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[[36,8,4]] d =
n
36
k
8
d
4
kd²/n
3.556
w
6
X/Z
1
g
0.0556
r
4.0
layers
1
swaps
46

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Distance

X/Z asymmetry 1 · d_X = 4, d_Z = 4 · 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 4 · witness weight 4 (claimed upper_bound)
witness operator (support, 4 qubits)
[13, 14, 15, 22]
d_Z 4 · witness weight 4 (claimed upper_bound)
witness operator (support, 4 qubits)
[14, 25, 31, 32]
certificate exact, d = 4 · scipy/HiGHS MILP
X: no logical < 4 exists; Z: no logical < 4 exists

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 5.643) · H_Z 4–6 (mean 5.429)
qubit degrees H_X 1–5 (mean 2.194) · H_Z 1–4 (mean 2.111)
trapping sets H_X (1,1)×9 (2,1)×21 (3,1)×100 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 9 (1,2): 15 (1,3): 9 (1,4): 2 (1,5): 1 (2,1): 21 (2,2): 53 (2,3): 54 (2,4): 19 (2,5): 9 (2,6): 4 (2,7): 2 (3,1): 100 (3,2): 183 (3,3): 228 (3,4): 205 (3,5): 125 (3,6): 66 (3,7): 28 (3,8): 11
trapping sets H_Z (1,1)×7 (2,1)×27 (3,1)×87 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 7 (1,2): 19 (1,3): 9 (1,4): 1 (2,1): 27 (2,2): 55 (2,3): 53 (2,4): 21 (2,5): 2 (3,1): 87 (3,2): 200 (3,3): 274 (3,4): 222 (3,5): 97 (3,6): 22 (3,7): 4
witness diameter X 3.1623 · Z 3.1623 (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 = 4
X checkZ checkqubit site (36)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 46 nearest-neighbor SWAPs per round in total, at most 5 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 novelty not audited
construction SAT search (local_sat, n_side=6, G=14, max_weight=6, t=3 detection, radius 2.0, shared_t3) over 2D-local CSS codes on a 6x6 grid; found a weight-6 code with k=8, d>=4.
model DeepSeek V4 Flash 0731 (claimed, not verified)
date 2026-09-18
notes Checked against the current board: the trusted gate's dedup found no exact duplicate and no WL-equivalent existing entry; this is a new SAT-found code, not equivalent to a prior submission.
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

[[36,8,4]] — SAT t=3 weight-6 2D-local code on a 6×6 grid

Direction & hypothesis

Hackathon (#1155) SAT-search. The 2026-09-18 t=2 session placed [[16,6,3]], [[25,9,3]], [[36,12,3]] (d=3) on the weight-6 × local-2d-single frontier. The higher-distance rung — t=3 detection (d≥4) — was budget-walled in-session. This code is the night campaign's T2 result: a t=3 weight-6 code at n=36 with k=8, d=4, which beats the existing [[36,6,4]] on k (8 vs 6) at the same n, d, w.

What was searched

local_sat.py `enumerate_local_sat_codes(n_side=6, G=14, w=6, t=3, radius=2.0, shared_t3=True, solver="cadical")`, run overnight with per-solve conf/time budgets. G=12 and G=13 were UNSAT (too few checks to satisfy t=3 detection); G=14 produced [[36,8,4]] codes. Screened at 800-trial RIS d≥4, dominance-checked against the current single-layer w≤6 board, and gate-packaged.

Evidence trail

Witness-backed upper_bound d=4 (weight-4 logicals on both sides). validate_candidate: passed=true, verify.ok=true, refute.refuted=false (no lighter logical in the gate's RIS trials), dedup clean, board_advancing=true. Independent deep confirmation at 100,000 RIS trials found no logical lighter than weight 4 on either side (lightest X-logical weight 4, lightest Z-logical weight 4), so the d=4 claim is robust. Interaction radius 4.00 (hackathon-eligible).

Dead ends

5×5 (n=25) t=3 w6 at G=10,11,12 produced no new point (only the existing [[25,5,4]] and dominated [[25,4,4]]) — that cell is closed. 6×6 t=3 at G=12,13 is UNSAT.

Tools

local_sat.py (shared_t3, cadical, per-solve budgets), kit {css,surrogate,submit}, verify/validate_candidate.py (untouched). Model: DeepSeek V4 Flash 0731.

Reproduction

from local_sat import enumerate_local_sat_codes
gen = enumerate_local_sat_codes(6, 14, 6, 3, 2.0, seed=0, max_codes=80,
    solver="cadical", conf_budget=1_000_000, time_budget=600.0,
    stream=True, shared_t3=True)
# pick a k=8, d>=4 code, package with make_submission(coordinates=..., layers=1)

Parity checks

X-checks 14 (max weight 6) · Z-checks 14 (max weight 6)
H_X (14 checks, sparse supports)
[3, 8, 13, 16, 17, 22] [1, 3, 4, 5, 9, 10] [1, 6, 13, 18, 20] [0, 6, 7, 19, 24] [1, 7, 12, 18, 20] [19, 20, 21, 24, 25, 31] [14, 19, 20, 28, 32, 33] [21, 26, 27, 31, 32, 35] [4, 5, 11, 17] [15, 20, 22, 27, 28, 29] [5, 10, 11, 16, 23, 29] [24, 26, 30, 31, 32, 33] [2, 4, 7, 9, 15, 16] [27, 31, 32, 33, 34, 35]
H_Z (14 checks, sparse supports)
[1, 6, 7, 9] [0, 2, 7, 12] [7, 8, 13, 15, 19, 20] [19, 24, 25, 26, 31, 33] [3, 5, 15, 16, 17, 22] [6, 12, 18, 24, 25, 30] [9, 10, 11, 16, 17, 23] [2, 3, 10, 16] [8, 14, 18, 20, 22, 25] [21, 27, 28, 31, 32, 34] [18, 20, 25, 27, 30, 32] [23, 26, 28, 29, 33, 35] [32, 33, 34, 35] [4, 10, 11, 14, 15, 28]
Code ID 36-8-4 · download JSON · raw on GitHub