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engine::course reads the course from wai-quantum/course/: 21 lessons from a first circuit through superposition, entanglement, interference, the standard algorithms, noise and mitigation, error correction and fault tolerance to resource estimates, each a Markdown text in English and Simplified Chinese and an exercise.json with a schema. A check runs each case of an exercise (a generator's inputs) with its intent and the verdict, measures its constraints (the gates allowed, counts, the T count, the critique's smells, the resource estimate's counts), and says what went wrong from the diagnostics, the verdict and the critique, never from the solution. The tests hold every solution to pass by proof, every known wrong answer to fail for its stated reason, and every locale to every text and message. wai-quantum learn shows, starts, checks, hints and explains a lesson, keeps progress only on this machine, and speaks the language --lang or LANG names; the command summaries and docs topics have Chinese translations held to the English they came from. The verdict gains of_diagnostic for a generator's refusal. llms.txt names the course. Co-Authored-By: Claude Opus 5.5 <[email protected]>
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错误缓解（mitigation）在不纠正错误的情况下改善有噪声设备给出的答案。方法之一是零噪声外推：先以线路自身的噪声运行，再把噪声按已知的倍数有意放大后运行，然后把测得的值外推回零噪声。
要在不改变线路计算内容的前提下放大噪声，就把它折叠（fold）：把门 G 换成 G G⁻¹ G。这三个门做的事与 G 相同，却承受三倍的噪声。折叠每一个双比特门，就把占主导地位的噪声放大 3 倍；只折叠其中一部分，可得到介于两者之间的倍数。
设 E(1) 是设备噪声下的期望值，E(3) 是门被折叠后的期望值，那么到零噪声的线性（Richardson）外推为
E(0) ≈ (3·E(1) − E(3)) / 2。
这里的意图是 equivalent（等价）：折叠后的程序必须与原程序是同一条线路，引擎用稳定子表证明这一点。Studio 的噪声字段，或命令行中的 --noise，可以并排运行两个版本，看着 ⟨Z0 Z1⟩ 随噪声放大而下降。