README.md

---
pretty_name: QLDPC FOM>12 Search Evidence
license: apache-2.0
language:
- en
- zh
tags:
- quantum-error-correction
- qldpc
- scientific-discovery
- expert-review
- tabular
configs:
- config_name: candidates
  data_files: data/candidates.jsonl
- config_name: round_summary
  data_files: data/round_summary.jsonl
- config_name: stage2_best_verified
  data_files: data/stage2_best_verified.jsonl
- config_name: historical_exact_fom11
  data_files: data/historical_exact_fom11.jsonl
- config_name: stage3_typed_exact_fom_gt_12
  data_files: data/stage3_typed_exact_fom_gt_12.jsonl
---

# 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`](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`](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`](docs/HISTORICAL_EXACT_FOM11.md).

## Snapshot summary

| Item | Value |
|---|---:|
| Selected candidates | 51 |
| Sealed trusted audits | 24 |
| Separate Stage 3 typed exact `FOM > 12` lane | 1 (`[[210,10,16]]`) |
| Exact non-winners | 3 |
| Rejected with replayable witness | 21 |
| Formally open lower-bound candidates | 27 |
| Advisory upper-bound-only signals | 0 |
| Exact `FOM > 12` | 0 |
| Exact `FOM = 12` | 0 |

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: **`k*d*d > 12*n`**. 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. [`docs/PIPELINE.md`](docs/PIPELINE.md) — what each automated stage does.
2. [`docs/METRICS.md`](docs/METRICS.md) — lower bounds, upper bounds, exact values, and search-only scores.
3. [`docs/EXPERT_REVIEW_CHECKLIST.md`](docs/EXPERT_REVIEW_CHECKLIST.md) — concrete independent checks.
4. [`data/candidates.jsonl`](data/candidates.jsonl) — one compact record per selected code.
5. [`evidence/proofs.jsonl`](evidence/proofs.jsonl) and [`matrices/`](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](https://gist.github.com/ShuxiangCao/aa35ff78f403ed7ab730e36e165c3cf1). Publishing this dataset does **not** imply that Shuxiang Cao, NVIDIA, or any cited author has reviewed or endorsed these candidates.