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[[11,3,3]] d ≤
n
11
k
3
d
3
kd²/n
2.45455
w
6
X/Z
1
g
0.0982
r
3.1623
layers
1
swaps
8

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Distance

X/Z asymmetry 1 · d_X ≤ 3, d_Z ≤ 3 · w_X = 6, 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 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[0, 3, 4]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[0, 1, 5]
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 4–6 (mean 5.5) · H_Z 5
qubit degrees H_X 1–3 (mean 2.0) · H_Z 1–3 (mean 1.818)
trapping sets H_X (1,1)×3 (2,1)×15 (3,0)×13 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 3 (1,2): 5 (1,3): 3 (2,1): 15 (2,2): 18 (2,3): 8 (3,0): 13 (3,1): 40 (3,2): 46 (3,3): 24 (3,4): 10
trapping sets H_Z (1,1)×4 (2,1)×14 (3,0)×12 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 4 (1,2): 5 (1,3): 2 (2,1): 14 (2,2): 15 (2,3): 6 (3,0): 12 (3,1): 36 (3,2): 36 (3,3): 18 (3,4): 8
witness diameter X 2.0 · Z 3.0 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Circuit tier

syndrome-extraction memory circuits committed under circuits/11-3-3-h/ · canonical noise recipe, 3 rounds, stim 1.16.0
d_circ ≤ 3 (min over bases; penalty-only, clamped to ≤ d)
d_circ^X 3 · fault-set witness of 3 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 3)
[8, 31, 100]
d_circ^Z 3 · fault-set witness of 3 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 3)
[0, 57, 144]
no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
layout contributed by @dorakingx · Simulated annealing over site assignments on an integer grid with the repo's own research/local2d/fold_layout.search_layout (max-diameter objective, several bounding boxes and seeds); single layer at radius 4 tried first, then two layers at 7. Radius and per-site occupancy re-measured with the verifier's rule. · 2026-09-26
r = 3.162
X checkZ checkqubit site (11)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 8 nearest-neighbor SWAPs per round in total, at most 3 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction E-PEEL q=9 X from 12-3-3.json
model Beam 1.0 (claimed, not verified)
date 2026-10-24
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. The layout is inherited from the parent and restricted to the qubits the child kept.
family other (a tag, not a ranking)
locality 2D-local single (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

[[11,3,3]] — priced-calculus E-PEEL

Direction & hypothesis

Aimed at the weight-6 / 2d-local track cell. Parent 12-3-3.json was transformed by a single E-PEEL move of the priced construction calculus; disconnected Tanner-graph instances were discarded and fresh X/Z logical witnesses were found.

What was searched

Single-move E-PEEL sweep over the qubits/checks of 12-3-3.json. Survivors were screened for X and Z logical witnesses up to weight 4 and validated with verify/validate_candidate.py.

Evidence trail

Witness-backed upper bounds: d_X <= 3, d_Z <= 3, so d <= 3. Validated by the challenge verifier (distance_not_refuted).

Dead ends

Instances that disconnected the Tanner graph or failed to yield witnesses were discarded. Other parents in the same sweep produced only dominated or d=1 codes.

Tools

Model: Beam 1.0. Priced construction calculus consumer (E-PEEL cell). Challenge verifier verify/qldpc_verify.py.

Reproduction

Parent: 12-3-3.json. Operation: E-PEEL q=9 X from 12-3-3.json. Witnesses as stored in the entry.

Parity checks

X-checks 4 (max weight 6) · Z-checks 4 (max weight 5)
H_X (4 checks, sparse supports)
[0, 2, 3, 4, 5, 7] [3, 6, 7, 10] [1, 4, 5, 6, 8, 10] [0, 1, 3, 4, 9, 10]
H_Z (4 checks, sparse supports)
[2, 7, 8, 9, 10] [0, 3, 5, 7, 8] [0, 2, 4, 6, 7] [0, 1, 3, 6, 9]
Code ID 11-3-3-h · download JSON · raw on GitHub