[[30,17,2]] · QEC Challenge

[[30,17,2]] d ≤

kd²/n

2.267

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 2, d_Z ≤ 2 · w_X = 8, w_Z = 8 (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)

[22, 24]

d_Z 2 · witness weight 2 (claimed upper_bound)

witness operator (support, 2 qubits)

[24, 27]

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 8 · H_Z 8

qubit degrees H_X 1–4 (mean 1.6) · H_Z 1–5 (mean 1.867)

trapping sets H_X (1,1)×22 (2,0)×45 (3,0)×75 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 22 (1,2): 3 (1,4): 5 (2,0): 45 (2,1): 30 (2,3): 60 (3,0): 75 (3,1): 174 (3,2): 331 (3,4): 70

trapping sets H_Z (1,1)×22 (2,0)×45 (3,1)×249 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 22 (1,3): 3 (1,5): 5 (2,0): 45 (2,2): 30 (2,4): 60 (2,6): 15 (3,1): 249 (3,3): 361 (3,5): 415

Circuit tier

syndrome-extraction memory circuits committed under circuits/30-17-2/ · canonical noise recipe, 2 rounds, stim 1.16.0

d_circ ≤ 2 (min over bases; penalty-only, clamped to ≤ d)

d_circ^X 2 · fault-set witness of 2 mechanisms (claimed upper_bound)

witness fault set (mechanism indices in the committed .dem, 2)

[1, 2]

d_circ^Z 2 · fault-set witness of 2 mechanisms (claimed upper_bound)

witness fault set (mechanism indices in the committed .dem, 2)

[267, 268]

no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see

Construction & provenance

authors @MathysRennela

provenance submitted through the challenge

novelty novelty not audited

construction C-DELETE-CHECK a1 from 30-16-2.json

model Beam 1.0 (claimed, not verified)

date 2026-10-19

family other (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight ≤ 8 (computed)

How this code was found

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

[[30,17,2]] C-DELETE-CHECK a1 from 30-16-2.json

Direction & hypothesis

Board-advancing code found by the priced construction calculus. Operation: C-DELETE-CHECK applied to a board entry, raising k / lowering check weight while keeping a witness-backed distance. Rule used: C-DELETE-CHECK.

What was searched

A single deletion move on an existing board code, validated by the trusted gate.

Evidence trail

Distance witnesses: X=[25, 27], Z=[18, 29]. The gate's refutation search found no lighter logical.

Dead ends

None recorded for this candidate.

Tools

Model: Beam 1.0. The local verdict is verify/validate_candidate.py.

Reproduction

Reconstruct the parent board code, delete the named check, and recompute n, k, and the witness-backed distance. The resulting checks are the submitted ones.

Parity checks

X-checks 6 (max weight 8) · Z-checks 7 (max weight 8)

H_X (6 checks, sparse supports)

[0, 1, 3, 16, 19, 22, 25, 28] [2, 4, 6, 15, 17, 20, 23, 26] [0, 1, 3, 18, 21, 24, 27, 29] [5, 7, 9, 15, 17, 20, 23, 26] [8, 10, 12, 15, 17, 20, 23, 26] [11, 13, 14, 15, 17, 20, 23, 26]

H_Z (7 checks, sparse supports)

[0, 2, 5, 8, 11, 15, 16, 18] [1, 4, 7, 10, 13, 15, 16, 18] [0, 2, 5, 8, 11, 17, 19, 21] [3, 6, 9, 12, 14, 15, 16, 18] [0, 2, 5, 8, 11, 20, 22, 24] [0, 2, 5, 8, 11, 23, 25, 27] [0, 2, 5, 8, 11, 26, 28, 29]

Code ID 30-17-2 · download JSON · raw on GitHub