plot_level_vs_ancilla.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical Result Part Figure 1: Recursive Level and Circuit Ancilla Usage\n",
    "\n",
    "Ancilla qubits number vs recursive level for much larger BQEs\n",
    "to demonstrate that the method could be powerful when more quantum resources are available.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-02-27 19:00:18,817 - generate_qc.py[line:34] - WARNING: **USING GPU SIMULATOR**\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pickle as pk\n",
    "import pandas as pd\n",
    "\n",
    "from utils import determine_oracle_ancilla_usage\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "###### WARNING: enable this part to recompute the output for drawing this figure #######\n",
    "# num_var, num_sol, seed, sols, EQs\n",
    "if 0:\n",
    "    eqs_df = pk.load(open(\"output/eqs.pkl\", \"rb\"))  # type: pd.DataFrame\n",
    "    save_file = \"output/figure1.pkl\"\n",
    "    cols = [\"num_var\", \"num_sol\", \"seed\", \"level\", \"num_ancilla\"]\n",
    "    result = pd.DataFrame(columns=cols)\n",
    "    if os.path.exists(save_file):\n",
    "        result = pk.load(open(save_file, \"rb\"))\n",
    "\n",
    "    levels = [1, 2, 3, 4]\n",
    "    split = 2\n",
    "    for idx, df in eqs_df.groupby(\"num_var\"):\n",
    "        for i, row in df.iterrows():\n",
    "            eqs = row[\"eqs\"]\n",
    "            num_var = row[\"num_var\"]\n",
    "            num_sol = row[\"num_sol\"]\n",
    "            seed = row[\"seed\"]\n",
    "            for level in levels:\n",
    "\n",
    "                part_size = int(np.ceil(len(eqs) / split))\n",
    "                num_ancilla = determine_oracle_ancilla_usage(part_size, level=level)\n",
    "\n",
    "                result = result.append(pd.DataFrame([[num_var, num_sol, seed, level, num_ancilla]], columns=cols), ignore_index=True)\n",
    "\n",
    "    pk.dump(result, open(save_file, \"wb+\"))\n",
    "    print(result)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>num_var</th>\n",
       "      <th>num_sol</th>\n",
       "      <th>seed</th>\n",
       "      <th>level</th>\n",
       "      <th>num_ancilla</th>\n",
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       "      <th>4</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>11854</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>6343</th>\n",
       "      <td>25</td>\n",
       "      <td>33</td>\n",
       "      <td>48899</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6344</th>\n",
       "      <td>25</td>\n",
       "      <td>36</td>\n",
       "      <td>96189</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
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       "    <tr>\n",
       "      <th>6345</th>\n",
       "      <td>25</td>\n",
       "      <td>36</td>\n",
       "      <td>96189</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>6346</th>\n",
       "      <td>25</td>\n",
       "      <td>36</td>\n",
       "      <td>96189</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>6347</th>\n",
       "      <td>25</td>\n",
       "      <td>36</td>\n",
       "      <td>96189</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6348 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     num_var num_sol   seed level num_ancilla\n",
       "0         10       1  85029     1           6\n",
       "1         10       1  85029     2           4\n",
       "2         10       1  85029     3           4\n",
       "3         10       1  85029     4           4\n",
       "4         10       1  11854     1           5\n",
       "...      ...     ...    ...   ...         ...\n",
       "6343      25      33  48899     4           5\n",
       "6344      25      36  96189     1          10\n",
       "6345      25      36  96189     2           5\n",
       "6346      25      36  96189     3           5\n",
       "6347      25      36  96189     4           5\n",
       "\n",
       "[6348 rows x 5 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph1_data = pk.load(open(\"output/figure1.pkl\", \"rb\"))\n",
    "cols = [\"num_var\", \"num_sol\", \"seed\", \"level\", \"num_ancilla\"]\n",
    "graph1_data = pd.DataFrame(graph1_data, columns=cols)\n",
    "# num_var, level, depth, qc.num_ancillas\n",
    "graph1_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "      <th rowspan=\"4\" valign=\"top\">15</th>\n",
       "      <th>1</th>\n",
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       "      <td>30</td>\n",
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       "      <th>2</th>\n",
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       "      <th>3</th>\n",
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       "      <th>1</th>\n",
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       "      <td>30</td>\n",
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       "      <th>3</th>\n",
       "      <td>30</td>\n",
       "      <td>30</td>\n",
       "      <td>30</td>\n",
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       "      <td>30</td>\n",
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       "      <th>1</th>\n",
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       "      <th>3</th>\n",
       "      <td>30</td>\n",
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       "      <td>30</td>\n",
       "    </tr>\n",
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       "      <th>4</th>\n",
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       "      <th>4</th>\n",
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      ],
      "text/plain": [
       "               seed  num_sol  num_ancilla\n",
       "num_var level                            \n",
       "10      1        30       30           30\n",
       "        2        30       30           30\n",
       "        3        30       30           30\n",
       "        4        30       30           30\n",
       "12      1        30       30           30\n",
       "        2        30       30           30\n",
       "        3        30       30           30\n",
       "        4        30       30           30\n",
       "15      1        30       30           30\n",
       "        2        30       30           30\n",
       "        3        30       30           30\n",
       "        4        30       30           30\n",
       "18      1        30       30           30\n",
       "        2        30       30           30\n",
       "        3        30       30           30\n",
       "        4        30       30           30\n",
       "20      1        30       30           30\n",
       "        2        30       30           30\n",
       "        3        30       30           30\n",
       "        4        30       30           30\n",
       "22      1        30       30           30\n",
       "        2        30       30           30\n",
       "        3        30       30           30\n",
       "        4        30       30           30\n",
       "25      1        15       15           15\n",
       "        2        15       15           15\n",
       "        3        15       15           15\n",
       "        4        15       15           15"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_first = graph1_data.groupby(['num_var', 'seed', 'level', \"num_sol\"]).first().reset_index()\n",
    "graph1_data = df_first\n",
    "df_first[df_first[\"num_sol\"] == 1].groupby([\"num_var\", \"level\"]).count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.12156862745098039, 0.4666666666666667, 0.7058823529411765)) for an unfilled marker ('+').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((1.0, 0.4980392156862745, 0.054901960784313725)) for an unfilled marker ('+').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.17254901960784313, 0.6274509803921569, 0.17254901960784313)) for an unfilled marker ('+').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.8392156862745098, 0.15294117647058825, 0.1568627450980392)) for an unfilled marker ('+').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.5803921568627451, 0.403921568627451, 0.7411764705882353)) for an unfilled marker ('+').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.5490196078431373, 0.33725490196078434, 0.29411764705882354)) for an unfilled marker ('+').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.8901960784313725, 0.4666666666666667, 0.7607843137254902)) for an unfilled marker ('+').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.6313725490196078, 0.788235294117647, 0.9568627450980393)) for an unfilled marker ('x').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.7019607843137254, 0.8862745098039215, 0.803921568627451)) for an unfilled marker ('x').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "/home/xli/.local/lib/python3.8/site-packages/seaborn/categorical.py:1728: UserWarning: You passed a edgecolor/edgecolors ((0.9921568627450981, 0.803921568627451, 0.6745098039215687)) for an unfilled marker ('x').  Matplotlib is ignoring the edgecolor in favor of the facecolor.  This behavior may change in the future.\n",
      "  ax.scatter(x, y, label=hue_level,\n",
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
      "Failed to find a Ghostscript installation.  Distillation step skipped.\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams.update({'font.size': 12})\n",
    "\n",
    "plt.rcParams['text.usetex'] = True\n",
    "plt.rcParams['text.latex.preamble'] = r'\\usepackage{amsmath}'\n",
    "\n",
    "df = graph1_data.copy()\n",
    "df[r\"\\# vars\"] = df[\"num_var\"]\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6,5))\n",
    "sns.pointplot(\n",
    "    data=df[df.num_sol==1], x=\"level\", y=\"num_ancilla\", hue=r\"\\# vars\",\n",
    "    ax=ax,\n",
    "    errorbar=(\"ci\", 95),\n",
    "    n_boot=15,\n",
    "    # errorbar=lambda x: (x.min(), x.max()),\n",
    "    dodge=0.,\n",
    "    capsize=.1,\n",
    "    markers=\"+\",\n",
    "    linestyles=[\"-\"] * 7,\n",
    "    scale=0.8,\n",
    "    errwidth=1.5,\n",
    ")\n",
    "\n",
    "df_theory = pd.DataFrame({\n",
    "    r\"\\# vars\": [25, 25, 25, 25, 50, 50, 50, 50, 100, 100, 100, 100],\n",
    "    \"level\": [1, 2, 3, 4] * 3,\n",
    "    \"num_ancilla\": [13, 6, 5, 5, 25, 8, 6, 6, 50, 11, 8, 7]\n",
    "})\n",
    "res3 = sns.pointplot(\n",
    "    data=df_theory[df_theory[r\"\\# vars\"] == 25], x=\"level\", y=\"num_ancilla\", hue=r\"\\# vars\",\n",
    "    ax=ax,\n",
    "    errorbar=None,\n",
    "    n_boot=None,\n",
    "    dodge=0.,\n",
    "    capsize=.1,\n",
    "    markers=\"x\",\n",
    "    palette=\"pastel\",\n",
    "    linestyles=[\"--\", \"--\", \"--\", \"--\"],\n",
    "    scale=1.2,\n",
    "    errwidth=1.5,\n",
    ")\n",
    "res2 = sns.pointplot(\n",
    "    data=df_theory[df_theory[r\"\\# vars\"] != 25], x=\"level\", y=\"num_ancilla\", hue=r\"\\# vars\",\n",
    "    ax=ax,\n",
    "    errorbar=None,\n",
    "    n_boot=None,\n",
    "    dodge=0.,\n",
    "    capsize=.1,\n",
    "    markers=\"x\",\n",
    "    palette=\"Pastel2\",\n",
    "    linestyles=[\"--\", \"--\", \"--\", \"--\"],\n",
    "    scale=0.8,\n",
    "    errwidth=1.5\n",
    ")\n",
    "\n",
    "\n",
    "# ax.set_yscale('log')\n",
    "ax.set_ylim(0, 55)\n",
    "# ax.set_yticks([3, 4, 5, 6, 8, 10, 15, 20, 25, 30])\n",
    "# ax.set_yticklabels([3, 4, 5, 6, 8, 10, 15, 20, 25, 30])\n",
    "\n",
    "ax.legend(loc='upper right', ncol=2, title=r\"\\# vars\")\n",
    "plt.title(\"\\# sols = 1, dashed = theroetical\", fontsize=14)\n",
    "plt.tight_layout()\n",
    "\n",
    "# Set the axis labels and title\n",
    "plt.xlabel(r'recursion level', fontsize=16)\n",
    "plt.ylabel(r'\\# ancillae', fontsize=16)\n",
    "# Show the plot\n",
    "plt.savefig(\"../figure/level-vs-ancillae.eps\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "b527f3c249422632fd979a2ca0dc809eaf644961d2ffc50a82a698b4eccd2dc3"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}