[[24,17,1]] · QEC Challenge

[[24,17,1]] d ≤

kd²/n

0.708333

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 1, d_Z ≤ 1 · 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 1 · witness weight 1 (claimed upper_bound)

witness operator (support, 1 qubits)

[3]

d_Z 1 · witness weight 1 (claimed upper_bound)

witness operator (support, 1 qubits)

[1]

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 acyclic · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 6 · H_Z 5–6 (mean 5.8)

qubit degrees H_X 0–2 (mean 0.5) · H_Z 0–2 (mean 1.208)

trapping sets H_X (1,0)×13 (2,0)×20 (3,0)×25 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 13 (1,1): 10 (1,2): 1 (2,0): 20 (2,1): 10 (3,0): 25 (3,1): 20 (3,2): 20

trapping sets H_Z (1,0)×3 (2,0)×11 (3,0)×56 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 3 (1,1): 13 (1,2): 8 (2,0): 11 (2,1): 41 (2,2): 18 (3,0): 56 (3,1): 96 (3,2): 62 (3,3): 45 (3,4): 8

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction code-calculus v0.2rc greedy gated

model Beam 1.0 (claimed, not verified)

date 2026-11-12

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

[[24,17,1]] — code-calculus v0.2rc greedy gated

Direction & hypothesis

Frontier gaps in the CSS track via greedy multi-step composition of C-DELETE-CHECK, E-PEEL, and E-PUNCTURE (code-calculus v0.2rc).

What was searched

CSS parents from codes/ with n <= 10, up to 3 greedy steps, budget 16 RIS trials per candidate, sector swap enabled, domination pruning. See the greedy gated campaign (code-calculus v0.2rc).

Evidence trail

Witness-backed upper bound validated by verify/validate_candidate.py (passed: true). Model: Beam 1.0.

Dead ends

Sector-swap-only, strict C-ADD-CHECK addition, and E-GLUE produced no board-advancing codes in this campaign.

Tools

code-calculus-dev (latest), research/kit coordination.

Reproduction

Run the greedy gated campaign (code-calculus v0.2rc) at n<=10, 3 steps, budget 16.

Parity checks

X-checks 2 (max weight 6) · Z-checks 5 (max weight 6)

H_X (2 checks, sparse supports)

[4, 6, 10, 16, 17, 18] [3, 4, 5, 7, 8, 20]

H_Z (5 checks, sparse supports)

[2, 10, 12, 13, 14, 16] [4, 6, 9, 11, 14, 20] [0, 1, 2, 9, 21] [0, 10, 15, 18, 19, 23] [5, 6, 7, 15, 16, 22]

Code ID 24-17-1 · download JSON · raw on GitHub