diff --git a/_sources/addition_on_ibmq.ipynb b/_sources/addition_on_ibmq.ipynb index 58ca6708..1ea81cf5 100644 --- a/_sources/addition_on_ibmq.ipynb +++ b/_sources/addition_on_ibmq.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d4d9c798", + "id": "e1fef5dc", "metadata": {}, "source": [ "# 【参考】足し算を実機で行う\n", @@ -19,7 +19,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9e959df", + "id": "e2fa7199", "metadata": { "tags": [ "remove-output" @@ -43,7 +43,7 @@ }, { "cell_type": "markdown", - "id": "974eb709", + "id": "ccd55db0", "metadata": {}, "source": [ "実習と同様、`'ibm-q/open/main'`のプロバイダでは(1, 1)の回路しか扱えないので、フェイクバックエンドを使います。" @@ -52,7 +52,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c245ab0", + "id": "bdb6f3f6", "metadata": { "tags": [ "remove-output", @@ -72,7 +72,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea1f18ab", + "id": "b44b5cf8", "metadata": { "tags": [ "remove-output" @@ -94,7 +94,7 @@ }, { "cell_type": "markdown", - "id": "1da8f041", + "id": "c54a74ca", "metadata": {}, "source": [ "実習と全く同じ`setup_addition`関数と、次のセルで効率化前の回路を返す`make_original_circuit`関数を定義します。" @@ -103,7 +103,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dca09621", + "id": "9133e1f6", "metadata": {}, "outputs": [], "source": [ @@ -165,7 +165,7 @@ }, { "cell_type": "markdown", - "id": "954bdcb6", + "id": "845aea2c", "metadata": {}, "source": [ "(4, 4)から(1, 1)までそれぞれオリジナルと効率化した回路の二通りを作り、全てリストにまとめてバックエンドに送ります。" @@ -174,7 +174,7 @@ { "cell_type": "code", "execution_count": null, - "id": "726ab688", + "id": "d7462357", "metadata": {}, "outputs": [], "source": [ @@ -217,7 +217,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b54076fc", + "id": "b2c85b6a", "metadata": { "tags": [ "remove-input" @@ -236,7 +236,7 @@ { "cell_type": "code", "execution_count": null, - "id": "37afb3b0", + "id": "37c204c9", "metadata": { "tags": [ "remove-output", @@ -276,7 +276,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0271748e", + "id": "c1d2b4d3", "metadata": { "tags": [ "remove-input" @@ -294,7 +294,7 @@ }, { "cell_type": "markdown", - "id": "8542b104", + "id": "19011701", "metadata": {}, "source": [ "ジョブが返ってきたら、正しい足し算を表しているものの割合を調べてみましょう。" @@ -303,7 +303,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e9f4fdda", + "id": "ebe8c2e2", "metadata": { "tags": [ "remove-output" @@ -339,7 +339,7 @@ }, { "cell_type": "markdown", - "id": "47af2c2b", + "id": "98c3b09b", "metadata": {}, "source": [ "ちなみに、`ibm_kawasaki`というマシンで同じコードを走らせると、下のような結果が得られます。\n", @@ -374,7 +374,7 @@ }, { "cell_type": "markdown", - "id": "ef0c03cf", + "id": "9d4d4a0d", "metadata": { "tags": [ "remove-input" @@ -395,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "783ec66f", + "id": "c5857d32", "metadata": {}, "source": [ "回路が均一にランダムに$0$から$2^{n_1 + n_2 + n_3} - 1$までの数を返す場合、レジスタ1と2のそれぞれの値の組み合わせに対して正しいレジスタ3の値が一つあるので、正答率は$2^{n_1 + n_2} / 2^{n_1 + n_2 + n_3} = 2^{-n_3}$となります。実機では、(4, 4)と(3, 3)でどちらの回路も正答率がほとんどこの値に近くなっています。(2, 2)では効率化回路で明らかにランダムでない結果が出ています。(1, 1)では両回路とも正答率8割です。\n", @@ -405,7 +405,7 @@ }, { "cell_type": "markdown", - "id": "8b6b37a6", + "id": "52b1cf5a", "metadata": {}, "source": [ "## Quantum Volume\n", @@ -424,7 +424,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db13ac0c", + "id": "cb21586f", "metadata": { "tags": [ "remove-output", @@ -443,7 +443,7 @@ { "cell_type": "code", "execution_count": null, - "id": "34035917", + "id": "fcf4bf4e", "metadata": { "tags": [ "remove-output", @@ -477,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "f95cf89e", + "id": "43e34cdb", "metadata": {}, "source": [ "QVから期待される正答率の序列にならないかもしれません。量子コンピュータという恐ろしく複雑な機械の性能を一つの数値で表すことの限界がここにあり、今のように単純な回路を実行する場合は、ケースバイケースで特定の量子ビットや特定のゲートのエラー率が結果に大きな影響を及ぼしたりするのです。\n", @@ -488,7 +488,7 @@ { "cell_type": "code", "execution_count": null, - "id": "00c518f7", + "id": "30a62548", "metadata": { "tags": [ "remove-output", @@ -509,7 +509,7 @@ }, { "cell_type": "markdown", - "id": "e6267166", + "id": "9119fb7f", "metadata": { "tags": [ "remove-output", @@ -543,7 +543,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e3851043", + "id": "559e76f3", "metadata": { "tags": [ "raises-exception", @@ -567,7 +567,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2272b30", + "id": "2567e7de", "metadata": { "tags": [ "remove-output", diff --git a/_sources/chsh_inequality.ipynb b/_sources/chsh_inequality.ipynb index a98ddc08..fb27ec74 100644 --- a/_sources/chsh_inequality.ipynb +++ b/_sources/chsh_inequality.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d9d93092", + "id": "52f22b74", "metadata": {}, "source": [ "# CHSH不等式の破れを確認する" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "8b659058", + "id": "fecfd07d", "metadata": {}, "source": [ "この最初の実習では、量子コンピュータにおいて量子力学的状態、特に「**エンタングルメント**」が実現しているか検証してみましょう。実習を通じて量子力学の概念と量子コンピューティングの基礎を紹介していきます。\n", @@ -30,7 +30,7 @@ }, { "cell_type": "markdown", - "id": "37c3aa50", + "id": "1fc514af", "metadata": {}, "source": [ "## 本当に量子コンピュータなのか?\n", @@ -42,7 +42,7 @@ }, { "cell_type": "markdown", - "id": "9f1fcdbc", + "id": "50448906", "metadata": {}, "source": [ "## CHSH不等式\n", @@ -54,7 +54,7 @@ }, { "cell_type": "markdown", - "id": "d2573316", + "id": "fcda119e", "metadata": {}, "source": [ "## Qiskitの基本構造\n", @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "8eb0ca53", + "id": "700bf294", "metadata": {}, "source": [ "### 量子ビット、量子レジスタ\n", @@ -155,7 +155,7 @@ }, { "cell_type": "markdown", - "id": "ff1f4c44", + "id": "2b2a8a44", "metadata": {}, "source": [ "### ゲート、回路、測定\n", @@ -190,7 +190,7 @@ }, { "cell_type": "markdown", - "id": "cadeb066", + "id": "29fa6869", "metadata": {}, "source": [ "### 量子計算結果の解析\n", @@ -204,7 +204,7 @@ }, { "cell_type": "markdown", - "id": "697dd839", + "id": "49472fb1", "metadata": {}, "source": [ "(common_gates)=\n", @@ -264,7 +264,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8756de7", + "id": "85893a78", "metadata": { "tags": [ "remove-output" @@ -290,7 +290,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0732ec9d", + "id": "ca0fa5a2", "metadata": {}, "outputs": [], "source": [ @@ -306,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "5c1f9f43", + "id": "f51a6415", "metadata": {}, "source": [ "最後のプリント文で、ゲートが3つなのにも関わらず \"5 operations\" と出てくるのは、各量子ビットの測定も一つのオペレーションとして数えられるからです。\n", @@ -369,7 +369,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9400004", + "id": "0f8fdd39", "metadata": {}, "outputs": [], "source": [ @@ -389,7 +389,7 @@ }, { "cell_type": "markdown", - "id": "b9acc9ee", + "id": "40c4477a", "metadata": {}, "source": [ "やや複雑ですが、また計算を追ってみましょう。まず角度$\\theta_1, \\theta_2, \\theta_3$は定義から以下の関係を満たします。\n", @@ -421,7 +421,7 @@ }, { "cell_type": "markdown", - "id": "01d26d1a", + "id": "a18a6a14", "metadata": {}, "source": [ "### 回路図の描き方と読み方\n", @@ -432,7 +432,7 @@ { "cell_type": "code", "execution_count": null, - "id": "80e23465", + "id": "a11d6317", "metadata": {}, "outputs": [], "source": [ @@ -441,7 +441,7 @@ }, { "cell_type": "markdown", - "id": "304cf161", + "id": "1141217c", "metadata": {}, "source": [ " ここで`draw()`の引数`'mpl'`はmatplotlibライブラリを使ってカラーで描くことを指定しています。実行環境によっては対応していないこともあるので、その場合は引数なしの`draw()`を使います。結果は`mpl`の場合に比べて見劣りしますが、内容は同じです。" @@ -450,7 +450,7 @@ { "cell_type": "code", "execution_count": null, - "id": "502e4237", + "id": "c83f0341", "metadata": {}, "outputs": [], "source": [ @@ -459,7 +459,7 @@ }, { "cell_type": "markdown", - "id": "051bd20e", + "id": "72f75b50", "metadata": {}, "source": [ "回路図は左から右に読んでいきます。水平の2本の実線が上からそれぞれ第0、第1量子ビットに対応し、その上にかぶさっている四角がゲート、最後にある矢印が下に伸びている箱が測定を表します。1ビットゲートから伸びている先端の丸い縦線は制御を表します。一番下の二重線は「古典レジスタ」(量子現象のない物理学を「古典物理学」と呼ぶので、量子でない通常のコンピュータにまつわる概念にはよく「古典 classical」という接頭辞をつけます)に対応し、測定結果の0/1が記録される部分です。" @@ -467,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "c4edf75b", + "id": "cb14a7a7", "metadata": {}, "source": [ "## CHSH不等式を計算する回路を書く\n", @@ -480,7 +480,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43ad8494", + "id": "246aca6c", "metadata": {}, "outputs": [], "source": [ @@ -534,7 +534,7 @@ }, { "cell_type": "markdown", - "id": "05fd7297", + "id": "992e83b0", "metadata": {}, "source": [ "それぞれの回路で2ビットレジスタの基底$\\ket{00}, \\ket{01}, \\ket{10}, \\ket{11}$が現れる確率を計算してみましょう。\n", @@ -632,7 +632,7 @@ }, { "cell_type": "markdown", - "id": "0dd47685", + "id": "c02c8671", "metadata": {}, "source": [ "## 回路を実機で実行する\n", @@ -643,7 +643,7 @@ { "cell_type": "code", "execution_count": null, - "id": "605b6de3", + "id": "de3f6087", "metadata": { "tags": [ "remove-output", @@ -664,7 +664,7 @@ }, { "cell_type": "markdown", - "id": "79c8951e", + "id": "bed7adb3", "metadata": {}, "source": [ "認証が済んだら、利用する量子コンピュータ(「バックエンド」と呼びます)を選びます。" @@ -673,7 +673,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59f8eb1b", + "id": "3c291458", "metadata": { "tags": [ "raises-exception", @@ -694,7 +694,7 @@ }, { "cell_type": "markdown", - "id": "855e3fed", + "id": "47dcac25", "metadata": {}, "source": [ "回路をバックエンドに送るには、`transpile`という関数とバックエンドの`run`というメソッドを使います。`transpile`については次回{ref}`transpilation`で説明するので、今は「おまじない」だと思ってください。`run`で回路を送るとき、前述したように同時にショット数を指定します。バックエンドごとに一度のジョブでの最大ショット数が決められており、8192、30000、100000などとさまざまです。回路をバックエンドに渡し、`shots`回実行させることをジョブと呼びます。" @@ -703,7 +703,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66c37369", + "id": "f4d014e2", "metadata": { "tags": [ "raises-exception", @@ -727,7 +727,7 @@ }, { "cell_type": "markdown", - "id": "977667d6", + "id": "7a35b37c", "metadata": {}, "source": [ "これで回路がバックエンドに送られ、キューに入りました。ジョブの実行結果は`run`メソッドの返り値であるジョブオブジェクトから参照します。\n", @@ -743,7 +743,7 @@ }, { "cell_type": "markdown", - "id": "a3d781f0", + "id": "a18ee1cf", "metadata": {}, "source": [ "## 量子測定結果の解析\n", @@ -754,7 +754,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da1b0343", + "id": "7d32f64a", "metadata": { "tags": [ "raises-exception", @@ -781,7 +781,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36d7380b", + "id": "776920ae", "metadata": { "tags": [ "remove-cell" @@ -805,7 +805,7 @@ }, { "cell_type": "markdown", - "id": "20008972", + "id": "8a560540", "metadata": {}, "source": [ "````{tip}\n", @@ -825,7 +825,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1743f15a", + "id": "8ed8131b", "metadata": {}, "outputs": [], "source": [ @@ -838,7 +838,7 @@ }, { "cell_type": "markdown", - "id": "67fe14de", + "id": "df78d8a4", "metadata": {}, "source": [ "$c^2/2 = (s + c)^2/4 = 0.427$, $s^2/2 = (s - c)^2 / 4 = 0.073$なので、得られた確率は当たらずとも遠からずというところでしょうか。\n", @@ -855,7 +855,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bac794f7", + "id": "02fb801c", "metadata": {}, "outputs": [], "source": [ @@ -883,7 +883,7 @@ }, { "cell_type": "markdown", - "id": "c7be497a", + "id": "a5891582", "metadata": {}, "source": [ "無事、$S$が2を超えました。" diff --git a/_sources/circuit_from_scratch.ipynb b/_sources/circuit_from_scratch.ipynb index 43b57cac..69576526 100644 --- a/_sources/circuit_from_scratch.ipynb +++ b/_sources/circuit_from_scratch.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "149fc322", + "id": "1e8a9d4e", "metadata": {}, "source": [ "# 単純な量子回路をゼロから書く" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "abeb5069", + "id": "d3e50ead", "metadata": {}, "source": [ "{doc}`chsh_inequality`で、量子回路の基本的な書き方と実機での実行の仕方を学びました。そこで出てきたように、QCでは量子レジスタに特定の量子状態を実現することが計算を行うこととなります。そこで今回は、基本的なゲートを組み合わせて様々な量子状態を作る実習を行います。\n", @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "38dc404f", + "id": "f3fdf274", "metadata": {}, "source": [ "## 状態ベクトルシミュレータで量子状態を調べる\n", @@ -38,7 +38,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cc837aad", + "id": "20b68749", "metadata": { "tags": [ "remove-output" @@ -61,7 +61,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f810d982", + "id": "8acec68a", "metadata": {}, "outputs": [], "source": [ @@ -71,7 +71,7 @@ }, { "cell_type": "markdown", - "id": "316d6562", + "id": "a2ae0504", "metadata": {}, "source": [ "シミュレートする回路を作ります。ここでは例として前半で登場した回路1を使います。測定以外のゲートをかけていきます。" @@ -80,7 +80,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf588aa7", + "id": "fe7fa013", "metadata": {}, "outputs": [], "source": [ @@ -94,7 +94,7 @@ }, { "cell_type": "markdown", - "id": "26c3e3ec", + "id": "6ce85a61", "metadata": {}, "source": [ "```{caution}\n", @@ -107,7 +107,7 @@ { "cell_type": "code", "execution_count": null, - "id": "74c75d90", + "id": "1f1c2d02", "metadata": {}, "outputs": [], "source": [ @@ -133,7 +133,7 @@ }, { "cell_type": "markdown", - "id": "e23565c6", + "id": "d6a29909", "metadata": {}, "source": [ "状態ベクトルは`np.asarray()`でnumpy配列に変換できます。データタイプは128ビットの複素数(実部と虚部それぞれ64ビット)です。配列のインデックスがそのまま二進数としてみなした計算基底の値に対応しています。\n", @@ -144,7 +144,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1affd48b", + "id": "bca43dcf", "metadata": {}, "outputs": [], "source": [ @@ -156,7 +156,7 @@ }, { "cell_type": "markdown", - "id": "37236392", + "id": "667e6675", "metadata": {}, "source": [ "前回より、{eq}`回路1 `は$\\frac{1}{\\sqrt{2}} (s\\ket{00} + c\\ket{01} - c\\ket{10} + s\\ket{11})$($s:=\\sin(\\pi/8)=0.271\\sqrt{2}$, $c:=\\cos(\\pi/8)=0.653\\sqrt{2}$)という状態を作るもののはずでした。実際に計算された終状態の状態ベクトルが一致しています。" @@ -164,7 +164,7 @@ }, { "cell_type": "markdown", - "id": "bfe20035", + "id": "f6874cc2", "metadata": {}, "source": [ "(other_gates)=\n", @@ -175,7 +175,7 @@ }, { "cell_type": "markdown", - "id": "9470ae92", + "id": "dbe37191", "metadata": {}, "source": [ "### 1、2量子ビット\n", @@ -225,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "6787e991", + "id": "b72b9dbf", "metadata": {}, "source": [ "### 3量子ビット以上\n", @@ -253,19 +253,21 @@ }, { "cell_type": "markdown", - "id": "fd2a57f2", + "id": "8981c154", "metadata": {}, "source": [ "## 量子状態生成\n", "\n", "それでは、これまでに登場したゲートを使って量子状態生成のエクササイズをしましょう。\n", "\n", - "実は`statevector_expr`関数には回路オブジェクトを直接渡すこともできるので(内部でシミュレータを実行し状態ベクトルオブジェクトを取得する)、ここからはその機能を利用します。また、コード中登場する`amp_norm`や`phase_norm`は、表示される数式において振幅や位相の共通因子をくくりだすために設定されています。" + "実は`statevector_expr`関数には回路オブジェクトを直接渡すこともできるので(内部でシミュレータを実行し状態ベクトルオブジェクトを取得する)、ここからはその機能を利用します。また、コード中登場する`amp_norm`や`phase_norm`は、表示される数式において振幅や位相の共通因子をくくりだすために設定されています。\n", + "\n", + "各問題のコードセルには、ヒントとして回路が一部分だけ書かれています。残りの`circuit.?`の部分を埋めてみましょう。答えは一行とは限りません。また、同じ状態を作る量子回路は無数に存在するので、ヒントを消して独自の実装をしても構いません。" ] }, { "cell_type": "markdown", - "id": "a6d4df8e", + "id": "648eedee", "metadata": {}, "source": [ "### 問題1: 1量子ビット、相対位相付き\n", @@ -284,7 +286,7 @@ { "cell_type": "code", "execution_count": null, - "id": "82f81276", + "id": "1c5be92a", "metadata": { "tags": [ "remove-output" @@ -308,7 +310,7 @@ }, { "cell_type": "markdown", - "id": "cbc86a1a", + "id": "8cd4e204", "metadata": {}, "source": [ "**解答**\n", @@ -335,7 +337,7 @@ }, { "cell_type": "markdown", - "id": "bf5bd643", + "id": "3962551d", "metadata": {}, "source": [ "### 問題2: ベル状態、相対位相付き\n", @@ -354,7 +356,7 @@ { "cell_type": "code", "execution_count": null, - "id": "665d75e3", + "id": "c849b8eb", "metadata": { "tags": [ "remove-output" @@ -379,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "e847ddad", + "id": "372aa682", "metadata": {}, "source": [ "**解答**\n", @@ -397,7 +399,7 @@ }, { "cell_type": "markdown", - "id": "3fe02630", + "id": "48bc41a8", "metadata": {}, "source": [ "### 問題3: GHZ状態\n", @@ -416,7 +418,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f66e024d", + "id": "5c0faf4e", "metadata": { "tags": [ "remove-output" @@ -441,7 +443,7 @@ }, { "cell_type": "markdown", - "id": "0304b024", + "id": "5323dd29", "metadata": { "tags": [ "hide-cell" @@ -463,7 +465,7 @@ }, { "cell_type": "markdown", - "id": "e4ff7483", + "id": "7640b851", "metadata": {}, "source": [ "### 問題4: Equal superposition\n", @@ -482,7 +484,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c7db5f0c", + "id": "b559f914", "metadata": { "tags": [ "remove-output" @@ -509,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "1baabfca", + "id": "c4b26564", "metadata": { "tags": [ "hide-cell" @@ -537,7 +539,7 @@ }, { "cell_type": "markdown", - "id": "7a3ca434", + "id": "447ae62a", "metadata": {}, "source": [ "### 問題5: 特定の基底の符号を反転させる\n", @@ -550,7 +552,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1fcd7de4", + "id": "3e98bc69", "metadata": { "tags": [ "remove-output" @@ -580,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "e7737270", + "id": "233ed44c", "metadata": { "tags": [ "hide-cell" @@ -611,7 +613,7 @@ }, { "cell_type": "markdown", - "id": "366da14f", + "id": "400666a1", "metadata": {}, "source": [ "(equal_superposition_with_phase)=\n", @@ -631,7 +633,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c37c1997", + "id": "23e6841e", "metadata": { "tags": [ "output_scroll", @@ -666,7 +668,7 @@ }, { "cell_type": "markdown", - "id": "a5e2f2d4", + "id": "cd0166ce", "metadata": { "tags": [ "hide-cell" @@ -714,7 +716,7 @@ }, { "cell_type": "markdown", - "id": "621fca28", + "id": "15bdc1c3", "metadata": {}, "source": [ "## 量子計算プリミティブ\n", @@ -724,7 +726,7 @@ }, { "cell_type": "markdown", - "id": "fd10917c", + "id": "966d62f8", "metadata": {}, "source": [ "### 条件分岐\n", @@ -741,7 +743,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c6de4d6", + "id": "31b53820", "metadata": {}, "outputs": [], "source": [ @@ -769,7 +771,7 @@ }, { "cell_type": "markdown", - "id": "ce439d5c", + "id": "5f268d35", "metadata": {}, "source": [ "測定オペレーションが入っているので、この回路をstatevector simulatorに渡すと、シミュレーションを実行するごとにレジスタ1の状態がランダムに決定されます。次のセルを複数回実行して、上の回路が狙い通り動いていることを確認してみましょう。\n", @@ -780,7 +782,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bfcd5269", + "id": "03931038", "metadata": {}, "outputs": [], "source": [ @@ -806,7 +808,7 @@ }, { "cell_type": "markdown", - "id": "1a58b3f7", + "id": "d17a0dfb", "metadata": {}, "source": [ "#### 条件分岐としての制御ゲート\n", @@ -819,7 +821,7 @@ { "cell_type": "code", "execution_count": null, - "id": "15cfefdf", + "id": "b5ebdfab", "metadata": {}, "outputs": [], "source": [ @@ -840,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "47ba7c0d", + "id": "29ae9182", "metadata": {}, "source": [ "今度は全ての分岐が重ね合わさった量子状態が実現しています。" @@ -849,7 +851,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d264f40c", + "id": "ee519964", "metadata": {}, "outputs": [], "source": [ @@ -859,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "f3d23f51", + "id": "57909bf5", "metadata": {}, "source": [ "### 関数\n", @@ -882,7 +884,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85dfffee", + "id": "a10c422b", "metadata": {}, "outputs": [], "source": [ @@ -910,7 +912,7 @@ { "cell_type": "code", "execution_count": null, - "id": "726dbf5e", + "id": "d3b00565", "metadata": {}, "outputs": [], "source": [ @@ -919,7 +921,7 @@ }, { "cell_type": "markdown", - "id": "2f553758", + "id": "ce5b2a45", "metadata": {}, "source": [ "入力レジスタの状態を色々変えて、状態ベクトルの変化を見てみましょう。\n", @@ -984,7 +986,7 @@ }, { "cell_type": "markdown", - "id": "bcd41953", + "id": "cf56204e", "metadata": {}, "source": [ "#### SWAPテスト\n", @@ -1002,7 +1004,7 @@ { "cell_type": "code", "execution_count": null, - "id": "943d60bc", + "id": "128a4608", "metadata": {}, "outputs": [], "source": [ @@ -1059,7 +1061,7 @@ { "cell_type": "code", "execution_count": null, - "id": "870dc42a", + "id": "7624d04b", "metadata": {}, "outputs": [], "source": [ @@ -1068,7 +1070,7 @@ }, { "cell_type": "markdown", - "id": "dcc1e48f", + "id": "337cda25", "metadata": {}, "source": [ "式{eq}`swap_test`を導いてみましょう。\n", @@ -1120,7 +1122,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ae85f646", + "id": "012d3d48", "metadata": {}, "outputs": [], "source": [ @@ -1130,7 +1132,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a0da4ac0", + "id": "bbbc00c6", "metadata": {}, "outputs": [], "source": [ @@ -1139,7 +1141,7 @@ }, { "cell_type": "markdown", - "id": "7ef5dd0f", + "id": "0e8b4fc7", "metadata": {}, "source": [ "で、$|\\braket{\\psi}{\\phi}|^2$は" @@ -1148,7 +1150,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07ffe2d6", + "id": "08cc1b1d", "metadata": {}, "outputs": [], "source": [ @@ -1159,7 +1161,7 @@ }, { "cell_type": "markdown", - "id": "5196bde8", + "id": "b9e8577a", "metadata": {}, "source": [ "それに対し上の回路を1000000回実行した時の$P_0 - P_1$は" @@ -1168,7 +1170,7 @@ { "cell_type": "code", "execution_count": null, - "id": "01578d25", + "id": "4bb2ca43", "metadata": {}, "outputs": [], "source": [ @@ -1183,7 +1185,7 @@ }, { "cell_type": "markdown", - "id": "f4bbc644", + "id": "345ddb32", "metadata": {}, "source": [ "です。" @@ -1191,7 +1193,7 @@ }, { "cell_type": "markdown", - "id": "86ab6bb2", + "id": "50c2a49a", "metadata": {}, "source": [ "(inverse_circuit)=\n", @@ -1212,7 +1214,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4704e8b", + "id": "1029ee00", "metadata": {}, "outputs": [], "source": [ @@ -1230,7 +1232,7 @@ }, { "cell_type": "markdown", - "id": "d5c4df86", + "id": "85eae3cb", "metadata": {}, "source": [ "ポイントは`psi_circuit.inverse()`で得られる`psi_circuit`の逆回路です。逆回路とは、ゲートの順番を反転させ、全てのゲートをその逆操作で置き換えたものです。$\\ket{0}$から$\\ket{\\psi}$を作る回路を$U_{\\psi}$と表すと、逆回路は$U_{\\psi}^{-1}$もしくは$U_{\\psi}^{\\dagger}$と書かれ、\n", @@ -1250,7 +1252,7 @@ }, { "cell_type": "markdown", - "id": "e88670b0", + "id": "54005903", "metadata": {}, "source": [ "```{toggle}\n", @@ -1305,7 +1307,7 @@ }, { "cell_type": "markdown", - "id": "ac11e862", + "id": "9373375f", "metadata": {}, "source": [ "上の回路で式{eq}`inverse_circuit`を確認しましょう。" @@ -1314,7 +1316,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9af8f84e", + "id": "7d087373", "metadata": {}, "outputs": [], "source": [ @@ -1328,7 +1330,7 @@ }, { "cell_type": "markdown", - "id": "d87221d8", + "id": "1bb84d77", "metadata": {}, "source": [ "## 複製不可能定理とテレポーテーション\n", @@ -1346,7 +1348,7 @@ }, { "cell_type": "markdown", - "id": "f79d628b", + "id": "14266afa", "metadata": {}, "source": [ "```{toggle}\n", @@ -1374,7 +1376,7 @@ }, { "cell_type": "markdown", - "id": "bc7bd9d7", + "id": "70712e73", "metadata": {}, "source": [ "複製不可能定理は量子回路で実行できる計算のクラスを大幅に制限します。例えば、何かの計算を途中で打ち切ってその時点での量子状態をなんらかのメモリデバイスに保存できたとして、その状態をコピーすることができないので、結局そこから計算を再開できるのは一度だけということになります。\n", @@ -1387,7 +1389,7 @@ { "cell_type": "code", "execution_count": null, - "id": "63dc8bb4", + "id": "c01c8416", "metadata": {}, "outputs": [], "source": [ @@ -1429,7 +1431,7 @@ }, { "cell_type": "markdown", - "id": "e75a044d", + "id": "9aca4ef0", "metadata": {}, "source": [ "入力ビットの状態は" @@ -1438,7 +1440,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b953d5e", + "id": "dbcbd129", "metadata": {}, "outputs": [], "source": [ @@ -1447,7 +1449,7 @@ }, { "cell_type": "markdown", - "id": "5731b6d9", + "id": "c405f5d3", "metadata": {}, "source": [ "回路の終状態は" @@ -1456,7 +1458,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8c089cb4", + "id": "1af1a5b0", "metadata": {}, "outputs": [], "source": [ @@ -1465,7 +1467,7 @@ }, { "cell_type": "markdown", - "id": "ef605d6e", + "id": "72322c1a", "metadata": {}, "source": [ "上のセルを何度か実行すると、右二つのレジスタは実行するごとにランダムに違う値を取るものの、二つの項で共通で、一番左のレジスタが$\\ket{\\text{in}}$と同じ状態にあることがわかります。このようにテレポーテーションが実際に起こることを、上の回路を元に数式でも確認してみるといいでしょう。" @@ -1516,63 +1518,63 @@ 124, 170, 194, - 202, - 216, - 231, - 254, - 268, - 284, - 298, - 312, - 330, - 344, - 358, - 378, - 398, - 406, - 429, - 452, - 467, - 494, - 534, - 540, - 552, - 573, - 579, - 598, - 606, - 620, - 624, - 627, - 645, - 667, + 204, + 218, + 233, + 256, + 270, + 286, + 300, + 314, + 332, + 346, + 360, + 380, + 400, + 408, + 431, + 454, + 469, + 496, + 536, + 542, + 554, + 575, + 581, + 600, + 608, + 622, + 626, + 629, + 647, 669, - 730, - 743, - 794, + 671, + 732, + 745, 796, - 843, - 847, + 798, + 845, 849, - 853, - 857, - 861, - 869, - 873, - 889, - 900, - 916, - 967, - 971, - 978, - 992, - 1016, - 1024, - 1059, - 1063, + 851, + 855, + 859, + 863, + 871, + 875, + 891, + 902, + 918, + 969, + 973, + 980, + 994, + 1018, + 1026, + 1061, 1065, - 1069, - 1071 + 1067, + 1071, + 1073 ] }, "nbformat": 4, diff --git a/_sources/circuit_from_scratch.md b/_sources/circuit_from_scratch.md index b889596a..89ff589f 100644 --- a/_sources/circuit_from_scratch.md +++ b/_sources/circuit_from_scratch.md @@ -199,6 +199,8 @@ circuit.mcry(theta, [i, j], k) 実は`statevector_expr`関数には回路オブジェクトを直接渡すこともできるので(内部でシミュレータを実行し状態ベクトルオブジェクトを取得する)、ここからはその機能を利用します。また、コード中登場する`amp_norm`や`phase_norm`は、表示される数式において振幅や位相の共通因子をくくりだすために設定されています。 +各問題のコードセルには、ヒントとして回路が一部分だけ書かれています。残りの`circuit.?`の部分を埋めてみましょう。答えは一行とは限りません。また、同じ状態を作る量子回路は無数に存在するので、ヒントを消して独自の実装をしても構いません。 + +++ ### 問題1: 1量子ビット、相対位相付き diff --git a/_sources/dynamics_simulation.ipynb b/_sources/dynamics_simulation.ipynb index 916cb410..dbad6e00 100644 --- a/_sources/dynamics_simulation.ipynb +++ b/_sources/dynamics_simulation.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5a7a3ce6", + "id": "3db99e81", "metadata": {}, "source": [ "# 物理系を表現する\n", @@ -25,7 +25,7 @@ }, { "cell_type": "markdown", - "id": "cb7a2583", + "id": "e45c8570", "metadata": {}, "source": [ "## 量子系のダイナミクスとは\n", @@ -55,7 +55,7 @@ }, { "cell_type": "markdown", - "id": "3bf94593", + "id": "b2a30dff", "metadata": {}, "source": [ "### 例:核磁気の歳差運動\n", @@ -116,7 +116,7 @@ }, { "cell_type": "markdown", - "id": "dfd48998", + "id": "27995e59", "metadata": {}, "source": [ "### 量子コンピュータ上での表現\n", @@ -136,7 +136,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c43e171", + "id": "8026403d", "metadata": { "tags": [ "remove-input" @@ -152,7 +152,7 @@ { "cell_type": "code", "execution_count": null, - "id": "46e13395", + "id": "1064f762", "metadata": { "tags": [ "remove-input" @@ -168,7 +168,7 @@ }, { "cell_type": "markdown", - "id": "04cf92c0", + "id": "6a747a8c", "metadata": {}, "source": [ "### ハミルトニアンの対角化\n", @@ -239,7 +239,7 @@ }, { "cell_type": "markdown", - "id": "91aa0441", + "id": "5b52e920", "metadata": {}, "source": [ "### 鈴木・トロッター分解\n", @@ -302,7 +302,7 @@ }, { "cell_type": "markdown", - "id": "63377f2f", + "id": "3139bd48", "metadata": {}, "source": [ "### なぜ量子コンピュータが量子ダイナミクスシミュレーションに向いているか\n", @@ -329,7 +329,7 @@ }, { "cell_type": "markdown", - "id": "98a3b486", + "id": "11e7d64b", "metadata": {}, "source": [ "## 実習:ハイゼンベルグモデルの時間発展\n", @@ -398,7 +398,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dc3fe51c", + "id": "b699ff27", "metadata": { "tags": [ "remove-input" @@ -415,7 +415,7 @@ }, { "cell_type": "markdown", - "id": "fab00b18", + "id": "195bab2e", "metadata": {}, "source": [ "によって、計算基底$\\ket{00}, \\ket{01}, \\ket{10}, \\ket{11}$はそれぞれ\n", @@ -448,7 +448,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a12ae07", + "id": "f8605180", "metadata": { "tags": [ "remove-input" @@ -469,7 +469,7 @@ }, { "cell_type": "markdown", - "id": "a487e947", + "id": "839781c2", "metadata": {}, "source": [ "最後に、$\\exp(\\frac{i \\omega \\Delta t}{2} \\sigma^Y_j\\sigma^Y_{j+1})$に対応する回路は" @@ -478,7 +478,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f4bbd96", + "id": "bae5cab3", "metadata": { "tags": [ "remove-input" @@ -503,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "aa407ad0", + "id": "f3775a18", "metadata": {}, "source": [ "です[^sgate]。\n", @@ -518,7 +518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef95642b", + "id": "22ec332c", "metadata": {}, "outputs": [], "source": [ @@ -537,7 +537,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ad2ddc4", + "id": "d9306599", "metadata": {}, "outputs": [], "source": [ @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "28679116", + "id": "86ee4864", "metadata": {}, "source": [ "量子回路シミュレーターで実行し、各ビットにおける$Z$方向スピンの期待値をプロットしましょう。プロット用の関数は比較的長くなってしまいますが実習の本質とそこまで関係しないので、[別ファイル](https://github.com/UTokyo-ICEPP/qc-workbook/blob/master/source/utils/dynamics.py)に定義してあります。関数はジョブの実行結果、系のスピンの数、初期状態、ステップ間隔を引数にとります。" @@ -601,7 +601,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43138394", + "id": "11c14a66", "metadata": {}, "outputs": [], "source": [ @@ -622,7 +622,7 @@ }, { "cell_type": "markdown", - "id": "598ce2b7", + "id": "466cd17a", "metadata": {}, "source": [ "ビット0でのスピンの不整合が徐々に他のビットに伝搬していく様子が観察できました。\n", @@ -635,7 +635,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b4e6a8f", + "id": "1884c30a", "metadata": { "tags": [ "raises-exception", @@ -661,7 +661,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3df5b835", + "id": "e3ca4be9", "metadata": { "tags": [ "raises-exception", @@ -682,7 +682,7 @@ { "cell_type": "code", "execution_count": null, - "id": "234b91d4", + "id": "e7e7a445", "metadata": { "tags": [ "raises-exception", diff --git a/_sources/extreme_simd.ipynb b/_sources/extreme_simd.ipynb index 502d98f2..d4c2825c 100644 --- a/_sources/extreme_simd.ipynb +++ b/_sources/extreme_simd.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e67c5d1f", + "id": "f9769b2c", "metadata": {}, "source": [ "# 計算をする量子回路の実装" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "1c5dc2b4", + "id": "feaac637", "metadata": {}, "source": [ "量子計算をする回路の感覚がつかめてきたところで、量子計算をするとはどういうことかに話を移して行きましょう。\n", @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "877e8d36", + "id": "dea26aa5", "metadata": {}, "source": [ "## 量子計算の特徴\n", @@ -53,7 +53,7 @@ }, { "cell_type": "markdown", - "id": "7c5dd431", + "id": "fe7e15ea", "metadata": {}, "source": [ "(QFT)=\n", @@ -86,7 +86,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1832ccec", + "id": "c6608add", "metadata": { "tags": [ "remove-output" @@ -113,7 +113,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9500ecf4", + "id": "e98684fa", "metadata": {}, "outputs": [], "source": [ @@ -169,7 +169,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c3ecf45", + "id": "cbdae420", "metadata": {}, "outputs": [], "source": [ @@ -182,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "b05174cb", + "id": "928d5f67", "metadata": {}, "source": [ "上の回路でどうQFTが実現できるのか、初見で一目でわかる人は世界で数人しかいないでしょう。実際に状態を書き下しながら回路を追ってみましょう。\n", @@ -283,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "aab0ea35", + "id": "58a00fbc", "metadata": {}, "source": [ "(fourier_addition)=\n", @@ -307,7 +307,7 @@ { "cell_type": "code", "execution_count": null, - "id": "571596f6", + "id": "9618e123", "metadata": { "tags": [ "remove-output" @@ -352,7 +352,7 @@ }, { "cell_type": "markdown", - "id": "7dc3afbc", + "id": "fb4a19a4", "metadata": {}, "source": [ "サブルーチンを具体的に数式で追ってみましょう。\n", @@ -428,7 +428,7 @@ { "cell_type": "code", "execution_count": null, - "id": "64d8371f", + "id": "211033ef", "metadata": {}, "outputs": [], "source": [ @@ -468,7 +468,7 @@ }, { "cell_type": "markdown", - "id": "722e3fea", + "id": "14e2efc5", "metadata": {}, "source": [ "再び`statevector_expr`関数を使って終状態を確認してみましょう。" @@ -477,7 +477,7 @@ { "cell_type": "code", "execution_count": null, - "id": "548bba40", + "id": "1b1c4eed", "metadata": {}, "outputs": [], "source": [ @@ -487,7 +487,7 @@ }, { "cell_type": "markdown", - "id": "1a1530b5", + "id": "efaa35c2", "metadata": {}, "source": [ "結果表示された状態は期待通り単一の計算基底$22:13:9$、つまりレジスタ1, 2, 3がそれぞれ$\\ket{9}, \\ket{13}, \\ket{22}$となっている状態です(回路全体でビットを右から書いて状態を表示するため、レジスタも右から左に並びます)。つまり、めでたく状態の変遷\n", @@ -501,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "9f6c6577", + "id": "e1fe1170", "metadata": {}, "source": [ "## 足し算の並列化\n", @@ -518,7 +518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d7beed2c", + "id": "1860e3a5", "metadata": {}, "outputs": [], "source": [ @@ -544,7 +544,7 @@ }, { "cell_type": "markdown", - "id": "b3c13ccd", + "id": "b4b145e0", "metadata": {}, "source": [ "2022年4月現在、IBMの持つ最大の量子コンピュータは127量子ビットです。このマシンを最大限利用するならば、$n_1 = n_2 = 42, n_3 = 43$で$2^{84}$通り、つまり約$2 \\times 10^{25}$(20𥝱)通りの足し算を同時に行うことができます。\n", @@ -559,7 +559,7 @@ { "cell_type": "code", "execution_count": null, - "id": "68ca704b", + "id": "5c83a463", "metadata": { "tags": [ "remove-output" @@ -578,7 +578,7 @@ }, { "cell_type": "markdown", - "id": "918a954a", + "id": "42eebf17", "metadata": {}, "source": [ "回路の効率化とは具体的にどういうことでしょうか。もともとの回路と効率化したものとを比べてみましょう。まずは、単純にオペレーションの数を比較します。ゲート一つ一つで一定の確率でエラーが起こるということは、同じことをする回路ならゲートの数が少ないほうがより正確な計算をしてくれます。" @@ -587,7 +587,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4576d5b", + "id": "71eca077", "metadata": {}, "outputs": [], "source": [ @@ -597,7 +597,7 @@ }, { "cell_type": "markdown", - "id": "30a87d0f", + "id": "47261126", "metadata": {}, "source": [ "効率化したはずの回路のほうがはるかにゲート数が多いという結果になりました。なぜでしょうか。" @@ -605,7 +605,7 @@ }, { "cell_type": "markdown", - "id": "f24b16cc", + "id": "8e5ffbde", "metadata": {}, "source": [ "(transpilation)=\n", @@ -649,7 +649,7 @@ }, { "cell_type": "markdown", - "id": "40717b13", + "id": "86880e10", "metadata": {}, "source": [ "### 回路の比較\n", @@ -664,7 +664,7 @@ { "cell_type": "code", "execution_count": null, - "id": "272c74ff", + "id": "d3f00ac7", "metadata": { "tags": [ "remove-output" @@ -695,7 +695,7 @@ { "cell_type": "code", "execution_count": null, - "id": "221aface", + "id": "050ce9ca", "metadata": { "tags": [ "remove-output" @@ -727,7 +727,7 @@ }, { "cell_type": "markdown", - "id": "71e106e1", + "id": "cfc6f6a1", "metadata": {}, "source": [ "上のセルを実行すると、今度は効率化回路のオペレーションの全数が元の回路の8割、CNOTの数は6割という結果になることがわかります。\n", @@ -740,7 +740,7 @@ { "cell_type": "code", "execution_count": null, - "id": "29be2b14", + "id": "a9ea38a1", "metadata": { "tags": [ "remove-output" @@ -796,7 +796,7 @@ }, { "cell_type": "markdown", - "id": "d0cb0f07", + "id": "19cf921f", "metadata": {}, "source": [ "両方の回路とも、正しい足し算の式がランダムに出現していることを確認してください。" @@ -805,6 +805,7 @@ ], "metadata": { "jupytext": { + "formats": "md:myst,ipynb", "notebook_metadata_filter": "all", "text_representation": { "extension": ".md", @@ -831,35 +832,35 @@ "version": "3.10.6" }, "source_map": [ - 23, - 27, - 39, - 62, - 90, - 109, - 159, - 165, - 262, - 281, - 317, - 388, - 421, - 425, - 428, - 438, - 450, - 469, - 479, - 489, - 493, - 496, - 500, - 540, - 550, - 573, - 596, - 604, - 651 + 24, + 28, + 40, + 63, + 91, + 110, + 160, + 166, + 263, + 282, + 318, + 389, + 422, + 426, + 429, + 439, + 451, + 470, + 480, + 490, + 494, + 497, + 501, + 541, + 551, + 574, + 597, + 605, + 652 ] }, "nbformat": 4, diff --git a/_sources/extreme_simd.md b/_sources/extreme_simd.md index dc689134..6424eea2 100644 --- a/_sources/extreme_simd.md +++ b/_sources/extreme_simd.md @@ -1,5 +1,6 @@ --- jupytext: + formats: md:myst,ipynb notebook_metadata_filter: all text_representation: extension: .md diff --git a/_sources/grover.ipynb b/_sources/grover.ipynb index 0f039990..2ce5762e 100644 --- a/_sources/grover.ipynb +++ b/_sources/grover.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "11e34aee", + "id": "acba69dc", "metadata": { "pycharm": { "name": "#%% md\n" @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "03638932", + "id": "f87e5235", "metadata": {}, "source": [ "ここでは、**グローバーのアルゴリズム**{cite}`grover_search,nielsen_chuang_search`の紹介と、そのアルゴリズムを使用して構造化されていないデータベースを検索する問題を考えます。アルゴリズムを説明した後に、Qiskitを使用してグローバーのアルゴリズムを実装します。\n", @@ -32,7 +32,7 @@ }, { "cell_type": "markdown", - "id": "4ed3b2a6", + "id": "66651270", "metadata": {}, "source": [ "## はじめに\n", @@ -42,7 +42,7 @@ }, { "cell_type": "markdown", - "id": "28b62bbb", + "id": "2fbbd4ec", "metadata": {}, "source": [ "(database)=\n", @@ -53,7 +53,7 @@ }, { "cell_type": "markdown", - "id": "96b74189", + "id": "3c160053", "metadata": {}, "source": [ "(grover)=\n", @@ -64,7 +64,7 @@ }, { "cell_type": "markdown", - "id": "ae5cebc7", + "id": "68947c97", "metadata": {}, "source": [ "(grover_phaseoracle)=\n", @@ -113,7 +113,7 @@ }, { "cell_type": "markdown", - "id": "49443124", + "id": "30adc592", "metadata": {}, "source": [ "(grover_circuit)=\n", @@ -150,7 +150,7 @@ }, { "cell_type": "markdown", - "id": "e5ae7251", + "id": "d1e67c36", "metadata": {}, "source": [ "(grover_superposition)=\n", @@ -166,7 +166,7 @@ }, { "cell_type": "markdown", - "id": "40cc94e9", + "id": "47d70bc3", "metadata": {}, "source": [ "(grover_geometry)=\n", @@ -200,7 +200,7 @@ }, { "cell_type": "markdown", - "id": "2215c12f", + "id": "7958c3d6", "metadata": {}, "source": [ "(grover_oracle)=\n", @@ -216,7 +216,7 @@ }, { "cell_type": "markdown", - "id": "96d186dd", + "id": "1d261ced", "metadata": {}, "source": [ "(grover_diffuser)=\n", @@ -281,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "563cc40d", + "id": "d297b150", "metadata": {}, "source": [ "(grover_amp)=\n", @@ -303,7 +303,7 @@ }, { "cell_type": "markdown", - "id": "fa623b3c", + "id": "b6fd9cc0", "metadata": {}, "source": [ "(grover_multidata)=\n", @@ -331,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "1f7b325c", + "id": "692f0e12", "metadata": { "pycharm": { "name": "#%% md\n" @@ -347,7 +347,7 @@ }, { "cell_type": "markdown", - "id": "2e0dfded", + "id": "4cd2ab6e", "metadata": {}, "source": [ "(imp_qiskit)=\n", @@ -359,7 +359,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9fe7e802", + "id": "d4f8d292", "metadata": { "jupyter": { "outputs_hidden": false @@ -389,7 +389,7 @@ }, { "cell_type": "markdown", - "id": "27cf3fee", + "id": "f13e7649", "metadata": {}, "source": [ "6量子ビットの回路`grover_circuit`を準備します。\n", @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "10062dc0", + "id": "2f1354ee", "metadata": { "jupyter": { "outputs_hidden": false @@ -452,7 +452,7 @@ }, { "cell_type": "markdown", - "id": "3c3e386a", + "id": "539f0cb4", "metadata": {}, "source": [ "**解答**\n", @@ -486,7 +486,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8964ad82", + "id": "f5e948c3", "metadata": { "jupyter": { "outputs_hidden": false @@ -526,7 +526,7 @@ }, { "cell_type": "markdown", - "id": "4bc0da50", + "id": "97c50687", "metadata": {}, "source": [ "**解答**\n", @@ -577,7 +577,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4ce2dde2", + "id": "943e4b1e", "metadata": { "jupyter": { "outputs_hidden": false @@ -620,7 +620,7 @@ }, { "cell_type": "markdown", - "id": "68e50c1e", + "id": "995b964a", "metadata": {}, "source": [ "正しく回路が実装できていれば、$\\ket{101101}=\\ket{45}$の状態を高い確率で測定できる様子を見ることができるでしょう。\n", @@ -630,7 +630,7 @@ }, { "cell_type": "markdown", - "id": "01f2f9ee", + "id": "b0e92706", "metadata": {}, "source": [ "(imp_qc)=\n", @@ -642,7 +642,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2dccafe6", + "id": "684768d7", "metadata": { "jupyter": { "outputs_hidden": false @@ -673,7 +673,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df03ff8e", + "id": "6b4d4125", "metadata": { "jupyter": { "outputs_hidden": false @@ -698,7 +698,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5465ae5e", + "id": "57ee1ab3", "metadata": { "jupyter": { "outputs_hidden": false @@ -721,7 +721,7 @@ }, { "cell_type": "markdown", - "id": "9753d87a", + "id": "80be0651", "metadata": {}, "source": [ "シミュレータに比べると結果は非常に悪いですね。。。残念ながら、今の量子コンピュータをそのまま使うとこういう結果になってしまいます。しかし、{ref}`エラー緩和 `等のテクニックを使うことである程度改善することはできます。" @@ -729,7 +729,7 @@ }, { "cell_type": "markdown", - "id": "997f1777", + "id": "712f6898", "metadata": { "pycharm": { "name": "#%% md\n" @@ -747,7 +747,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ccf8ebef", + "id": "a186854d", "metadata": { "pycharm": { "name": "#%%\n" @@ -770,7 +770,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5994337", + "id": "5c930d6e", "metadata": { "pycharm": { "name": "#%%\n" @@ -786,7 +786,7 @@ }, { "cell_type": "markdown", - "id": "a93ea585", + "id": "9b9f887e", "metadata": { "pycharm": { "name": "#%% md\n" @@ -801,7 +801,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2abd0fb1", + "id": "98e87253", "metadata": { "pycharm": { "name": "#%%\n" @@ -837,7 +837,7 @@ }, { "cell_type": "markdown", - "id": "704d752c", + "id": "66d6de72", "metadata": { "pycharm": { "name": "#%% md\n" @@ -849,7 +849,7 @@ }, { "cell_type": "markdown", - "id": "a4e71be4", + "id": "bf456c3d", "metadata": { "pycharm": { "name": "#%% md\n" @@ -861,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "f047a0ff", + "id": "449ca7f4", "metadata": { "pycharm": { "name": "#%% md\n" @@ -879,7 +879,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c73225b", + "id": "b7cebecc", "metadata": { "pycharm": { "name": "#%%\n" @@ -945,7 +945,7 @@ }, { "cell_type": "markdown", - "id": "0eda7d93", + "id": "dc3e2cac", "metadata": { "pycharm": { "name": "#%% md\n" diff --git a/_sources/grover_number_light.ipynb b/_sources/grover_number_light.ipynb index bc9a2a08..9665c9fd 100644 --- a/_sources/grover_number_light.ipynb +++ b/_sources/grover_number_light.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "817e5f40", + "id": "49d6b0e7", "metadata": {}, "source": [ "# 【課題】ビット反転ボードの操作を見つける\n", @@ -12,7 +12,7 @@ }, { "cell_type": "markdown", - "id": "c573a0c1", + "id": "17300409", "metadata": { "pycharm": { "name": "#%% md\n" @@ -50,7 +50,7 @@ }, { "cell_type": "markdown", - "id": "56d2fa00", + "id": "6999c871", "metadata": { "pycharm": { "name": "#%% md\n" @@ -77,7 +77,7 @@ { "cell_type": "code", "execution_count": null, - "id": "82aafebd", + "id": "565fdb2b", "metadata": { "jupyter": { "outputs_hidden": false @@ -96,7 +96,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5f93041", + "id": "ff8d198a", "metadata": { "jupyter": { "outputs_hidden": false @@ -122,7 +122,7 @@ }, { "cell_type": "markdown", - "id": "4f6d57ed", + "id": "75b5fc3b", "metadata": {}, "source": [ "以下の回路の中身を書いてください。" @@ -131,7 +131,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cf45cfcf", + "id": "88c4e673", "metadata": { "jupyter": { "outputs_hidden": false @@ -157,7 +157,7 @@ }, { "cell_type": "markdown", - "id": "ea5e2597", + "id": "7ebf55bd", "metadata": {}, "source": [ "コードをシミュレータで実行して、答えを確認する。\n", @@ -167,7 +167,7 @@ { "cell_type": "code", "execution_count": null, - "id": "86b1b79f", + "id": "e3a81e80", "metadata": { "jupyter": { "outputs_hidden": false @@ -198,7 +198,7 @@ }, { "cell_type": "markdown", - "id": "ea81e4c1", + "id": "c4835e55", "metadata": { "pycharm": { "name": "#%% md\n" diff --git a/_sources/more_dynamics.ipynb b/_sources/more_dynamics.ipynb index 4f249a29..1949427d 100644 --- a/_sources/more_dynamics.ipynb +++ b/_sources/more_dynamics.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "0a9e60d3", + "id": "b444678b", "metadata": {}, "source": [ "# 【課題】量子ダイナミクスシミュレーション・続\n", @@ -21,7 +21,7 @@ }, { "cell_type": "markdown", - "id": "5253c529", + "id": "7bb397d4", "metadata": {}, "source": [ "## 問題1: ハイゼンベルグモデル、X方向のスピン" @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "008c7c81", + "id": "1273571a", "metadata": {}, "source": [ "### 問題\n", @@ -44,7 +44,7 @@ { "cell_type": "code", "execution_count": null, - "id": "25cab10d", + "id": "5412c80f", "metadata": { "tags": [ "raises-exception", @@ -66,7 +66,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49b24da7", + "id": "6c70312e", "metadata": { "tags": [ "remove-output" @@ -149,7 +149,7 @@ }, { "cell_type": "markdown", - "id": "002cadcf", + "id": "f20b476e", "metadata": {}, "source": [ "**提出するもの**\n", @@ -160,7 +160,7 @@ }, { "cell_type": "markdown", - "id": "4183ee1c", + "id": "8caddcd0", "metadata": {}, "source": [ "### おまけ: スピン総和\n", @@ -180,7 +180,7 @@ }, { "cell_type": "markdown", - "id": "de9f347d", + "id": "09047ffe", "metadata": {}, "source": [ "## 問題2: シュウィンガーモデル\n", @@ -190,7 +190,7 @@ }, { "cell_type": "markdown", - "id": "be01d3c3", + "id": "51d9e914", "metadata": {}, "source": [ "### シュウィンガーモデルの物理\n", @@ -240,7 +240,7 @@ }, { "cell_type": "markdown", - "id": "23b493b8", + "id": "1ad6247f", "metadata": {}, "source": [ "### ハミルトニアンを物質場のみで記述する\n", @@ -285,7 +285,7 @@ }, { "cell_type": "markdown", - "id": "94aa2ae8", + "id": "be917c1d", "metadata": {}, "source": [ "### ハミルトニアンをパウリ行列で表現する\n", @@ -326,7 +326,7 @@ }, { "cell_type": "markdown", - "id": "2a7a490b", + "id": "f283069a", "metadata": {}, "source": [ "### 問題\n", @@ -371,7 +371,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2445dc09", + "id": "34c23372", "metadata": { "tags": [ "raises-exception", @@ -476,7 +476,7 @@ }, { "cell_type": "markdown", - "id": "6e2d78a3", + "id": "8e7a08a5", "metadata": { "tags": [ "remove-output" diff --git a/_sources/numerics.ipynb b/_sources/numerics.ipynb index 991815d2..67d87476 100644 --- a/_sources/numerics.ipynb +++ b/_sources/numerics.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e16df406", + "id": "943fb2b4", "metadata": {}, "source": [ "# 予備知識:数値表現\n", @@ -18,7 +18,7 @@ }, { "cell_type": "markdown", - "id": "d924fa5f", + "id": "ee0078af", "metadata": {}, "source": [ "(signed_binary)=\n", @@ -33,7 +33,7 @@ }, { "cell_type": "markdown", - "id": "967c5fb9", + "id": "3c403249", "metadata": {}, "source": [ "(nonintegral_fourier)=\n", @@ -61,13 +61,13 @@ { "cell_type": "code", "execution_count": 1, - "id": "bd169524", + "id": "2c82cf18", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 1, diff --git a/_sources/prerequisites.ipynb b/_sources/prerequisites.ipynb index 99cea4c4..b4d6298c 100644 --- a/_sources/prerequisites.ipynb +++ b/_sources/prerequisites.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d3b5b93c", + "id": "6aa854eb", "metadata": {}, "source": [ "# 実習の準備\n", @@ -16,7 +16,7 @@ }, { "cell_type": "markdown", - "id": "68a0f36a", + "id": "0a278d34", "metadata": {}, "source": [ "## IBM Quantum\n", @@ -42,7 +42,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "0c19edf6", + "id": "6aa89a94", "metadata": { "tags": [ "raises-exception", @@ -70,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "d8558190", + "id": "eb1d625c", "metadata": {}, "source": [ "トークンを保存することで、プログラム中でのIBM Quantumへの認証(IBMProviderの取得)は\n", diff --git a/_sources/python_intro.ipynb b/_sources/python_intro.ipynb index f454ab55..190fa53a 100644 --- a/_sources/python_intro.ipynb +++ b/_sources/python_intro.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "6864ff16", + "id": "fb4aabc1", "metadata": {}, "source": [ "# 予備知識:Python\n", @@ -16,7 +16,7 @@ }, { "cell_type": "markdown", - "id": "338decda", + "id": "5e01416f", "metadata": {}, "source": [ "## 基礎編\n", @@ -39,7 +39,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "43c9c219", + "id": "92d72c56", "metadata": { "tags": [ "remove-output" @@ -54,7 +54,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "9ccd9ec1", + "id": "53c4198b", "metadata": { "tags": [ "remove-output" @@ -69,7 +69,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "4aecad90", + "id": "bf846598", "metadata": { "tags": [ "remove-output" @@ -91,7 +91,7 @@ }, { "cell_type": "markdown", - "id": "c1d8f061", + "id": "09cb8e8b", "metadata": {}, "source": [ "あとで解説する関数やクラスの定義、`if`、`for`、`try`/`except`などの複合文では、全ての行を一定数の空白文字分(通常スペース4つ、流儀によっては2つ。タブ文字は使うべきでない)だけインデントさせます。" @@ -100,7 +100,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "e469a621", + "id": "ab4dde10", "metadata": { "tags": [ "remove-output" @@ -134,7 +134,7 @@ }, { "cell_type": "markdown", - "id": "c9f85903", + "id": "7f732fb7", "metadata": {}, "source": [ "インデントしたブロックの中で、さらにインデントを必要とする文を書く場合は、スペース8つ、12個、と入れ子状にインデントします。各レベルでのインデンテーション解消がブロックの終わりを意味します。" @@ -143,7 +143,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "9c5c8ba5", + "id": "43afb7fc", "metadata": { "tags": [ "remove-output" @@ -182,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "e1a4e558", + "id": "4cf73b03", "metadata": {}, "source": [ "```{admonition} インデンテーション\n", @@ -192,7 +192,7 @@ }, { "cell_type": "markdown", - "id": "6fb8f90a", + "id": "3f0750f6", "metadata": {}, "source": [ "### 変数\n", @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "ee4994c5", + "id": "b3025a3e", "metadata": { "tags": [ "remove-output" @@ -233,7 +233,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "02e7d455", + "id": "027c527c", "metadata": { "tags": [ "remove-output" @@ -247,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "cbd69cee", + "id": "5dbe1733", "metadata": {}, "source": [ "```{admonition} 文字列\n", @@ -262,7 +262,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "596399a9", + "id": "c24cf057", "metadata": { "tags": [ "remove-output" @@ -278,7 +278,7 @@ }, { "cell_type": "markdown", - "id": "214201d9", + "id": "f4015079", "metadata": {}, "source": [ "### 演算子\n", @@ -289,7 +289,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "809c5a90", + "id": "2559752e", "metadata": { "tags": [ "remove-output" @@ -370,7 +370,7 @@ }, { "cell_type": "markdown", - "id": "ffef0588", + "id": "49a451be", "metadata": {}, "source": [ "他にもビットシフト演算子などが存在しますが、このワークブックでは使用しないので割愛します。\n", @@ -385,7 +385,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "4909addd", + "id": "19d88f35", "metadata": { "tags": [ "remove-output" @@ -416,7 +416,7 @@ }, { "cell_type": "markdown", - "id": "98846d16", + "id": "037cdf88", "metadata": {}, "source": [ "### 基本のデータ型\n", @@ -433,7 +433,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "c14c7dd6", + "id": "fed11d26", "metadata": { "tags": [ "remove-output" @@ -471,7 +471,7 @@ }, { "cell_type": "markdown", - "id": "4c334aaf", + "id": "69c0dbcb", "metadata": {}, "source": [ "#### 文字列型 str\n", @@ -482,7 +482,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "ee067e4a", + "id": "5a7705a4", "metadata": { "tags": [ "remove-output" @@ -503,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "8a0e4090", + "id": "a139c87a", "metadata": {}, "source": [ "同じことを例えばdouble quotesだけで表現することもできます。その場合、文字列中のクオーテーション記号にバックスラッシュを付け、文字列を囲む記号と区別します。" @@ -512,7 +512,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "f0968b80", + "id": "ff477394", "metadata": { "tags": [ "remove-output" @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "9fa8ba0d", + "id": "dfd6a691", "metadata": {}, "source": [ "上に比べて少しコードが読みにくくなることがわかります。\n", @@ -544,7 +544,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "0212fa16", + "id": "4133f0b9", "metadata": { "tags": [ "remove-output" @@ -566,7 +566,7 @@ }, { "cell_type": "markdown", - "id": "a98854f6", + "id": "31825544", "metadata": {}, "source": [ "これもまた読みにくいので、実はsingle quotesとdouble quotes以外にそれらの記号を3つ並べた`'''`や`\"\"\"`(三重クオート)でテキストを囲み、改行を含む文字列をそのまま書くこともできます。" @@ -575,7 +575,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "5450a80e", + "id": "435def83", "metadata": { "tags": [ "remove-output" @@ -607,7 +607,7 @@ }, { "cell_type": "markdown", - "id": "e835b1a8", + "id": "c0108622", "metadata": {}, "source": [ "改行やクオーテーション以外にも「特殊文字」があり、全てバックスラッシュで始まります。実際、通常の文字列中でバックスラッシュが一つ登場すると、Pythonはそのバックスラッシュと次の文字(場合によっては複数字)を組み合わせて特殊文字として解釈します。なので、実際のバックスラッシュをテキスト中に登場させたい場合(LaTeXのテキストを書いているときなど)は、一つだけ書くと解釈されないので、`\\\\`という特殊文字を利用します。" @@ -616,7 +616,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "bccafb3c", + "id": "2ad2189d", "metadata": { "tags": [ "remove-output" @@ -637,7 +637,7 @@ }, { "cell_type": "markdown", - "id": "21feaef7", + "id": "f66cced7", "metadata": {}, "source": [ "これも読みにくいテキストになってしまうので、バックスラッシュがたくさん使われる文字列を書く場合は、`r`というプレフィックスをクオーテーションの前にくっつけます。`r`のついた文字列中では、バックスラッシュが特殊文字として解釈されません。" @@ -646,7 +646,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "507a27dd", + "id": "18ba7658", "metadata": { "tags": [ "remove-output" @@ -667,7 +667,7 @@ }, { "cell_type": "markdown", - "id": "dee478fd", + "id": "73a2e648", "metadata": {}, "source": [ "ときどき、文字列型以外の変数を文字列に変換する必要が出てきます。例えば、`\"The value of variable x is \"`という文字列の後に、`x`という変数の値を付け加えたいとします。`x`が整数型だと`+`演算子を使ったらエラーになります。" @@ -676,7 +676,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "85e142a4", + "id": "15af6cab", "metadata": { "tags": [ "remove-output", @@ -706,7 +706,7 @@ }, { "cell_type": "markdown", - "id": "9b8c7a46", + "id": "3adefca4", "metadata": {}, "source": [ "文字列と整数の足し算は定義されていないためです。このような場合は、`str(x)`として`x`の10進数表現の文字列を作ります。" @@ -715,7 +715,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "0b6420e0", + "id": "38719378", "metadata": { "tags": [ "remove-output" @@ -737,7 +737,7 @@ }, { "cell_type": "markdown", - "id": "0e955800", + "id": "e6f527c3", "metadata": {}, "source": [ "ただ、この方法で変数の文字列表現をたくさん作ると、下のようにコードが冗長になりやすい問題があります。" @@ -746,7 +746,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "c7ecd0af", + "id": "ee0a5268", "metadata": { "tags": [ "remove-output" @@ -767,7 +767,7 @@ }, { "cell_type": "markdown", - "id": "8dda4a2e", + "id": "9d8047b3", "metadata": {}, "source": [ "そこで、Pythonでは文字列中に変数のプレースホルダーを入れ、後から変数値を代入することができるようになっています。ただ、歴史的経緯から、4つの異なる方法が実装されていて、少し厄介です。このワークブックでは2通りのみ使用することにします。\n", @@ -778,7 +778,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "cd20cce9", + "id": "3d341794", "metadata": { "tags": [ "remove-output" @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "b15e1173", + "id": "3d832ba8", "metadata": {}, "source": [ "f-stringは、実は変数に限らず、その場で評価可能な任意のプログラムコードを扱えます。中括弧の中にさらに文字列リテラルが入る場合は、全体の文字列に使っていないクオーテーション記号を使います。" @@ -808,7 +808,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "b9dedd25", + "id": "b9f1a455", "metadata": { "tags": [ "remove-output" @@ -833,7 +833,7 @@ }, { "cell_type": "markdown", - "id": "e068bfa4", + "id": "32900fb5", "metadata": {}, "source": [ "このようにf-stringで大体の目的は達成できますが、厄介になるのは実際に中括弧を含む文字列を作りたい場合です。f-string中の中括弧は二重にして表現するので、簡単な文字列でもコードが非常に読みにくくなります。" @@ -842,7 +842,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "f028666a", + "id": "41f7d267", "metadata": { "tags": [ "remove-output" @@ -867,7 +867,7 @@ }, { "cell_type": "markdown", - "id": "e3bdb51c", + "id": "eb2aafda", "metadata": {}, "source": [ "そこで、このワークブックでは中括弧を含む文字列に変数値を代入するときに限り、最も古い方式である%-formattingを使います。この方式でのプレースホルダーは、整数値を代入したいときは`%d`、実数値なら`%f`、文字列なら`%s`など、`%`文字と代入したいデータの型の識別子の組み合わせでできます。変数値を代入するには、文字列のすぐ後に` % 変数`をくっつけます。\n", @@ -880,7 +880,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "30dd1bb9", + "id": "8cf1e7fb", "metadata": { "tags": [ "remove-output" @@ -901,7 +901,7 @@ }, { "cell_type": "markdown", - "id": "f0741533", + "id": "fb39a76a", "metadata": {}, "source": [ "#### 配列型 tuple, list\n", @@ -912,7 +912,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "be5c4de4", + "id": "12c91409", "metadata": { "tags": [ "remove-output" @@ -938,7 +938,7 @@ }, { "cell_type": "markdown", - "id": "b765f8f7", + "id": "305d87ba", "metadata": {}, "source": [ "タプルやリストの要素を一つ参照するときは、鉤括弧でインデックス(要素の番号)を指定します。インデックスは0から始まるので、長さnの配列に対して有効なインデックスは0からn-1までです。" @@ -947,7 +947,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "590fa9c1", + "id": "e967d897", "metadata": { "tags": [ "remove-output" @@ -973,7 +973,7 @@ }, { "cell_type": "markdown", - "id": "dd15408f", + "id": "b6ecf8e1", "metadata": {}, "source": [ "リストでは要素を新しい値にすることができます。" @@ -982,7 +982,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "6270a713", + "id": "a8cbe53a", "metadata": { "tags": [ "remove-output" @@ -1006,7 +1006,7 @@ }, { "cell_type": "markdown", - "id": "6625b807", + "id": "32a92085", "metadata": {}, "source": [ "あとで説明するfor文を使って、配列の要素を順番に参照することもできます。" @@ -1015,7 +1015,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "efd4b732", + "id": "41347b27", "metadata": { "tags": [ "remove-output" @@ -1040,7 +1040,7 @@ }, { "cell_type": "markdown", - "id": "ce508f0f", + "id": "37100044", "metadata": {}, "source": [ "タプルやリストの長さ(要素数)は`len()`関数でわかります。" @@ -1049,7 +1049,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "f33a70b5", + "id": "855b7ec8", "metadata": { "tags": [ "remove-output" @@ -1072,7 +1072,7 @@ }, { "cell_type": "markdown", - "id": "7597ccba", + "id": "77869886", "metadata": {}, "source": [ "タプル同士やリスト同士は足し算で繋ぎ合わせられます。" @@ -1081,7 +1081,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "32272c01", + "id": "147899c8", "metadata": { "tags": [ "remove-output" @@ -1111,7 +1111,7 @@ }, { "cell_type": "markdown", - "id": "e055813c", + "id": "d6c9545c", "metadata": {}, "source": [ "数値に対してと同様、足し算での更新も可能です。" @@ -1120,7 +1120,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "862e2120", + "id": "f1d7d8ce", "metadata": { "tags": [ "remove-output" @@ -1145,7 +1145,7 @@ }, { "cell_type": "markdown", - "id": "af16d597", + "id": "ac1ae726", "metadata": {}, "source": [ "リストの最後に新たな要素を足すには、`append()`というメソッド(後の解説を参照)を使います。" @@ -1154,7 +1154,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "c406ef63", + "id": "dcc1823b", "metadata": { "tags": [ "remove-output" @@ -1176,7 +1176,7 @@ }, { "cell_type": "markdown", - "id": "cfe0748a", + "id": "6219751d", "metadata": {}, "source": [ "すでに説明した通り、タプルには要素を足せないので、対応するメソッドがありません。" @@ -1184,7 +1184,7 @@ }, { "cell_type": "markdown", - "id": "d9a52bbe", + "id": "c88e534a", "metadata": {}, "source": [ "#### 辞書型 dict\n", @@ -1195,7 +1195,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "a9e16052", + "id": "1cf47675", "metadata": { "tags": [ "remove-output" @@ -1213,7 +1213,7 @@ }, { "cell_type": "markdown", - "id": "40c5dbac", + "id": "cee74441", "metadata": {}, "source": [ "辞書型の要素を参照するときは鉤括弧にキーを入れます。辞書型と同様、要素の値を入れ替えることができます。また、全く新しいキーを加えることもできます。" @@ -1222,7 +1222,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "c290eedf", + "id": "15497393", "metadata": { "tags": [ "remove-output" @@ -1247,7 +1247,7 @@ }, { "cell_type": "markdown", - "id": "b9b42b35", + "id": "3c704ec8", "metadata": {}, "source": [ "辞書型に対しても`len()`が使えます。" @@ -1256,7 +1256,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "dcc0b968", + "id": "56ae3cfc", "metadata": { "tags": [ "remove-output" @@ -1277,7 +1277,7 @@ }, { "cell_type": "markdown", - "id": "b2bc1a39", + "id": "313b5a6d", "metadata": {}, "source": [ "#### 真理値型 bool\n", @@ -1288,7 +1288,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "d148ff21", + "id": "346b04ff", "metadata": { "tags": [ "remove-output" @@ -1340,7 +1340,7 @@ }, { "cell_type": "markdown", - "id": "07c9e6aa", + "id": "ef5a9fbf", "metadata": {}, "source": [ "#### None型\n", @@ -1350,7 +1350,7 @@ }, { "cell_type": "markdown", - "id": "61dda2af", + "id": "58bf6a5f", "metadata": {}, "source": [ "### 関数\n", @@ -1369,7 +1369,7 @@ { "cell_type": "code", "execution_count": 37, - "id": "5aa1daf2", + "id": "55fb25ef", "metadata": { "tags": [ "remove-output" @@ -1400,7 +1400,7 @@ }, { "cell_type": "markdown", - "id": "6b4897bf", + "id": "8edc1003", "metadata": {}, "source": [ "関数の引数にはデフォルトの値を持たせることができます。そのような引数には、関数実行時に値を指定されなければ、設定されたデフォルト値が代入されます。\n", @@ -1415,7 +1415,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "537fa1f7", + "id": "4b698af7", "metadata": { "tags": [ "remove-output" @@ -1455,7 +1455,7 @@ }, { "cell_type": "markdown", - "id": "7a02336b", + "id": "657da2f9", "metadata": {}, "source": [ "### if文(条件文)\n", @@ -1466,7 +1466,7 @@ { "cell_type": "code", "execution_count": 39, - "id": "5e4ff44b", + "id": "5807b695", "metadata": { "tags": [ "remove-output" @@ -1494,7 +1494,7 @@ { "cell_type": "code", "execution_count": 40, - "id": "abff49d7", + "id": "16b27b97", "metadata": { "tags": [ "remove-output" @@ -1517,7 +1517,7 @@ { "cell_type": "code", "execution_count": 41, - "id": "e59225a5", + "id": "47941695", "metadata": { "tags": [ "raises-exception", @@ -1544,7 +1544,7 @@ }, { "cell_type": "markdown", - "id": "b19d3852", + "id": "2b8d54e3", "metadata": {}, "source": [ "```{admonition} 変数のスコープ\n", @@ -1557,7 +1557,7 @@ { "cell_type": "code", "execution_count": 42, - "id": "c396383b", + "id": "d0e8cce5", "metadata": { "tags": [ "remove-output" @@ -1584,7 +1584,7 @@ }, { "cell_type": "markdown", - "id": "eca3a443", + "id": "0f90088e", "metadata": {}, "source": [ "### for文、while文(ループ)\n", @@ -1595,7 +1595,7 @@ { "cell_type": "code", "execution_count": 43, - "id": "479228cd", + "id": "f702c759", "metadata": { "tags": [ "remove-output" @@ -1646,7 +1646,7 @@ }, { "cell_type": "markdown", - "id": "55b501ac", + "id": "99d9713e", "metadata": {}, "source": [ "### クラス、オブジェクト、メソッド\n", @@ -1659,7 +1659,7 @@ { "cell_type": "code", "execution_count": 44, - "id": "a2990b3f", + "id": "671da90f", "metadata": { "tags": [ "remove-output" @@ -1673,7 +1673,7 @@ }, { "cell_type": "markdown", - "id": "b79aa8d9", + "id": "144fedba", "metadata": {}, "source": [ "このままでは`EmptyClass`というクラスがプログラムの中で定義されているという他、何の役割も果たしません。プログラムによってはあるクラスが存在するだけでいいということもありますが、通常は属性(インスタンスに付随するデータ)を足したり、「メソッド」を定義したりします。メソッドというのはクラスに対して定義される関数のことです。インスタンスを自動的に引数に取るため、挙動がインスタンスごとに異なります。" @@ -1682,7 +1682,7 @@ { "cell_type": "code", "execution_count": 45, - "id": "5bebae8c", + "id": "12126e92", "metadata": { "tags": [ "remove-output" @@ -1723,7 +1723,7 @@ }, { "cell_type": "markdown", - "id": "e7ac9820", + "id": "1c9664b7", "metadata": {}, "source": [ "### モジュールのインポート\n", @@ -1734,7 +1734,7 @@ { "cell_type": "code", "execution_count": 46, - "id": "f2343ae8", + "id": "a694a80d", "metadata": { "tags": [ "remove-output" @@ -1764,7 +1764,7 @@ }, { "cell_type": "markdown", - "id": "07a60a20", + "id": "af312b2c", "metadata": {}, "source": [ "Pythonの非常に大きな強みが、ユーザーベースの広さとオープンソースのライブラリの多さです。Pythonでやりたいと思うことは大体誰かがすでに実装していて、[PyPI](https://pypi.org)などでパッケージとして公開しているので、ユーザーはパッケージをインストールしてプログラム中からモジュールを`import`すればいい、という具合です。" @@ -1772,7 +1772,7 @@ }, { "cell_type": "markdown", - "id": "9a5e9624", + "id": "b43f751f", "metadata": {}, "source": [ "### 例外(exception)\n", @@ -1783,7 +1783,7 @@ { "cell_type": "code", "execution_count": 47, - "id": "8f97bcd5", + "id": "497fca4d", "metadata": { "tags": [ "remove-output" @@ -1816,7 +1816,7 @@ }, { "cell_type": "markdown", - "id": "56c2d9f6", + "id": "45bc4b6a", "metadata": {}, "source": [ "上の例にあるように、例外にも型があり、例外発生のさまざまな理由を区別できるようになっています。例外とその処理はPythonの正常なプログラムフローの一部として捉えるべきで、`try``except`を上手に使うことでより「Pythonらしい」コードが書けると言われています。\n", @@ -1827,7 +1827,7 @@ { "cell_type": "code", "execution_count": 48, - "id": "3a30e0be", + "id": "7cb6bafb", "metadata": { "tags": [ "remove-output" @@ -1855,7 +1855,7 @@ }, { "cell_type": "markdown", - "id": "ab1cbbc1", + "id": "e67457c6", "metadata": {}, "source": [ "## 実用編\n", @@ -1870,7 +1870,7 @@ { "cell_type": "code", "execution_count": 49, - "id": "d734d903", + "id": "0e1ba10c", "metadata": { "tags": [ "remove-output" @@ -1930,7 +1930,7 @@ }, { "cell_type": "markdown", - "id": "8db188e1", + "id": "9a732983", "metadata": {}, "source": [ "文字列(`str`)、リスト(`list`)、タプル(`tuple`)、辞書(`dict`)などの組み込み型でよく使うメソッドも紹介しておきます。" @@ -1939,7 +1939,7 @@ { "cell_type": "code", "execution_count": 50, - "id": "8824960f", + "id": "1cee5815", "metadata": { "tags": [ "remove-output" @@ -1991,7 +1991,7 @@ }, { "cell_type": "markdown", - "id": "ec67deae", + "id": "cc6e4386", "metadata": {}, "source": [ "リスト、タプル、辞書などを生成するときに時々使う構文を紹介します。" @@ -2000,7 +2000,7 @@ { "cell_type": "code", "execution_count": 51, - "id": "64718f46", + "id": "62f4b0ca", "metadata": {}, "outputs": [ { @@ -2027,7 +2027,7 @@ }, { "cell_type": "markdown", - "id": "578879e8", + "id": "a925370d", "metadata": {}, "source": [ "### NumPy\n", @@ -2040,7 +2040,7 @@ { "cell_type": "code", "execution_count": 52, - "id": "2476db65", + "id": "07436bda", "metadata": { "tags": [ "remove-output" @@ -2053,7 +2053,7 @@ }, { "cell_type": "markdown", - "id": "c0bf2b0a", + "id": "ce141cd2", "metadata": {}, "source": [ "#### 配列を作る\n", @@ -2066,7 +2066,7 @@ { "cell_type": "code", "execution_count": 53, - "id": "c8160cd5", + "id": "4c18323d", "metadata": { "tags": [ "remove-output" @@ -2097,7 +2097,7 @@ }, { "cell_type": "markdown", - "id": "3aca13f9", + "id": "1bb97a3a", "metadata": {}, "source": [ "#### 配列の要素を参照する" @@ -2106,7 +2106,7 @@ { "cell_type": "code", "execution_count": 54, - "id": "031496e8", + "id": "c4b40c6f", "metadata": { "tags": [ "remove-output" @@ -2144,7 +2144,7 @@ }, { "cell_type": "markdown", - "id": "f5294fc5", + "id": "bea0c0df", "metadata": {}, "source": [ "#### 配列を操作する" @@ -2153,7 +2153,7 @@ { "cell_type": "code", "execution_count": 55, - "id": "5157ae9c", + "id": "028d2ff4", "metadata": { "tags": [ "remove-output" @@ -2187,7 +2187,7 @@ }, { "cell_type": "markdown", - "id": "fa5400b0", + "id": "48bbad74", "metadata": {}, "source": [ "#### 配列に対して計算を施す\n", @@ -2198,7 +2198,7 @@ { "cell_type": "code", "execution_count": 56, - "id": "bad49a30", + "id": "2ec86f09", "metadata": { "tags": [ "remove-output" @@ -2229,7 +2229,7 @@ }, { "cell_type": "markdown", - "id": "c828e447", + "id": "90c4591d", "metadata": {}, "source": [ "のようになります。これだと簡単なことをするために何行もコードがいるだけでなく、実は非常に非効率です。というのも、Pythonには、コード一行一行の実行が比較的遅いという弱点があるからです。これはPythonがCやJavaのようにプログラム全体を「コンパイル」して最初から機械言語に変換して実行する言語ではないことに起因します。上のようにループを回すと、ループの繰り返しごと、一行ごとに書かれている命令を解釈し直すので、時間がかかります。無論繰り返し数3のループではCなどとPythonの間で人間が感知できるような時間の差はありませんが、配列の大きさが例えば数十万を超えてくると、明らかに違いが見えてきます。\n", @@ -2240,7 +2240,7 @@ { "cell_type": "code", "execution_count": 57, - "id": "8015cc9c", + "id": "03279829", "metadata": { "tags": [ "remove-output" @@ -2266,7 +2266,7 @@ }, { "cell_type": "markdown", - "id": "4b837075", + "id": "e3c3e013", "metadata": {}, "source": [ "となります。コードの行数が少なくなっただけでなく、実はこの場合はCなどと同じ速さで計算が行われます。NumPyはPythonから扱えるモジュールですが、中身はコンパイルされて極度に最適化されたライブラリなのです。\n", @@ -2277,7 +2277,7 @@ { "cell_type": "code", "execution_count": 58, - "id": "f624b04a", + "id": "7df9292f", "metadata": { "tags": [ "remove-output" @@ -2328,7 +2328,7 @@ }, { "cell_type": "markdown", - "id": "3eed53e8", + "id": "11080eb1", "metadata": {}, "source": [ "要素ごとではなく配列全体にかかる関数もあります。" @@ -2337,7 +2337,7 @@ { "cell_type": "code", "execution_count": 59, - "id": "c0f80f51", + "id": "f8d30490", "metadata": { "tags": [ "remove-output" @@ -2365,7 +2365,7 @@ }, { "cell_type": "markdown", - "id": "7f02fced", + "id": "603cd0ed", "metadata": {}, "source": [ "NumPyで実装されている関数はあまりにも多いので、このワークブックで使われている分でもここで紹介しきれていないかもしれません。残りは[NumPyのドキュメンテーション](https://numpy.org/doc/stable/)を参照してください。" @@ -2373,7 +2373,7 @@ }, { "cell_type": "markdown", - "id": "536415ec", + "id": "63b52ed8", "metadata": {}, "source": [ "### Matplotlib\n", @@ -2386,7 +2386,7 @@ { "cell_type": "code", "execution_count": 60, - "id": "76131ba4", + "id": "bd4f4218", "metadata": { "tags": [ "remove-output" @@ -2400,7 +2400,7 @@ }, { "cell_type": "markdown", - "id": "5fc20577", + "id": "12fadfea", "metadata": {}, "source": [ "Matplotlibには「図」(Figure)と「グラフ描画領域」(Axes)という概念があります。一つのFigureの中に複数のAxesが存在でき、各Axesに一つのプロットが描画される構造になっています。\n", @@ -2411,7 +2411,7 @@ { "cell_type": "code", "execution_count": 61, - "id": "7dfa35fe", + "id": "7c80926d", "metadata": { "tags": [ "remove-output" @@ -2461,7 +2461,7 @@ }, { "cell_type": "markdown", - "id": "8cc2f12b", + "id": "e111d5e0", "metadata": {}, "source": [ "こうして作ったFigureやAxesオブジェクトの様々なメソッドを使ってグラフを描くことができますが、実は単にxとyのデータがあって一つスキャッタープロットを作りたいという時などは、もっと簡単な方法を取ることもできます。" @@ -2470,7 +2470,7 @@ { "cell_type": "code", "execution_count": 62, - "id": "24dd8dd6", + "id": "2d1d4da8", "metadata": { "tags": [ "remove-output" @@ -2480,7 +2480,7 @@ { "data": { "text/plain": [ - "[]" + "[]" ] }, "execution_count": 62, @@ -2514,7 +2514,7 @@ { "cell_type": "code", "execution_count": 63, - "id": "5a2a03df", + "id": "465593c3", "metadata": { "tags": [ "remove-output" @@ -2524,7 +2524,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 63, @@ -2558,7 +2558,7 @@ }, { "cell_type": "markdown", - "id": "96beb574", + "id": "ba0c55d1", "metadata": {}, "source": [ "`plt.plot`や`plt.scatter`を複数実行すると、同じAxesにグラフが重なってプロットされます。実行の際に`label='some text'`という引数を足し、`plt.legend()`を呼ぶと、凡例が表示されます。また`plt.xlabel()`や`plt.ylabel()`でX, Y軸にタイトルをつけたり、`plt.title()`でプロット全体にタイトルをつけたりできます。" @@ -2566,7 +2566,7 @@ }, { "cell_type": "markdown", - "id": "20738ec9", + "id": "a4056044", "metadata": {}, "source": [ "### Jupyter\n", @@ -2579,14 +2579,14 @@ { "cell_type": "code", "execution_count": 64, - "id": "e0a0e816", + "id": "6e29a609", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Using matplotlib backend: \n" + "Using matplotlib backend: \n" ] } ], @@ -2608,7 +2608,7 @@ { "cell_type": "code", "execution_count": 65, - "id": "8755251f", + "id": "3f263427", "metadata": {}, "outputs": [ { @@ -2634,7 +2634,7 @@ { "cell_type": "code", "execution_count": 66, - "id": "b0510ae7", + "id": "ee4b64ac", "metadata": {}, "outputs": [ { diff --git a/_sources/qkc_machine_learning.ipynb b/_sources/qkc_machine_learning.ipynb index 37e7dad8..2b4786c9 100644 --- a/_sources/qkc_machine_learning.ipynb +++ b/_sources/qkc_machine_learning.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "a8f76021", + "id": "6a7cbf7e", "metadata": { "pycharm": { "name": "#%% md\n" @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "0387e33d", + "id": "bbb3dadc", "metadata": { "pycharm": { "name": "#%% md\n" @@ -35,7 +35,7 @@ }, { "cell_type": "markdown", - "id": "e6f5ed77", + "id": "efa52de7", "metadata": { "pycharm": { "name": "#%% md\n" @@ -62,7 +62,7 @@ }, { "cell_type": "markdown", - "id": "1fc0b22d", + "id": "1ff40ed9", "metadata": { "pycharm": { "name": "#%% md\n" @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "ddb49e12", + "id": "f22af115", "metadata": { "pycharm": { "name": "#%% md\n" @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "bc6b076c", + "id": "020ebc5b", "metadata": { "pycharm": { "name": "#%% md\n" @@ -202,7 +202,7 @@ }, { "cell_type": "markdown", - "id": "9c2f3572", + "id": "4a7429dc", "metadata": { "pycharm": { "name": "#%% md\n" @@ -256,7 +256,7 @@ }, { "cell_type": "markdown", - "id": "0f7bdd0b", + "id": "36d12fc7", "metadata": { "pycharm": { "name": "#%% md\n" @@ -274,7 +274,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51b70050", + "id": "f43db253", "metadata": {}, "outputs": [], "source": [ @@ -297,7 +297,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3bc9006a", + "id": "d9854d37", "metadata": { "jupyter": { "outputs_hidden": false @@ -355,7 +355,7 @@ }, { "cell_type": "markdown", - "id": "c030d8f9", + "id": "3c9a452b", "metadata": { "pycharm": { "name": "#%% md\n" @@ -373,7 +373,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c29159a7", + "id": "4b654932", "metadata": { "jupyter": { "outputs_hidden": false @@ -401,7 +401,7 @@ }, { "cell_type": "markdown", - "id": "0b965d76", + "id": "d3f81737", "metadata": { "pycharm": { "name": "#%% md\n" @@ -444,7 +444,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c36857d", + "id": "e72906ea", "metadata": { "jupyter": { "outputs_hidden": false @@ -470,7 +470,7 @@ }, { "cell_type": "markdown", - "id": "67d2a851", + "id": "6c01bf57", "metadata": { "pycharm": { "name": "#%% md\n" @@ -483,7 +483,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5dc95e4", + "id": "29a708cf", "metadata": { "jupyter": { "outputs_hidden": false @@ -510,7 +510,7 @@ }, { "cell_type": "markdown", - "id": "45cdb1f7", + "id": "90d085d2", "metadata": {}, "source": [ "次に同じことを`FidelityQuantumKernel`クラスを利用して行います。" @@ -519,7 +519,7 @@ { "cell_type": "code", "execution_count": null, - "id": "20e225aa", + "id": "356b15ef", "metadata": { "jupyter": { "outputs_hidden": false @@ -548,7 +548,7 @@ }, { "cell_type": "markdown", - "id": "d1fbf890", + "id": "617fd046", "metadata": { "pycharm": { "name": "#%% md\n" @@ -565,7 +565,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62241e67", + "id": "ab7939bf", "metadata": { "jupyter": { "outputs_hidden": false @@ -593,7 +593,7 @@ }, { "cell_type": "markdown", - "id": "6234fa71", + "id": "bf19cfa2", "metadata": { "pycharm": { "name": "#%% md\n" @@ -610,7 +610,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8640d96", + "id": "b37bd1ee", "metadata": { "jupyter": { "outputs_hidden": false @@ -637,7 +637,7 @@ }, { "cell_type": "markdown", - "id": "db111d78", + "id": "9aa1617d", "metadata": { "pycharm": { "name": "#%% md\n" diff --git a/_sources/quantum_computation.ipynb b/_sources/quantum_computation.ipynb index 382cb4b4..7edef77b 100644 --- a/_sources/quantum_computation.ipynb +++ b/_sources/quantum_computation.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5fe4d9f2", + "id": "9ff33a7d", "metadata": {}, "source": [ "# 【課題】アダマールテスト\n", @@ -20,7 +20,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f9213fec", + "id": "e1dc2cd9", "metadata": { "tags": [ "remove-output" @@ -40,7 +40,7 @@ }, { "cell_type": "markdown", - "id": "2f3f0097", + "id": "f11415d9", "metadata": {}, "source": [ "## 問題1: アダマールテストで状態ベクトルを同定する\n", @@ -115,7 +115,7 @@ { "cell_type": "code", "execution_count": null, - "id": "29ac763f", + "id": "ca72084c", "metadata": {}, "outputs": [], "source": [ @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "6831deb9", + "id": "daa8edeb", "metadata": {}, "source": [ "Qiskitでは、`QuantumCircuit`オブジェクトで表される量子回路を、`to_gate()`メソッドで一つのゲートオブジェクトに変換することができます。さらにそのゲートに対して`control(n)`メソッドを用いると、元の回路をn量子ビットで制御する制御ゲートを作ることができます。" @@ -148,7 +148,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7d61fecc", + "id": "9e262e31", "metadata": {}, "outputs": [], "source": [ @@ -158,7 +158,7 @@ }, { "cell_type": "markdown", - "id": "e99a267d", + "id": "16f0c3a1", "metadata": {}, "source": [ "$U^{-1}_k$とその制御ゲート化は$k$の関数として定義しておきます。" @@ -167,7 +167,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8c192bc8", + "id": "91aba088", "metadata": {}, "outputs": [], "source": [ @@ -192,7 +192,7 @@ }, { "cell_type": "markdown", - "id": "60d74886", + "id": "997c6ba8", "metadata": {}, "source": [ "ゲートオブジェクトは`QuantumCircuit`オブジェクトに`append()`で組み込むことができます。制御ゲートを埋め込む場合は、制御ビットが組み込み先の最初のnビットとなるので、`append()`の`qargs`引数で正しく対応づけします。\n", @@ -203,7 +203,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17c89437", + "id": "60990a54", "metadata": { "tags": [ "remove-output" @@ -265,7 +265,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72be29e1", + "id": "0128a00e", "metadata": { "tags": [ "remove-output" @@ -281,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "577a3998", + "id": "544de0ab", "metadata": {}, "source": [ "得られた結果と状態ベクトルシミュレータで計算される状態ベクトルとを比較してみましょう。" @@ -290,7 +290,7 @@ { "cell_type": "code", "execution_count": null, - "id": "64f9c874", + "id": "240a5f0c", "metadata": { "tags": [ "remove-output" @@ -317,7 +317,7 @@ }, { "cell_type": "markdown", - "id": "c9e1763c", + "id": "06c7a175", "metadata": {}, "source": [ "## 問題2: 符号が反転している基底を見つける\n", @@ -348,7 +348,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b804836a", + "id": "186495e0", "metadata": {}, "outputs": [], "source": [ @@ -375,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "764168e6", + "id": "f4ad07d8", "metadata": {}, "source": [ "ここまでは{doc}`circuit_from_scratch`の問題5と同じです。\n", @@ -386,7 +386,7 @@ { "cell_type": "code", "execution_count": null, - "id": "361de8dc", + "id": "e2588674", "metadata": {}, "outputs": [], "source": [ @@ -398,7 +398,7 @@ }, { "cell_type": "markdown", - "id": "9b973e05", + "id": "87735584", "metadata": {}, "source": [ "それでは、この制御ブラックボックスゲートを利用して、equal superpositionにある`haystack`レジスタで干渉を起こして、観測で`needle`が識別できるような回路を書いてください。\n", @@ -409,7 +409,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4581d79d", + "id": "46c45b25", "metadata": { "tags": [ "remove-output" @@ -442,7 +442,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b269877", + "id": "ade324a3", "metadata": { "tags": [ "remove-output" @@ -456,7 +456,7 @@ }, { "cell_type": "markdown", - "id": "f0121f2e", + "id": "cad0b7d4", "metadata": {}, "source": [ "回路が完成したら、`qasm_simulator`で実行し、ヒストグラムをプロットしてください。" @@ -465,7 +465,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f013c872", + "id": "2bff98ef", "metadata": { "tags": [ "remove-output" @@ -482,7 +482,7 @@ }, { "cell_type": "markdown", - "id": "bc0fa10b", + "id": "42fafb6b", "metadata": {}, "source": [ "**提出するもの**\n", @@ -496,6 +496,7 @@ ], "metadata": { "jupytext": { + "formats": "md:myst,ipynb", "notebook_metadata_filter": "all", "text_representation": { "extension": ".md", @@ -522,29 +523,29 @@ "version": "3.10.6" }, "source_map": [ - 23, - 36, - 47, - 117, - 134, - 138, - 141, - 145, - 163, - 169, - 223, - 230, - 234, - 252, - 278, - 298, - 304, - 309, - 315, - 340, - 345, - 349, - 357 + 24, + 37, + 48, + 118, + 135, + 139, + 142, + 146, + 164, + 170, + 224, + 231, + 235, + 253, + 279, + 299, + 305, + 310, + 316, + 341, + 346, + 350, + 358 ] }, "nbformat": 4, diff --git a/_sources/quantum_computation.md b/_sources/quantum_computation.md index 669ee885..313ad981 100644 --- a/_sources/quantum_computation.md +++ b/_sources/quantum_computation.md @@ -1,5 +1,6 @@ --- jupytext: + formats: md:myst,ipynb notebook_metadata_filter: all text_representation: extension: .md diff --git a/_sources/shor.ipynb b/_sources/shor.ipynb index cf13ab6c..34fdf19e 100644 --- a/_sources/shor.ipynb +++ b/_sources/shor.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "f3daf0b3", + "id": "d75605c1", "metadata": { "pycharm": { "name": "#%% md\n" @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "59a668c5", + "id": "2cd99635", "metadata": {}, "source": [ "この実習では**ショアのアルゴリズム**を学習します。名前を聞いたことがある人もいるかもしれませんが、ショアのアルゴリズム{cite}`shor,nielsen_chuang_qft_app`は最も有名な量子アルゴリズムと言っても良いでしょう。ショアのアルゴリズムの元になっている**量子位相推定**と呼ばれる手法を学んだ後、ショアのアルゴリズムの各ステップを実例とともに紹介します。最後に、Qiskitを使用してショアのアルゴリズムを実装し、実際に素因数分解を行ってみます。\n", @@ -40,7 +40,7 @@ }, { "cell_type": "markdown", - "id": "e08ed2d0", + "id": "471cf722", "metadata": {}, "source": [ "(qpe)=\n", @@ -56,7 +56,7 @@ }, { "cell_type": "markdown", - "id": "63959221", + "id": "924c3757", "metadata": {}, "source": [ "(qpe_1qubit)=\n", @@ -87,7 +87,7 @@ }, { "cell_type": "markdown", - "id": "09bc0f90", + "id": "e57c970e", "metadata": { "pycharm": { "name": "#%% md\n" @@ -137,7 +137,7 @@ }, { "cell_type": "markdown", - "id": "9021074d", + "id": "c40111d4", "metadata": { "pycharm": { "name": "#%% md\n" @@ -155,7 +155,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a466efd8", + "id": "e35ed770", "metadata": { "pycharm": { "name": "#%%\n" @@ -181,7 +181,7 @@ }, { "cell_type": "markdown", - "id": "e6353728", + "id": "9e31a012", "metadata": { "pycharm": { "name": "#%% md\n" @@ -194,7 +194,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bbd309d4", + "id": "43e98bd5", "metadata": { "pycharm": { "name": "#%%\n" @@ -228,7 +228,7 @@ }, { "cell_type": "markdown", - "id": "a0a517d0", + "id": "d24ce021", "metadata": { "pycharm": { "name": "#%% md\n" @@ -243,7 +243,7 @@ { "cell_type": "code", "execution_count": null, - "id": "56757838", + "id": "6d55d2ef", "metadata": { "pycharm": { "name": "#%%\n" @@ -278,7 +278,7 @@ }, { "cell_type": "markdown", - "id": "0b515921", + "id": "729bfb4b", "metadata": {}, "source": [ "**解答**\n", @@ -320,7 +320,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69b57498", + "id": "e29c7127", "metadata": { "tags": [ "remove-input", @@ -367,7 +367,7 @@ }, { "cell_type": "markdown", - "id": "c5a5d1ee", + "id": "aabfc40e", "metadata": { "pycharm": { "name": "#%% md\n" @@ -383,7 +383,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c765d1c9", + "id": "a944f2df", "metadata": { "pycharm": { "name": "#%%\n" @@ -421,7 +421,7 @@ }, { "cell_type": "markdown", - "id": "af708cbb", + "id": "d5ebfc3a", "metadata": { "pycharm": { "name": "#%% md\n" @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "8304910d", + "id": "b67ef560", "metadata": { "pycharm": { "name": "#%% md\n" @@ -454,7 +454,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ceb6162", + "id": "3edf34c2", "metadata": { "pycharm": { "name": "#%%\n" @@ -482,7 +482,7 @@ { "cell_type": "code", "execution_count": null, - "id": "006a685e", + "id": "306643e1", "metadata": { "pycharm": { "name": "#%%\n" @@ -503,7 +503,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36cd2598", + "id": "a5f6cdfb", "metadata": { "pycharm": { "name": "#%%\n" @@ -523,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "9e75bfe2", + "id": "1c900347", "metadata": {}, "source": [ "(shor_algo)=\n", @@ -551,7 +551,7 @@ }, { "cell_type": "markdown", - "id": "cf19f7bc", + "id": "1d1c13dd", "metadata": { "pycharm": { "name": "#%% md\n" @@ -580,7 +580,7 @@ }, { "cell_type": "markdown", - "id": "8c83b5ea", + "id": "c1ec75eb", "metadata": {}, "source": [ "(shor_circuit)=\n", @@ -646,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "3c4d34e1", + "id": "b64e69c0", "metadata": {}, "source": [ "(shor_measurement)=\n", @@ -706,7 +706,7 @@ }, { "cell_type": "markdown", - "id": "ecb67052", + "id": "41a1b0d7", "metadata": {}, "source": [ "(continued_fractions)=\n", @@ -718,7 +718,7 @@ }, { "cell_type": "markdown", - "id": "f0d1d6f6", + "id": "649cc308", "metadata": {}, "source": [ "(modular_exponentiation)=\n", @@ -756,7 +756,7 @@ }, { "cell_type": "markdown", - "id": "0512b07b", + "id": "1e4f68b6", "metadata": { "pycharm": { "name": "#%% md\n" @@ -776,7 +776,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2df82275", + "id": "745a2d71", "metadata": { "jupyter": { "outputs_hidden": false @@ -811,7 +811,7 @@ }, { "cell_type": "markdown", - "id": "08188ca8", + "id": "1c321251", "metadata": {}, "source": [ "(shor_imp_oracle)=\n", @@ -829,7 +829,7 @@ { "cell_type": "code", "execution_count": null, - "id": "947a5c0c", + "id": "ef0f3496", "metadata": { "jupyter": { "outputs_hidden": false @@ -876,7 +876,7 @@ }, { "cell_type": "markdown", - "id": "e6755d2c", + "id": "b7af70d4", "metadata": { "pycharm": { "name": "#%% md\n" @@ -1008,7 +1008,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d923cf68", + "id": "26939ab0", "metadata": { "jupyter": { "outputs_hidden": false @@ -1053,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "701f8e03", + "id": "781d8f1d", "metadata": { "pycharm": { "name": "#%% md\n" @@ -1069,7 +1069,7 @@ { "cell_type": "code", "execution_count": null, - "id": "975b23f9", + "id": "7778ce46", "metadata": { "jupyter": { "outputs_hidden": false @@ -1115,7 +1115,7 @@ }, { "cell_type": "markdown", - "id": "950c4e08", + "id": "048c355b", "metadata": {}, "source": [ "シミュレータで実行して、結果を確認してみます。" @@ -1124,7 +1124,7 @@ { "cell_type": "code", "execution_count": null, - "id": "89a50455", + "id": "a27bdd08", "metadata": { "jupyter": { "outputs_hidden": false @@ -1144,7 +1144,7 @@ }, { "cell_type": "markdown", - "id": "02f49d26", + "id": "00487a86", "metadata": { "pycharm": { "name": "#%% md\n" @@ -1159,7 +1159,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6ecf290d", + "id": "925fb40d", "metadata": { "jupyter": { "outputs_hidden": false @@ -1188,7 +1188,7 @@ }, { "cell_type": "markdown", - "id": "ca3297ac", + "id": "ab6c8ef0", "metadata": {}, "source": [ "得られた位相の情報から、連分数アルゴリズムを使用して$s$と$r$を見つけることができます。Pythonの組み込みの`fractions`(分数)モジュールを使用して、小数を`Fraction`オブジェクトに変換できます。" @@ -1197,7 +1197,7 @@ { "cell_type": "code", "execution_count": null, - "id": "94a108b2", + "id": "38778732", "metadata": { "jupyter": { "outputs_hidden": false @@ -1223,7 +1223,7 @@ }, { "cell_type": "markdown", - "id": "4d1567d8", + "id": "05b76a60", "metadata": {}, "source": [ "`limit_denominator`メソッドを使って、分母が特定の値(ここでは15)を下回る分数で、最も位相の値に近いものを得ています。\n", diff --git a/_sources/spectrum_estimation.ipynb b/_sources/spectrum_estimation.ipynb index 29e98d0d..444a4f30 100644 --- a/_sources/spectrum_estimation.ipynb +++ b/_sources/spectrum_estimation.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d0ee5821", + "id": "d4744b49", "metadata": {}, "source": [ "# 【課題】位相推定によるスペクトル分解\n", @@ -18,7 +18,7 @@ }, { "cell_type": "markdown", - "id": "12c185dc", + "id": "2a195495", "metadata": {}, "source": [ "## エネルギースペクトルを求める\n", @@ -32,7 +32,7 @@ }, { "cell_type": "markdown", - "id": "5dbb2026", + "id": "dd1a72f2", "metadata": {}, "source": [ "## ハイゼンベルグモデル再考\n", @@ -59,7 +59,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2d1c12c1", + "id": "80c0fb71", "metadata": { "tags": [ "remove-output" @@ -83,7 +83,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3513b101", + "id": "22420437", "metadata": {}, "outputs": [], "source": [ @@ -120,7 +120,7 @@ }, { "cell_type": "markdown", - "id": "2715c889", + "id": "bde6fd94", "metadata": {}, "source": [ "最後の部分で、[`show_state`関数](https://github.com/UTokyo-ICEPP/qc-workbook/tree/master/source/qc_workbook/show_state.py)を利用して固有値と固有ベクトルを表示しました。最低エネルギー状態(固有値$-2J$)に対応する独立な固有ベクトルが3つあることがわかります。したがって、これらの固有ベクトルの任意の線形和もまた最低エネルギー状態です。励起状態(固有値$6J$)は$1/\\sqrt{2} (-\\ket{01} + \\ket{10})$です。" @@ -128,7 +128,7 @@ }, { "cell_type": "markdown", - "id": "44341c2d", + "id": "71dbe4c6", "metadata": {}, "source": [ "## 位相推定によるスペクトル分解\n", @@ -225,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "76aee91f", + "id": "9c72c831", "metadata": {}, "source": [ "## 問題1: スペクトル推定を実装し、厳密解と照らし合わせる\n", @@ -240,7 +240,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ea49f76", + "id": "141db0da", "metadata": { "jupyter": { "outputs_hidden": false @@ -300,7 +300,7 @@ }, { "cell_type": "markdown", - "id": "77b931e1", + "id": "3b7dfa08", "metadata": {}, "source": [ "次のセルでスペクトル推定のアルゴリズムを実装しています。この関数は状態レジスタ、読み出しレジスタ、時間発展回路を引数に取り、スペクトル推定の量子回路を返します。" @@ -309,7 +309,7 @@ { "cell_type": "code", "execution_count": null, - "id": "feb4e7a1", + "id": "186e594f", "metadata": { "jupyter": { "outputs_hidden": false @@ -365,7 +365,7 @@ }, { "cell_type": "markdown", - "id": "9b8fb8d6", + "id": "cf42062b", "metadata": {}, "source": [ "この問題では、上で厳密解を求めた$n=2, g=0$のケースを調べます。今回はすでにエネルギー固有値を知っているので、ハミルトニアンの規格化定数を$\\hbar \\omega = 16J$として、読み出しレジスタの終状態が単純になるようにします。このとき読み出しは符号付きで、最大絶対値が$2^{n_R} (6/16)$なので、$n_R = 1 + 3$とすればオーバーフローを回避できます。\n", @@ -376,7 +376,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b691ae3", + "id": "8e53ea56", "metadata": {}, "outputs": [], "source": [ @@ -400,7 +400,7 @@ }, { "cell_type": "markdown", - "id": "5dbb3d1d", + "id": "9a6a0c65", "metadata": {}, "source": [ "上で正しく関数をかけているか確認しておきましょう。" @@ -409,7 +409,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5ab667dd", + "id": "179b7b1a", "metadata": { "tags": [ "remove-output" @@ -424,7 +424,7 @@ { "cell_type": "code", "execution_count": null, - "id": "147df17a", + "id": "cc665139", "metadata": { "tags": [ "remove-output" @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "f42b7538", + "id": "db547f0b", "metadata": {}, "source": [ "状態レジスタの初期状態を\n", @@ -454,7 +454,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b8b3a83", + "id": "aef3724d", "metadata": { "tags": [ "remove-output" @@ -485,7 +485,7 @@ }, { "cell_type": "markdown", - "id": "14337d90", + "id": "59cd4902", "metadata": {}, "source": [ "最後に全てを組み合わせます。" @@ -494,7 +494,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e000e90", + "id": "f0d21a07", "metadata": { "jupyter": { "outputs_hidden": false @@ -519,7 +519,7 @@ }, { "cell_type": "markdown", - "id": "65a0604d", + "id": "610f98c0", "metadata": {}, "source": [ "シミュレータで実行してヒストグラムを得ます。" @@ -528,7 +528,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47ad161e", + "id": "0dd4b4b2", "metadata": { "jupyter": { "outputs_hidden": false @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "dec60a4e", + "id": "1d103d60", "metadata": {}, "source": [ "状態レジスタの初期状態が式{eq}`two_qubit_init`なので、回路の終状態は\n", @@ -573,7 +573,7 @@ }, { "cell_type": "markdown", - "id": "ed0dbea6", + "id": "0d5336af", "metadata": {}, "source": [ "## 問題2: 非自明な系の振る舞いを調べる\n", @@ -636,7 +636,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4735b04a", + "id": "b28c912c", "metadata": {}, "outputs": [], "source": [ @@ -715,7 +715,7 @@ }, { "cell_type": "markdown", - "id": "0826955a", + "id": "5278a753", "metadata": {}, "source": [ "読み出しレジスタのビット数を決めます。スピンの数が4なので、$\\hbar \\omega = 8(3 + |g|)J$と取ります。すると、$g=0$のとき、上の議論によると$\\Theta$の固有値の予想される最小絶対値は$1/24$ですが、実は系の対称性からその$n=4$倍の$1/6$が最小値になると予測できます。$|g| \\ll 1$しか考えないので、外部磁場を摂動として考えて、結局$2^{n_R} / 6$が1より十分大きくなるように$n_R=5$とします。\n", @@ -726,7 +726,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3fdbac6", + "id": "78b73135", "metadata": { "tags": [ "remove-output" @@ -768,7 +768,7 @@ }, { "cell_type": "markdown", - "id": "ac1c1244", + "id": "dd19d5d3", "metadata": {}, "source": [ "得られた$P(k)$分布を、$k$をエネルギーに換算してプロットしてみましょう。" @@ -777,7 +777,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5617cd98", + "id": "f401cc33", "metadata": { "tags": [ "remove-output" @@ -792,7 +792,7 @@ }, { "cell_type": "markdown", - "id": "03c7433d", + "id": "d4880dbe", "metadata": {}, "source": [ "続いて、同じ関数を$g=0.1, 0.2, 0.3, 0.4, 0.5$について実行して、それぞれのスペクトルから系のエネルギー固有値と$g$の関係をプロットしてください。" @@ -801,7 +801,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1f0e871e", + "id": "6091ba3a", "metadata": { "tags": [ "remove-output" @@ -816,7 +816,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc7fc443", + "id": "732cb76f", "metadata": { "tags": [ "remove-output" @@ -842,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "18f2f319", + "id": "d720c5b7", "metadata": {}, "source": [ "**提出するもの**\n", diff --git a/_sources/toffoli_shor_code.ipynb b/_sources/toffoli_shor_code.ipynb index 414b7fc8..27c9f5ea 100644 --- a/_sources/toffoli_shor_code.ipynb +++ b/_sources/toffoli_shor_code.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "eec187b3", + "id": "68542765", "metadata": {}, "source": [ "# ToffoliゲートとShorコード\n", @@ -21,7 +21,7 @@ }, { "cell_type": "markdown", - "id": "6752e79a", + "id": "dfa78534", "metadata": {}, "source": [ "## 量子エラー訂正\n", @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "7097c26a", + "id": "294d9a2f", "metadata": {}, "source": [ "## Toffoliゲート\n", @@ -60,7 +60,7 @@ { "cell_type": "code", "execution_count": null, - "id": "39345758", + "id": "0b79b29b", "metadata": { "tags": [ "remove-input" @@ -77,7 +77,7 @@ }, { "cell_type": "markdown", - "id": "013a2842", + "id": "e4f60432", "metadata": {}, "source": [ "Toffoliゲートはエラー訂正だけでなく、多重制御ゲートの基本パーツとなるため、さまざまな場面で登場します。また理論的には、ToffoliゲートとHadamardゲートの組み合わせで全ての量子演算が実現できる(普遍ゲートセットとなる)ことから、Toffoliゲートは特別重要な存在です。\n", @@ -88,7 +88,7 @@ { "cell_type": "code", "execution_count": null, - "id": "13af4507", + "id": "775e47e7", "metadata": {}, "outputs": [], "source": [ @@ -105,7 +105,7 @@ { "cell_type": "code", "execution_count": null, - "id": "109bb8f7", + "id": "c139619d", "metadata": {}, "outputs": [], "source": [ @@ -128,7 +128,7 @@ }, { "cell_type": "markdown", - "id": "6f77cf57", + "id": "a797200e", "metadata": {}, "source": [ "## CPゲート\n", @@ -169,7 +169,7 @@ { "cell_type": "code", "execution_count": null, - "id": "327a68fc", + "id": "0aa59491", "metadata": { "tags": [ "remove-output" @@ -199,7 +199,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9c1e48b5", + "id": "c6601802", "metadata": { "tags": [ "raises-exception", @@ -215,7 +215,7 @@ }, { "cell_type": "markdown", - "id": "30fc9b61", + "id": "4af28671", "metadata": {}, "source": [ "$CP$は`QuantumCircuit`オブジェクトにもメソッド`cp`として備わっているので、以下では(回路図の見やすさを考慮して)標準メソッドを使うことにします。" @@ -223,7 +223,7 @@ }, { "cell_type": "markdown", - "id": "babb6352", + "id": "60d10149", "metadata": {}, "source": [ "## CCZゲート\n", @@ -239,7 +239,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8734a60", + "id": "171ea824", "metadata": { "tags": [ "remove-output" @@ -270,7 +270,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c7d09810", + "id": "eece8c58", "metadata": { "tags": [ "remove-output" @@ -283,7 +283,7 @@ }, { "cell_type": "markdown", - "id": "872566db", + "id": "3b0c92f3", "metadata": {}, "source": [ "## Hadamardゲート\n", @@ -305,7 +305,7 @@ { "cell_type": "code", "execution_count": null, - "id": "93666271", + "id": "7119ea4d", "metadata": { "tags": [ "remove-output" @@ -331,7 +331,7 @@ { "cell_type": "code", "execution_count": null, - "id": "40c372ff", + "id": "f35b96f4", "metadata": { "tags": [ "remove-output" @@ -344,7 +344,7 @@ }, { "cell_type": "markdown", - "id": "886d4efe", + "id": "c9dca8d2", "metadata": {}, "source": [ "## Toffoliゲート\n", @@ -355,7 +355,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8da04159", + "id": "174f5885", "metadata": { "tags": [ "remove-output" @@ -383,7 +383,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e67c2776", + "id": "396d65e2", "metadata": { "tags": [ "remove-output" @@ -396,7 +396,7 @@ }, { "cell_type": "markdown", - "id": "fa43d3f4", + "id": "e685773e", "metadata": {}, "source": [ "## 量子エラーとエラー訂正\n", @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "ad3440b1", + "id": "5e13444c", "metadata": {}, "source": [ "### ビット反転($X$)エラー\n", @@ -428,7 +428,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7c20164", + "id": "df662fde", "metadata": { "tags": [ "remove-output" @@ -482,7 +482,7 @@ { "cell_type": "code", "execution_count": null, - "id": "778e8c4b", + "id": "38248ad9", "metadata": { "tags": [ "remove-output" @@ -495,7 +495,7 @@ }, { "cell_type": "markdown", - "id": "b6cf967c", + "id": "751c0311", "metadata": {}, "source": [ "第1と第2量子ビット(Qiskitの順番なので左二桁)の状態が同一である=第3量子ビットとのエンタングルメントが切れていれば、正しくデコードされています。第0ビットの状態をエラーのない単一量子ビット回路のものと比較します。" @@ -504,7 +504,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26beff41", + "id": "c9d3aae2", "metadata": {}, "outputs": [], "source": [ @@ -517,7 +517,7 @@ }, { "cell_type": "markdown", - "id": "ace86f57", + "id": "f9a0f45a", "metadata": {}, "source": [ "### 位相反転($Z$)エラー\n", @@ -528,7 +528,7 @@ { "cell_type": "code", "execution_count": null, - "id": "159f0af3", + "id": "041e58df", "metadata": { "tags": [ "remove-output" @@ -579,7 +579,7 @@ { "cell_type": "code", "execution_count": null, - "id": "298635a1", + "id": "e904181c", "metadata": { "tags": [ "remove-output" @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "c764a99a", + "id": "bc1bf862", "metadata": {}, "source": [ "### Shorコード\n", @@ -603,7 +603,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d2b39cc", + "id": "e18f8721", "metadata": { "tags": [ "remove-output" @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "022d9ac1", + "id": "3236baa0", "metadata": { "tags": [ "remove-output" diff --git a/_sources/vqc_machine_learning.ipynb b/_sources/vqc_machine_learning.ipynb index 4102bfec..2f852134 100644 --- a/_sources/vqc_machine_learning.ipynb +++ b/_sources/vqc_machine_learning.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7d1bc48e", + "id": "985242f3", "metadata": {}, "source": [ "# 量子機械学習を使った新しい素粒子現象の探索" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "12a9abb0", + "id": "7cc058a5", "metadata": {}, "source": [ "この実習では、**量子・古典ハイブリッドアルゴリズム**の応用である**量子機械学習**の基本的な実装を学んだのち、その活用例として、**素粒子実験での新粒子探索**への応用を考えます。ここで学ぶ量子機械学習の手法は、変分量子アルゴリズムの応用として提案された、**量子回路学習**と呼ばれる学習手法{cite}`quantum_circuit_learning`です。\n", @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "058db0a1", + "id": "86ec9a74", "metadata": {}, "source": [ "## はじめに \n", @@ -40,7 +40,7 @@ }, { "cell_type": "markdown", - "id": "b01f3daa", + "id": "5350d3cf", "metadata": {}, "source": [ "## 機械学習と深層学習 \n", @@ -89,7 +89,7 @@ }, { "cell_type": "markdown", - "id": "955098d4", + "id": "de1be9d9", "metadata": {}, "source": [ "## 量子回路学習\n", @@ -119,7 +119,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ee7db6d", + "id": "97c93712", "metadata": { "jupyter": { "outputs_hidden": false @@ -150,7 +150,7 @@ }, { "cell_type": "markdown", - "id": "5f922258", + "id": "e2062ef5", "metadata": {}, "source": [ "## 初歩的な例\n", @@ -165,7 +165,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c75de542", + "id": "45112319", "metadata": { "jupyter": { "outputs_hidden": false @@ -205,7 +205,7 @@ }, { "cell_type": "markdown", - "id": "0ddb4c27", + "id": "47f0d663", "metadata": {}, "source": [ "### 量子状態の生成\n", @@ -222,7 +222,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41431e96", + "id": "7a2a57e2", "metadata": { "jupyter": { "outputs_hidden": false @@ -247,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "4ed1b668", + "id": "eacc6b84", "metadata": {}, "source": [ "### 変分フォームを使った状態変換\n", @@ -281,7 +281,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c2de4e7f", + "id": "a8ad59ec", "metadata": { "jupyter": { "outputs_hidden": false @@ -333,7 +333,7 @@ }, { "cell_type": "markdown", - "id": "616a2e8a", + "id": "93a21ba0", "metadata": {}, "source": [ "### 測定とモデル出力\n", @@ -344,7 +344,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5658b167", + "id": "4e22f26a", "metadata": { "jupyter": { "outputs_hidden": false @@ -369,7 +369,7 @@ { "cell_type": "code", "execution_count": null, - "id": "68fd80aa", + "id": "eeca1bce", "metadata": { "pycharm": { "name": "#%%\n" @@ -408,7 +408,7 @@ }, { "cell_type": "markdown", - "id": "637ea108", + "id": "d34de434", "metadata": {}, "source": [ "コスト関数$L$として、モデルの予測値$y(x_i, \\theta)$と真の値$y_i$の平均2乗誤差の総和を使っています。\n", @@ -419,7 +419,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2df7077", + "id": "2ddf65ff", "metadata": { "jupyter": { "outputs_hidden": false @@ -443,7 +443,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50d03322", + "id": "52b432ca", "metadata": { "tags": [ "remove-input" @@ -460,7 +460,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8077eee", + "id": "9ee60679", "metadata": { "jupyter": { "outputs_hidden": false @@ -484,7 +484,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b8b9756", + "id": "1060bff9", "metadata": { "tags": [ "remove-input" @@ -503,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "d63332d9", + "id": "9ce8b3d5", "metadata": {}, "source": [ "コスト値の推移をプロットします。" @@ -512,7 +512,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8cce3f7", + "id": "1a2f99be", "metadata": {}, "outputs": [], "source": [ @@ -521,7 +521,7 @@ }, { "cell_type": "markdown", - "id": "b8d60f39", + "id": "c2b3b923", "metadata": { "jupyter": { "outputs_hidden": false @@ -537,7 +537,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1beda7ae", + "id": "7604fbeb", "metadata": { "jupyter": { "outputs_hidden": false @@ -561,7 +561,7 @@ }, { "cell_type": "markdown", - "id": "c2467e8f", + "id": "73b0ffae", "metadata": {}, "source": [ "生成された図を確認してください。ノイズを印加した学習データの分布から、元の関数$f(x)=x^3$をおおよそ導き出せていることが分かると思います。\n", @@ -571,7 +571,7 @@ }, { "cell_type": "markdown", - "id": "1c509d29", + "id": "a3973f8d", "metadata": {}, "source": [ "## 素粒子現象の探索への応用\n", @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "ce3e5525", + "id": "6204bf92", "metadata": {}, "source": [ "### 学習データの準備\n", @@ -605,7 +605,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf053847", + "id": "8c086727", "metadata": { "jupyter": { "outputs_hidden": false @@ -669,7 +669,7 @@ }, { "cell_type": "markdown", - "id": "8284b81b", + "id": "b5a03203", "metadata": { "pycharm": { "name": "#%% md\n" @@ -710,7 +710,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27a668ac", + "id": "b5e16930", "metadata": { "jupyter": { "outputs_hidden": false @@ -728,7 +728,7 @@ }, { "cell_type": "markdown", - "id": "bc085688", + "id": "d6fb88d9", "metadata": {}, "source": [ "### 変分フォームを使った状態変換\n", @@ -745,7 +745,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2fd8070a", + "id": "a2049bd3", "metadata": { "jupyter": { "outputs_hidden": false @@ -763,7 +763,7 @@ }, { "cell_type": "markdown", - "id": "ca81e9b6", + "id": "54efb35a", "metadata": {}, "source": [ "### 測定とモデル出力\n", @@ -776,7 +776,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dce872d3", + "id": "6849a592", "metadata": { "jupyter": { "outputs_hidden": false @@ -836,7 +836,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8895a189", + "id": "e64534fa", "metadata": { "tags": [ "remove-input" @@ -852,7 +852,7 @@ { "cell_type": "code", "execution_count": null, - "id": "672eed28", + "id": "e1bbc171", "metadata": { "jupyter": { "outputs_hidden": false @@ -876,7 +876,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07ca81e0", + "id": "8464d9a1", "metadata": { "tags": [ "remove-input" @@ -904,7 +904,7 @@ { "cell_type": "code", "execution_count": null, - "id": "809bde31", + "id": "76531ce8", "metadata": { "jupyter": { "outputs_hidden": false @@ -924,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "fdc3c1f6", + "id": "18c745cf", "metadata": { "pycharm": { "name": "#%% md\n" diff --git a/_sources/vqe.ipynb b/_sources/vqe.ipynb index f52f58c1..f27d5be3 100644 --- a/_sources/vqe.ipynb +++ b/_sources/vqe.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e1655988", + "id": "a40638d6", "metadata": {}, "source": [ "# 変分法と変分量子固有値ソルバー法を学習する" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "b593c06c", + "id": "546c70d5", "metadata": {}, "source": [ "この実習では、変分法の基本的な考え方と、その方法に基づいた変分量子アルゴリズムと呼ばれる量子計算の手法を学びます。特に、量子計算と古典計算を組み合わせた「**量子・古典ハイブリッドアルゴリズム**」としての変分量子アルゴリズムに着目します。この手法を用いて、近似的な固有値計算を可能にする**変分量子固有値ソルバー法**と呼ばれる方法へ拡張していきます。\n", @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "aec2c449", + "id": "76ceb7f1", "metadata": {}, "source": [ "## はじめに\n", @@ -46,7 +46,7 @@ }, { "cell_type": "markdown", - "id": "2caeceb2", + "id": "d234fda6", "metadata": {}, "source": [ "## 量子力学における変分法\n", @@ -91,7 +91,7 @@ }, { "cell_type": "markdown", - "id": "ada8a952", + "id": "7cc609e3", "metadata": {}, "source": [ "(vqa)=\n", @@ -102,7 +102,7 @@ }, { "cell_type": "markdown", - "id": "ea7b83c9", + "id": "e6b0aaf5", "metadata": {}, "source": [ "### 変分量子回路\n", @@ -115,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "c3e1ee98", + "id": "62a22997", "metadata": {}, "source": [ "### 単純な変分フォーム\n", @@ -132,7 +132,7 @@ }, { "cell_type": "markdown", - "id": "94f8ffa8", + "id": "19fe90da", "metadata": {}, "source": [ "### パラメータの最適化\n", @@ -147,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "6bb085c0", + "id": "02b4b190", "metadata": {}, "source": [ "### 変分フォームを使った実例\n", @@ -171,7 +171,7 @@ { "cell_type": "code", "execution_count": null, - "id": "add066df", + "id": "008df22b", "metadata": { "jupyter": { "outputs_hidden": false @@ -194,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "bb3168b5", + "id": "9995d3a0", "metadata": {}, "source": [ "最初に、ターゲットとなる量子状態ベクトルをランダムに生成する関数と、状態ベクトルから$X, Y, Z$の期待値を計算する関数を定義します。状態ベクトルはQiskitのStatevectorというクラスで表現し、パウリ演算子にはSparsePauliOpを使用します。" @@ -203,7 +203,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6269ab6a", + "id": "22864507", "metadata": { "jupyter": { "outputs_hidden": false @@ -234,7 +234,7 @@ }, { "cell_type": "markdown", - "id": "a236130e", + "id": "7df348f0", "metadata": {}, "source": [ "次に、変分フォーム回路を定義します。このとき、$U$ゲートの回転角として、具体的な数値を設定せず、QiskitのParameterというオブジェクトを利用します。Parameterはあとから数値を代入できる名前のついた箱として使えます。" @@ -243,7 +243,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87e43867", + "id": "be4d15e7", "metadata": { "tags": [ "remove-output" @@ -260,7 +260,7 @@ }, { "cell_type": "markdown", - "id": "5cb6d3e1", + "id": "2c1b99a3", "metadata": {}, "source": [ "Parameterに値を代入するには、回路の`bind_parameters`メソッドを利用します。" @@ -269,7 +269,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f05372b", + "id": "ac0d277c", "metadata": {}, "outputs": [], "source": [ @@ -280,7 +280,7 @@ { "cell_type": "code", "execution_count": null, - "id": "73ed8942", + "id": "e261ac55", "metadata": {}, "outputs": [], "source": [ @@ -290,7 +290,7 @@ }, { "cell_type": "markdown", - "id": "aab889cc", + "id": "73d23693", "metadata": {}, "source": [ "変分フォーム回路が作る状態における$X, Y, Z$の期待値を測定するための回路を定義します。" @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e80d8ef", + "id": "60ad83af", "metadata": {}, "outputs": [], "source": [ @@ -323,7 +323,7 @@ }, { "cell_type": "markdown", - "id": "0b7d5b2f", + "id": "bcb8ac97", "metadata": {}, "source": [ "それぞれの回路を通常通りバックエンドの`run()`メソッドで実行し、結果から期待値を計算する関数を定義します。" @@ -332,7 +332,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0d67dba3", + "id": "dde082d4", "metadata": {}, "outputs": [], "source": [ @@ -357,7 +357,7 @@ }, { "cell_type": "markdown", - "id": "4ea8ab05", + "id": "8e9f6572", "metadata": {}, "source": [ "最小化する目的関数を定義します。" @@ -366,7 +366,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2fd2b2b0", + "id": "c190615a", "metadata": {}, "outputs": [], "source": [ @@ -389,7 +389,7 @@ }, { "cell_type": "markdown", - "id": "a0efc1b6", + "id": "0832f698", "metadata": {}, "source": [ "最適化には使用しませんが、解を得たあとで変分フォームの終状態とターゲット状態とのフィデリティ$|\\langle \\psi_0 | \\psi(\\theta, \\phi) \\rangle|^2$を計算する関数も定義しておきます。厳密に最適化が成功すれば、この関数の返り値は1になります。" @@ -398,7 +398,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db047182", + "id": "beb17654", "metadata": {}, "outputs": [], "source": [ @@ -417,7 +417,7 @@ }, { "cell_type": "markdown", - "id": "a2626162", + "id": "cd1a769d", "metadata": {}, "source": [ "最後にCOBYLAオプティマイザーのインスタンスを作成し、アルゴリズムを実行します。" @@ -426,7 +426,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b7613fe7", + "id": "9e0e47ba", "metadata": {}, "outputs": [], "source": [ @@ -444,7 +444,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e34aa118", + "id": "042f4926", "metadata": { "tags": [ "remove-input" @@ -462,7 +462,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6a7af5e4", + "id": "2226c330", "metadata": { "tags": [ "raises-exception", @@ -485,7 +485,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c33144a0", + "id": "a7e9b322", "metadata": { "tags": [ "remove-input" @@ -503,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "c632b4fb", + "id": "bfcabc11", "metadata": {}, "source": [ "最適化プロセスにおけるロス(目的関数の返り値)の推移をプロットします。" @@ -512,7 +512,7 @@ { "cell_type": "code", "execution_count": null, - "id": "51ee25c8", + "id": "738d9774", "metadata": {}, "outputs": [], "source": [ @@ -521,7 +521,7 @@ }, { "cell_type": "raw", - "id": "d3e9bd3d", + "id": "96c11aca", "metadata": {}, "source": [ "`optimizer.minimize()`の返り値の`min_result`から最適化過程の様々な情報(目的関数の呼び出し回数や最適化に要したステップ数など)にアクセスできます。特に、最適化されたパラメータ値が`min_result.x`から得られるので、それを使ってフィデリティを計算してみます。" @@ -530,7 +530,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5120d038", + "id": "10646485", "metadata": {}, "outputs": [], "source": [ @@ -539,7 +539,7 @@ }, { "cell_type": "raw", - "id": "0fdc96e3", + "id": "838a0836", "metadata": {}, "source": [ "ショット数が有限なので統計誤差の影響から最適パラメータは厳密解とは一致しません。ショット数やステップ数を変えて、解の一致具合を確認してみてください。" @@ -547,7 +547,7 @@ }, { "cell_type": "markdown", - "id": "f78bf917", + "id": "bdf83f81", "metadata": {}, "source": [ "#### Estimatorの利用\n", @@ -558,7 +558,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1310da3e", + "id": "880a3b28", "metadata": {}, "outputs": [], "source": [ @@ -579,7 +579,7 @@ }, { "cell_type": "markdown", - "id": "8e5a3022", + "id": "27f236ab", "metadata": {}, "source": [ "Estimatorを使った目的関数を定義します。" @@ -588,7 +588,7 @@ { "cell_type": "code", "execution_count": null, - "id": "37b8359b", + "id": "bf13415b", "metadata": {}, "outputs": [], "source": [ @@ -609,7 +609,7 @@ }, { "cell_type": "markdown", - "id": "eb579031", + "id": "0b2fb02c", "metadata": {}, "source": [ "上の目的関数を最適化します。" @@ -618,7 +618,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4d22b0a5", + "id": "93a8dd42", "metadata": {}, "outputs": [], "source": [ @@ -636,7 +636,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a68d5473", + "id": "d4bca742", "metadata": { "tags": [ "remove-input" @@ -653,7 +653,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea6c801f", + "id": "1b8ccee6", "metadata": { "tags": [ "raises-exception", @@ -676,7 +676,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1629c135", + "id": "4db19e0c", "metadata": { "tags": [ "remove-input" @@ -694,7 +694,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bca8aa88", + "id": "2ac95440", "metadata": {}, "outputs": [], "source": [ @@ -703,7 +703,7 @@ }, { "cell_type": "markdown", - "id": "f2619947", + "id": "c5ed2adc", "metadata": {}, "source": [ "### エンタングルメントの導入\n", @@ -722,7 +722,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b44e4c7", + "id": "2cfb456b", "metadata": { "tags": [ "remove-output" @@ -741,7 +741,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eba86314", + "id": "6ce3ecbc", "metadata": {}, "outputs": [], "source": [ @@ -766,7 +766,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41cd99c2", + "id": "911cf6b3", "metadata": { "jupyter": { "outputs_hidden": false @@ -797,7 +797,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0986bc39", + "id": "f7dad0c2", "metadata": { "tags": [ "remove-input" @@ -814,7 +814,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4048a07a", + "id": "09cdfc12", "metadata": { "jupyter": { "outputs_hidden": false @@ -837,7 +837,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66a28237", + "id": "2a276c8e", "metadata": { "tags": [ "remove-input" @@ -855,7 +855,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b3b0215", + "id": "1e63697d", "metadata": { "jupyter": { "outputs_hidden": false @@ -871,7 +871,7 @@ }, { "cell_type": "markdown", - "id": "bb49dc26", + "id": "46f9175e", "metadata": {}, "source": [ "やってみると分かりますが、結果は1量子ビットの場合と比べて良くないですね。どうすれば良くなるでしょうか?(やり方は複数あると思います)" @@ -879,7 +879,7 @@ }, { "cell_type": "markdown", - "id": "dae69b29", + "id": "700534a8", "metadata": {}, "source": [ "**一つの解決策:変分フォームにエンタングルメントを導入する**\n", @@ -896,7 +896,7 @@ }, { "cell_type": "markdown", - "id": "d882d368", + "id": "2f7b7c52", "metadata": {}, "source": [ "2量子ビットの一般の状態では2つのビットがエンタングルしているので、変分フォームに2量子ビットゲートを入れると近似精度が良くなるのはある意味当然です。例えば、ベル状態([CHSH不等式の破れを確認する](https://utokyo-icepp.github.io/qc-workbook/chsh_inequality.html#id14)を参照)を再現したいときにこの状況をクリアに見ることができます。上で\n", @@ -924,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "e93ac8a5", + "id": "0ab3c047", "metadata": { "pycharm": { "name": "#%% md\n" @@ -990,7 +990,7 @@ }, { "cell_type": "markdown", - "id": "5991c4b1", + "id": "faff5cf2", "metadata": { "pycharm": { "name": "#%% md\n" @@ -1011,7 +1011,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af245f71", + "id": "2b4d6170", "metadata": {}, "outputs": [], "source": [ @@ -1023,7 +1023,7 @@ { "cell_type": "code", "execution_count": null, - "id": "acf87658", + "id": "9dfcccda", "metadata": {}, "outputs": [], "source": [ @@ -1058,7 +1058,7 @@ { "cell_type": "code", "execution_count": null, - "id": "013ae9ee", + "id": "0d681cd4", "metadata": {}, "outputs": [], "source": [ @@ -1090,7 +1090,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d5cdc4a5", + "id": "fda72065", "metadata": { "tags": [ "remove-input" @@ -1107,7 +1107,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9884c256", + "id": "a0555a0c", "metadata": { "tags": [ "raises-exception", @@ -1125,7 +1125,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4790d04b", + "id": "0ac15845", "metadata": { "tags": [ "remove-input" @@ -1142,7 +1142,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fdd041ab", + "id": "08c2a952", "metadata": { "jupyter": { "outputs_hidden": false @@ -1162,7 +1162,7 @@ }, { "cell_type": "markdown", - "id": "9ad760ce", + "id": "8d9a6e90", "metadata": { "pycharm": { "name": "#%% md\n" diff --git a/_sources/vqe_tracking.ipynb b/_sources/vqe_tracking.ipynb index 9d26fb09..8538b3df 100644 --- a/_sources/vqe_tracking.ipynb +++ b/_sources/vqe_tracking.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "2b921307", + "id": "a0bbd9fe", "metadata": {}, "source": [ "# 【課題】高エネルギー実験で生成された荷電粒子の飛跡を見つける" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "aee470f6", + "id": "de693b9e", "metadata": {}, "source": [ "この課題では、変分量子固有値ソルバー法を物理実験に応用することを考えてみます。特に高エネルギー物理の実験に着目し、その必須技術である「**荷電粒子飛跡の再構成**」を変分量子固有値ソルバー法を使って実現することを目指します。\n", @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "7cd8293e", + "id": "e7116374", "metadata": {}, "source": [ "## はじめに\n", @@ -35,7 +35,7 @@ }, { "cell_type": "markdown", - "id": "545a29ed", + "id": "fcb31467", "metadata": {}, "source": [ "(hep)=\n", @@ -57,7 +57,7 @@ }, { "cell_type": "markdown", - "id": "4a14e992", + "id": "a3559f26", "metadata": {}, "source": [ "(hep_detect)=\n", @@ -77,7 +77,7 @@ }, { "cell_type": "markdown", - "id": "fcaa1112", + "id": "445cc9a2", "metadata": {}, "source": [ "(ML_challenge)=\n", @@ -90,7 +90,7 @@ }, { "cell_type": "markdown", - "id": "c96c5509", + "id": "9cf7e966", "metadata": {}, "source": [ "(tracking)=\n", @@ -101,7 +101,7 @@ }, { "cell_type": "markdown", - "id": "f17e7937", + "id": "4ef383ad", "metadata": {}, "source": [ "まず、必要なライブラリを最初にインポートします。" @@ -110,7 +110,7 @@ { "cell_type": "code", "execution_count": null, - "id": "adb87012", + "id": "9a8855f1", "metadata": { "jupyter": { "outputs_hidden": false @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "f06d51ed", + "id": "fad35fca", "metadata": {}, "source": [ "(hamiltonian_form)=\n", @@ -150,7 +150,7 @@ }, { "cell_type": "markdown", - "id": "b635886a", + "id": "a8278185", "metadata": {}, "source": [ "(pre_processing)=\n", @@ -176,7 +176,7 @@ }, { "cell_type": "markdown", - "id": "38cae6f1", + "id": "e21964c1", "metadata": {}, "source": [ "#### QUBO\n", @@ -197,7 +197,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ac26566", + "id": "31e42f5f", "metadata": {}, "outputs": [], "source": [ @@ -214,7 +214,7 @@ }, { "cell_type": "markdown", - "id": "fc415f30", + "id": "03328bd6", "metadata": {}, "source": [ "#### Ising形式\n", @@ -239,7 +239,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f328957c", + "id": "1e7117b3", "metadata": {}, "outputs": [], "source": [ @@ -261,7 +261,7 @@ }, { "cell_type": "markdown", - "id": "5168e223", + "id": "16707cde", "metadata": {}, "source": [ "次に、この係数をもとに、VQEに渡すハミルトニアンをSparsePauliOpとして定義します。{ref}`vqe_imp`ではSparsePauliOpは単一のパウリ積$ZXY$を表現するのに使いましたが、実はパウリ積の和も同じクラスを使って表現できます。例えば\n", @@ -282,7 +282,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fa29518", + "id": "307c2799", "metadata": { "tags": [ "raises-exception", @@ -309,7 +309,7 @@ }, { "cell_type": "markdown", - "id": "94895cd9", + "id": "54af2340", "metadata": {}, "source": [ "(tracking_vqe)=\n", @@ -321,7 +321,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dea76f57", + "id": "6208b517", "metadata": { "pycharm": { "name": "#%%\n" @@ -346,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "f50e515a", + "id": "12b8cd5f", "metadata": {}, "source": [ "`optimal_segments_diag`のリストで1になっている量子ビットが、目的関数を最小化するセグメントの選択に対応します。\n", @@ -357,7 +357,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4e6c7f53", + "id": "cafb10fc", "metadata": { "pycharm": { "name": "#%%\n" @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "3cc99b49", + "id": "00763469", "metadata": { "pycharm": { "name": "#%% md\n" @@ -424,7 +424,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f1c91b07", + "id": "14589ef7", "metadata": { "pycharm": { "name": "#%%\n" @@ -472,7 +472,7 @@ }, { "cell_type": "markdown", - "id": "cc09c302", + "id": "548f5395", "metadata": {}, "source": [ "**提出するもの**\n", diff --git a/circuit_from_scratch.html b/circuit_from_scratch.html index 56d48788..fc71d02e 100644 --- a/circuit_from_scratch.html +++ b/circuit_from_scratch.html @@ -841,6 +841,7 @@

3量子ビット以上量子状態生成

それでは、これまでに登場したゲートを使って量子状態生成のエクササイズをしましょう。

実はstatevector_expr関数には回路オブジェクトを直接渡すこともできるので(内部でシミュレータを実行し状態ベクトルオブジェクトを取得する)、ここからはその機能を利用します。また、コード中登場するamp_normphase_normは、表示される数式において振幅や位相の共通因子をくくりだすために設定されています。

+

各問題のコードセルには、ヒントとして回路が一部分だけ書かれています。残りのcircuit.?の部分を埋めてみましょう。答えは一行とは限りません。また、同じ状態を作る量子回路は無数に存在するので、ヒントを消して独自の実装をしても構いません。

問題1: 1量子ビット、相対位相付き

問題

diff --git a/numerics.html b/numerics.html index a17d9bdf..9f2bc2ed 100644 --- a/numerics.html +++ b/numerics.html @@ -493,7 +493,7 @@

予備知識:数値表現 -
<matplotlib.legend.Legend at 0x7fc978cf0dc0>
+
<matplotlib.legend.Legend at 0x7fdaf464adf0>
 
_images/numerics_3_1.png diff --git a/python_intro.html b/python_intro.html index 114a125c..7d71544a 100644 --- a/python_intro.html +++ b/python_intro.html @@ -1867,7 +1867,7 @@

Jupyter -
Using matplotlib backend: <object object at 0x7f9a1167dc60>
+
Using matplotlib backend: <object object at 0x7ff722497c30>
 
diff --git a/searchindex.js b/searchindex.js index be7174ee..ab6fe4fb 100644 --- a/searchindex.js +++ b/searchindex.js @@ -1 +1 @@ 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