Amazon Braket のサンプルノートブックです（日本語版）

0_Getting_started-workshop.ipynb

1_Running_quantum_circuits_on_simulators-workshop.ipynb

2_QPU_devices.ipynb

3_Dwave_MaximumCut-workshop.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# D-Wave の基本：最大カット問題を Braket で使う"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "このチュートリアルでは、Amazon BraketのD-Waveデバイスを使用して、有名な __Maximum-Cut (MaxCut)__ 問題の小さなインスタンスを解決します。 MaxCut問題は、組合せ最適化で最も有名なNP困難問題の1つです。 頂点セット $V$ とエッジセット $E$ を持つ無向グラフ $G(V, E)$ が与えられた場合、MaxCut問題は、2つのセット間のエッジの数が最も大きくなるように、 $V$ を2つのセットに分割しようとします。 \n",
    "\n",
    "この MaxCut 問題の実アプリケーションとしては、例えばマーケティング目的のクラスタリング問題や、金融のポートフォリオ最適化問題になどが考えられています。\n",
    "\n",
    "このハンズオンを実行するのに、0.3019ドル（1タスク + 10ショット 0.0019ドル）かかりますので、予めご了承ください。ジョブを複数投げると、その分コストが発生しますのでご利用の際はご注意ください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "免責事項：この例に示されているコードは、[こちら](https://github.com/dwave-examples/maximum-cut) の Github で入手可能な D-Wave チュートリアルから抜粋したものであり、著作権は D-Wave Systems、Inc. にあります。 Apacheライセンスの下でライセンスされています。 下記のスクリプトの目的は、D-Wave の Ocean tool suite を使用する既存のコードを、最小限のコード変更で Amazon Braket で簡単に実行できることを示すことです。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "from braket.aws import AwsDevice\n",
    "from braket.ocean_plugin import BraketSampler, BraketDWaveSampler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "# magic word for producing visualizations in notebook\n",
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "import dwave_networkx as dnx\n",
    "from dimod.binary_quadratic_model import BinaryQuadraticModel\n",
    "from dwave.system.composites import EmbeddingComposite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [入力必須] __注__：以下にS3バケットとキーを入力してください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Please enter the S3 bucket you created during onboarding in the code below\n",
    "my_bucket = \"amazon-braket-Your-Bucket-Name\" # the name of the bucket\n",
    "my_prefix = \"braket-handson/d-wave\" \n",
    "s3_folder = (my_bucket, my_prefix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# session and device\n",
    "device = AwsDevice(\"arn:aws:braket:::device/qpu/d-wave/DW_2000Q_6\")\n",
    "print('Device:', device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 最大カット問題の設定"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# helper function to plot graph\n",
    "def get_graph(graph, pos):\n",
    "    \"\"\"\n",
    "    plot colored graph for given solution\n",
    "    \"\"\"\n",
    "    # positions for all nodes\n",
    "    # pos = nx.spring_layout(graph)\n",
    "\n",
    "    # nodes\n",
    "    nx.draw_networkx_nodes(graph, pos, node_size=700)\n",
    "\n",
    "    # edges\n",
    "    nx.draw_networkx_edges(graph, pos)\n",
    "\n",
    "    # labels\n",
    "    nx.draw_networkx_labels(graph, pos, font_size=20, font_family='sans-serif')\n",
    "\n",
    "    # plot the graph\n",
    "    plt.axis('off')\n",
    "    #plt.savefig(\"figures/random_graph.png\") # save as png\n",
    "    plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Copyright 2019 D-Wave Systems, Inc.\n",
    "#\n",
    "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "#     http://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License.\n",
    "\n",
    "# ------ Import necessary packages ----\n",
    "from collections import defaultdict\n",
    "\n",
    "# from dwave.system.samplers import DWaveSampler\n",
    "# from dwave.system.composites import EmbeddingComposite\n",
    "\n",
    "# ------- Set up our graph -------\n",
    "\n",
    "# Create empty graph\n",
    "G = nx.Graph()\n",
    "\n",
    "# Add edges to the graph (also adds nodes)\n",
    "G.add_edges_from([(1,2),(1,3),(2,4),(3,4),(3,5),(4,5)])\n",
    "\n",
    "# plot graph\n",
    "pos = nx.spring_layout(G)\n",
    "# plot graph with labels\n",
    "get_graph(G, pos)\n",
    "\n",
    "# ------- Set up our QUBO dictionary -------\n",
    "\n",
    "# Initialize our Q matrix\n",
    "Q = defaultdict(int)\n",
    "\n",
    "# Update Q matrix for every edge in the graph\n",
    "for u, v in G.edges:\n",
    "    Q[(u,u)]+= -1\n",
    "    Q[(v,v)]+= -1\n",
    "    Q[(u,v)]+= 2\n",
    "\n",
    "# print Q matrix\n",
    "print('Show Q matrix:', Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 最大カット問題をD-Wave 2000 で解く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ------- Run our QUBO on the QPU -------\n",
    "# Set up QPU parameters\n",
    "chainstrength = 8\n",
    "numruns = 10\n",
    "\n",
    "# Run the QUBO on the Braket solver from your config file\n",
    "# set sampler\n",
    "sampler = BraketDWaveSampler(s3_folder,'arn:aws:braket:::device/qpu/d-wave/DW_2000Q_6')\n",
    "sampler = EmbeddingComposite(sampler)\n",
    "response = sampler.sample_qubo(Q, chain_strength=chainstrength, num_reads=numruns)\n",
    "energies = iter(response.data())\n",
    "\n",
    "# ------- Print results to user -------\n",
    "print('-' * 60)\n",
    "print('{:>15s}{:>15s}{:^15s}{:^15s}'.format('Set 0','Set 1','Energy','Cut Size'))\n",
    "print('-' * 60)\n",
    "for line in response:\n",
    "    S0 = [k for k,v in line.items() if v == 0]\n",
    "    S1 = [k for k,v in line.items() if v == 1]\n",
    "    E = next(energies).energy\n",
    "    print('{:>15s}{:>15s}{:^15s}{:^15s}'.format(str(S0),str(S1),str(E),str(int(-1*E))))\n",
    "\n",
    "# ------- Display results to user -------\n",
    "# Grab best result\n",
    "# Note: \"best\" result is the result with the lowest energy\n",
    "# Note2: the look up table (lut) is a dictionary, where the key is the node index\n",
    "#   and the value is the set label. For example, lut[5] = 1, indicates that\n",
    "#   node 5 is in set 1 (S1).\n",
    "lut = response.lowest().first.sample\n",
    "\n",
    "# Interpret best result in terms of nodes and edges\n",
    "S0 = [node for node in G.nodes if not lut[node]]\n",
    "S1 = [node for node in G.nodes if lut[node]]\n",
    "cut_edges = [(u, v) for u, v in G.edges if lut[u]!=lut[v]]\n",
    "uncut_edges = [(u, v) for u, v in G.edges if lut[u]==lut[v]]\n",
    "\n",
    "# Display best result\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw_networkx_nodes(G, pos, nodelist=S0, node_color='r')\n",
    "nx.draw_networkx_nodes(G, pos, nodelist=S1, node_color='c')\n",
    "nx.draw_networkx_edges(G, pos, edgelist=cut_edges, style='dashdot', alpha=0.5, width=3)\n",
    "nx.draw_networkx_edges(G, pos, edgelist=uncut_edges, style='solid', width=3)\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "\n",
    "filename = \"maxcut_plot.png\"\n",
    "plt.savefig(filename, bbox_inches='tight')\n",
    "print(\"\\nYour plot is saved to {}\".format(filename))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__DISCUSSION__：このトイプロブレムの最適なカットサイズは5です。上記の破線で表示されているように、異なる色のノードを接続するすべてのエッジについて、ポイントをスコアリングします（つまり、このエッジをカットします）。 ここでは最大で5つのエッジをカットできます。 このおもちゃの例では、ノード5に優先する色がないため、明らかな$ Z_ {2} $対称性（つまり、2つのサブセットの色の選択は任意）を除いて、複数の最適な縮退解が見つかります。この問題は同等です。 フラストレーションの存在下で、反強磁性基底状態を見つけること（ノード3-4-5のサブグラフにここに存在するように）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## APPENDIX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original MaxCut example from here: https://github.com/dwave-examples/maximum-cut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Copyright 2019 D-Wave Systems, Inc.\n",
    "# #\n",
    "# # Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# # you may not use this file except in compliance with the License.\n",
    "# # You may obtain a copy of the License at\n",
    "# #\n",
    "# #     http://www.apache.org/licenses/LICENSE-2.0\n",
    "# #\n",
    "# # Unless required by applicable law or agreed to in writing, software\n",
    "# # distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# # See the License for the specific language governing permissions and\n",
    "# # limitations under the License.\n",
    "\n",
    "# # ------ Import necessary packages ----\n",
    "# from collections import defaultdict\n",
    "\n",
    "# from dwave.system.samplers import DWaveSampler\n",
    "# from dwave.system.composites import EmbeddingComposite\n",
    "# import networkx as nx\n",
    "\n",
    "# import matplotlib\n",
    "# matplotlib.use(\"agg\")\n",
    "# from matplotlib import pyplot as plt\n",
    "\n",
    "# # ------- Set up our graph -------\n",
    "\n",
    "# # Create empty graph\n",
    "# G = nx.Graph()\n",
    "\n",
    "# # Add edges to the graph (also adds nodes)\n",
    "# G.add_edges_from([(1,2),(1,3),(2,4),(3,4),(3,5),(4,5)])\n",
    "\n",
    "# # ------- Set up our QUBO dictionary -------\n",
    "\n",
    "# # Initialize our Q matrix\n",
    "# Q = defaultdict(int)\n",
    "\n",
    "# # Update Q matrix for every edge in the graph\n",
    "# for u, v in G.edges:\n",
    "#     Q[(u,u)]+= -1\n",
    "#     Q[(v,v)]+= -1\n",
    "#     Q[(u,v)]+= 2\n",
    "\n",
    "# # ------- Run our QUBO on the QPU -------\n",
    "# # Set up QPU parameters\n",
    "# chainstrength = 8\n",
    "# numruns = 10\n",
    "\n",
    "# # Run the QUBO on the solver from your config file\n",
    "# sampler = EmbeddingComposite(DWaveSampler(solver={'qpu': True}))\n",
    "# response = sampler.sample_qubo(Q, chain_strength=chainstrength, num_reads=numruns)\n",
    "# energies = iter(response.data())\n",
    "\n",
    "# # ------- Print results to user -------\n",
    "# print('-' * 60)\n",
    "# print('{:>15s}{:>15s}{:^15s}{:^15s}'.format('Set 0','Set 1','Energy','Cut Size'))\n",
    "# print('-' * 60)\n",
    "# for line in response:\n",
    "#     S0 = [k for k,v in line.items() if v == 0]\n",
    "#     S1 = [k for k,v in line.items() if v == 1]\n",
    "#     E = next(energies).energy\n",
    "#     print('{:>15s}{:>15s}{:^15s}{:^15s}'.format(str(S0),str(S1),str(E),str(int(-1*E))))\n",
    "\n",
    "# # ------- Display results to user -------\n",
    "# # Grab best result\n",
    "# # Note: \"best\" result is the result with the lowest energy\n",
    "# # Note2: the look up table (lut) is a dictionary, where the key is the node index\n",
    "# #   and the value is the set label. For example, lut[5] = 1, indicates that\n",
    "# #   node 5 is in set 1 (S1).\n",
    "# lut = response.lowest().first.sample\n",
    "\n",
    "# # Interpret best result in terms of nodes and edges\n",
    "# S0 = [node for node in G.nodes if not lut[node]]\n",
    "# S1 = [node for node in G.nodes if lut[node]]\n",
    "# cut_edges = [(u, v) for u, v in G.edges if lut[u]!=lut[v]]\n",
    "# uncut_edges = [(u, v) for u, v in G.edges if lut[u]==lut[v]]\n",
    "\n",
    "# # Display best result\n",
    "# pos = nx.spring_layout(G)\n",
    "# nx.draw_networkx_nodes(G, pos, nodelist=S0, node_color='r')\n",
    "# nx.draw_networkx_nodes(G, pos, nodelist=S1, node_color='c')\n",
    "# nx.draw_networkx_edges(G, pos, edgelist=cut_edges, style='dashdot', alpha=0.5, width=3)\n",
    "# nx.draw_networkx_edges(G, pos, edgelist=uncut_edges, style='solid', width=3)\n",
    "# nx.draw_networkx_labels(G, pos)\n",
    "\n",
    "# filename = \"maxcut_plot.png\"\n",
    "# plt.savefig(filename, bbox_inches='tight')\n",
    "# print(\"\\nYour plot is saved to {}\".format(filename))"
   ]
  }
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