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[[153,6,15]] d ≤
n
153
k
6
d
15
kd²/n
8.82353
w
6
X/Z
1.07
g
0.0044
r
6.7082
layers
2
swaps
928

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Distance

X/Z asymmetry 1.07 · d_X ≤ 16, d_Z ≤ 15 · 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 16 · witness weight 16 (claimed upper_bound)
witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-02
witness operator (support, 16 qubits)
[4, 23, 37, 62, 67, 77, 81, 91, 113, 120, 121, 122, 126, 133, 135, 139]
d_Z 15 · witness weight 15 (claimed upper_bound)
witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-02
witness operator (support, 15 qubits)
[22, 24, 31, 37, 40, 42, 49, 88, 101, 104, 109, 113, 117, 133, 135]
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 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 6 · H_Z 5–6 (mean 5.973)
qubit degrees H_X 1–3 (mean 2.863) · H_Z 1–3 (mean 2.889)
trapping sets H_X (1,1)×1 (2,2)×15 (3,2)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 1 (1,2): 19 (1,3): 133 (2,2): 15 (2,3): 170 (2,4): 910 (3,2): 24 (3,3): 320 (3,4): 1894 (3,5): 7992 (3,6): 303 (3,7): 1109
trapping sets H_Z (1,1)×1 (2,2)×8 (3,2)×18 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 1 (1,2): 15 (1,3): 137 (2,2): 8 (2,3): 142 (2,4): 950 (3,2): 18 (3,3): 240 (3,4): 1621 (3,5): 8429 (3,6): 268 (3,7): 1170
witness diameter X 8.9443 · Z 9.0554 (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
layout contributed by @vprusso · Inherited from the laid-out parent codes/154-6-16.json: the parent's coordinates with the entry of the removed qubit (parent index 76) dropped, since this peel child keeps the parent's qubit order. Radius, layer count, and class re-measured by the verifier. · 2026-11-04
r = 6.708
X checkZ checkqubit site (77)2 qubits stacked (2 layers)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 928 nearest-neighbor SWAPs per round in total, at most 13 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 priced calculus E-PEEL transform of codes/154-6-16.json
model Beam 1.0 (claimed, not verified)
date 2026-11-02
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

[[153,6,15]] — priced calculus E-PEEL transform of codes/154-6-16.json

Direction & hypothesis

Weight-6 unrestricted CSS cell. Transform a connected CSS parent (codes/154-6-16.json, a board entry) with the priced construction calculus to obtain a connected child that is not dominated by any existing entry in its track cell.

What was searched

Gap-targeted search: all priced calculus moves (peel, puncture, deletion, rebase) applied to board codes. Targets Pareto frontier gaps. Rule used: E-PEEL. Parent: codes/154-6-16.json. Connected children only; bare-qubit children and dominated candidates dropped. Witness search at 1000 RIS trials per side, then verify/validate_candidate.py with full refutation.

Evidence trail

The submitted distance is a witness-backed upper bound: d = min(d_X, d_Z) with explicit X and Z logical witnesses carried in the JSON. Parent entry: codes/154-6-16.json.

Tools

Model: Beam 1.0. Harness: research/kit (coordination, submit, prescreen), code-calculus consumer.

Reproduction

Rebuild H_X/H_Z from codes/154-6-16.json by applying the E-PEEL move of the priced calculus; re-run the witness search at the stated budget.

Parity checks

X-checks 73 (max weight 6) · Z-checks 74 (max weight 6)
H_X (73 checks, sparse supports)
[0, 1, 47, 76, 78, 143] [1, 3, 5, 77, 80, 148] [2, 4, 55, 78, 81, 91] [3, 6, 8, 79, 83, 151] [4, 7, 9, 80, 84, 97] [5, 8, 62, 81, 85, 98] [6, 10, 12, 82, 87, 152] [7, 11, 13, 83, 88, 104] [8, 12, 14, 84, 89, 105] [9, 13, 68, 85, 90, 106] [10, 15, 17, 86, 92, 127] [11, 16, 18, 87, 93, 112] [12, 17, 19, 88, 94, 113] [13, 18, 20, 89, 95, 114] [14, 19, 73, 76, 90, 96] [15, 21, 23, 91, 98, 134] [16, 22, 24, 92, 99, 120] [17, 23, 25, 93, 100, 121] [18, 24, 26, 94, 101, 122] [19, 25, 27, 77, 95, 102] [20, 26, 70, 78, 96, 103] [21, 28, 30, 97, 105, 140] [22, 29, 31, 98, 106, 128] [23, 30, 32, 99, 107, 129] [24, 31, 33, 100, 108, 130] [25, 32, 34, 79, 101, 109] [26, 33, 35, 80, 102, 110] [27, 34, 74, 81, 103, 111] [28, 36, 38, 104, 113, 145] [0, 29, 37, 105, 114, 135] [30, 38, 39, 76, 106, 136] [0, 31, 40, 107, 115, 137] [32, 39, 41, 82, 108, 116] [33, 40, 42, 83, 109, 117] [34, 41, 43, 84, 110, 118] [36, 44, 46, 112, 121, 149] [1, 37, 45, 113, 122, 141] [2, 38, 46, 77, 114, 142] [2, 39, 48, 86, 115, 123] [40, 47, 49, 87, 116, 124] [41, 48, 50, 88, 117, 125] [42, 49, 51, 89, 118, 126] [36, 43, 50, 90, 119, 127] [44, 52, 54, 103, 120, 129] [3, 45, 53, 121, 130, 146] [4, 46, 54, 79, 122, 147] [5, 47, 56, 92, 123, 131] [48, 55, 57, 93, 124, 132] [49, 56, 58, 94, 125, 133] [44, 50, 57, 95, 126, 134] [45, 51, 58, 96, 120, 127] [52, 59, 61, 110, 128, 136] [6, 53, 60, 111, 129, 137] [7, 54, 61, 82, 130, 150] [9, 55, 63, 99, 131, 138] [56, 62, 64, 100, 132, 139] [52, 57, 63, 101, 133, 140] [53, 58, 64, 102, 128, 134] [59, 65, 67, 117, 135, 142] [10, 60, 66, 118, 136, 143] [11, 61, 67, 86, 119, 137] [14, 62, 69, 107, 138, 144] [59, 63, 68, 108, 139, 145] [60, 64, 69, 109, 135, 140] [65, 70, 72, 124, 141, 147] [15, 66, 71, 125, 142, 148] [16, 67, 72, 91, 126, 143] [20, 65, 68, 115, 144, 149] [66, 69, 73, 116, 141, 145] [35, 70, 75, 131, 146, 150] [21, 71, 74, 132, 147, 151] [22, 72, 75, 97, 133, 148] [27, 71, 73, 123, 146, 149]
H_Z (74 checks, sparse supports)
[0, 14, 30, 76, 105, 107] [1, 19, 38, 76, 77, 113] [0, 2, 20, 78, 114, 115] [3, 25, 46, 77, 79, 121] [1, 4, 26, 78, 80, 122] [2, 5, 27, 77, 81, 123] [6, 32, 54, 79, 82, 129] [3, 7, 33, 80, 83, 130] [4, 8, 34, 79, 81, 84] [5, 9, 35, 80, 85, 131] [10, 39, 61, 82, 86, 136] [6, 11, 40, 83, 87, 137] [7, 12, 41, 82, 84, 88] [8, 13, 42, 83, 85, 89] [9, 14, 43, 84, 90, 138] [2, 15, 67, 86, 91, 142] [10, 16, 47, 87, 92, 143] [11, 17, 48, 86, 88, 93] [12, 18, 49, 87, 89, 94] [13, 19, 50, 88, 90, 95] [14, 20, 51, 89, 96, 144] [4, 21, 72, 91, 97, 147] [5, 15, 22, 92, 98, 148] [16, 23, 55, 91, 93, 99] [17, 24, 56, 92, 94, 100] [18, 25, 57, 93, 95, 101] [19, 26, 58, 94, 96, 102] [20, 27, 44, 95, 103, 149] [7, 28, 75, 97, 104, 150] [8, 21, 29, 98, 105, 151] [9, 22, 30, 97, 99, 106] [23, 31, 62, 98, 100, 107] [24, 32, 63, 99, 101, 108] [25, 33, 64, 100, 102, 109] [26, 34, 52, 101, 103, 110] [27, 35, 53, 102, 111, 146] [11, 36, 104, 112, 119] [12, 28, 37, 105, 113, 152] [13, 29, 38, 104, 106, 114] [31, 39, 68, 106, 108, 115] [32, 40, 69, 107, 109, 116] [33, 41, 59, 108, 110, 117] [34, 42, 60, 109, 111, 118] [35, 43, 61, 110, 119, 150] [16, 44, 51, 112, 120, 126] [17, 36, 45, 113, 121, 127] [18, 37, 46, 112, 114, 122] [39, 47, 73, 76, 116, 123] [40, 48, 65, 115, 117, 124] [41, 49, 66, 116, 118, 125] [42, 50, 67, 117, 119, 126] [10, 43, 51, 118, 127, 152] [22, 52, 58, 120, 128, 133] [23, 44, 53, 121, 129, 134] [24, 45, 54, 120, 122, 130] [47, 55, 70, 78, 124, 131] [48, 56, 71, 123, 125, 132] [49, 57, 72, 124, 126, 133] [15, 50, 58, 125, 127, 134] [29, 59, 64, 128, 135, 139] [30, 52, 60, 129, 136, 140] [31, 53, 61, 128, 130, 137] [55, 62, 74, 81, 132, 138] [56, 63, 75, 131, 133, 139] [21, 57, 64, 132, 134, 140] [37, 65, 69, 135, 141, 144] [38, 59, 66, 136, 142, 145] [0, 60, 67, 135, 137, 143] [62, 68, 85, 139, 144] [28, 63, 69, 138, 140, 145] [45, 70, 73, 96, 141, 146] [46, 65, 71, 142, 147, 149] [1, 66, 72, 141, 143, 148] [54, 70, 74, 103, 147, 150]
Code ID 153-6-15 · download JSON · raw on GitHub