humanfia-lab/qcode

QLDPC FOM>12 Search Evidence

This repository contains the original human-review snapshot plus separately versioned result lanes. It includes twisted-torus CSS quantum-code candidates, their check matrices, replay-oriented evidence summaries, and a readable description of the automated search pipeline.

Status at snapshot: in progress. Sealed rounds: 1–4. Certified novel candidates with exact FOM > 12: 0.

Stage 3 typed exact FOM>12 update (2026-08-19)

The separate stage3_typed_exact_fom_gt_12 configuration publishes one [[210,10,16]] CSS-BB code with exact Stage 3 FOM 256/21 ~= 12.19047619047619. The integer target check is 10*16^2 = 2560 > 2520 = 12*210.

The lower result is bound to a pinned DistQLDPC/MaxCDCL binary and the upper bound is a replayable weight-16 X-logical witness. The typed Stage 3 handoff replayed successfully, but the run used --no-certify: Stage 4 and Stage 5 publication gates were not run, and no portable DRAT/LRAT lower-bound proof is available. It is therefore labelled STAGE3_TYPED_EXACT_PENDING_STRICT_GATE, not CERTIFIED_EXACT_WIN. See `docs/STAGE3_TYPED_EXACT_FOM_GT_12.md`.

Stage 2 verified near-miss update (2026-08-16)

A separate stage2_best_verified configuration now publishes 13 fully replayed Stage 2 near-misses. All are [[254,2,d<=39]], with verified upper-bound FOM 1521/127 ~= 11.97638. They are rejections, not wins, and their exact distances remain unknown. See `docs/STAGE2_BEST_RESULT.md`.

The latest source boundary contained 102 raw-score ties; only the 13 released rows completed the full replay used here. The dataset does not claim that all 102 raw ties have the same evidence level.

Historical exact-distance reference (2026-08-17)

The separate historical_exact_fom11 configuration contains one canonical-deduplicated [[288,50,8]] CSS-BB code with legacy exact FOM 100/9 ~= 11.1111. The Campaign 4 source reports d_X=d_Z=8 and all 100 logical MILPs optimal. This is a historical exact non-winner, not a current Stage 2 result. Its identity and matrices were replayed with the current code, but the legacy run did not preserve a portable proof artifact under the modern certificate schema. See `docs/HISTORICAL_EXACT_FOM11.md`.

Snapshot summary

Best formally open item in this snapshot: 158bf9b332c9012345f8: [[90,12,d]], 5 ≤ d ≤ 10, FOM ∈ [3.33333, 13.3333]. “Open” means the current rigorous interval has not excluded the target; it is not a proof of high distance.

Objective

For a quantum code [[n,k,d]], this project uses

FOM = k d² / n.

The strict target is checked with integer arithmetic: *`kdd > 12n`**. Equality is not a win. A candidate is promoted only when its distance evidence and novelty checks cross the appropriate trust boundary.

Read this first

1. 1.`docs/PIPELINE.md` — what each automated stage does.
2. 2.`docs/METRICS.md` — lower bounds, upper bounds, exact values, and search-only scores.
3. 3.`docs/EXPERT_REVIEW_CHECKLIST.md` — concrete independent checks.
4. 4.`data/candidates.jsonl` — one compact record per selected code.
5. 5.`evidence/proofs.jsonl` and `matrices/` — evidence and H_X/H_Z matrices.

Run git lfs pull --include='matrices/**' and then python -B scripts/verify_dataset.py . to validate every checksum, matrix, CSS commutation relation, reconstructed k, FOM field, and included logical witness, including the separate Stage 3 typed-exact lane.

中文说明

这是供人类专家复核的进行中数据集。原 rounds 1–4 快照仍没有通过完整 Stage 4/5 发布门的 FOM>12 候选；新增独立配置发布了一个 Stage 3 typed exact 的 [[210,10,16]] 结果，FOM 为 256/21。其下界依赖固定版本的 DistQLDPC/MaxCDCL，且本轮使用了 --no-certify，所以等待后续严格发布门。

Attribution and non-endorsement

The challenge target follows Shuxiang Cao's public gist. Publishing this dataset does not imply that Shuxiang Cao, NVIDIA, or any cited author has reviewed or endorsed these candidates.