{"type":"rich","author_url":"https://blog.hatena.ne.jp/derwind/","published":"2022-02-05 21:52:32","author_name":"derwind","url":"https://randommemory.hatenablog.com/entry/2022/02/05/215232","version":"1.0","blog_url":"https://randommemory.hatenablog.com/","image_url":"https://cdn-ak.f.st-hatena.com/images/fotolife/d/derwind/20220205/20220205230129.png","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2022%2F02%2F05%2F215232\" title=\"Qiskit (36) \u2015 Shor \u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","categories":["quantum_computing"],"provider_name":"Hatena Blog","provider_url":"https://hatena.blog","title":"Qiskit (36) \u2015 Shor \u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","width":"100%","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","description":"\u66f8\u7c4d p.146 \u306e\u4e0b\u306e\u307b\u3046\u306e\u8a18\u8ff0\u3092\u691c\u8a3c\u3057\u3066\u304a\u3053\u3046:$$ \\begin{align*} \\sqrt{r} \\sum_{j = 0}^{r - 1} \\ket{u_j} &= \\sum_{k = 0}^{r - 1} \\sum_{j = 0}^{r - 1} e^{- 2 \\pi i \\frac{jk}{r}} \\ket{x^k \\bmod{N}} \\\\ &= r \\ket{1} + \\sum_{k = 1}^{r - 1} \\frac{1 - e^{- 2 \\pi i \\frac{kr}{r}}}{1 - e^{- 2 \\pi i \\frac{k}{r}}} \\ket{x^k \\bmod{N}\u2026","height":"190"}