noise_entropy_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Experiments to classify entropy, noise, other characteristics of QRNG vs PRNG datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from modules.feature_extraction_functions import *\n",
    "from modules.data_preprocessing import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>binary_string</th>\n",
       "      <th>quantum</th>\n",
       "      <th>QPU</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1011001111011110101101000100010011001010110000...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0011111010111000011001001000110100101000101100...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1111001100100100001110110101101101000100000010...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0000110100111010000011000011110101010001000000...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0101111101001110011100100101110001101101001011...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399995</th>\n",
       "      <td>1100101011110111000101001100100110010000010100...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399996</th>\n",
       "      <td>1110001110111101010011001110110110110001011001...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399997</th>\n",
       "      <td>0100011001001001101111110000010001100110100010...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399998</th>\n",
       "      <td>1000100001011011100010110101100101101101110111...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399999</th>\n",
       "      <td>0001110000001110010001000111010110011011101111...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>400000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                            binary_string  quantum  \\\n",
       "0       1011001111011110101101000100010011001010110000...  quantum   \n",
       "1       0011111010111000011001001000110100101000101100...  quantum   \n",
       "2       1111001100100100001110110101101101000100000010...  quantum   \n",
       "3       0000110100111010000011000011110101010001000000...  quantum   \n",
       "4       0101111101001110011100100101110001101101001011...  quantum   \n",
       "...                                                   ...      ...   \n",
       "399995  1100101011110111000101001100100110010000010100...  quantum   \n",
       "399996  1110001110111101010011001110110110110001011001...  quantum   \n",
       "399997  0100011001001001101111110000010001100110100010...  quantum   \n",
       "399998  1000100001011011100010110101100101101101110111...  quantum   \n",
       "399999  0001110000001110010001000111010110011011101111...  quantum   \n",
       "\n",
       "                 QPU  \n",
       "0       ibm_brisbane  \n",
       "1       ibm_brisbane  \n",
       "2       ibm_brisbane  \n",
       "3       ibm_brisbane  \n",
       "4       ibm_brisbane  \n",
       "...              ...  \n",
       "399995      ibm_kyiv  \n",
       "399996      ibm_kyiv  \n",
       "399997      ibm_kyiv  \n",
       "399998      ibm_kyiv  \n",
       "399999      ibm_kyiv  \n",
       "\n",
       "[400000 rows x 3 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/IBM_Superposition_QRNG_100qubit_large.txt', names=['binary_number', 'quantum', 'QPU'], sep=' ')\n",
    "df_QPU = data[data['quantum'] == 'quantum']\n",
    "df_QPU.reset_index(inplace=True)\n",
    "df_QPU = df_QPU.drop('index', axis=1)\n",
    "\n",
    "df_QPU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'quantum_data' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[10], line 6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Step 1: get 1 and 0 counts for each qubit (100 qubit QRNG circuit).\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m# Since it's binary data, getting the counts of all 1s will give us a distribution of 1s and 0s\u001b[39;00m\n\u001b[1;32m      4\u001b[0m qubit_one_counts \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m0\u001b[39m] \u001b[38;5;241m*\u001b[39m \u001b[38;5;241m100\u001b[39m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m binary_string \u001b[38;5;129;01min\u001b[39;00m \u001b[43mquantum_data\u001b[49m[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mbinary_string\u001b[39m\u001b[38;5;124m'\u001b[39m]:\n\u001b[1;32m      7\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m100\u001b[39m):\n\u001b[1;32m      8\u001b[0m         \u001b[38;5;28;01mif\u001b[39;00m binary_string[i] \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m1\u001b[39m\u001b[38;5;124m'\u001b[39m:\n",
      "\u001b[0;31mNameError\u001b[0m: name 'quantum_data' is not defined"
     ]
    }
   ],
   "source": [
    "# Step 1: get 1 and 0 counts for each qubit (100 qubit QRNG circuit).\n",
    "# Since it's binary data, getting the counts of all 1s will give us a distribution of 1s and 0s\n",
    "\n",
    "qubit_one_counts = [0] * 100\n",
    "\n",
    "for binary_string in quantum_data['binary_number']:\n",
    "    for i in range(100):\n",
    "        if binary_string[i] == '1':\n",
    "            qubit_one_counts[i] += 1\n",
    "\n",
    "qubit_one_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 3000x1500 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [i for i in range(100)]\n",
    "\n",
    "plt.bar(x, height=qubit_one_counts)\n",
    "\n",
    "plt.xlabel('Qubit #')\n",
    "plt.ylabel('1 count')\n",
    "\n",
    "plt.figure(figsize=(30, 15))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Baseline entropy measurements for QRNG vs PRNG data (treating all QPUs as 1 label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shannon Entropy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>binary_number</th>\n",
       "      <th>quantum</th>\n",
       "      <th>QPU</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1011001111011110101101000100010011001010110000...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0011111010111000011001001000110100101000101100...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1111001100100100001110110101101101000100000010...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0000110100111010000011000011110101010001000000...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0101111101001110011100100101110001101101001011...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_brisbane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399995</th>\n",
       "      <td>1100101011110111000101001100100110010000010100...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399996</th>\n",
       "      <td>1110001110111101010011001110110110110001011001...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399997</th>\n",
       "      <td>0100011001001001101111110000010001100110100010...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399998</th>\n",
       "      <td>1000100001011011100010110101100101101101110111...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>399999</th>\n",
       "      <td>0001110000001110010001000111010110011011101111...</td>\n",
       "      <td>quantum</td>\n",
       "      <td>ibm_kyiv</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>400000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                            binary_number  quantum  \\\n",
       "0       1011001111011110101101000100010011001010110000...  quantum   \n",
       "1       0011111010111000011001001000110100101000101100...  quantum   \n",
       "2       1111001100100100001110110101101101000100000010...  quantum   \n",
       "3       0000110100111010000011000011110101010001000000...  quantum   \n",
       "4       0101111101001110011100100101110001101101001011...  quantum   \n",
       "...                                                   ...      ...   \n",
       "399995  1100101011110111000101001100100110010000010100...  quantum   \n",
       "399996  1110001110111101010011001110110110110001011001...  quantum   \n",
       "399997  0100011001001001101111110000010001100110100010...  quantum   \n",
       "399998  1000100001011011100010110101100101101101110111...  quantum   \n",
       "399999  0001110000001110010001000111010110011011101111...  quantum   \n",
       "\n",
       "                 QPU  \n",
       "0       ibm_brisbane  \n",
       "1       ibm_brisbane  \n",
       "2       ibm_brisbane  \n",
       "3       ibm_brisbane  \n",
       "4       ibm_brisbane  \n",
       "...              ...  \n",
       "399995      ibm_kyiv  \n",
       "399996      ibm_kyiv  \n",
       "399997      ibm_kyiv  \n",
       "399998      ibm_kyiv  \n",
       "399999      ibm_kyiv  \n",
       "\n",
       "[400000 rows x 3 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Loading of data in proper format: \n",
    "\n",
    "data = pd.read_csv('data/IBM_Superposition_QRNG_100qubit_large.txt', names=['binary_number', 'quantum', 'QPU'], sep=' ')\n",
    "df_QRNG = data[data['quantum'] == 'quantum']\n",
    "df_QRNG.reset_index(inplace=True)\n",
    "df_QRNG = df_QRNG.drop('index', axis=1)\n",
    "                     \n",
    "df_PRNG = data[data['quantum'] == 'non-quantum']\n",
    "df_PRNG.reset_index(inplace=True)\n",
    "df_PRNG = df_PRNG.drop('index', axis=1)\n",
    "\n",
    "df_QRNG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find entropy for input strings from 100 - 10000, chunk size 1 - 10 to evaluate differences\n",
    "# Choose random entry\n",
    "\n",
    "chunk_sizes = [1, 2, 4, 5, 10, 20]\n",
    "num_concats_sizes = [1, 10, 20, 40, 50, 100, 200]\n",
    "\n",
    "for num_concats in num_concats_sizes:   #Number of conacts (baseline string length is 100)\n",
    "    for chunk_size in chunk_sizes: \n",
    "        cur_df_QRNG = concatenate_data(df_QRNG, num_concats)\n",
    "        cur_df_PRNG = concatenate_data(df_PRNG, num_concats)\n",
    "\n",
    "        input_string_QRNG = cur_df_QRNG.sample(1).iloc[0][0]\n",
    "        input_string_PRNG = cur_df_PRNG.sample(1).iloc[0][0]\n",
    "\n",
    "        QRNG_entropy = shannon_entropy(input_string_QRNG, '01', chunk_size)\n",
    "        PRNG_entropy = shannon_entropy(input_string_PRNG, '01', chunk_size)\n",
    "\n",
    "        print(f'Entropy for input length = {100*num_concats} and chunk size = {chunk_size}:\\nQRNG:{QRNG_entropy}\\nPRNG:{PRNG_entropy}\\n\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**On first glance, the Shannon entropy seems pretty random even for larger input lengths and chunk sizes - no apparent difference between PRNG and QRNG**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To confirm our results, we will perform randomized trials on what should theoretically yield high non-trivial entropy - input length 100000 bit strings with chunk size of 1, 2, 5, 10, 20. For each trial, we will take the average of 20 random index selections to avoid random sampling error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/kj/xbj7kgl124b7r16_d8j8zsww0000gn/T/ipykernel_82092/2195505110.py:9: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  QRNG_string = random_sample_QRNG.iloc[i][0]\n",
      "/var/folders/kj/xbj7kgl124b7r16_d8j8zsww0000gn/T/ipykernel_82092/2195505110.py:10: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  PRNG_string = random_sample_PRNG.iloc[i][0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For chunk size = 1 and input length = 100000, the average QRNG entropy = 0.9998347304940454 and the average PRNG entropy = 0.9998325782853069\n",
      "\n",
      "\n",
      "For chunk size = 2 and input length = 100000, the average QRNG entropy = 1.999670894654929 and the average PRNG entropy = 1.9996494082728453\n",
      "\n",
      "\n",
      "For chunk size = 5 and input length = 100000, the average QRNG entropy = 4.997931158316204 and the average PRNG entropy = 4.997859685886725\n",
      "\n",
      "\n",
      "For chunk size = 10 and input length = 100000, the average QRNG entropy = 9.92188289205087 and the average PRNG entropy = 9.921901372608428\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Concatenated_QRNG = concatenate_data(df_QRNG, 1000)\n",
    "Concatenated_PRNG = concatenate_data(df_PRNG, 1000)\n",
    "for chunk_size in [1, 2, 5, 10]:\n",
    "    QRNG_entropies = []\n",
    "    PRNG_entropies = []\n",
    "    random_sample_QRNG = Concatenated_QRNG.sample(20)\n",
    "    random_sample_PRNG = Concatenated_QRNG.sample(20)\n",
    "    for i in range(20):\n",
    "        QRNG_string = random_sample_QRNG.iloc[i][0]\n",
    "        PRNG_string = random_sample_PRNG.iloc[i][0]\n",
    "        QRNG_entropies.append(shannon_entropy(QRNG_string, '10', chunk_size))\n",
    "        PRNG_entropies.append(shannon_entropy(PRNG_string, '10', chunk_size))\n",
    "    QRNG_entropy = sum(QRNG_entropies) / len(QRNG_entropies)\n",
    "    PRNG_entropy = sum(PRNG_entropies) / len(PRNG_entropies)\n",
    "    print(f'For chunk size = {chunk_size} and input length = 100000, the average QRNG entropy = {QRNG_entropy} and the average PRNG entropy = {PRNG_entropy}\\n\\n')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next entropy test we will perform is to measure entropy for groupings of every 100th bit - in other words, find the entropy of each individual device qubit's measurements and check for differences (all datasets we are using are generated from 100 qubit IBM circuits)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/kj/xbj7kgl124b7r16_d8j8zsww0000gn/T/ipykernel_82092/3541382400.py:9: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  binary_string = df_QRNG.iloc[row][0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qubit 0 entropy: 4.998881114849497\n",
      "qubit 1 entropy: 4.999642326267536\n",
      "qubit 2 entropy: 4.99955479137855\n",
      "qubit 3 entropy: 4.999663093659567\n",
      "qubit 4 entropy: 4.999146426857126\n",
      "qubit 5 entropy: 4.9997086823696995\n",
      "qubit 6 entropy: 4.999049930293405\n",
      "qubit 7 entropy: 4.99927445162009\n",
      "qubit 8 entropy: 4.998583539197197\n",
      "qubit 9 entropy: 4.996991106812206\n",
      "qubit 10 entropy: 4.999728800026849\n",
      "qubit 11 entropy: 4.998402818749085\n",
      "qubit 12 entropy: 4.988031440710408\n",
      "qubit 13 entropy: 4.999537467018678\n",
      "qubit 14 entropy: 4.999542033656393\n",
      "qubit 15 entropy: 4.998876565137906\n",
      "qubit 16 entropy: 4.998138280052424\n",
      "qubit 17 entropy: 4.998564629663232\n",
      "qubit 18 entropy: 4.999091294889859\n",
      "qubit 19 entropy: 4.990622268601436\n",
      "qubit 20 entropy: 4.9994798061682655\n",
      "qubit 21 entropy: 4.999583783488863\n",
      "qubit 22 entropy: 4.996999645888314\n",
      "qubit 23 entropy: 4.990794618463553\n",
      "qubit 24 entropy: 4.9997446785338235\n",
      "qubit 25 entropy: 4.999200448395679\n",
      "qubit 26 entropy: 4.999462197569888\n",
      "qubit 27 entropy: 4.9987239780537776\n",
      "qubit 28 entropy: 4.999204229551657\n",
      "qubit 29 entropy: 4.9722400958025785\n",
      "qubit 30 entropy: 4.999516203502375\n",
      "qubit 31 entropy: 4.999562736244661\n",
      "qubit 32 entropy: 4.999340172485493\n",
      "qubit 33 entropy: 4.968446439719023\n",
      "qubit 34 entropy: 4.999741591242923\n",
      "qubit 35 entropy: 4.994000692858815\n",
      "qubit 36 entropy: 4.966183754489466\n",
      "qubit 37 entropy: 4.999531300005741\n",
      "qubit 38 entropy: 4.999494790706281\n",
      "qubit 39 entropy: 4.999754860627022\n",
      "qubit 40 entropy: 4.999651697800591\n",
      "qubit 41 entropy: 4.998840308815639\n",
      "qubit 42 entropy: 4.999724775822589\n",
      "qubit 43 entropy: 4.9918205828348405\n",
      "qubit 44 entropy: 4.998658250985714\n",
      "qubit 45 entropy: 4.999554248131644\n",
      "qubit 46 entropy: 4.999757979814235\n",
      "qubit 47 entropy: 4.999606950019696\n",
      "qubit 48 entropy: 4.999395272911676\n",
      "qubit 49 entropy: 4.999565530407821\n",
      "qubit 50 entropy: 4.998537536347909\n",
      "qubit 51 entropy: 4.999448443688739\n",
      "qubit 52 entropy: 4.999412430495561\n",
      "qubit 53 entropy: 4.9994814572995505\n",
      "qubit 54 entropy: 4.999482301941887\n",
      "qubit 55 entropy: 4.9997291783226\n",
      "qubit 56 entropy: 4.999730585334322\n",
      "qubit 57 entropy: 4.999572046519806\n",
      "qubit 58 entropy: 4.999618727657216\n",
      "qubit 59 entropy: 4.999674780722398\n",
      "qubit 60 entropy: 4.998875239168976\n",
      "qubit 61 entropy: 4.994362607743425\n",
      "qubit 62 entropy: 4.995110159699689\n",
      "qubit 63 entropy: 4.998710812044028\n",
      "qubit 64 entropy: 4.999487915508154\n",
      "qubit 65 entropy: 4.999808955988484\n",
      "qubit 66 entropy: 4.999616707568673\n",
      "qubit 67 entropy: 4.999434808345205\n",
      "qubit 68 entropy: 4.998774951958487\n",
      "qubit 69 entropy: 4.9993144133383565\n",
      "qubit 70 entropy: 4.999789321722672\n",
      "qubit 71 entropy: 4.9979334789337555\n",
      "qubit 72 entropy: 4.9984218729789855\n",
      "qubit 73 entropy: 4.99919916214542\n",
      "qubit 74 entropy: 4.999515554824002\n",
      "qubit 75 entropy: 4.9079307184080205\n",
      "qubit 76 entropy: 4.999418235416773\n",
      "qubit 77 entropy: 4.999699521407865\n",
      "qubit 78 entropy: 4.99969245586584\n",
      "qubit 79 entropy: 4.997559742048585\n",
      "qubit 80 entropy: 4.997411556195405\n",
      "qubit 81 entropy: 4.999780097054766\n",
      "qubit 82 entropy: 4.999360748884127\n",
      "qubit 83 entropy: 4.998259573063279\n",
      "qubit 84 entropy: 4.997580054269615\n",
      "qubit 85 entropy: 4.999527966586058\n",
      "qubit 86 entropy: 4.999688156326755\n",
      "qubit 87 entropy: 4.999152677033403\n",
      "qubit 88 entropy: 4.999719246811562\n",
      "qubit 89 entropy: 4.998666399792421\n",
      "qubit 90 entropy: 4.998688006409842\n",
      "qubit 91 entropy: 4.999709741457994\n",
      "qubit 92 entropy: 4.997913454958846\n",
      "qubit 93 entropy: 4.99568146095494\n",
      "qubit 94 entropy: 4.994476355090044\n",
      "qubit 95 entropy: 4.998896771051824\n",
      "qubit 96 entropy: 4.999660667102986\n",
      "qubit 97 entropy: 4.9992448666370235\n",
      "qubit 98 entropy: 4.998986463711777\n",
      "qubit 99 entropy: 4.9984460961682045\n"
     ]
    }
   ],
   "source": [
    "# To do this we will extract the data from the existing dataframes \n",
    "# (without concatenation) to create large input strings for each \n",
    "# individual qubit, similar to how we extract features for each qubit\n",
    "# in the model building notebook.\n",
    "\n",
    "qb_measurements = [[] for _ in range(100)]\n",
    "\n",
    "for row in range(len(df_QRNG)):\n",
    "    binary_string = df_QRNG.iloc[row][0]\n",
    "    for count, meas in enumerate(binary_string):\n",
    "        qb_measurements[count].append(meas)\n",
    "\n",
    "for count, entry in enumerate(qb_measurements):\n",
    "    qb_string = ''.join(entry)\n",
    "    entropy = shannon_entropy(qb_string, '10', 5)\n",
    "    print(f'qubit {count} entropy: {entropy}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final part of the entropy measurements of this notebook is to convert chunks of QRNG data into base 10 integers (using simple binary multiplication). This will allow us to measure entropy for much larger input strings as well as \"chunk size\" because every possible binary string of QRNG data for length x will be represented by a unique integer - and now we don't have to use a cartesian product to find all possible binary substrings, which results in exponential runtime slow down, especially for chunk size > 10. Instead, we can iterate once through the entire binary string, converting each chunk to an integer as we go, and calculate the frequencies for entropy that way. See the function documentation in the modules directory for more information on the actual implementation. Note that the below code is exactly the same as the previous entropy section except now we are using the entropy function that converts binary to decimal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/kj/xbj7kgl124b7r16_d8j8zsww0000gn/T/ipykernel_7698/2015138874.py:9: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  QRNG_string = random_sample_QRNG.iloc[i][0]\n",
      "/var/folders/kj/xbj7kgl124b7r16_d8j8zsww0000gn/T/ipykernel_7698/2015138874.py:10: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  PRNG_string = random_sample_PRNG.iloc[i][0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For chunk size = 1 and input length = 100000, the average QRNG entropy = 0.9998808854398321 and the average PRNG entropy = 0.9998365225327243\n",
      "\n",
      "\n",
      "For chunk size = 2 and input length = 100000, the average QRNG entropy = 1.9996237844832028 and the average PRNG entropy = 1.9996623493956296\n",
      "\n",
      "\n",
      "For chunk size = 5 and input length = 100000, the average QRNG entropy = 4.997778174058462 and the average PRNG entropy = 4.997859279277032\n",
      "\n",
      "\n",
      "For chunk size = 10 and input length = 100000, the average QRNG entropy = 9.9216314772832 and the average PRNG entropy = 9.920096222934522\n",
      "\n",
      "\n",
      "For chunk size = 20 and input length = 100000, the average QRNG entropy = 12.282532379549448 and the average PRNG entropy = 12.283312379549448\n",
      "\n",
      "\n",
      "For chunk size = 25 and input length = 100000, the average QRNG entropy = 11.965634284662908 and the average PRNG entropy = 11.965534284662894\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Concatenated_QRNG = concatenate_data(df_QRNG, 1000)\n",
    "Concatenated_PRNG = concatenate_data(df_PRNG, 1000)\n",
    "for chunk_size in [1, 2, 5, 10, 20, 25]:\n",
    "    QRNG_entropies = []\n",
    "    PRNG_entropies = []\n",
    "    random_sample_QRNG = Concatenated_QRNG.sample(20)\n",
    "    random_sample_PRNG = Concatenated_QRNG.sample(20)\n",
    "    for i in range(20):\n",
    "        QRNG_string = random_sample_QRNG.iloc[i][0]\n",
    "        PRNG_string = random_sample_PRNG.iloc[i][0]\n",
    "        QRNG_entropies.append(shannon_entropy_integer(QRNG_string, chunk_size))\n",
    "        PRNG_entropies.append(shannon_entropy_integer(PRNG_string, chunk_size))\n",
    "    QRNG_entropy = sum(QRNG_entropies) / len(QRNG_entropies)\n",
    "    PRNG_entropy = sum(PRNG_entropies) / len(PRNG_entropies)\n",
    "    print(f'For chunk size = {chunk_size} and input length = 100000, the average QRNG entropy = {QRNG_entropy} and the average PRNG entropy = {PRNG_entropy}\\n\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We have now basically proved that, as expected, entropy is essentially indistinguishable between PRNg and QRNG at levels of data complexity that we can realistically test on local machines**"
   ]
  }
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