[[32,24,1]] · QEC Challenge

[[32,24,1]] d ≤

kd²/n

0.75

X/Z

Share this result

Distance

X/Z asymmetry 3 · d_X ≤ 1, d_Z ≤ 3 · w_X = 12, 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)

[27]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[22, 26, 28]

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

check weights H_X 6–12 (mean 10.0) · H_Z 6

qubit degrees H_X 1–5 (mean 1.875) · H_Z 0–1 (mean 0.375)

trapping sets H_X (1,1)×18 (2,0)×30 (3,0)×40 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 18 (1,2): 8 (1,4): 4 (1,5): 2 (2,0): 30 (2,1): 48 (2,2): 17 (2,3): 72 (2,4): 66 (2,5): 8 (3,0): 40 (3,1): 250 (3,2): 784 (3,3): 764 (3,4): 308 (3,5): 196 (3,6): 52

trapping sets H_Z (1,0)×20 (2,0)×30 (3,1)×40 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 20 (1,1): 12 (2,0): 30 (3,1): 40

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 > 8 (computed)

How this code was found

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

[[32,24,1]] — 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 6 (max weight 12) · Z-checks 2 (max weight 6)

H_X (6 checks, sparse supports)

[15, 16, 17, 18, 19, 20] [21, 22, 23, 24, 25, 26] [0, 1, 5, 6, 10, 11, 15, 16, 21, 22, 27, 28] [0, 2, 5, 7, 10, 12, 15, 17, 21, 23, 27, 29] [0, 3, 5, 8, 10, 13, 15, 18, 21, 24, 27, 30] [0, 4, 5, 9, 10, 14, 15, 19, 21, 25, 27, 31]

H_Z (2 checks, sparse supports)

[15, 16, 17, 18, 19, 20] [21, 22, 23, 24, 25, 26]

Code ID 32-24-1 · download JSON · raw on GitHub