<feat> 新增 QECClosedForm:量子纠错码闭式参数预测(与 QECNoise 闭环) - #49
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QECClosedForm 对 AG 完备码族 [[2^m, k, 2^{r+1}]](Reed-Muller CSS 码)
由组合闭式直接给出全套纠错参数——无需电路、无需模拟:
- 码参数与编码率:[[2^m, n-2·dim RM(r,m), 2^{r+1}]]
- 损失闭式 loss(θ)=c_d·θ^d(指数 d ∈ {4,8,16,32},系数全闭式)
- 零损失边界 k ≤ ⌊(d-1)/2⌋
- 逻辑算符计数(AG 平坦数)
- 检测率 p_det(θ) = sin²(θ/2)
与 QECNoise(PR OriginQ#48,QPanda3 模拟 θ⁴ 标度)闭环:预测指数 4 与
模拟 slope ≈ 4.04 一致。包含 demo、预测-模拟对比、可视化(2 图)
与 9 个单元测试(闭式 vs 已发布精确值)。
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Summary
新增 QECClosedForm 模块:量子纠错码闭式参数预测(零电路、零模拟)。对 AG 完备码族
[[2^m, k, 2^{r+1}]](Reed-Muller CSS 码),由组合闭式秒算全套纠错参数。与 QECNoise 的闭环(合并故事)
QECNoise(PR #48)QECClosedForm(本 PR)闭环:QECClosedForm 预测
loss(θ) = c_d·θ^d(指数 d、系数 c_d 全闭式),QECNoise 模拟确认 log-log 斜率 ≈ 4 —— 预测与验证一致(实测 [[7,1,3]]
slope=4.04),一台电脑完成纠错码设计全流程。
功能
[[2^m, n-2·dim RM(r,m), 2^{r+1}]],编码率(m=20 时 99.996%)loss(θ) = c_d·θ^d,c_d = C(n,w0)·P(w0)·fail(w0)·κ·2^{-2w0}(定理 10.35.1.07)——
[[1024,252,32]]在 θ=0.01 时 loss 7.5e-57k ≤ ⌊(d-1)/2⌋(注入零损失定理)p_det(θ) = sin²(θ/2)(与码无关)演示与验证
逻辑计数、检测率)
说明
两者共同覆盖"设计 → 验证"的纠错码开发流程