[[36,23,2]] · QEC Challenge

[[36,23,2]] d ≤

kd²/n

2.55556

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)

[15, 31]

d_Z 2 · witness weight 2 (claimed upper_bound)

witness operator (support, 2 qubits)

[15, 31]

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 1–2 (mean 1.111) · H_Z 1–2 (mean 1.778)

trapping sets H_X (1,1)×32 (2,0)×102 (3,0)×64 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 32 (1,2): 4 (2,0): 102 (2,1): 32 (3,0): 64 (3,1): 224 (3,2): 52

trapping sets H_Z (1,1)×8 (2,0)×54 (3,1)×184 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 8 (1,2): 28 (2,0): 54 (2,1): 32 (2,2): 96 (3,1): 184 (3,2): 684

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

[[36,23,2]] — 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 5 (max weight 8) · Z-checks 8 (max weight 8)

H_X (5 checks, sparse supports)

[0, 1, 16, 17, 18, 19, 34, 35] [2, 4, 6, 9, 20, 22, 24, 27] [3, 5, 7, 10, 21, 23, 25, 28] [7, 10, 12, 14, 25, 28, 30, 32] [8, 11, 13, 15, 26, 29, 31, 33]

H_Z (8 checks, sparse supports)

[0, 1, 2, 4, 18, 19, 20, 22] [2, 4, 6, 9, 20, 22, 24, 27] [3, 5, 7, 10, 21, 23, 25, 28] [3, 5, 6, 9, 21, 23, 24, 27] [7, 10, 12, 14, 25, 28, 30, 32] [8, 11, 13, 15, 26, 29, 31, 33] [8, 11, 12, 14, 26, 29, 30, 32] [13, 15, 16, 17, 31, 33, 34, 35]

Code ID 36-23-2 · download JSON · raw on GitHub