{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Precomptued Analysis\n",
    "\n",
    "Use precomputed optimal angles to measure the expected value of $\\langle C \\rangle$ across a variety of problem types, sizes, $p$-depth, and random instances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load in Raw Data\n",
    "Go through each record, load in supporting objects, flatten everything into records, and put into a massive dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>timestamp</th>\n",
       "      <th>bitstrings</th>\n",
       "      <th>qubits</th>\n",
       "      <th>final_qubits</th>\n",
       "      <th>circuit</th>\n",
       "      <th>violation_indices</th>\n",
       "      <th>problem</th>\n",
       "      <th>problem_type</th>\n",
       "      <th>dataset_id</th>\n",
       "      <th>device_name</th>\n",
       "      <th>...</th>\n",
       "      <th>generation_task.dataset_id</th>\n",
       "      <th>generation_task.device_name</th>\n",
       "      <th>instance_i</th>\n",
       "      <th>n_qubits</th>\n",
       "      <th>optimum.p</th>\n",
       "      <th>f_val</th>\n",
       "      <th>gammas</th>\n",
       "      <th>betas</th>\n",
       "      <th>min_c</th>\n",
       "      <th>max_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2020-04-08 13:11:32.151452</td>\n",
       "      <td>[[0, 0, 0, 0], [0, 0, 1, 0], [1, 1, 1, 1], [0,...</td>\n",
       "      <td>[(5, 3), (6, 2), (6, 3), (6, 4)]</td>\n",
       "      <td>[(5, 3), (6, 2), (6, 3), (6, 4)]</td>\n",
       "      <td>[(PhX(-0.824)^0.5((5, 3)), PhX(-0.824)^0.5((6,...</td>\n",
       "      <td>[]</td>\n",
       "      <td>(2, 0, 1, 3)</td>\n",
       "      <td>HardwareGridProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>...</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Sycamore23</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>-2.616073</td>\n",
       "      <td>[0.47109541452232295, 0.5900885654628348]</td>\n",
       "      <td>[-0.44860990386986666, -0.29400122107756244]</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2020-04-08 13:11:32.520129</td>\n",
       "      <td>[[0, 1, 1, 0], [0, 0, 0, 1], [0, 0, 0, 0], [1,...</td>\n",
       "      <td>[(5, 3), (6, 2), (6, 3), (6, 4)]</td>\n",
       "      <td>[(5, 3), (6, 2), (6, 3), (6, 4)]</td>\n",
       "      <td>[(PhX(-0.644)^0.39663553581308286((5, 3)), PhX...</td>\n",
       "      <td>[]</td>\n",
       "      <td>(2, 0, 1, 3)</td>\n",
       "      <td>HardwareGridProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>...</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Sycamore23</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>-3.000000</td>\n",
       "      <td>[0.3047317419709853, 0.6664224586095869, 0.607...</td>\n",
       "      <td>[-0.5760240058080092, -0.36261585803438645, -0...</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2020-04-08 13:11:31.499590</td>\n",
       "      <td>[[0, 0, 0, 0], [1, 0, 1, 1], [0, 1, 0, 0], [1,...</td>\n",
       "      <td>[(5, 3), (6, 2), (6, 3), (6, 4)]</td>\n",
       "      <td>[(5, 3), (6, 2), (6, 3), (6, 4)]</td>\n",
       "      <td>[(PhX(0.806)^0.3587079604881125((5, 3)), PhX(0...</td>\n",
       "      <td>[]</td>\n",
       "      <td>(2, 0, 1, 3)</td>\n",
       "      <td>HardwareGridProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>...</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Sycamore23</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>-1.632993</td>\n",
       "      <td>[0.4776585668842565]</td>\n",
       "      <td>[-0.3926990816996555]</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2020-04-08 13:11:31.077127</td>\n",
       "      <td>[[1, 0], [1, 0], [0, 1], [1, 0], [1, 0], [1, 0...</td>\n",
       "      <td>[(5, 3), (6, 3)]</td>\n",
       "      <td>[(5, 3), (6, 3)]</td>\n",
       "      <td>[(PhX(0.163)^0.27171459224559236((5, 3)), PhX(...</td>\n",
       "      <td>[]</td>\n",
       "      <td>(1, 0)</td>\n",
       "      <td>HardwareGridProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>...</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Sycamore23</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>[0.6283182637521854, 0.7853973288957912]</td>\n",
       "      <td>[-0.3926989532796281, -0.07854016690845925]</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2020-04-08 13:11:31.247321</td>\n",
       "      <td>[[1, 0], [1, 0], [0, 1], [0, 1], [0, 1], [1, 0...</td>\n",
       "      <td>[(5, 3), (6, 3)]</td>\n",
       "      <td>[(5, 3), (6, 3)]</td>\n",
       "      <td>[(PhX(-0.14)^0.5((5, 3)), PhX(-0.5)^0.5((6, 3)...</td>\n",
       "      <td>[]</td>\n",
       "      <td>(1, 0)</td>\n",
       "      <td>HardwareGridProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>...</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Sycamore23</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>[0.5620701143250424, 0.7076351823020001, 0.798...</td>\n",
       "      <td>[-0.4199391572618354, -0.1086414306397252, -0....</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1.0</td>\n",
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       "<p>5 rows × 25 columns</p>\n",
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      ],
      "text/plain": [
       "                   timestamp  \\\n",
       "0 2020-04-08 13:11:32.151452   \n",
       "1 2020-04-08 13:11:32.520129   \n",
       "2 2020-04-08 13:11:31.499590   \n",
       "3 2020-04-08 13:11:31.077127   \n",
       "4 2020-04-08 13:11:31.247321   \n",
       "\n",
       "                                          bitstrings  \\\n",
       "0  [[0, 0, 0, 0], [0, 0, 1, 0], [1, 1, 1, 1], [0,...   \n",
       "1  [[0, 1, 1, 0], [0, 0, 0, 1], [0, 0, 0, 0], [1,...   \n",
       "2  [[0, 0, 0, 0], [1, 0, 1, 1], [0, 1, 0, 0], [1,...   \n",
       "3  [[1, 0], [1, 0], [0, 1], [1, 0], [1, 0], [1, 0...   \n",
       "4  [[1, 0], [1, 0], [0, 1], [0, 1], [0, 1], [1, 0...   \n",
       "\n",
       "                             qubits                      final_qubits  \\\n",
       "0  [(5, 3), (6, 2), (6, 3), (6, 4)]  [(5, 3), (6, 2), (6, 3), (6, 4)]   \n",
       "1  [(5, 3), (6, 2), (6, 3), (6, 4)]  [(5, 3), (6, 2), (6, 3), (6, 4)]   \n",
       "2  [(5, 3), (6, 2), (6, 3), (6, 4)]  [(5, 3), (6, 2), (6, 3), (6, 4)]   \n",
       "3                  [(5, 3), (6, 3)]                  [(5, 3), (6, 3)]   \n",
       "4                  [(5, 3), (6, 3)]                  [(5, 3), (6, 3)]   \n",
       "\n",
       "                                             circuit violation_indices  \\\n",
       "0  [(PhX(-0.824)^0.5((5, 3)), PhX(-0.824)^0.5((6,...                []   \n",
       "1  [(PhX(-0.644)^0.39663553581308286((5, 3)), PhX...                []   \n",
       "2  [(PhX(0.806)^0.3587079604881125((5, 3)), PhX(0...                []   \n",
       "3  [(PhX(0.163)^0.27171459224559236((5, 3)), PhX(...                []   \n",
       "4  [(PhX(-0.14)^0.5((5, 3)), PhX(-0.5)^0.5((6, 3)...                []   \n",
       "\n",
       "        problem         problem_type        dataset_id      device_name  ...  \\\n",
       "0  (2, 0, 1, 3)  HardwareGridProblem  2020-03-tutorial  Syc23-simulator  ...   \n",
       "1  (2, 0, 1, 3)  HardwareGridProblem  2020-03-tutorial  Syc23-simulator  ...   \n",
       "2  (2, 0, 1, 3)  HardwareGridProblem  2020-03-tutorial  Syc23-simulator  ...   \n",
       "3        (1, 0)  HardwareGridProblem  2020-03-tutorial  Syc23-simulator  ...   \n",
       "4        (1, 0)  HardwareGridProblem  2020-03-tutorial  Syc23-simulator  ...   \n",
       "\n",
       "   generation_task.dataset_id  generation_task.device_name  instance_i  \\\n",
       "0            2020-03-tutorial                   Sycamore23           4   \n",
       "1            2020-03-tutorial                   Sycamore23           4   \n",
       "2            2020-03-tutorial                   Sycamore23           4   \n",
       "3            2020-03-tutorial                   Sycamore23           4   \n",
       "4            2020-03-tutorial                   Sycamore23           4   \n",
       "\n",
       "  n_qubits  optimum.p     f_val  \\\n",
       "0        4          2 -2.616073   \n",
       "1        4          3 -3.000000   \n",
       "2        4          1 -1.632993   \n",
       "3        2          2 -1.000000   \n",
       "4        2          3 -1.000000   \n",
       "\n",
       "                                              gammas  \\\n",
       "0          [0.47109541452232295, 0.5900885654628348]   \n",
       "1  [0.3047317419709853, 0.6664224586095869, 0.607...   \n",
       "2                               [0.4776585668842565]   \n",
       "3           [0.6283182637521854, 0.7853973288957912]   \n",
       "4  [0.5620701143250424, 0.7076351823020001, 0.798...   \n",
       "\n",
       "                                               betas  min_c  max_c  \n",
       "0       [-0.44860990386986666, -0.29400122107756244]   -3.0    3.0  \n",
       "1  [-0.5760240058080092, -0.36261585803438645, -0...   -3.0    3.0  \n",
       "2                              [-0.3926990816996555]   -3.0    3.0  \n",
       "3        [-0.3926989532796281, -0.07854016690845925]   -1.0    1.0  \n",
       "4  [-0.4199391572618354, -0.1086414306397252, -0....   -1.0    1.0  \n",
       "\n",
       "[5 rows x 25 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import recirq\n",
    "import cirq\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from recirq.qaoa.experiments.precomputed_execution_tasks import \\\n",
    "    DEFAULT_BASE_DIR, DEFAULT_PROBLEM_GENERATION_BASE_DIR, DEFAULT_PRECOMPUTATION_BASE_DIR\n",
    "\n",
    "records = []\n",
    "for record in recirq.iterload_records(dataset_id=\"2020-03-tutorial\", base_dir=DEFAULT_BASE_DIR):\n",
    "    dc_task = record['task']\n",
    "    apre_task = dc_task.precomputation_task\n",
    "    pgen_task = apre_task.generation_task\n",
    "    \n",
    "    problem = recirq.load(pgen_task, base_dir=DEFAULT_PROBLEM_GENERATION_BASE_DIR)['problem']\n",
    "    record['problem'] = problem.graph\n",
    "    record['problem_type'] = problem.__class__.__name__\n",
    "    record['optimum'] = recirq.load(apre_task, base_dir=DEFAULT_PRECOMPUTATION_BASE_DIR)['optimum']\n",
    "    record['bitstrings'] = record['bitstrings'].bits\n",
    "    recirq.flatten_dataclass_into_record(record, 'task')\n",
    "    recirq.flatten_dataclass_into_record(record, 'precomputation_task')    \n",
    "    recirq.flatten_dataclass_into_record(record, 'generation_task')    \n",
    "    recirq.flatten_dataclass_into_record(record, 'optimum')\n",
    "    records.append(record)\n",
    "df_raw = pd.DataFrame(records)    \n",
    "df_raw['timestamp'] = pd.to_datetime(df_raw['timestamp'])\n",
    "df_raw.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Narrow down to Relevant Data\n",
    "Drop unnecessary metadata and use bitstrings to compute the expected value of the energy. In general, it's better to save the raw data and lots of metadata so we can use it if it becomes necessary in the future."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>2020-04-08 13:08:23.360051</td>\n",
       "      <td>SKProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>50000</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>-7.888209</td>\n",
       "      <td>-9.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-1.53480</td>\n",
       "      <td>0.020784</td>\n",
       "      <td>0.170533</td>\n",
       "      <td>0.002309</td>\n",
       "      <td>0.876468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>2020-04-08 13:08:16.029073</td>\n",
       "      <td>SKProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>50000</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>-5.318905</td>\n",
       "      <td>-9.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-3.02000</td>\n",
       "      <td>0.019369</td>\n",
       "      <td>0.335556</td>\n",
       "      <td>0.002152</td>\n",
       "      <td>0.590989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>2020-04-08 13:09:02.773520</td>\n",
       "      <td>SKProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>50000</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>-6.942368</td>\n",
       "      <td>-9.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-2.36920</td>\n",
       "      <td>0.020491</td>\n",
       "      <td>0.263244</td>\n",
       "      <td>0.002277</td>\n",
       "      <td>0.771374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>2020-04-08 13:09:06.524879</td>\n",
       "      <td>SKProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>50000</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>-7.888209</td>\n",
       "      <td>-9.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-1.50696</td>\n",
       "      <td>0.020841</td>\n",
       "      <td>0.167440</td>\n",
       "      <td>0.002316</td>\n",
       "      <td>0.876468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>2020-04-08 13:08:59.681882</td>\n",
       "      <td>SKProblem</td>\n",
       "      <td>2020-03-tutorial</td>\n",
       "      <td>Syc23-simulator</td>\n",
       "      <td>50000</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>-5.318905</td>\n",
       "      <td>-9.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>-3.04136</td>\n",
       "      <td>0.019464</td>\n",
       "      <td>0.337929</td>\n",
       "      <td>0.002163</td>\n",
       "      <td>0.590989</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 18 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                     timestamp         problem_type        dataset_id  \\\n",
       "0   2020-04-08 13:11:32.151452  HardwareGridProblem  2020-03-tutorial   \n",
       "1   2020-04-08 13:11:32.520129  HardwareGridProblem  2020-03-tutorial   \n",
       "2   2020-04-08 13:11:31.499590  HardwareGridProblem  2020-03-tutorial   \n",
       "3   2020-04-08 13:11:31.077127  HardwareGridProblem  2020-03-tutorial   \n",
       "4   2020-04-08 13:11:31.247321  HardwareGridProblem  2020-03-tutorial   \n",
       "..                         ...                  ...               ...   \n",
       "145 2020-04-08 13:08:23.360051            SKProblem  2020-03-tutorial   \n",
       "146 2020-04-08 13:08:16.029073            SKProblem  2020-03-tutorial   \n",
       "147 2020-04-08 13:09:02.773520            SKProblem  2020-03-tutorial   \n",
       "148 2020-04-08 13:09:06.524879            SKProblem  2020-03-tutorial   \n",
       "149 2020-04-08 13:08:59.681882            SKProblem  2020-03-tutorial   \n",
       "\n",
       "         device_name  n_shots  structured  echoed  p  instance_i  n_qubits  \\\n",
       "0    Syc23-simulator    50000        True   False  2           4         4   \n",
       "1    Syc23-simulator    50000        True   False  3           4         4   \n",
       "2    Syc23-simulator    50000        True   False  1           4         4   \n",
       "3    Syc23-simulator    50000        True   False  2           4         2   \n",
       "4    Syc23-simulator    50000        True   False  3           4         2   \n",
       "..               ...      ...         ...     ... ..         ...       ...   \n",
       "145  Syc23-simulator    50000        True   False  3           0         7   \n",
       "146  Syc23-simulator    50000        True   False  1           0         7   \n",
       "147  Syc23-simulator    50000        True   False  2           1         7   \n",
       "148  Syc23-simulator    50000        True   False  3           1         7   \n",
       "149  Syc23-simulator    50000        True   False  1           1         7   \n",
       "\n",
       "        f_val  min_c  max_c   energy       err  energy_ratio  err_ratio  \\\n",
       "0   -2.616073   -3.0    3.0 -1.89004  0.007524      0.630013   0.002508   \n",
       "1   -3.000000   -3.0    3.0 -1.85736  0.007451      0.619120   0.002484   \n",
       "2   -1.632993   -3.0    3.0 -1.39456  0.007291      0.464853   0.002430   \n",
       "3   -1.000000   -1.0    1.0 -0.89096  0.002031      0.890960   0.002031   \n",
       "4   -1.000000   -1.0    1.0 -0.85592  0.002313      0.855920   0.002313   \n",
       "..        ...    ...    ...      ...       ...           ...        ...   \n",
       "145 -7.888209   -9.0   11.0 -1.53480  0.020784      0.170533   0.002309   \n",
       "146 -5.318905   -9.0   11.0 -3.02000  0.019369      0.335556   0.002152   \n",
       "147 -6.942368   -9.0   11.0 -2.36920  0.020491      0.263244   0.002277   \n",
       "148 -7.888209   -9.0   11.0 -1.50696  0.020841      0.167440   0.002316   \n",
       "149 -5.318905   -9.0   11.0 -3.04136  0.019464      0.337929   0.002163   \n",
       "\n",
       "     f_val_ratio  \n",
       "0       0.872024  \n",
       "1       1.000000  \n",
       "2       0.544331  \n",
       "3       1.000000  \n",
       "4       1.000000  \n",
       "..           ...  \n",
       "145     0.876468  \n",
       "146     0.590989  \n",
       "147     0.771374  \n",
       "148     0.876468  \n",
       "149     0.590989  \n",
       "\n",
       "[150 rows x 18 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from recirq.qaoa.simulation import hamiltonian_objectives, hamiltonian_objective_avg_and_err\n",
    "import cirq.google as cg\n",
    "\n",
    "def compute_energy_w_err(row):\n",
    "    permutation = []\n",
    "    for i, q in enumerate(row['qubits']):\n",
    "        fi = row['final_qubits'].index(q)\n",
    "        permutation.append(fi)\n",
    "    \n",
    "    energy, err = hamiltonian_objective_avg_and_err(row['bitstrings'], row['problem'], permutation)\n",
    "    return pd.Series([energy, err], index=['energy', 'err'])\n",
    "    \n",
    "\n",
    "# Start cleaning up the raw data\n",
    "df = df_raw.copy()\n",
    "\n",
    "# Don't need these columns for present analysis\n",
    "df = df.drop(['gammas', 'betas', 'circuit', 'violation_indices',\n",
    "              'precomputation_task.dataset_id',\n",
    "              'generation_task.dataset_id',\n",
    "              'generation_task.device_name'], axis=1)\n",
    "\n",
    "# p is specified twice (from a parameter and from optimum)\n",
    "assert (df['optimum.p'] == df['p']).all()\n",
    "df = df.drop('optimum.p', axis=1)\n",
    "\n",
    "# Compute energies\n",
    "df = df.join(df.apply(compute_energy_w_err, axis=1))\n",
    "df = df.drop(['bitstrings', 'qubits', 'final_qubits', 'problem'], axis=1)\n",
    "\n",
    "# Normalize\n",
    "df['energy_ratio'] = df['energy'] / df['min_c']\n",
    "df['err_ratio'] = df['err'] * np.abs(1/df['min_c'])\n",
    "df['f_val_ratio'] = df['f_val'] / df['min_c']\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style('ticks')\n",
    "\n",
    "plt.rc('axes', labelsize=16, titlesize=16)\n",
    "plt.rc('xtick', labelsize=14)\n",
    "plt.rc('ytick', labelsize=14)\n",
    "plt.rc('legend', fontsize=14, title_fontsize=16)\n",
    "\n",
    "# theme colors\n",
    "QBLUE = '#1967d2'\n",
    "QRED = '#ea4335ff'\n",
    "QGOLD = '#fbbc05ff'\n",
    "QGREEN = '#34a853ff'\n",
    "\n",
    "QGOLD2 = '#ffca28'\n",
    "QBLUE2 = '#1e88e5'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = r'\\langle C \\rangle'\n",
    "CMIN = r'C_\\mathrm{min}'\n",
    "COVERCMIN = f'${C}/{CMIN}$'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def percentile(n):\n",
    "    def percentile_(x):\n",
    "        return np.nanpercentile(x, n)\n",
    "    percentile_.__name__ = 'percentile_%s' % n\n",
    "    return percentile_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Raw swarm plots of all data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "pretty_problem = {\n",
    "    'HardwareGridProblem': 'Hardware Grid',\n",
    "    'SKProblem': 'SK Model',\n",
    "    'ThreeRegularProblem': '3-Regular MaxCut'\n",
    "}\n",
    "\n",
    "for problem_type in ['HardwareGridProblem', 'SKProblem', 'ThreeRegularProblem']:\n",
    "    df1 = df\n",
    "    df1 = df1[df1['problem_type'] == problem_type]\n",
    "\n",
    "    for p in sorted(df1['p'].unique()):\n",
    "        dfb = df1\n",
    "        dfb = dfb[dfb['p'] == p]\n",
    "        dfb = dfb.sort_values(by='n_qubits')    \n",
    "\n",
    "        plt.subplots(figsize=(7,5))\n",
    "\n",
    "        n_instances = dfb.groupby('n_qubits').count()['energy_ratio'].unique()\n",
    "        if len(n_instances) == 1:\n",
    "            n_instances = n_instances[0]\n",
    "            label = f'{n_instances}'\n",
    "        else:\n",
    "            label = f'{min(n_instances)} - {max(n_instances)}'\n",
    "\n",
    "        #sns.boxplot(dfb['n_qubits'], dfb['energy_ratio'], color=QBLUE, saturation=1)\n",
    "        #sns.boxplot(dfb['n_qubits'], dfb['f_val_ratio'], color=QGREEN, saturation=1)\n",
    "        sns.swarmplot(dfb['n_qubits'], dfb['energy_ratio'], color=QBLUE)\n",
    "        sns.swarmplot(dfb['n_qubits'], dfb['f_val_ratio'], color=QGREEN)\n",
    "\n",
    "        plt.axhline(1, color='grey', ls='-')\n",
    "        plt.axhline(0, color='grey', ls='-')\n",
    "\n",
    "        plt.title(f'{pretty_problem[problem_type]}, {label} instances, p={p}')\n",
    "        plt.xlabel('# Qubits')\n",
    "        plt.ylabel(COVERCMIN)\n",
    "        plt.tight_layout()\n",
    "        plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare SK and Hardware Grid vs. $n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pretty_problem = {\n",
    "    'HardwareGridProblem': 'Hardware Grid',\n",
    "    'SKProblem': 'SK Model',\n",
    "    'ThreeRegularProblem': '3-Regular MaxCut'\n",
    "}\n",
    "\n",
    "df1 = df\n",
    "df1 = df1[\n",
    "    ((df1['problem_type'] == 'SKProblem') & (df1['p'] == 3))\n",
    "    | ((df1['problem_type'] == 'HardwareGridProblem') & (df1['p'] == 3))\n",
    "    ]\n",
    "df1 = df1.sort_values(by='n_qubits')\n",
    "\n",
    "MINQ = 3\n",
    "df1 = df1[df1['n_qubits'] >= MINQ]\n",
    "\n",
    "plt.subplots(figsize=(8, 6))\n",
    "plt.xlim((8, 23))\n",
    "\n",
    "# SK\n",
    "dfb = df1\n",
    "dfb = dfb[dfb['problem_type'] == 'SKProblem']\n",
    "sns.swarmplot(dfb['n_qubits'], dfb['energy_ratio'], s=5, linewidth=0.5, edgecolor='k', color=QRED)\n",
    "sns.swarmplot(dfb['n_qubits'], dfb['f_val_ratio'], s=5, linewidth=0.5, edgecolor='k', color=QRED,\n",
    "              marker='s')\n",
    "dfg = dfb.groupby('n_qubits').mean().reset_index()\n",
    "# --------\n",
    "\n",
    "\n",
    "# Hardware\n",
    "dfb = df1\n",
    "dfb = dfb[dfb['problem_type'] == 'HardwareGridProblem']\n",
    "sns.swarmplot(dfb['n_qubits'], dfb['energy_ratio'], s=5, linewidth=0.5, edgecolor='k', color=QBLUE)\n",
    "sns.swarmplot(dfb['n_qubits'], dfb['f_val_ratio'], s=5, linewidth=0.5, edgecolor='k', color=QBLUE,\n",
    "              marker='s')\n",
    "dfg = dfb.groupby('n_qubits').mean().reset_index()\n",
    "# -------\n",
    "\n",
    "\n",
    "plt.axhline(1, color='grey', ls='-')\n",
    "plt.axhline(0, color='grey', ls='-')\n",
    "\n",
    "plt.xlabel('# Qubits')\n",
    "plt.ylabel(COVERCMIN)\n",
    "\n",
    "from matplotlib.patches import Patch\n",
    "from matplotlib.lines import Line2D\n",
    "from matplotlib.legend_handler import HandlerTuple\n",
    "\n",
    "lelements = [\n",
    "    Line2D([0], [0], color=QBLUE, marker='o', ms=7, ls='', ),\n",
    "    Line2D([0], [0], color=QRED, marker='o', ms=7, ls='', ),\n",
    "\n",
    "    Line2D([0], [0], color='k', marker='s', ms=7, ls='', markerfacecolor='none'),\n",
    "    Line2D([0], [0], color='k', marker='o', ms=7, ls='', markerfacecolor='none'),\n",
    "]\n",
    "\n",
    "plt.legend(lelements, ['Hardware Grid', 'SK Model', 'Noiseless', 'Experiment', ], loc='best',\n",
    "           title=f'p = 3',\n",
    "           handler_map={tuple: HandlerTuple(ndivide=None)}, framealpha=1.0)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hardware Grid vs. $p$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "p1    0.25\n",
       "p2    0.60\n",
       "p3    0.15\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfb = df\n",
    "dfb = dfb[dfb['problem_type'] == 'HardwareGridProblem']\n",
    "dfb = dfb[['p', 'instance_i', 'n_qubits', 'energy_ratio', 'f_val_ratio']]\n",
    "P_LIMIT = max(dfb['p'])\n",
    "\n",
    "def max_over_p(group):\n",
    "    i = group['energy_ratio'].idxmax()\n",
    "    return group.loc[i][['energy_ratio', 'p']]\n",
    "\n",
    "def count_p(group):\n",
    "    new = {}\n",
    "    for i, c in enumerate(np.bincount(group['p'], minlength=P_LIMIT+1)):\n",
    "        if i == 0:\n",
    "            continue\n",
    "        new[f'p{i}'] = c\n",
    "    return pd.Series(new)\n",
    "    \n",
    "\n",
    "dfgy = dfb.groupby(['n_qubits', 'instance_i']).apply(max_over_p).reset_index()\n",
    "dfgz = dfgy.groupby(['n_qubits']).apply(count_p).reset_index()\n",
    "# In the paper, we restrict to n > 10\n",
    "# dfgz = dfgz[dfgz['n_qubits'] > 10]\n",
    "dfgz = dfgz.set_index('n_qubits').sum(axis=0)\n",
    "dfgz /= (dfgz.sum())\n",
    "dfgz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfb = df\n",
    "dfb = dfb[dfb['problem_type'] == 'HardwareGridProblem']\n",
    "dfb = dfb[['p', 'instance_i', 'n_qubits', 'energy_ratio', 'f_val_ratio']]\n",
    "# In the paper, we restrict to n > 10\n",
    "# dfb = dfb[dfb['n_qubits'] > 10]\n",
    "dfg = dfb.groupby('p').agg(['median', percentile(25), percentile(75), 'mean', 'std']).reset_index()\n",
    "\n",
    "plt.subplots(figsize=(5.5,4))\n",
    "plt.errorbar(x=dfg['p'], y=dfg['f_val_ratio', 'mean'],\n",
    "             yerr=(dfg['f_val_ratio', 'std'],\n",
    "                   dfg['f_val_ratio', 'std']),\n",
    "             fmt='o-',\n",
    "             capsize=7,\n",
    "             color=QGREEN,\n",
    "             label='Noiseless'\n",
    "           )\n",
    "plt.errorbar(x=dfg['p'], y=dfg['energy_ratio', 'mean'],\n",
    "             yerr=(dfg['energy_ratio', 'std'],\n",
    "                   dfg['energy_ratio', 'std']),\n",
    "             fmt='o-',\n",
    "             capsize=7,\n",
    "             color=QBLUE,\n",
    "             label='Experiment'\n",
    "           )\n",
    "plt.xlabel('p')\n",
    "plt.ylabel('Mean ' + COVERCMIN)\n",
    "plt.ylim((0, 1))\n",
    "plt.text(0.05, 0.9, r'Hardware Grid', fontsize=16, transform=plt.gca().transAxes, ha='left', va='bottom')\n",
    "plt.legend(loc='center right')\n",
    "\n",
    "ax2 = plt.gca().twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "dfgz_p = [int(s[1:]) for s in dfgz.index]\n",
    "dfgz_y = dfgz.values\n",
    "ax2.bar(dfgz_p, dfgz_y, color=QBLUE, width=0.9, lw=1, ec='k')\n",
    "ax2.tick_params(axis='y')\n",
    "ax2.set_ylim((0, 2))\n",
    "ax2.set_yticks([0, 0.25, 0.50])\n",
    "ax2.set_yticklabels(['0%', None, '50%'])\n",
    "ax2.set_ylabel('Fraction best' + ' ' * 41, fontsize=14)\n",
    "\n",
    "plt.tight_layout()"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}