[[36,21,1]] · QEC Challenge

[[36,21,1]] d ≤

kd²/n

0.583333

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 1, d_Z ≤ 1 · w_X = 5, w_Z = 5 (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)

[29]

d_Z 1 · witness weight 1 (claimed upper_bound)

witness operator (support, 1 qubits)

[16]

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 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 5 · H_Z 5

qubit degrees H_X 0–2 (mean 1.111) · H_Z 0–2 (mean 0.972)

trapping sets H_X (1,0)×7 (2,0)×13 (3,0)×45 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 7 (1,1): 18 (1,2): 11 (2,0): 13 (2,1): 46 (2,2): 21 (3,0): 45 (3,1): 97 (3,2): 67 (3,3): 39 (3,4): 8

trapping sets H_Z (1,0)×9 (2,0)×19 (3,0)×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): 9 (1,1): 19 (1,2): 8 (2,0): 19 (2,1): 38 (2,2): 13 (3,0): 40 (3,1): 80 (3,2): 49 (3,3): 24 (3,4): 5

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 https://qecdb.org/codes/67a4b0149edf81e4b7e670ae (isomorphic record; research/provenance/derived.json)

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

[[36,21,1]] — 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 8 (max weight 5) · Z-checks 7 (max weight 5)

H_X (8 checks, sparse supports)

[12, 22, 28, 30, 35] [0, 2, 7, 31, 35] [3, 9, 26, 29, 32] [8, 14, 21, 23, 28] [6, 14, 18, 24, 29] [3, 4, 20, 22, 27] [5, 11, 17, 18, 30] [10, 23, 26, 31, 34]

H_Z (7 checks, sparse supports)

[9, 15, 16, 25, 32] [4, 17, 18, 20, 24] [11, 15, 22, 27, 30] [9, 21, 23, 26, 33] [0, 1, 10, 13, 31] [13, 20, 21, 22, 28] [7, 16, 19, 31, 34]

Code ID 36-21-1 · download JSON · raw on GitHub