,2): 816 (3,3): 616 (3,4): 264 (3,5): 56 (3,6): 8

trapping sets H_Z (1,1)×48 (2,0)×64 (3,0)×128 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,1): 48 (1,2): 48 (1,3): 32 (2,0): 64 (2,1): 128 (2,2): 160 (2,3): 96 (2,4): 64 (3,0): 128 (3,1): 288 (3,2): 688 (3,3): 816 (3,4): 448 (3,5): 192

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction code-calculus v0.2rc C-DELETE-CHECK

model Beam 1.0 (claimed, not verified)

date 2026-11-13

notes Generated by the priced construction calculus. Distance is reported only with witness-backed upper bounds; lower interval bounds are kept in the separate local ledger.

family other (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight ≤ 6 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[128,52,2]] greedy 3 from 128-48-2

Direction & hypothesis

Unrestricted-weight CSS parents with 99 <= n <= 400, searched with the priced construction calculus (code-calculus v0.2rc) greedy multi-step composition. The rule used on this step is C-DELETE-CHECK.

What was searched

Greedy multi-step composition of C-DELETE-CHECK / E-PEEL / E-PUNCTURE with sector-targeted planning, sector swap, bounded support search, and Pareto ranking. This candidate is step 3 of a chain from codes/128-48-2.json (target sector X).

Evidence trail

Staged deep-verify (2k -> 20k -> 200k -> 2M trials, multi-seed) kept the screened distance unchanged; the witness-backed upper bound is d_X <= 2, d_Z <= 2. No downgrade at any depth.

Dead ends

Parents whose display carries a dependent generator produce no derivable child; candidates whose deep-verified slug collides with an existing board entry are skipped.

Tools

Model: Beam 1.0. Harness: code-calculus v0.2rc greedy gated campaign with the verifier's staged deep-verify used before submission.

Reproduction

Start from codes/128-48-2.json, apply C-DELETE-CHECK on the target sector, and repeat greedily with Pareto ranking and staged deep-verify.

Parity checks

X-checks 36 (max weight 6) · Z-checks 40 (max weight 6)

H_X (36 checks, sparse supports)

[0, 2, 64, 66, 115, 127] [1, 22, 64, 65, 71, 76] [3, 12, 67, 76, 124, 125] [4, 13, 65, 68, 77, 86] [5, 14, 69, 73, 78, 106] [6, 15, 70, 79, 93, 121] [7, 8, 66, 67, 72, 86] [9, 42, 68, 73, 87, 96] [10, 43, 69, 74, 88, 97] [11, 44, 70, 75, 89, 98] [16, 32, 71, 72, 80, 96] [17, 33, 81, 87, 90, 97] [18, 34, 82, 98, 109, 112] [19, 35, 74, 83, 99, 107] [20, 36, 75, 84, 100, 108] [21, 37, 85, 94, 101, 122] [23, 26, 77, 80, 90, 106] [24, 27, 78, 81, 91, 107] [25, 28, 79, 82, 92, 108] [29, 57, 83, 93, 109, 116] [30, 58, 84, 94, 110, 117] [31, 59, 85, 95, 111, 118] [38, 52, 88, 91, 102, 116] [39, 53, 89, 92, 103, 117] [40, 54, 104, 110, 113, 118] [41, 55, 95, 105, 119, 123] [45, 48, 83, 93, 109, 116] [46, 49, 84, 94, 110, 117] [47, 50, 85, 95, 111, 118] [45, 48, 99, 102, 112, 121] [46, 49, 100, 103, 113, 122] [47, 50, 101, 104, 114, 123] [51, 63, 105, 115, 124, 126] [56, 62, 111, 114, 120, 126] [60, 61, 105, 115, 124, 126] [60, 61, 119, 120, 125, 127]

H_Z (40 checks, sparse supports)

[0, 1, 2, 7, 64, 66] [1, 4, 7, 13, 65, 86] [0, 2, 8, 22, 64, 66] [3, 8, 12, 22, 67, 76] [4, 9, 13, 23, 68, 77] [5, 10, 14, 24, 69, 78] [6, 11, 15, 25, 70, 79] [1, 7, 16, 32, 71, 72] [5, 9, 14, 23, 73, 106] [10, 19, 24, 35, 74, 107] [11, 20, 25, 36, 75, 108] [4, 13, 26, 42, 68, 77] [5, 14, 27, 43, 69, 78] [6, 15, 28, 44, 70, 79] [16, 26, 32, 42, 80, 96] [17, 27, 33, 43, 81, 97] [18, 28, 34, 44, 82, 98] [19, 29, 35, 45, 83, 99] [20, 30, 36, 46, 84, 100] [21, 31, 37, 47, 85, 101] [9, 17, 23, 33, 87, 90] [10, 24, 38, 52, 88, 91] [11, 25, 39, 53, 89, 92] [6, 15, 29, 45, 93, 121] [21, 30, 37, 46, 94, 122] [31, 41, 47, 55, 95, 123] [19, 35, 48, 57, 83, 99] [20, 36, 49, 58, 84, 100] [21, 37, 50, 59, 85, 101] [38, 48, 52, 57, 102, 116] [39, 49, 53, 58, 103, 117] [40, 50, 54, 59, 104, 118] [41, 51, 55, 60, 105, 119] [18, 29, 34, 45, 109, 112] [30, 40, 46, 54, 110, 113] [31, 47, 56, 62, 111, 114] [0, 2, 51, 60, 115, 127] [41, 55, 61, 63, 105, 119] [56, 61, 62, 63, 120, 126] [3, 12, 51, 60, 124, 125]

Code ID 128-52-2 · download JSON · raw on GitHub