docs/tutorials/07_squeezing_in_qudits.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Squeezing in atomic qudits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we will see how it is possible to detect entanglement in cold atomic experiments through the squeezing of the measured histograms. The notebook is structured as follows:\n",
    "\n",
    "1. We start with a simple motivational example of two qubits, where we see that entanglement can reduce fluctuations in certain cases.\n",
    "2. Next, we discuss an experimental implementation, where 500 atoms were condensed into a Bose-Einstein condensate and squeezing was observed.\n",
    "3. We will then study how you can simulate the experiments on your own laptop through `qiskt-cold-atom`.\n",
    "4. In the last section, we show how to send such calculations to a cloud simulator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two correlated coins - a toy example for squeezing \n",
    "\n",
    "To understand the motivation for studying squeezing, we start out with a two-qubit quantum circuit. In a first step, we put both qubits into a 50-50 superposition as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 496.776x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "\n",
    "circuit = QuantumCircuit(2)\n",
    "\n",
    "# initialization to create a 50 - 50 superposition\n",
    "circuit.h(0)\n",
    "circuit.h(1)\n",
    "\n",
    "# measurement\n",
    "circuit.measure_all()\n",
    "circuit.draw(\"mpl\", style='clifford')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each execution of such a circuit corresponds to flipping two coins. By writing down the outcomes of many executions we obtain a histogram of the counts where 0 and 1 could be interpreted as heads and tails, respectively (or vice versa)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import Aer\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "def bit_counts_to_Lz(counts):\n",
    "    \"\"\"transform bitstring counts to collective counts.\n",
    "\n",
    "    Args:\n",
    "        counts: a dict whose keys are the observed integers for the spin\n",
    "                and whose values is the number of observations\n",
    "\n",
    "    Returns:\n",
    "        counts: a dict whose keys are the observed integers for the total observed numbers of up\n",
    "                and whose values is the number of observations\n",
    "    \"\"\"\n",
    "    lz_counts = {}\n",
    "    for bitstring, count in counts.items():\n",
    "        measured_label = bitstring.count(\"1\")\n",
    "        if str(measured_label) in lz_counts:\n",
    "            lz_counts[str(measured_label)] += count\n",
    "        else:\n",
    "            lz_counts[str(measured_label)] = count\n",
    "\n",
    "    return lz_counts\n",
    "\n",
    "\n",
    "qasm_simulator = Aer.get_backend(\"aer_simulator\")\n",
    "job = qasm_simulator.run(circuit, shots=1000)\n",
    "counts = job.result().get_counts()\n",
    "lz_counts_uncorrelated = bit_counts_to_Lz(counts)\n",
    "plot_histogram(lz_counts_uncorrelated)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The histogram above shows the probability of obtaining the collective counts, i.e. the number of 1's in each measured bit-string. For example, since each state 00, 01, 10, and 11 has a 25\\% probability of occuring we have a 50\\% probability of measuring 1 (i.e. states 01 and 10) and a 25% probability of measuring 2 (i.e. state 11). In the next step we will start correlating, i.e. entangling the qubits, and see how this correlation is visible in the histogram. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 580.387x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(2)\n",
    "\n",
    "# initialization on x\n",
    "circuit.h(0)\n",
    "circuit.x(1)\n",
    "circuit.cx(0, 1)\n",
    "\n",
    "# measurement\n",
    "circuit.measure_all()\n",
    "circuit.draw(\"mpl\", style='clifford')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kAwcOyN/fv1Tzys7OVmBgoOx2uwICAsrWHHANGTW7smeAqmrhhMqeAVA9VET2qPZvYZdkxYoVOnbsmP7yl7+4w2NZfPrppzp58qSeeOIJd3iUpLCwMI0bN05ZWVn68ssvy2PKAAAA1UKNDZCLFi2SJD322GPFbt+wYYNmzpypWbNmacWKFTp16lSx49atWydJiomJKbKt8K3x9evXl8OMAQAAqodqvwayOL/++qtWr16tsLAw9evXr9gxF6+bDAoK0pw5czRs2DCPempqqiSpZcuWRfZRWCscU5y8vDzl5eW5P87OzpYkORwOORwOSZLVapXNZlNBQYGcTqd7bGE9Pz9fF640sNlsslqtJdYL91vIy+v8pzk/P79UdW9vbzmdThUUFLhrFotFXl5eJdZLmjs90dOV9iR5CyiOw+Hg+4me6KmUPZW3Ghkg4+Li5HQ6NWLECNlsNo9tN998sz744AP16NFDjRs3VmZmpr755hu99NJLGjFihIKCgnTXXXe5x9vtdklSYGBgkeMUriMoHFOcGTNmKDY2tkg9KSlJ1113nSSpadOmat++vXbt2qW0tDT3mNatW6tNmzZKTk7W0aNH3fXIyEiFh4drw4YNysnJcde7dOmiBg0aKCkpyeOLJTo6Wr6+vkpISPCYQ//+/XXmzBmtXbvWXfPy8tKAAQOUlZWlzZs3u+v+/v7q2bOn0tPTlZKS4q7Xr19fXbt2VWpqqvbu3euu0xM9lVdP0t0CipOQkMD3Ez3RUyl62r59u8pbjbuIxul0KiIiQunp6dq/f78iIiJK9brVq1erT58+uvHGG7Vr1y53vVWrVkpNTZXD4XD/9lDI4XCoVq1auummm7Rz585i91vcGcgmTZooKyvLHUCv1d+G6ImeStPTmLc5A4nivTOWM5D0RE+l6en48eMKDg4u14toatwZyFWrViktLU29evUqdXiUpF69eqlFixbavXu3srOz3f/AhWce7Xa7goODPV5T+HZ0cWcnC/n4+MjHx6dI3dvbW97env8x2my2ImdMJRUJrperX7zfstStVqus1qJLZEuqlzR3eqIn03pJcwcuduHXD99P9ERP5j1diRr3U/pyF89cSkhIiCTp9OnT7tql1jlean0kAABATVWjAuSxY8f01VdfqV69err33nuNXpubm6s9e/bIz8/PHSQlKSoqStL5NYsXS0xM9BgDAABwLahRAXLJkiU6d+6cHnnkkWLfNs7JydG+ffuK1M+cOaNRo0YpJydHgwYN8jjVO2jQIAUGBmru3LnKyMhw1zMyMjRv3jyFhIQYh1UAAIDqrEatgXz//fcllfz29bFjx9SmTRt17NhRbdu2VaNGjXTkyBGtWrVKGRkZateunWbNmuXxmrp162revHkaOnSoOnTooMGDB0s6/yjDY8eOafny5aV+Cg0AAEBNUGMCZHJysn788Ud16tRJ7dq1K3ZMvXr1NGbMGCUnJyshIUEnTpyQr6+v2rZtq/Hjx2vcuHHy9fUt8rpHHnlEISEhmj59uuLi4mSxWHTLLbdo0qRJ6t27d0W3BgAAUKXUuNv4VHU8Cxsww7OwURKehQ2UDs/CBgAAQKUjQAIAAMAIARIAAABGCJAAAAAwQoAEAACAEQIkAAAAjBAgAQAAYIQACQAAACMESAAAABghQAIAAMAIARIAAABGCJAAAAAwQoAEAACAEQIkAAAAjBAgAQAAYIQACQAAACMESAAAABghQAIAAMAIARIAAABGCJAAAAAwQoAEAACAEQIkAAAAjBAgAQAAYIQACQAAACMESAAAABghQAIAAMAIARIAAABGCJAAAAAwQoAEAACAEQIkAAAAjBAgAQAAYIQACQAAACMESAAAABghQAIAAMAIARIAAABGyhwgN2zYoLS0tEuOSU9P14YNG8p6CAAAAFRBZQ6Q0dHRio+Pv+SYDz/8UNHR0WU9BAAAAKqgMgdIl8t12TFOp1MWi6WshwAAAEAVVKFrIFNTUxUYGFiRhwAAAMBV5mUy+G9/+5vHxytWrNChQ4eKjCsoKHCvf7zzzjuvaIIAAACoWowC5IVrHi0Wi1JSUpSSklLsWIvFoo4dO+rNN9+8kvkBAACgijEKkAcPHpR0fv1j8+bNNWHCBD355JNFxtlsNtWtW1d+fn7lM0sAAABUGUYBMjw83P33uLg4tW/f3qMGAACAms8oQF5o+PDh5TkPAAAAVBNlDpCFkpOTtW3bNp08eVIFBQVFtlssFr344otXehgAAABUEWUOkMePH9c999yjjRs3XvKekARIAACAmqXMAXLixIn6/vvv1aNHDw0fPlxhYWHy8rriE5oAAACo4sqc+L755ht16tRJq1ev5mkzAAAA15AyP4nmzJkz6t69O+ERAADgGlPmABkZGVnsU2gAAABQs5U5QE6ePFlff/21tmzZUp7zAQAAQBVX5jWQmZmZGjBggKKiojRkyBB16NBBAQEBxY4dNmxYmScIAACAqsXiutQ9eC7BarXKYrF43MLn4vWQLpdLFoul2PtDXquys7MVGBgou91eYuAG8H9Gza7sGaCqWjihsmcAVA8VkT3KfAYyLi6uXCYAAACA6oVHGQIAAMBImS+iAQAAwLWpzGcg09LSSj22adOmZT0MAAAAqpgyB8hmzZqV6ibiFotF+fn5ZT0MAAAAqpgyB8hhw4YVGyDtdrt27typgwcPKioqSs2aNbuS+QEAAKCKKXOAjI+PL3Gby+XS66+/rldffVXvv/9+WQ8BAACAKqhCLqKxWCz6xz/+oT//+c965plnKuIQAAAAqCQVehX2rbfeqjVr1lTkIQAAAHCVVWiA3L9/PxfQAAAA1DBlXgNZEqfTqd9++03x8fH66quv1KtXr/I+BAAAACpRmQNk4bOwS+JyuVS3bl29/vrrZT0EAAAAqqAyB8ju3bsXGyCtVqvq1q2rjh07auTIkWrQoMEVTRAAAABVS5kD5Lp168pxGgAAAKgueBY2AAAAjJTLRTQbN25USkqKsrOzFRAQoMjISHXr1q08dg0AAIAq5ooC5KZNmzRy5Ej98ssvks5fOFO4LrJly5aKi4tTly5drnyWAAAAqDLKHCD37NmjmJgYnT59Wn369FF0dLQaN26szMxMrV27VklJSerbt6+2bNmiG264oTznDAAAgEpU5gD58ssv69y5c0pISFC/fv08tj377LP69ttvddddd+nll1/WsmXLrniiAAAAqBrKfBHNunXrdP/99xcJj4X69eun+++/X2vXri3z5AAAAFD1lDlA2u12RUREXHJMRESE7HZ7WQ9Ras2aNZPFYin2T48ePYqMz8vL08svv6yWLVuqdu3aCg0N1ejRo/XHH3+UeIx///vf6tSpk/z8/FS3bl395S9/0Y4dOyqwKwAAgKqpzG9hh4aGasuWLZccs3XrVoWGhpb1EEYCAwM1YcKEIvVmzZp5fOx0OnX33XcrMTFRt912mwYOHKjU1FQtWrRIq1ev1pYtW1S/fn2P10ybNk2TJk1SeHi4/v73vysnJ0fLli1T165dtXr1aq44BwAA15QyB8i77rpLc+fO1YsvvqgXXnhBtWvXdm87e/asZsyYobVr12r8+PHlMtHLCQoK0pQpUy47bvHixUpMTNRDDz2kf//73+6rxt977z39x3/8hyZNmqT58+e7x6empmrKlClq1aqVkpOTFRgYKEkaM2aMbrvtNo0aNUo//vijrFZuqQkAAK4NFpfL5SrLC48dO6bOnTvr4MGDCg4OVqdOndSwYUMdOXJE27Zt09GjR9W8eXMlJyerXr165T1vD4VnGQ8dOnTZsV27dtXmzZt16NAhhYeHu+sul0t/+tOfdOTIER09elS+vr6SpOeff14zZszQ4sWLNWzYMI99jRw5UvHx8Vq/fr26d+9eqrlmZ2crMDBQdrtdAQEBpWsQuIaNml3ZM0BVtXBCZc8AqB4qInuU+QxkcHCwtmzZov/8z//UsmXLlJCQ4N5Wu3ZtjRw5UjNnzqzw8FgoLy9P8fHxOnz4sAICAtSxY0d17tzZY8zZs2e1detWtW7d2iM8SpLFYlGfPn00f/58/c///I/uuOMOSf/3yMaYmJgix+zbt+9lA2ReXp7y8vLcH2dnZ0uSHA6HHA6HpPPPD7fZbCooKJDT6XSPLazn5+frwpxvs9lktVpLrBfut5CX1/lPc35+fqnq3t7ecjqdKigo8Pj38fLyKrFe0tzpiZ6utCfJW0BxHA4H30/0RE+l7Km8XdGNxENCQvTBBx9o/vz5+vnnn91PomnTpo28va/uD/3MzEyNHDnSo9axY0d9/PHHatGihSRp//79cjqdatmyZbH7KKynpqa6A2Rqaqrq1KmjRo0aXXJ8SWbMmKHY2Ngi9aSkJF133XWSpKZNm6p9+/batWuX0tLS3GNat26tNm3aKDk5WUePHnXXIyMjFR4erg0bNignJ8dd79Klixo0aKCkpCSPL5bo6Gj5+vp6hHxJ6t+/v86cOeNxpbyXl5cGDBigrKwsbd682V339/dXz549lZ6erpSUFHe9fv366tq1q1JTU7V37153nZ7oqbx6ku4WUJyEhAS+n+iJnkrR0/bt21XejN/CnjZtmnJzcxUbG1tiSDx37pxiY2Pl7++vf/7zn+Uy0UuJjY3VHXfcoRtvvFF16tTRvn379MYbb2jJkiUKDw/X7t275e/vr02bNqlbt24aMmSIli5dWmQ/Cxcu1OjRo/XGG2/oqaeekiTVqlVLDRo0UEZGRpHxqampatWqle666y599dVXxc6tuDOQTZo0UVZWlvs08rX62xA90VNpehrzNmcgUbx3xnIGkp7oqTQ9HT9+XMHBwZX3FvaqVav00ksv6dVXX73kGcZatWopODhYzzzzjDp37qzo6OgrnuilTJ482ePjyMhIffjhh5KkJUuWaOHChZo4cWKFzqEkPj4+8vHxKVL39vYu8m9os9lks9mKjC38oittvaTPjUndarUWe2FQSfWS5k5P9GRaL2nuwMUu/Prh+4me6Mm8pyth9FP6ww8/VN26dTVu3LjLjh07dqzq1aunuLi4Mk/uSj3++OOSpI0bN0qS+wrqku5NWbg+sXBc4d9NxgMAANR0RgFy06ZN6t27d7Fn1C7m4+Oj3r17u8NbZQgJCZEk5ebmSpKaN28uq9Va4prFwvqFayRbtmypU6dOKTMzs1TjAQAAajqjAHn48GE1b9681OMjIiL0+++/G0+qvGzdulXS/93mx9fXV506ddLevXv166+/eox1uVxauXKl/Pz8dOutt7rrUVFRks5f9HKxxMREjzEAAADXAqMAWdxi0UtxOBwVvpbp559/1unTp4utP/vss5Kkhx9+2F0fPXq0JOm5557zWAw7f/58HThwQEOGDHHfA1I6f69HLy8vTZs2zeOt7JSUFH388cdq27atbr/99nLvCwAAoKoyWlUZGhqqH3/8sdTjf/zxR11//fXGkzKxbNkyvfHGG+revbvCw8Pl5+enffv2KSEhQQ6HQ88995zHPRqHDx+u5cuX6+OPP9bBgwcVFRWlX375RV988YUiIiI0depUj/23atVKU6ZM0aRJk3TzzTdr4MCB7kcZSuev3GbBPwAAuJYYBcg77rhDS5cu1aFDh4o8Y/pihw4d0po1a4o8vaW8RUdH66efftIPP/yg7777TqdPn1ZISIj69++vMWPGFLkBuNVq1VdffaV//etfWrJkid58803Vq1dPjz76qKZOnVrkOdiS9MILL6hZs2aaPXu23n33XdWqVUt33HGHXnnlFXXo0KFC+wMAAKhqjO4DuWPHDt16663q0KGDvv32W/dFKhc7duyY+vXrpx07dmjbtm2ErAvwKEPADI8yREl4lCFQOpX+KMMOHTpowoQJmj17tm644Qb9/e9/V3R0tMLCwiRJv/32m1avXq0FCxbo6NGjmjhxIuERAACghjG+s+Trr7+u2rVra9asWZo2bZqmTZvmsd3lcslms+m5554rsp4QAAAA1Z9xgLRYLJo+fboeffRRxcXFadOmTe57JDZq1EjdunXTiBEj3M+fBgAAQM1S5mfbtGjRgjOMAAAA1yDuPwMAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARgiQAAAAMEKABAAAgBECJAAAAIwQIAEAAGCEAAkAAAAjBEgAAAAYIUACAADACAESAAAARqp9gPztt980e/ZsxcTEqGnTpqpVq5YaNWqkgQMHauvWrUXGT5kyRRaLpcQ/hw4dKvY4iYmJioqKkr+/vwICAhQdHa3Vq1dXcHcAAABVj1dlT+BKzZ07VzNnzlSLFi0UExOj+vXrKzU1VStWrNCKFSv00UcfafDgwUVeN3z4cDVr1qxIPSgoqEht6dKlGjp0qOrXr68RI0ZIkpYvX64+ffrok08+0f3331/OXQEAAFRdFpfL5arsSVyJL774QsHBwYqKivKof/fdd+rVq5fq1Kmj33//XT4+PpLOn4GMjY3V2rVr1aNHj8vu/8SJE2revLm8vLz0ww8/KCwsTJKUkZGh9u3bS5IOHDggf3//Us03OztbgYGBstvtCggIMOgUuDaNml3ZM0BVtXBCZc8AqB4qIntU+7ew77vvviLhUZLuuOMORUdH68SJE9q9e3eZ9//pp5/q5MmTeuKJJ9zhUZLCwsI0btw4ZWVl6csvvyzz/gEAAKqbah8gL8Xb21uS5OVV9J36DRs2aObMmZo1a5ZWrFihU6dOFbuPdevWSZJiYmKKbOvbt68kaf369eU0YwAAgKqv2q+BLElaWppWrVqlxo0bq127dkW2T5482ePjoKAgzZkzR8OGDfOop6amSpJatmxZZB+FtcIxxcnLy1NeXp774+zsbEmSw+GQw+GQJFmtVtlsNhUUFMjpdLrHFtbz8/N14UoDm80mq9VaYr1wv4UKA3R+fn6p6t7e3nI6nSooKHDXLBaLvLy8SqyXNHd6oqcr7UnyFlAch8PB9xM90VMpeypvNTJAOhwODR06VHl5eZo5c6ZsNpt7280336wPPvhAPXr0UOPGjZWZmalvvvlGL730kkaMGKGgoCDddddd7vF2u12SFBgYWOQ4hesICscUZ8aMGYqNjS1ST0pK0nXXXSdJatq0qdq3b69du3YpLS3NPaZ169Zq06aNkpOTdfToUXc9MjJS4eHh2rBhg3Jyctz1Ll26qEGDBkpKSvL4YomOjpavr68SEhI85tC/f3+dOXNGa9eudde8vLw0YMAAZWVlafPmze66v7+/evbsqfT0dKWkpLjr9evXV9euXZWamqq9e/e66/RET+XVk3S3gOIkJCTw/URP9FSKnrZv367yVu0vormY0+nU0KFD9dFHH2nUqFFasGBBqV63evVq9enTRzfeeKN27drlrrdq1UqpqalyOBxF3gp3OByqVauWbrrpJu3cubPY/RZ3BrJJkybKyspyB9Br9bcheqKn0vQ05m3OQKJ474zlDCQ90VNpejp+/LiCg4PL9SKaGnUG0ul06m9/+5s++ugjPfLII3rvvfdK/dpevXqpRYsW2r17t7Kzs93/wIVnHu12u4KDgz1eU/h2dHFnJwv5+Pi4rwC/kLe3t3uNZiGbzeZxtrRQcWs4L1W/eL9lqVutVlmtRZfIllQvae70RE+m9ZLmDlzswq8fvp/oiZ7Me7oSNeantNPp1MiRI7V48WI99NBDio+PN/5PKCQkRJJ0+vRpd+1S6xwvtT4SAACgpqoRAbIwPH744YcaPHiwlixZUmwCv5Tc3Fzt2bNHfn5+7iApyX2LoKSkpCKvSUxM9BgDAABwLaj2AbLwbesPP/xQDzzwgJYuXVpieMzJydG+ffuK1M+cOaNRo0YpJydHgwYN8jjVO2jQIAUGBmru3LnKyMhw1zMyMjRv3jyFhITo3nvvLf/GAAAAqqhqvwby5Zdf1uLFi1WnTh21atVKU6dOLTLmnnvuUWRkpI4dO6Y2bdqoY8eOatu2rRo1aqQjR45o1apVysjIULt27TRr1iyP19atW1fz5s3T0KFD1aFDB/djEZcvX65jx45p+fLlpX4KDQAAQE1Q7QPkoUOHJEmnTp3StGnTih3TrFkzRUZGql69ehozZoySk5OVkJCgEydOyNfXV23bttX48eM1btw4+fr6Fnn9I488opCQEE2fPl1xcXGyWCy65ZZbNGnSJPXu3bsi2wMAAKhyatxtfKo6noUNmOFZ2CgJz8IGSodnYQMAAKDSESABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAiQAAACMECABAABghAAJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkAAAADBCgAQAAIARAqSBbdu2qX///goKCpKfn59uu+02ffLJJ5U9LQAAgKvKq7InUF2sXbtWffv2Ve3atfXggw/K399fn3/+uQYPHqz09HQ9/fTTlT1FAACAq8LicrlclT2Jqi4/P19t2rRRRkaGtmzZosjISEmS3W5Xp06ddOjQIe3bt0/h4eGX3Vd2drYCAwNlt9sVEBBQwTMHqr9Rsyt7BqiqFk6o7BkA1UNFZA/ewi6FNWvWaP/+/Xr44Yfd4VGSAgMD9fzzz+vcuXNavHhx5U0QAADgKiJAlsK6deskSTExMUW29e3bV5K0fv36qzklAACASsMayFJITU2VJLVs2bLItkaNGqlOnTruMRfLy8tTXl6e+2O73S5JOn78uBwOhyTJarXKZrOpoKBATqfTPbawnp+frwtXGthsNlmt1hLrhfst5OV1/tOcn59fqrq3t7ecTqcKCgrcNYvFIi8vrxLrJc2dnujpSns6d9ZbQHGOHXPw/URP9FSKno4fPy5JKs9ViwTIUigMfYGBgcVuDwgIcI+52IwZMxQbG1ukHhERUX4TBIBr0IfPVfYMgOrl2LFjJWYZUwTICvbcc89p4sSJ7o9Pnjyp8PBwpaWlldsnEcC1ITs7W02aNFF6ejoX4QEoNbvdrqZNm6pevXrltk8CZCkUBr2SzjJmZ2erbt26xW7z8fGRj49PsfvkPwAAZREQEMDPDwDGrNbyu/SFi2hKoXDtY3HrHDMzM3Xq1Kli10cCAADURATIUoiKipIkJSUlFdmWmJjoMQYAAKCmI0CWQq9evdS8eXN99NFHSklJcdftdrumT5+uWrVqadiwYaXal4+PjyZPnlzs29oAcCn8/ABQFhXxs4Mn0ZRSSY8y/PXXX/Xaa6/xKEMAAHDNIEAaSE5O1uTJk7Vp0yY5HA61a9dOEydO1ODBgyt7agAAAFcNARIAAABGWAMJAAAAIwRIAAAAGCFAAgAAwAgBEgAAAEYIkBWo8PokrlMCAABXi9PprPBjECArkMVikcvlksViUWZm5lX5hAIAgGvbhc+8rqiTWF4VslcoPz9fGzdu1AcffKB9+/bJarXK19dXkZGRuu+++9S1a9fKniIAAKhBdu3apWXLlul///d/ddttt2ngwIFq2bJlhRyL+0BWkNdee02vvPKKcnJy1KJFC3l5eWnv3r3u7W3atNHo0aP14IMPqlGjRpU4UwBVWeG7GABwKZ988onGjx+vP/74w10LDAzUvHnzNGTIkHI/HgGyAhw8eFDt2rVThw4dtHjxYtWqVUsNGzZUZmamvv76a3322Wdat26dJKlnz5569dVX1aFDh8qdNIAq4cyZM0pLS1PTpk3l6+tb2dMBUA2kpaW539l866235OPjo++//14zZ85UixYt9M0336h169ZyOp3ut7cLl9Vd+Ha3CdZAVoC4uDj5+flp8uTJioiI0PXXXy+bzaawsDCNGTNGa9as0c6dOzV06FBt3LhRDz/8sLZv317Z0wZQBcyZM0ePPPKIZs+erbVr1+rw4cMqKCi45GuysrKUn59/lWYIoKp57733lJubqzfeeEP33XefBgwYoBkzZujjjz/W/v37FRsbK+l8WCw8b5iSkqJFixZ5nLE0wRnICjBw4EClpKRo7dq1atq0qfLz8+Xl5SWXyyWn0ymbzeYeO2fOHD311FMaPny44uLiKnHWAKqCsLAwHT58WDabTYGBgeratatiYmLUuXNnNW/eXMHBwR7jc3NzNWXKFB07dkyLFi0q89kEANVXZGSkIiIiNH/+fDVo0EAOh8P9s+C+++7TunXrlJCQoG7dukmS8vLy9PTTT+vdd9/V6dOn5ePjY3xMftJUgPbt2+vgwYM6deqUJMnL6/y1ShaLxR0eC3P7k08+qfvuu09r1qzRgQMHKmfCAKqEffv2yW63q0uXLpo9e7Zuv/12bd26VePHj9cDDzygp59+WkuXLtWePXt08uRJSdKPP/6ohQsX6vjx44RH4Bp04MAB2e12NWzYUA0aNJAkeXt7y2azyWaz6cknn9S5c+f0wQcfuF9z8OBBfffdd4qJiSlTeJQIkBUiOjpakjRkyBCtWbNG586dK3Zc4dtSrVu3VlZWljtwArg27du3T2fPnlVMTIzGjh2rOXPmaMmSJZo8ebLCw8P1+eefa+TIkXr44YcVGxurxMREff7558rOztaoUaMqe/oAKkFOTo7sdrv8/PwkqciSl549e6p379764osv9NNPP0mSkpOTtXv3bo0ZM6bMxyVAVoDbbrtNEydO1M6dOzVu3DgtXLhQR44c8RhTeDbyxIkTysjIkJ+fn2666aZKmjGAquDs2bMqKChQ27ZtJUnh4eGKiYnR888/r/fff1/x8fEaO3asLBaL3nnnHQ0cOFBvv/22goKCNGDAgEqePYDK0KhRI0VGRqpJkyaS5LFMrjBMjhs3Tna7XQsXLpQkrVq1SnXq1NFf//rXMh+XNZAVaP78+Zo1a5YOHDig0NBQ3XvvvbrzzjvVpEkT2Ww2BQUFae7cuZo9e7bGjBmj119/vbKnDKASuVwu/fzzz6pdu7YiIiKKvYVPbm6u9u3bp7179youLk4rV67UuHHj9NZbb1XSrAFUtiNHjuiPP/5Qu3btimwrvA6jZ8+e2r9/v6ZOnaqXX35Z3bt31/vvv1/mYxIgK5DL5dIvv/yihQsXatmyZcrIyJAkNWjQQN7e3vr999/ldDr10EMPaebMmQoLC6vkGQOoqooLk+PHj9e8efO0fft2tW/fvpJmBqA6WLZsmYYOHaobbrhBu3fv1tatW9WxY8cy748AeZXk5uYqOTlZX3/9tQ4fPqw//vhDAQEBGjRokAYOHKjatWtX9hQBVAOF93E7dOiQ7r77bp04cUJpaWmVPS0AVVxubq769u2rTZs2qXnz5vrll1+uaH88yvAq8fPzU3R0tKKjo+VwOOTt7V3ZUwJQDRVeaf3bb7/J4XBc0SJ4ANcGl8slPz8/Pfnkk9q7d6/Gjh17xfvkDCQAVEMul0sZGRmqV6+e++pLALgUl8ul9PR0hYSE6LrrrruifREgAQAAYITb+AAAAMAIARIAAABGCJAAAAAwQoAEAACAEQIkAAAAjBAgAQAAYIQACQAAACMESAAAABghQAIAAMDI/wNflLXDQdD5RgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job = qasm_simulator.run(circuit, shots=1000)\n",
    "counts = job.result().get_counts()\n",
    "counts[\"00\"] = 0\n",
    "counts[\"11\"] = 0\n",
    "squeezed_lz_counts = bit_counts_to_Lz(counts)\n",
    "plot_histogram(squeezed_lz_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see quite nicely the correlations between the qubits are inducing a reduction in the width of the observed histogram. It is this reduction that is called **squeezing** and its relation to quantum entanglement has motivated a large body of literature [1] and experimental work on this topic, which we will slightly touch on in the following example ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimental implementation with 500 cold atoms\n",
    "\n",
    "We now discuss some results from a [paper](https://arxiv.org/abs/1507.03782) on squeezing with cold atoms by Strobel et al. [2]. In this paper, $N_{at} = 500$ atoms were cooled down to form a Bose-Einstein condensate. In this state, they are indistinguishable and each of the atoms can be controlled to be in one of two internal states. Altogether the system can be described in terms of angular momentum operators $\\hat{L}_i$ of length $\\ell = \\frac{N_{at}}{2}$. This system evolves under the Hamiltonian:\n",
    "\n",
    "$$ H_{\\text{OAT}}(\\chi, \\Delta, \\Omega) =  \\chi L_{z}^2 + \\Delta L_{z} + \\Omega L_{x}$$\n",
    "\n",
    "- The first term arises from the interactions between the atoms. It is called *one-axis-twisting Hamiltonian*.\n",
    "- The second term stems from an externally applied magnetic field and microwave. It introduces rotations around the z axis of the collective Bloch sphere. It's strength $\\Delta$ is hence quite easily switched through the frequency of the externally applied magnetic field.\n",
    "- The third term describes the Rabi coupling and its strength $\\Omega$ is directly controlled through the amplitude of the applied microwave signal.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To observe squeezing the following actions were performed in the experiment. \n",
    "\n",
    "0. __Preparation__: We prepare the collective spin such that the Bloch-sphere-vector points to one of the poles. \n",
    "\n",
    "1. __First step__: The vector is rotated onto the equator by applying a very fast Rabi pulse such that only the third term of the Hamiltonian is of practical relevance. We can hence describe it by an $\\mathcal{R}_y$ rotation.\n",
    "\n",
    "2. __Second step__: The state is squeezed such that it starts to wrap around the Bloch-sphere. This happens under the evolution of the above Hamiltonian with suitably chosen parameters. A $\\pi$-pulse in the middle is suppressing certain unwanted noise to improve the observed squeezing. The evolution can hence be described by the unitary:\n",
    "\n",
    "$$\\hat{U}_{oat} = e^{i\\hat{H}_{oat}t}$$\n",
    "\n",
    "3. __Third step__: In the last step we rotate the state around the $X$-axis. This rotation corresponds to the angle $\\alpha$ in this notebook.\n",
    "\n",
    "We can summarize this experiments with `qiskit-cold-atom` as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit_cold_atom.providers import ColdAtomProvider\n",
    "from qiskit_cold_atom.spins.spins_gate_library import OATGate\n",
    "from qiskit.circuit import Parameter\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "provider = ColdAtomProvider()\n",
    "backend = provider.get_backend(\"collective_spin_simulator\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 747.609x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "\n",
    "alpha = Parameter(\"α\")\n",
    "beta = Parameter(\"β\")\n",
    "gamma = Parameter(\"γ\")\n",
    "\n",
    "qc.rly(np.pi / 2, 0)\n",
    "qc.append(OATGate(chi=gamma, delta=0, omega=beta), qargs=[0])\n",
    "qc.rlx(np.pi, 0)\n",
    "qc.append(OATGate(chi=gamma, delta=0, omega=beta), qargs=[0])\n",
    "qc.rlx(alpha, 0)\n",
    "qc.measure_all()\n",
    "\n",
    "qc.draw(\"mpl\", style='clifford')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This circuit is run multiple times and the collective spin is observed for two evolution times. Let us simulate such an experiment for two extreme cases of angles with large and small squeezing. The parameters are chosen from the experimental paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Number of atoms\n",
    "Nat = 100\n",
    "\n",
    "# The length of the spin\n",
    "l = Nat / 2\n",
    "\n",
    "# Strength of the rotation around x \n",
    "omegax = 2 * np.pi * 20\n",
    "\n",
    "# Time of the evolution\n",
    "time = 15e-3\n",
    "\n",
    "# Strength of the Lz-squared operator\n",
    "Lambda = 1.5\n",
    "chi = Lambda * abs(omegax) / Nat;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "alphas = np.array([50, 140]) / 180 * np.pi\n",
    "\n",
    "circuit = qc.assign_parameters(\n",
    "    {\n",
    "        alpha: np.pi - alphas[0],\n",
    "        beta: omegax * time / 2,\n",
    "        gamma: chi * time / 2,\n",
    "    },\n",
    "    inplace=False,\n",
    ")\n",
    "\n",
    "job = backend.run(circuit, shots=1000, spin=Nat / 2)\n",
    "counts1 = job.result().get_counts()\n",
    "\n",
    "\n",
    "circuit = qc.assign_parameters(\n",
    "    {\n",
    "        alpha: np.pi - alphas[1],\n",
    "        beta: omegax * time / 2,\n",
    "        gamma: chi * time / 2,\n",
    "    },\n",
    "    inplace=False,\n",
    ")\n",
    "\n",
    "job = backend.run(circuit, shots=1000, spin=Nat / 2)\n",
    "counts2 = job.result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import binom\n",
    "\n",
    "f, ax = plt.subplots()\n",
    "\n",
    "obs_num = np.array([int(key) for key in counts1.keys()])\n",
    "obs_vals = np.array([val for val in counts1.values()])\n",
    "\n",
    "ax.bar(\n",
    "    obs_num - Nat / 2,\n",
    "    obs_vals / obs_vals.sum(),\n",
    "    align=\"center\",\n",
    "    alpha=0.5,\n",
    "    label=\"squeezed\",\n",
    ")\n",
    "\n",
    "obs_num = np.array([int(key) for key in counts2.keys()])\n",
    "obs_vals = np.array([val for val in counts2.values()])\n",
    "\n",
    "ax.bar(\n",
    "    obs_num - Nat / 2,\n",
    "    obs_vals / obs_vals.sum(),\n",
    "    align=\"center\",\n",
    "    alpha=0.5,\n",
    "    label=\"anti-squeezed\",\n",
    ")\n",
    "\n",
    "# and compare to the binomial distribution;\n",
    "ks = np.arange(Nat)\n",
    "pk = binom(Nat, ks) * 0.5 ** ks * 0.5 ** (Nat - ks)\n",
    "ax.plot(ks - Nat / 2, pk, label=\"uncorrelated noise\", c=\"C2\")\n",
    "ax.legend()\n",
    "ax.set_ylabel(\"Probability\")\n",
    "ax.set_xlabel(r\"$L_z$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The observed variance $\\Delta^2$ is then compared to the variance of uncorrelated coin tosses, i.e. of a binomial distribution with $50%$ success probability, $\\Delta^2_{SN} = \\frac{N_{at}}{4}$. The observed squeezing $\\Delta$ is then quantified in *dB* through the squeezing parameter:\n",
    "$$\\xi = 10 \\log\\left(\\frac{\\Delta^2}{\\Delta^2_{SN}}\\right)$$\n",
    "In the histogram above we can see a squeezed state with a reduced variance. At this stage, we have discussed all the necessary ingredients to understand the experimental observations of the paper by Strobel. We will therefore simulate the observations at the reported evolution times ($t_1 = 15$ms, $t_1 = 25$ms) and compare the observed squeezing parameters to our simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "t1 = 15e-3\n",
    "t2 = 25e-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def mean_var_from_counts(counts):\n",
    "    \"\"\"calculate mean and variance from the counts.\n",
    "\n",
    "    Args:\n",
    "        counts: a dict whose keys are the observed integers for the spin\n",
    "                and whose values is the number of observations\n",
    "\n",
    "    Returns:\n",
    "        mean, var: mean and variance of the observed counts\n",
    "    \"\"\"\n",
    "    mean, var, count_sum = 0, 0, 0\n",
    "\n",
    "    for k, v in counts.items():\n",
    "        mean += int(k) * v\n",
    "        count_sum += v\n",
    "\n",
    "    mean = mean / count_sum\n",
    "    for k, v in counts.items():\n",
    "        var += (int(k) - mean) ** 2 * v / count_sum\n",
    "    return mean, var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now run the circuits for all the experimental data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "alphas = np.linspace(0, np.pi, 15)\n",
    "variances_1 = np.zeros(len(alphas))\n",
    "variances_2 = np.zeros(len(alphas))\n",
    "\n",
    "for ii in range(len(alphas)):\n",
    "\n",
    "    # first time step\n",
    "    circuit = qc.assign_parameters(\n",
    "        {\n",
    "            alpha: alphas[ii],\n",
    "            beta: omegax * t1 / 2,\n",
    "            gamma: chi * t1 / 2,\n",
    "        },\n",
    "        inplace=False,\n",
    "    )\n",
    "\n",
    "    job = backend.run(circuit, shots=1000, spin=Nat / 2, seed=14)\n",
    "    counts = job.result().get_counts()\n",
    "    mean, var = mean_var_from_counts(counts)\n",
    "    variances_1[ii] = var\n",
    "\n",
    "    # and the second time step\n",
    "    circuit = qc.assign_parameters(\n",
    "        {\n",
    "            alpha: alphas[ii],\n",
    "            beta: omegax * t2 / 2,\n",
    "            gamma: chi * t2 / 2,\n",
    "        },\n",
    "        inplace=False,\n",
    "    )\n",
    "\n",
    "    job = backend.run(circuit, shots=1000, spin=Nat / 2, seed=14)\n",
    "    counts = job.result().get_counts()\n",
    "    mean, var = mean_var_from_counts(counts)\n",
    "    variances_2[ii] = var;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the data from the paper for comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Import the data from the paper by Strobel et al.\n",
    "strobel_15_dB = np.array(\n",
    "    [\n",
    "        0.51993068,\n",
    "        10.39861352,\n",
    "        20.5372617,\n",
    "        30.41594454,\n",
    "        40.81455806,\n",
    "        45.49393414,\n",
    "        50.6932409,\n",
    "        56.152513,\n",
    "        60.05199307,\n",
    "        69.93067591,\n",
    "        79.80935875,\n",
    "        90.98786828,\n",
    "        100.08665511,\n",
    "        109.96533795,\n",
    "        120.36395147,\n",
    "        130.24263432,\n",
    "        139.86135182,\n",
    "        150.51993068,\n",
    "        160.13864818,\n",
    "        170.01733102,\n",
    "        180.1559792,\n",
    "    ]\n",
    ")\n",
    "\n",
    "strobel_15_alpha = np.array(\n",
    "    [\n",
    "        9.27455357,\n",
    "        8.03571429,\n",
    "        6.19419643,\n",
    "        3.54910714,\n",
    "        -0.46875,\n",
    "        -2.27678571,\n",
    "        -4.11830357,\n",
    "        -4.01785714,\n",
    "        -2.94642857,\n",
    "        1.30580357,\n",
    "        4.55357143,\n",
    "        6.99776786,\n",
    "        8.50446429,\n",
    "        9.140625,\n",
    "        10.41294643,\n",
    "        10.546875,\n",
    "        10.64732143,\n",
    "        10.27901786,\n",
    "        9.74330357,\n",
    "        9.40848214,\n",
    "        8.27008929,\n",
    "    ]\n",
    ")\n",
    "\n",
    "# and the values for 25ms\n",
    "strobel_25_dB = np.array(\n",
    "    [\n",
    "        0.51993068,\n",
    "        10.39861352,\n",
    "        20.5372617,\n",
    "        30.41594454,\n",
    "        40.81455806,\n",
    "        45.49393414,\n",
    "        50.6932409,\n",
    "        56.152513,\n",
    "        60.05199307,\n",
    "        69.93067591,\n",
    "        79.80935875,\n",
    "        90.98786828,\n",
    "        100.08665511,\n",
    "        109.96533795,\n",
    "        120.36395147,\n",
    "        130.24263432,\n",
    "        139.86135182,\n",
    "        150.51993068,\n",
    "        160.13864818,\n",
    "        170.01733102,\n",
    "        180.1559792,\n",
    "    ]\n",
    ")\n",
    "\n",
    "strobel_25_alpha = np.array(\n",
    "    [\n",
    "        16.07142857,\n",
    "        15.46875,\n",
    "        14.02901786,\n",
    "        11.71875,\n",
    "        8.40401786,\n",
    "        4.72098214,\n",
    "        2.20982143,\n",
    "        -0.46875,\n",
    "        0.0,\n",
    "        2.74553571,\n",
    "        7.734375,\n",
    "        10.98214286,\n",
    "        13.39285714,\n",
    "        14.89955357,\n",
    "        15.73660714,\n",
    "        16.50669643,\n",
    "        17.00892857,\n",
    "        17.31026786,\n",
    "        17.24330357,\n",
    "        16.77455357,\n",
    "        15.80357143,\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and calculate the variance as presented above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def number_squeezing_factor_to_db(var_CSS, var):\n",
    "    \"\"\"Calcululate the squeezing parameter from the observed variance.\"\"\"\n",
    "    return 10 * np.log10(var / var_CSS)\n",
    "\n",
    "f, ax = plt.subplots()\n",
    "ax.set_title(\"Number Squeezing\")\n",
    "\n",
    "ax.plot(\n",
    "    np.rad2deg(np.pi - alphas),\n",
    "    number_squeezing_factor_to_db(l / 2, variances_1),\n",
    "    \"r-\",\n",
    "    lw=5,\n",
    "    label=\"simulated  15ms\",\n",
    "    alpha=0.5,\n",
    ")\n",
    "ax.plot(strobel_15_dB, strobel_15_alpha, \"ro\", label=\"1experiment 5ms\", markersize=4)\n",
    "ax.plot(\n",
    "    np.rad2deg(np.pi - alphas),\n",
    "    number_squeezing_factor_to_db(l / 2, variances_2),\n",
    "    \"b-\",\n",
    "    lw=5,\n",
    "    label=\"simulated  25ms\",\n",
    "    alpha=0.5,\n",
    ")\n",
    "ax.plot(strobel_25_dB, strobel_25_alpha, \"bo\", label=\"experiment 25ms\", markersize=4)\n",
    "ax.axhline(y=0, color=\"g\", linestyle=\"--\")\n",
    "ax.set_ylabel(r\"Number Squeezing in $dB$\")\n",
    "ax.set_xlabel(r\"tomography angle $\\alpha$\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see the experiments are well understood as a quantum information circuit with specifically chosen parmeters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optional: Working on a cloud simulator\n",
    "\n",
    "We would also like to send such circuits to some real hardware and investigate these results. In this last section, we will present this possibility with the [alqor](https://qlued.alqor.io) provider. \n",
    "\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note:</b> To run the cells in this part of the tutorial that interface with a remote device backend, you'll need to have a registered account with a valid username and token for this provider. You can obtain such credentials by visiting the <a href ='https://qlued.alqor.io/accounts/login/'>sign-up page</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a first step, it is necessary to import the cold atom provider."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_cold_atom.providers import ColdAtomProvider\n",
    "from pprint import pprint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Saving/enabling your backend credentials (Optional if not alreayd done)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# save an account to disk\n",
    "#provider = ColdAtomProvider.save_account(\n",
    "#    url=[\n",
    "#        \"https://qlued.alqor.io/api/v2/singlequdit\",\n",
    "#        \"https://qlued.alqor.io/api/v2/multiqudit\",\n",
    "#        \"https://qlued.alqor.io/api/v2/fermions\",\n",
    "#    ],\n",
    "#    username=\"name\",\n",
    "#    token=\"token\",\n",
    "#    overwrite=True\n",
    "#)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# or enable an account in the current session\n",
    "#provider = ColdAtomProvider.enable_account(\n",
    "#    url=[\n",
    "#        \"https://qlued.alqor.io/api/v2/singlequdit\",\n",
    "#        \"https://qlued.alqor.io/api/v2/multiqudit\",\n",
    "#        \"https://qlued.alqor.io/api/v2/fermions\",\n",
    "#    ],\n",
    "#    username=\"name\",\n",
    "#    token=\"token\",\n",
    "#    overwrite=True\n",
    "#)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now load the necessary backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['rlx', 'rlz', 'rlz2', 'barrier', 'measure', 'load']\n"
     ]
    }
   ],
   "source": [
    "provider = ColdAtomProvider.load_account()\n",
    "\n",
    "spin_device_backend = provider.get_backend(\"alqor_singlequdit_simulator\")\n",
    "pprint(spin_device_backend.configuration().supported_instructions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see from above the simulator backend does not provide the OAT gate that we used previously. However, we will simply trotterize it in the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nat = 200\n",
    "l = Nat / 2  # spin length\n",
    "omegax = 2 * np.pi * 20\n",
    "t1 = 15e-3\n",
    "t2 = 25e-3\n",
    "Lambda = 1.5\n",
    "\n",
    "chi = Lambda * abs(omegax) / Nat\n",
    "\n",
    "Ntrott = 15\n",
    "alphas = np.linspace(0, np.pi, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2192.12x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = Parameter(\"α\")\n",
    "beta = Parameter(\"β\")\n",
    "gamma = Parameter(\"γ\")\n",
    "\n",
    "qc_trott = QuantumCircuit(1, 1)\n",
    "qc_trott.load_spins(Nat, 0)\n",
    "qc_trott.rlx(np.pi / 2, 0)\n",
    "qc_trott.rlz(np.pi / 2, 0)\n",
    "for ii in range(Ntrott):\n",
    "    qc_trott.rlx(beta, 0)\n",
    "    qc_trott.rlz2(gamma, 0)\n",
    "qc_trott.rlx(alpha, 0)\n",
    "qc_trott.measure(0, 0)\n",
    "qc_trott.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as before we are now ready to send the job to the back-end and run it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "circuit1_list = [\n",
    "    qc_trott.assign_parameters(\n",
    "        {alpha: -a % (2 * np.pi), gamma: chi * t1 / Ntrott, beta: omegax * t1 / Ntrott},\n",
    "        inplace=False,\n",
    "    )\n",
    "    for a in alphas\n",
    "]\n",
    "job1 = spin_device_backend.run(circuit1_list, shots=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can now verify that it was successfully run through its job id. This comes in especially hand for longer jobs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'20230407_084217-singlequdit-fred-613a5'"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job1.job_id()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "job status:  JobStatus.DONE\n"
     ]
    }
   ],
   "source": [
    "job_retrieved1 = spin_device_backend.retrieve_job(job_id=job1.job_id())\n",
    "\n",
    "print(\"job status: \", job_retrieved1.status())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the job status has switch towards done, the counts can be retrieved and analyzed. In the meantime we can send out the job for the other time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "circuit2_list = [\n",
    "    qc_trott.assign_parameters(\n",
    "        {alpha: -a % (2 * np.pi), gamma: chi * t2 / Ntrott, beta: omegax * t2 / Ntrott},\n",
    "        inplace=False,\n",
    "    )\n",
    "    for a in alphas\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "job2 = spin_device_backend.run(circuit2_list, shots=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'20230407_084317-singlequdit-fred-c8f9c'"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job2.job_id()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "job status:  JobStatus.INITIALIZING\n"
     ]
    }
   ],
   "source": [
    "job_retrieved2 = spin_device_backend.retrieve_job(job_id=job2.job_id())\n",
    "\n",
    "print(\"job status: \", job_retrieved2.status())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of the job can be accessed by directly calling `job.result()` which returns a `Qiskit.Result` object and be transformed into the necessary variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "result1 = job_retrieved1.result()\n",
    "result2 = job_retrieved2.result()\n",
    "\n",
    "outcomes1 = [result1.get_memory(i) for i in range(len(circuit1_list))]\n",
    "outcomes2 = [result2.get_memory(i) for i in range(len(circuit2_list))]\n",
    "\n",
    "variances_1 = [np.var(np.array(counts1, dtype=float)) for counts1 in outcomes1]\n",
    "variances_2 = [np.var(np.array(counts2, dtype=float)) for counts2 in outcomes2]\n",
    "\n",
    "variances_1 = np.array(variances_1)\n",
    "variances_2 = np.array(variances_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1696f7640>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots()\n",
    "ax.set_title(\"Number Squeezing\")\n",
    "plt.plot(\n",
    "    np.rad2deg(alphas),\n",
    "    number_squeezing_factor_to_db(l / 2, variances_1),\n",
    "    \"r-\",\n",
    "    lw=5,\n",
    "    label=\"simulated  15ms\",\n",
    "    alpha=0.5,\n",
    ")\n",
    "plt.plot(\n",
    "    np.rad2deg(alphas),\n",
    "    number_squeezing_factor_to_db(l / 2, variances_2),\n",
    "    \"b-\",\n",
    "    lw=5,\n",
    "    label=\"simulated  25ms\",\n",
    "    alpha=0.5,\n",
    ")\n",
    "\n",
    "plt.plot(strobel_15_dB, strobel_15_alpha, \"ro\", label=\"15ms\", markersize=4)\n",
    "plt.plot(strobel_25_dB, strobel_25_alpha, \"bo\", label=\"25ms\", markersize=4)\n",
    "\n",
    "\n",
    "ax.axhline(y=0, color=\"g\", linestyle=\"--\")\n",
    "ax.set_ylabel(r\"Number Squeezing in $dB$\")\n",
    "ax.set_xlabel(r\"tomography angle $\\alpha$\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "[1] [Luca Pezze et al.](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.90.035005) *Quantum metrology with nonclassical states of atomic ensembles*. Reviews of Modern Physics 90, 035005 (2018). \n",
    "\n",
    "[2] [Helmut Strobel et al.](https://doi.org/10.1126/science.1250147) *Fisher information and entanglement of non-Gaussian spin states*. Science 345, 424 (2014). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Software</th><th>Version</th></tr><tr><td><code>qiskit</code></td><td>0.45.1</td></tr><tr><td><code>qiskit_nature</code></td><td>0.7.1</td></tr><tr><td><code>qiskit_cold_atom</code></td><td>0.1.0</td></tr><tr><td><code>qiskit_aer</code></td><td>0.12.0</td></tr><tr><td><code>qiskit_algorithms</code></td><td>0.2.1</td></tr><tr><th colspan='2'>System information</th></tr><tr><td>Python version</td><td>3.9.16</td></tr><tr><td>Python compiler</td><td>MSC v.1916 64 bit (AMD64)</td></tr><tr><td>Python build</td><td>main, Jan 11 2023 16:16:36</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>63.724937438964844</td></tr><tr><td colspan='2'>Tue Jan 09 14:46:20 2024 W. Europe Standard Time</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "\n",
    "%qiskit_version_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}