[[36,29,1]] · QEC Challenge

[[36,29,1]] d ≤

kd²/n

0.805556

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 1, d_Z ≤ 1 · w_X = 9, w_Z = 9 (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)

[7]

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

check weights H_X 9 · H_Z 8–9 (mean 8.6)

qubit degrees H_X 0–2 (mean 0.5) · H_Z 0–2 (mean 1.194)

trapping sets H_X (1,0)×20 (2,0)×43 (3,0)×98 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 20 (1,1): 14 (1,2): 2 (2,0): 43 (2,1): 28 (3,0): 98 (3,1): 84 (3,2): 84

trapping sets H_Z (1,0)×5 (2,0)×33 (3,0)×165 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 5 (1,1): 19 (1,2): 12 (2,0): 33 (2,1): 88 (2,2): 38 (3,0): 165 (3,1): 344 (3,2): 246 (3,3): 134 (3,4): 20

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty known parameter set; see provenance notes

construction code-calculus v0.2rc greedy gated

model Beam 1.0 (claimed, not verified)

builds on arXiv:2610.13880

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

[[36,29,1]] — 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 9) · Z-checks 5 (max weight 9)

H_X (2 checks, sparse supports)

[2, 3, 9, 11, 14, 18, 20, 31, 34] [4, 5, 7, 12, 15, 18, 20, 33, 35]

H_Z (5 checks, sparse supports)

[0, 1, 3, 16, 19, 23, 29, 34] [0, 1, 5, 6, 17, 21, 25, 27, 35] [2, 3, 4, 18, 22, 26, 31, 32] [2, 4, 5, 6, 20, 24, 28, 30, 33] [8, 10, 13, 15, 17, 19, 28, 29, 33]

Code ID 36-29-1 · download JSON · raw on GitHub