fb230d8a62
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]>
11 lines
1,016 B
Markdown
11 lines
1,016 B
Markdown
<!-- 机器辅助翻译（machine-assisted translation）：在对外推广之前，须由熟练的读者审校。 -->
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量子傅里叶变换（QFT）把一个数写进相位里。在 n 个量子比特上，它把基态 |x⟩ 变成
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Σᵧ e^{2πi·xy/2ⁿ} |y⟩ / √2ⁿ：
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每个结果等可能，信息全部在相对相位之中。这条线路只需 n(n+1)/2 个门：每个量子比特上一个 Hadamard 门、成对量子比特之间的受控相位旋转 `cp(π/2ᵏ)`，以及最后把量子比特顺序倒过来的交换门。
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在相位估计中，正是 QFT 这一步把相位变成可以读出的数，因而在因数分解中也是如此。相位估计反过来使用它：*逆* QFT。
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这道练习的意图是 *equivalent*（等价）：你的整个程序必须与恒等线路在相差一个全局相位的意义下是同一条线路。引擎在全部 8 个基态上逐一判定，由证明检查。角度 π/2 和 π/4 是二进分数（dyadic），所以这个程序也能逐位精确地运行。
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