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[[33,7,1]] d ≤
n
33
k
7
d
1
kd²/n
0.212121
w
6
X/Z
7
g
0.0007
r
5.831
layers
1
swaps
168

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Distance

X/Z asymmetry 7 · d_X ≤ 1, d_Z ≤ 7 · w_X = 6, 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 found by @mathysrennela · gf2_fast · found at 2×105 trials · 2026-11-13
witness operator (support, 1 qubits)
[32]
d_Z 7 · witness weight 7 (claimed upper_bound)
witness operator (support, 7 qubits)
[3, 15, 23, 26, 28, 29, 32]
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 6 · H_Z 6
qubit degrees H_X 1–4 (mean 2.545) · H_Z 0–4 (mean 2.182)
trapping sets H_X (1,1)×4 (2,1)×10 (3,0)×2 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 4 (1,2): 15 (1,3): 6 (1,4): 8 (2,1): 10 (2,2): 34 (2,3): 34 (2,4): 61 (2,5): 36 (2,6): 23 (3,0): 2 (3,1): 23 (3,2): 94 (3,3): 203 (3,4): 398 (3,5): 413 (3,6): 326 (3,7): 116 (3,8): 62 (3,9): 21 (3,10): 5
trapping sets H_Z (1,0)×1 (2,0)×1 (3,0)×5 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,0): 1 (1,1): 8 (1,2): 11 (1,3): 10 (1,4): 3 (2,0): 1 (2,1): 16 (2,2): 35 (2,3): 50 (2,4): 42 (2,5): 25 (2,6): 3 (3,0): 5 (3,1): 41 (3,2): 136 (3,3): 284 (3,4): 358 (3,5): 282 (3,6): 135 (3,7): 35 (3,8): 22 (3,9): 4
witness diameter X 0.0 · Z 5.831 (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)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 5.831
X checkZ checkqubit site (33)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 168 nearest-neighbor SWAPs per round in total, at most 9 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 code-calculus v0.2rc greedy gated
model Beam 1.0 (claimed, not verified)
builds on https://qecdb.org/codes/67a42e519d65c7b4098269c3 (isomorphic record; research/provenance/derived.json)
date 2026-11-13
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 bilayer (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

[[33,7,1]] code-calculus v0.2rc greedy gated

Code-calculus v0.2rc greedy gated campaign (cc-distance-raise). Witness-backed upper bound on distance.

Parity checks

X-checks 14 (max weight 6) · Z-checks 12 (max weight 6)
H_X (14 checks, sparse supports)
[2, 11, 18, 19, 21, 27] [5, 9, 21, 25, 26, 28] [6, 10, 22, 26, 27, 29] [7, 11, 23, 27, 28, 30] [8, 12, 24, 28, 29, 31] [1, 13, 17, 29, 30, 32] [0, 14, 16, 18, 30, 31] [9, 15, 19, 25, 31, 32] [3, 12, 19, 20, 22, 28] [4, 13, 20, 21, 23, 29] [5, 14, 21, 22, 24, 30] [6, 15, 17, 22, 23, 31] [2, 8, 17, 18, 24, 25] [1, 3, 16, 17, 19, 26]
H_Z (12 checks, sparse supports)
[6, 12, 14, 15, 22, 31] [0, 1, 7, 14, 16, 30] [0, 8, 9, 15, 25, 31] [0, 2, 10, 11, 18, 27] [3, 9, 11, 12, 19, 28] [4, 10, 12, 13, 20, 29] [5, 11, 13, 14, 21, 30] [1, 2, 3, 15, 17, 19] [2, 4, 5, 9, 21, 25] [3, 5, 6, 10, 22, 26] [4, 6, 7, 11, 23, 27] [5, 7, 8, 12, 24, 28]
Code ID 33-7-1 · download JSON · raw on GitHub