---
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
---

# QLDPC FOM>12 Search Evidence

This is a **human-review snapshot**, not a winner announcement. It contains a compact selection of twisted-torus CSS quantum-code candidates, their check matrices, replay-oriented evidence summaries, and a readable description of the automated five-stage search pipeline.

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

## 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.


## Snapshot summary

| Item | Value |
|---|---:|
| Selected candidates | 51 |
| Sealed trusted audits | 24 |
| 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 `python -B scripts/verify_dataset.py .` to validate every checksum, matrix, CSS commutation relation, reconstructed `k`, FOM field, and included logical witness.

## 中文说明

这是供人类专家复核的**进行中快照**，不是“已经发现新纪录码”的声明。数据集收录精选 twisted-torus CSS 候选、`H_X/H_Z`、证据等级、FOM 区间、每轮统计和五阶段流水线说明。当前没有任何新候选被严格认证为 `FOM>12`。BP/OSD 的较大数值只是启发式距离上界，不能当作性能下界或最终结果。

## 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.