[[63,22,5]] · QEC Challenge

[[63,22,5]] d ≤

kd²/n

8.73016

X/Z

1.4

Share this result

Distance

X/Z asymmetry 1.4 · d_X ≤ 7, d_Z ≤ 5 · w_X = 16, w_Z = 16 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 7 · witness weight 7 (claimed upper_bound)

witness found by @vprusso · research/kit/surrogate.lightest_logical · found at 2000 trials · survived 2000 trials · 2026-11-03

witness operator (support, 7 qubits)

[2, 10, 26, 38, 46, 53, 61]

d_Z 5 · witness weight 5 (claimed upper_bound)

witness found by @vprusso · research/kit/surrogate.lightest_logical · found at 2000 trials · survived 2000 trials · 2026-11-03

witness operator (support, 5 qubits)

[8, 21, 37, 41, 56]

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 15–16 (mean 15.6) · H_Z 16

qubit degrees H_X 2–8 (mean 4.952) · H_Z 1–8 (mean 5.333)

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

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

(1,2): 3 (1,3): 9 (1,4): 10 (1,5): 18 (1,6): 15 (1,7): 5 (1,8): 3 (2,1): 2 (2,2): 6 (2,3): 24 (2,4): 70 (2,5): 157 (2,6): 248 (2,7): 327 (2,8): 258 (2,9): 202 (2,10): 97 (2,11): 28 (2,12): 6 (2,13): 3 (3,1): 2 (3,2): 25 (3,3): 155 (3,4): 489 (3,5): 1329 (3,6): 2929 (3,7): 4603 (3,8): 5809 (3,9): 5878 (3,10): 4752 (3,11): 3149 (3,12): 1629 (3,13): 635 (3,14): 172 (3,15): 38 (3,16): 4 (3,17): 2

trapping sets H_Z (1,1)×1 (2,2)×3 (3,1)×4 (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 (1,3): 6 (1,4): 12 (1,5): 15 (1,6): 14 (1,7): 10 (1,8): 5 (2,2): 3 (2,3): 17 (2,4): 42 (2,5): 117 (2,6): 212 (2,7): 303 (2,8): 289 (2,9): 247 (2,10): 145 (2,11): 82 (2,12): 25 (2,13): 6 (3,1): 4 (3,2): 8 (3,3): 70 (3,4): 324 (3,5): 912 (3,6): 2086 (3,7): 3693 (3,8): 5275 (3,9): 6014 (3,10): 5655 (3,11): 4336 (3,12): 2616 (3,13): 1235 (3,14): 497 (3,15): 134 (3,16): 31 (3,17): 3

Circuit tier

syndrome-extraction memory circuits committed under circuits/63-22-5/ · canonical noise recipe, 5 rounds, stim 1.16.0

d_circ ≤ 5 (min over bases; penalty-only, clamped to ≤ d)

d_circ^X 5 · fault-set witness of 5 mechanisms (claimed upper_bound)

witness fault set (mechanism indices in the committed .dem, 5)

[25701, 25728, 25776, 25806, 29890]

d_circ^Z 5 · fault-set witness of 5 mechanisms (claimed upper_bound)

witness fault set (mechanism indices in the committed .dem, 5)

[34754, 34776, 34845, 34866, 37927]

no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see

Construction & provenance

authors @vprusso

provenance submitted through the challenge

novelty novelty not audited

construction Priced construction calculus C-DELETE-CHECK of codes/63-21-7.json ([[63,21,7]], max check weight 16; itself Mathys Rennela's priced-calculus E-PEEL of codes/64-20-8.json, the depth-one universal code grown from the [[24,8,4]] seed in arXiv:2610.06730): delete X check a4 (rows numbered in file order after dropping dependent rows, as machine/priced_calculus.py labels them) and keep every qubit at its parent index. Consumer: github.com/unitaryfoundation/code-calculus @ 1b9a942, machine/priced_calculus.py.

model Claude Fable 5.1 (claimed, not verified)

builds on arXiv:2610.06730

date 2026-11-04

notes Single-step priced-calculus C-DELETE-CHECK child of board entry 63-21-7. verify/validate_candidate.py found no board entry sharing this code's fingerprint or Weisfeiler-Leman signature, local-Hadamard images included.

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

[[63,22,5]] priced calculus C-DELETE-CHECK of codes/63-21-7.json

Direction & hypothesis

Unrestricted weight-9plus CSS cell. The priced construction calculus was applied one move deep to every CSS entry on the board, and this code is the C-DELETE-CHECK of codes/63-21-7.json ([[63,21,7]], max check weight 16; itself Mathys Rennela's priced-calculus E-PEEL of codes/64-20-8.json, the depth-one universal code grown from the [[24,8,4]] seed in arXiv:2610.06730). Deleting X check a4 raises k from 21 to 22 and lowers the witnessed distance bound from 7 to 5; n = 63 and the max check weight 16 are unchanged.

What was searched

Every C-DELETE-CHECK, E-PEEL, and E-PUNCTURE move on each of the 2,783 CSS board entries as of 2026-11-02, 1,684,787 moves in all, with the consumer at github.com/unitaryfoundation/code-calculus @ 1b9a942. Children with a bare qubit, a disconnected Tanner graph, a Weisfeiler-Leman signature equal to a board entry or to an earlier child, or parameters already dominated inside the parent's cell were dropped before any search, leaving 334,191 distinct children. Children with n <= 60 and an inherited distance bound of at least 2, and children with 61 <= n <= 100 and a bound of at least 5, were screened with research/kit/surrogate.lightest_logical at 2,000 RIS trials per side; the survivors the kit's novelty pre-check called board-advancing were staged with research/kit/submit.py and gated with verify/validate_candidate.py, one representative per distinct (n, k, d, max weight, locality) point. This code is that representative for [[63,22,5]] at max check weight 16. The thirteen points audited first went to the board on 2026-11-04 (PRs #4588 to #4600); this one is from the remainder, re-checked against the board of 2026-11-04 with the gate's structural, deduplication, and novelty stages before the ladder below was run. The screen distance is a witness-backed upper bound; the rungs below are the independent confirmation runs on the staged file.

Evidence trail

Confirmation ladder for the submitted code, each rung a fresh seed unless marked otherwise, reading the lightest logical found:

| budget (trials/side) | lightest logical | | ---: | ---: | | 2,000 (staging screen, seeds 1 and 2) | 5 | | 1,000,000 (seed 101) | 5 | | 1,000,000 (seed 102) | 5 | | 10,000,000 (seed 103) | 5 |

4 fresh-seed rung(s) agree at the best bound, the deepest of them at 10,000,000 trials per side. The submitted witness reproduces it: X: d <= 7 (upper_bound), Z: d <= 5 (upper_bound).

Dead ends

None recorded for this candidate.

Tools

Model: Claude Fable 5.1 (Claude Code). Repo tooling: research/kit/coordination.py, research/kit/submit.py, research/kit/surrogate.py, research/audits/leader_audit.py. The local verdict is verify/validate_candidate.py; the bundle was assembled by research/kit/promote.py.

Reproduction

Load codes/63-21-7.json and delete X check a4, where the X rows are numbered a1, a2, ... in file order after dropping rows dependent on earlier ones, as CodeState.from_challenge in machine/priced_calculus.py labels them; every qubit keeps its index. In github.com/unitaryfoundation/code-calculus @ 1b9a942 this is apply_operation(state, {'op': 'C-DELETE-CHECK', 'row_id': 'a4'}). Then run research/audits/leader_audit.py ladder on the result with --ladder 1000000:101,102 10000000:103 to reproduce the confirmation rungs; the witnesses in the entry are the ones those runs validated.

Parity checks

X-checks 20 (max weight 16) · Z-checks 21 (max weight 16)

H_X (20 checks, sparse supports)

[5, 7, 12, 14, 16, 18, 24, 26, 31, 33, 40, 42, 52, 54, 59, 61] [32, 34, 35, 37, 40, 42, 43, 45, 48, 50, 51, 53, 56, 58, 59, 61] [2, 4, 9, 15, 17, 22, 25, 27, 34, 36, 39, 45, 47, 53, 58, 60] [3, 5, 10, 12, 20, 25, 27, 31, 37, 40, 46, 47, 53, 56, 62] [1, 7, 10, 12, 20, 23, 29, 34, 36, 39, 45, 48, 54, 57, 59] [4, 6, 12, 14, 17, 24, 26, 32, 34, 40, 42, 51, 53, 59, 61] [3, 7, 11, 15, 18, 21, 25, 29, 31, 35, 39, 43, 48, 52, 56, 60] [0, 3, 12, 15, 16, 27, 30, 35, 38, 39, 42, 51, 54, 55, 58] [17, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46] [3, 4, 9, 14, 17, 21, 26, 27, 31, 38, 41, 44, 49, 52, 55, 62] [2, 7, 11, 14, 18, 22, 26, 29, 34, 37, 41, 46, 50, 53, 57, 62] [2, 5, 8, 15, 19, 24, 29, 31, 38, 41, 44, 48, 53, 58, 59] [4, 6, 8, 10, 17, 28, 30, 31, 33, 43, 45, 52, 54, 56, 58] [0, 2, 13, 15, 19, 21, 24, 26, 36, 38, 39, 41, 48, 50, 59, 61] [9, 10, 12, 15, 17, 18, 19, 22, 39, 42, 44, 45, 47, 50, 52, 53] [8, 9, 10, 11, 19, 20, 21, 22, 43, 44, 45, 46, 47, 48, 49, 50] [1, 2, 9, 10, 16, 23, 26, 35, 38, 43, 46, 52, 53, 60, 61] [1, 3, 5, 7, 8, 10, 12, 14, 16, 18, 19, 21, 24, 26, 28, 30] [1, 3, 9, 11, 16, 18, 23, 25, 32, 34, 40, 42, 47, 49, 55, 57] [4, 6, 13, 15, 20, 22, 27, 29, 32, 34, 39, 41, 47, 49, 56, 58]

H_Z (21 checks, sparse supports)

[2, 3, 4, 5, 16, 17, 21, 22, 39, 40, 45, 46, 57, 58, 59, 60] [5, 7, 9, 11, 20, 22, 24, 26, 32, 34, 44, 46, 48, 50, 60, 62] [0, 2, 5, 7, 8, 10, 13, 15, 47, 49, 52, 54, 55, 57, 60, 62] [4, 5, 6, 7, 19, 20, 21, 22, 39, 40, 41, 42, 55, 56, 57, 58] [9, 10, 13, 14, 17, 18, 20, 21, 32, 33, 36, 37, 56, 57, 60, 61] [8, 9, 14, 15, 25, 26, 27, 28, 31, 32, 37, 38, 49, 50, 51, 52] [1, 3, 13, 15, 16, 18, 27, 29, 31, 33, 43, 45, 48, 50, 60, 62] [2, 6, 10, 14, 16, 19, 23, 27, 33, 37, 41, 45, 47, 51, 55, 59] [1, 4, 8, 13, 17, 19, 23, 28, 34, 37, 41, 46, 50, 53, 57, 62] [2, 4, 8, 14, 18, 19, 23, 29, 33, 35, 39, 45, 49, 51, 55, 61] [1, 4, 11, 14, 16, 20, 25, 30, 34, 37, 40, 43, 49, 54, 55, 60] [0, 3, 5, 6, 24, 25, 27, 30, 32, 33, 35, 38, 55, 58, 60, 61] [2, 7, 8, 13, 16, 20, 25, 30, 33, 38, 39, 44, 47, 52, 57, 62] [1, 7, 9, 15, 17, 22, 24, 30, 33, 35, 41, 43, 49, 51, 57, 59] [10, 11, 12, 13, 23, 24, 29, 30, 41, 42, 43, 44, 55, 56, 61, 62] [2, 3, 12, 13, 21, 22, 23, 24, 31, 32, 45, 46, 51, 52, 57, 58] [0, 5, 11, 14, 16, 20, 26, 29, 33, 38, 40, 43, 49, 54, 56, 59] [4, 7, 8, 11, 17, 18, 28, 29, 36, 37, 40, 41, 47, 50, 59, 62] [0, 6, 8, 14, 18, 19, 25, 27, 34, 36, 42, 44, 48, 54, 56, 62] [2, 3, 12, 13, 16, 17, 29, 30, 31, 32, 45, 46, 49, 50, 59, 60] [5, 7, 9, 11, 19, 21, 23, 25, 35, 37, 39, 41, 52, 54, 56, 58]

Code ID 63-22-5 · download JSON · raw on GitHub