examples/analog_hamiltonian_simulation/04_Maximum_Independent_Sets_with_Analog_Hamiltonian_Simulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximum Independent Sets with Analog Hamiltonian Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to the maximum independent set problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we'll demonstrate how to set up a unit disk graph and solve for its maximum independent set using the Amazon Braket analog Hamiltonian simulation (AHS) local simulator. This code can then be generalized to run on the actual AHS device, QuEra's Aquila.\n",
    "\n",
    "Finding a maximum independent set (MIS) is a common problem in graph theory with many real-life applications. What is an \"independent set\", let alone a \"maximum\" one? Consider a graph with vertices $V$ and edges $E$. An independent set is any subset $V_{is}$ of $V$ such that no pair of vertices in $V_{is}$ are connected by an edge in $E$. The *maximum* independent set is the largest such subset. Let's make this a little more concrete with a visual example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Raw graph](py_graph.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can select vertices to be part of the maximum independent set:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![MIS graph](mis_graph.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we see that the vertices in the MIS (the red ones) are not connected by any edge. We can also see there is no way to add another vertex to the set without it being connected to another vertex already present. We can also determine that no larger independent set can be found through brute-force enumeration of all possible independent sets (not shown)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finding maximum independent sets is a problem with many applications. Consider, for example, a business owner who wants to put branches of their chain store on as many street corners as possible so that potential customers never have to walk very far to find a location. However, the owner doesn't want to have multiple branches at the same intersection — this is inefficient. Maximizing the number of branches in a city, given its particular street grid, while avoiding opening branches which are too close together is an example of the MIS problem. There are many other applications, including to \"knapsack packing\" style problems, routing, and others."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit disk graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A unit disk graph is a graph in which, if and only if any two vertices are within a unit disk radius of each other, they are connected. This type of graph is very well suited for AHS devices because it can be simulated with no overhead — the number of atoms needed in the trap corresponds exactly to the total number of vertices in the graph. The phenomenon of Rydberg blockade enforces the condition that vertices connected by an edge cannot both be in the independent set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [],
   "source": [
    "# necessary imports\n",
    "import networkx as nx\n",
    "\n",
    "from braket.ahs.atom_arrangement import AtomArrangement\n",
    "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n",
    "\n",
    "from braket.timings.time_series import TimeSeries\n",
    "from braket.ahs.driving_field import DrivingField\n",
    "from braket.ahs.local_detuning import LocalDetuning\n",
    "from braket.ahs.field import Field\n",
    "from braket.devices import LocalSimulator\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import numpy as np\n",
    "\n",
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [],
   "source": [
    "# constants\n",
    "atoms_w = 3\n",
    "atoms_l = 4\n",
    "blockade_radius = 7.5\n",
    "np.random.seed(92)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function generates both the `AtomArrangement`, which will be passed to the simualtor or AHS device, and the graph it corresponds to. We set up the atoms in a square grid, such that nearest- (horizontal or vertical neighbors) and next-nearest-neighbors (diagonal neighbors) are within the unit disk range. In the graph this means the next-nearest-neighbors are connected by an edge. We perform a random dropout on this square grid — removing some of the atoms — to generate a more interesting graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [],
   "source": [
    "def generate_unit_disk(atoms_l: int, atoms_w: int, scale=4.0*1e-6, dropout=0.45):\n",
    "    atom_list = []\n",
    "    edge_dict = {}\n",
    "    atom_to_edge = {}\n",
    "    for ii in range(atoms_l):\n",
    "        for jj in range(atoms_w):\n",
    "            atom_list.append((ii*scale, jj*scale))\n",
    "            atom_to_edge[(ii*scale, jj*scale)] = ii*atoms_w + jj\n",
    "            edge_dict[ii*atoms_w + jj] = []\n",
    "            if jj < atoms_w - 1:\n",
    "                edge_dict[ii*atoms_w + jj].append(ii*atoms_w + jj + 1)\n",
    "            if ii < atoms_l - 1:\n",
    "                edge_dict[ii*atoms_w + jj].append((ii+1)*atoms_w + jj)\n",
    "            if ii < atoms_l - 1 and jj < atoms_w - 1:\n",
    "                # nearest neighbor\n",
    "                edge_dict[ii*atoms_w + jj].append((ii+1)*atoms_w + jj + 1)\n",
    "            if jj > 0 and ii < atoms_l - 1:\n",
    "                # nearest neighbor\n",
    "                edge_dict[ii*atoms_w + jj].append((ii+1)*atoms_w + jj - 1)\n",
    "\n",
    "    graph = nx.from_dict_of_lists(edge_dict)\n",
    "    \n",
    "    # perform dropout\n",
    "    new_len = int(np.round(len(atom_list) * (1 - dropout)))\n",
    "    atom_arr = np.empty(len(atom_list), dtype=object)\n",
    "    atom_arr[:] = atom_list\n",
    "    remaining_atom_list = np.random.choice(atom_arr, new_len, replace=False)\n",
    "    \n",
    "    dropped_edge_dict = {}\n",
    "    atoms = AtomArrangement()\n",
    "    for atom in remaining_atom_list:\n",
    "        atoms.add(atom)\n",
    "    graph.remove_nodes_from([atom_to_edge[atom] for atom in  set(atom_list) - set(list(remaining_atom_list))])\n",
    "\n",
    "    return atoms, graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [],
   "source": [
    "atoms, graph = generate_unit_disk(atoms_l, atoms_w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [
    {
     "data": {
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OnTrxHUqFRo4cifDwcEyePBkXL16s9W2ZJ0+eYM6cOXj69CnOnTsHe3t7OUUqf97e3pg+fbrKFbcpD810iUKEhITAysoKL168gEgkwsSJE5U24QKqs61006ZNkMlkWL9+fY3bkMlk+P3339GjRw/07t0bkZGRSp1wVbq4TXn4vr9B1Mv7K9+qUlz66dOnzNDQUGW2lWZkZLAWLVrU6P7mgwcPWN++fVmvXr1U5sWYQUFBrH///nyHITc00yVy8+HK94gRI/gOqUpUbVupmZkZAgICMGPGDKSkpFTpnOLiYvz000/o3bs3XF1dcePGDXTt2lWxgcqJqnwKqTK+sz5RfSUr3+bm5iw0NJTvcKpFJpOxjh07quTrcrZt28Z69OjBCgoKKj0uNjaW2dnZscGDB7Pk5GSOopOPkuI2inwDBddopktqjH2w8h0fH4/+/fvzHVa13Lx5Ezo6OnBycuI7lGpbsmQJ2rZti8WLF5f7c7FYjO+//x5DhgzB/PnzcenSJbRr147bIGvp4MGDGD9+POrVq8d3KHKj+kuBhBclK99paWlKv/JdGVXeVioQCODt7Q17e3scPnwYX3zxxbufhYeHw93dHV26dEFcXByaNWvGY6Q1I5PJ4O3tDT8/P75DkS++p9pEtUilUubp6cmMjY3Zpk2beC9QUxsl20qfP3/Odyi1Eh8fz4yNjVl8fDzLzc1lCxcuZM2aNWPHjh1Tyk0oVRUaGsq6deum0v+G8tBMl1TZ33//DQ8PD0gkEoSFhanMQkxFAgMDMXDgQJiamvIdSq1YWVlh27ZtGD58OLS0tODs7AyhUAgjIyO+Q6sVVf4UUhm6p0s+6v2V73HjxuHmzZsqn3CB/13Uqu7Nmze4du0asrKy0Lp1axw4cEDlE252djbOnDmDqVOn8h2K3FHSJZWKi4uDk5MTrly5gnv37mHRokVKU6CmNhISEpCamgoXFxe+Q6mVEydOwNLSEg0aNEBycjLy8/OxY8cOvsOqtYCAAAwePFj1i9uUh+/7G0Q5FRQUsNWrVzNjY2Pm5eWldvfVvvnmG7Zq1Sq+w6ix9PR0Nm7cONa5c2d248aNd99PTk5mpqam7ObNmzxGV3sODg4sODiY7zAUgma6pIzw8HB0794dCQkJiIuLw8yZM9XqvpoqbytljOHgwYOwtrZGp06dEBsbi08++eTdz9u1awdvb2+4ubnJtTAOl4RCIZ49e6YWxW3KQwtp5J28vDysXr0ax44dw65duzBu3Di1SrYl/vzzT1hYWKBjx458h1ItKSkp+Oqrr/DixQtcvHgR3bt3L/e4ESNGYNq0aZg0aRIuXbqkcreDSorbqFrcVUUzXQIAuHTpEqysrJCVlQWhUAhXV1e1TLiA6m0rlclk2L17N+zt7TFgwABERERUmHBLbNiwAQKBAGvXruUoSvkoKiqCr6+vSn4KqTK+728Qfr1+/ZpNnz6dtW7dmp0/f57vcBSuZFupqhS3SUxMZH369GF9+vRhiYmJ1Tr3+fPnrGXLluzMmTMKik7+jh07xgYMGMB3GApFM10NduLECXTr1g3169eHSCRSutfUKIKqFLeRSCTYunUrPvnkE7i5ueH69euwsLCoVhumpqYIDAyEu7s7kpOTFRSpfKnap5Aa4TvrE+6VrHx36tSJXb9+ne9wOCOTyZi5uTm7c+cO36FUKjo6mtna2jIXFxeWkpJS6/a2b9/O7OzsPloYh2+pqalqV9ymPDTT1SDsvZXvjh07Ii4uDn379uU7LM7cuHEDderUgaOjI9+hlEssFmPVqlVwcXHB4sWLcf78ebRp06bW7S5atAgdOnTAwoUL5RCl4hw8eBATJkxQq+I25aGnFzTE+yvfFy5cgJ2dHd8hcU6Zt5XevHkT7u7usLa2Rnx8PJo2bSq3tgUCAfbv3w8HBwccPHgQ06ZNk1vb8lJS3CYgIIDvUBSP76k2USypVMp27drFjIyM2NatW1lRURHfIfEiKyuLGRgYsBcvXvAdSik5OTls3rx5rHnz5uz48eMK7UsoFDJjY2MWFxen0H5q4urVq8zKykrtNuGUh2a6auz+/fvw8PAAYww3b96s9kKMOgkMDMSgQYOUalvphQsX8NVXX2HQoEEQiURo3LixQvuztLTE9u3bMW7cOERGRsLAwECh/VVHyQKaMn4KkTu+sz6Rv6KiIrZlyxZmZGTEdu/ezaRSKd8h8c7R0bFG7xRThJcvX7Ivv/yStW3bll26dInz/ufMmcPGjh2rNLPKN2/eMAMDA5aZmcl3KJyghTQ1ExMTA0dHR4SFhSEyMhLz58+HlpZmD7NIJEJaWhrv20oZYwgKCoKVlRUMDQ0hFAoxZMgQzuPYsWMHnjx5gl9//ZXzvssTEBCAIUOGwNjYmO9QuMF31ifyUVBQwL799ltmYmLCfHx8lGYWowyWLFnCvvvuO15jePbsGfv888+ZhYUFu3XrFq+xMMZYSkoKMzU1VYpHBu3t7TViY04JzZ4CqYmbN2/CxsYGSUlJiI+Px7Rp0zTj3lgV8F3chjEGb29v2NjYoFu3boiJiUHv3r15ieV9bdq0gY+PDyZNmoSMjAze4oiPj0dGRgYvM36+0EKaCsvNzcWqVatw4sQJ/Pbbbxg7dizfISmds2fPomvXrjA3N+e870ePHmH27Nl48+YNLl++DBsbG85jqMywYcMwc+ZMuLm54cqVK9DR4T4dqHtxm/LQTFdFXbhwAZaWlsjPz0dCQgIl3Arwsa1UKpVi586dcHBwwJAhQ3Dnzh2lS7gl1q1bhzp16uD777/nvO/CwkL1L25THr7vb5DqKVn5btOmDbt48SLf4Si1kuI2XG4rTUhIYL169WJ9+/ZlDx484Kzf2njx4gVr1aoVO336NKf9Hj16lDk7O3PapzKgma6KYB+sfItEIt5X45XdwYMHMX78eE62lUokEmzevBn9+/fHF198gdDQUHTq1Enh/cqDiYkJAgMD4eHhgYcPH3LWr0YUtykP31mffNz7K9+q/hoWrkilUtahQwd29+5dhfcVGRnJrK2t2bBhw9jjx48V3p+i7Ny5k9na2rL8/HyF9/XkyRPWpEkTTvpSNjTTVWLsvZXvrl27IiYmBn369OE7LJVw/fp16Ovrw8HBQWF9FBQUYOXKlRg+fDiWL1+Oc+fOoXXr1grrT9EWLFiATp06YcGCBQrvy8fHBxMnToS+vr7C+1I29PSCkipZ+X79+jUuXboEW1tbvkNSKYreVhoWFgYPDw/06NEDQqEQpqamCumHSyWFcRwdHXHgwAGFLXDJZDIcOHAAR48eVUj7So/vqTYprbi4mO3YsYMZGRmxH3/8kUkkEr5DUjmKLG6TnZ3N5syZw1q0aMFOnTol9/aVgUgkYsbGxiwmJkYh7YeEhDBra2uN3cBDM10l8tdff8HDwwM6OjoIDw9XmYUYZRMQEIDBgwfLvbhNcHAw5syZAxcXF4hEIhgaGsq1fWXRrVs37Ny5E66uroiMjJT7v1OjituUh++sT/4tULNp0yZmZGTEPD09qUBNLTk4OLDg4GC5tZeZmcmmTJnC2rdvz65cuSK3dpXdvHnz2OjRo+U6Iy0pbvPy5Uu5talqaCGNZ5GRkbC3t8etW7cQHR2NuXPnanyBmtoQCoV49uyZXB6nY4whMDAQVlZWMDU1RXx8PAYNGiSHKFXDtm3bkJ6ejl9++UVubfr7+2Po0KEwMjKSW5sqh++sr6ny8/PZ8uXLmampKTt8+LDG3t+St8WLF7PVq1fXup20tDQ2atQo1rVrV3b79m05RKaaHj9+zMzMzFhoaKhc2uvRowe7cOGCXNpSVTSl4kFYWBisra3x+PFjCIVCTJ06VXPvb8lRUVFRrbeVMsawb98+2Nraonv37oiOjkbPnj3lGKVqad26NQ4ePIjJkycjPT29Vm3FxcXhxYsXGDx4sJyiU020kMahnJwcrFy5EmfOnIGnpyfGjBnDd0hq5cyZM+jWrRs6dOhQo/MfPnyIWbNmITc3F1evXoWVlZWcI1RNLi4umDVrFtzc3BASElLjwjiaWNymPDTT5UhwcDAsLS0hkUiQkJBACVcBarqtVCqV4tdff4WTkxNGjBiB27dvU8L9wJo1a6Cnp4fvvvuuRucXFhbCz88P06dPl29gqojv+xvqrmTlu127dhq18s211NTUGhW3EQqFzNHRkfXv35/9888/CopOPWRmZrLWrVuzkydPVvvcwMBANnDgQPkHpYJopqsg7IOVb6FQqFEr31wr2VZa1eI2RUVF2LBhA5ydneHu7o6rV6/yUnNXlRgbG+Po0aOYPXs2kpKSqnWul5cX3N3dFRSZiuE766sjWvnmllQqZe3bt2cRERFVOv7u3bvM0tKSffbZZyw1NVXB0amf3bt3MxsbmyoXq3n8+LHGFrcpD8105Yi9t/Jta2ur8SvfXAkLC0P9+vVhb29f6XH5+flYtmwZRo0ahe+++w5nzpxBy5YtOYpSfcybNw9dunTBvHnzqnS8j48P3NzcNLK4TXno6YUPvMwrRFBUGu5n5CBHXIxGejqwaNoI43u0hFGDuhWe9/7Kd0hICKytrTmMWnOUNz6xoeFwmz6r0sfurl27hlmzZsHJyQlCoVDuW4Q1iUAgwL59++Do6FjqtkF5Y9PZrCG8/Y7huK8Pv0ErEQFjjPEdhDKIS82CZ2gSwv7OBAAUFsve/UxPRwsMwIDOJpjb3xw2rQzf/azk1Sxbt27Ft99+i8WLF/Pyril1V9n4MEkh6urpwdnCtMz4ZGdnY8WKFQgODsaePXswcuRIrkNXW4mJiejXrx88A/7ElWfa5Y6Nrta/Bd6HWrXEvAGlx0ZTUdIFcOROCrYE34e4WIrKfhsCAaCno43Vwy0wtWdbiEQiuLu7Q19fH/v376eFGAWp6ficPXsWc+fOxYgRI/DTTz/BwMCAu6A1xGLP4ziVogWBTh1Ulkg+HBtNpvFJ998LOhEFEtnHD/4vPV0tdGfJuLJ3PTZv3oxZs2ZRvQQFqdH46Gih+fPbSL3mj3379mHAgAGKC1CD1WRs9HW1sHp4F41OvBqddONSs+C27w4KJNJ338uJOou3whAUZaagfpf+MP5sSbnnCmQS7JvYFYPtqPyiopQ3PiUkr5/imdd81LfoA+ORy8r8XJtJ4e/hCEfzplyEqnEqGpsn21xL/TcrLkLD7sPRZOicd9/T19VG4OyesG5pyEWoSkejp2eeoUkQF5f+o9FpYASD3hPRwHpI5Sdr6yLorxwFRkfKG58Sry/tRd1mHSs8V6alDe87aYoKTeNVNDatlwa9+2q54AgEOnVQz+KTUseIi6XYE1q953zVicYm3Zd5hQj7O7PMPcJ6nXujXqde0NJvVOn5jAHXHmTiVV6hAqPUXBWNDwC8/SsMWnr1odfGpsLzaXwUp7KxeV/+g1vQrmeAuq26lfq+po+NxibdoKjaz4IEAIKiaTalCBWNj6wwH1k3fNF44Md3N9H4KEZVr508YQjqWw4s91E+TR4bjU269zNySj3aUhPiYhnup+fKKSLyvorGJ+v6YTSwGQqdRh9/zpbGRzGqcu0UZ79AYaoI9a3K3/quyWOjsUk3R1wsl3Z8j52AQCCgLzl/+R07WeZ3XfQ8GeLHcWjkMJrGR8nG5kN5oquo27IrdA0rXsjMEUuqPI7qRGOTbiM9+WxgmDJ+LBhj9CXnr8njPy/zuxY/EaI4+znS9sxA6u6pyIk4ifwH4Ug/sIjGh+ex+dBb0VU0sBxY6TGN9HQ/foGpIY3dOmXRtBHq6mSU+ZjEZFKg5IvJwIqLAC1tCLTKFl7W09GCRbOGXIWsUcobnwa2Lqjfpd+7/86JOIHi7Odo4lJ+DQAaH8Wo6NopIU5LhDTvVZmnFt6nyWOjsTNd1x7lFzrJvhWAJ/8Zi5w7QXibcA1P/jMW2bcCyj2WAXC1o4IpiuDaoyUYK708rqWrB+0Gjd99CXT1INCpA+165e80o/FRjIqunRJvRSGo16k3tOpWXGZTk8dGY2e6xg3qon8nE1xOfI73r23DvlNg2HfKR88XCADnziaVFsEhNRd39yaKHscCLawAQflzg8rGicZHcSq6dkoYfTq/0vM1fWw0dqYLAPMGmENPp2bva9LT0cbcAVRrQd6ysrLg4eGBGTNmYMVnNtCvU7P7fjQ+ikXXTs1pdNK1aWWI1cMtoK9bvV/Dv/vHLTR2G6OinDp1CpaWlqhbty5EIhHmThxB46Ok6NqpOY29vVCipPDGluD7KCiSVPhRFqBKSYry/PlzLFiwALGxsfDz80O/fv9bLHt/fD5aZQwMrLgIiwbT+HCh1NhIpFRlrIo0eqZbYmrPtjgyoweKU6JRR1sAPZ3SvxY9HS3U1dGCS1czBM7uqfF/NPLCGMPhw4dhbW2N9u3bIy4urlTCLTG1Z1sEzu4Jl65mqKujVfH4dGsKZ1kczmxbBpmsdhtfSNWUjI253lsIZFK6dqpAo6uMvS8oKAienp4IOnsBQdFpuJ+eixyxBI30dGHRrCFc7Sp/cwSpnidPnmDOnDl49uwZvLy80KNHjyqd9yqvsNLxkUgkcHZ2xqefforvv/9ewf8KUsLOzg7fb/oRmQ070LXzMYwwxhgbNmwYO3ToEN9hqD2pVMo8PT2ZsbEx27x5MysqKpJ7H2lpaaxp06bs8uXLcm+blBUdHc1at27NpFIp36GoBJrpAkhLS4O1tTXS0tKq/ApvUn0PHjzArFmzUFxcDC8vL3Tp0kVhfV29ehVTpkzBvXv36OWTCrZgwQIYGRlh/fr1fIeiEuieLv59W+nEiRMp4SpIcXExfvzxR/Tp0weurq64ceOGQhMuAAwcOBALFy7EhAkTUFRUpNC+NJlYLIa/vz9mzJjBdygqQ+OTrkwmw4EDBzBz5ky+Q1FLsbGxcHJywtWrVxEZGYmFCxdCW7tmz3dW18qVK2FkZIQVK1Zw0p8mOnXqFLp37442bdrwHYrK0PikGxYWhvr168Pe3p7vUNSKWCzG6tWrMXToUCxYsAAXL15E27ZtOY1BS0sLhw4dwpkzZ3D06FFO+9YU77+CnVSNxj+n6+3tjZkzZ0IgKFtomdRMeHg43N3d0aVLF8TFxaFZs2a8xdK4cWMEBQXBxcUF1tbWsLCw4C0WdZOSkoKYmBiMGTOG71BUikYvpGVlZaFt27ZISkqCsbEx3+GovLy8PHz33XcICgrC7t27MW7cOL5Demffvn3YsWMH7t69iwYNGvAdjlpYv349Xr16hd27d/MdikrR6NsLAQEBGDJkCCVcObh06RKsrKyQk5MDkUikVAkXADw8PODg4ICvvvqqTPUyUn20FlJzGp106X5U7b1+/RozZszA7NmzsXfvXvj4+KBJkyZ8h1WGQCDAnj17IBKJ8Pvvv/MdjsoLCQmBkZERunfvzncoKkdjk258fDwyMjIwZMhHXrVOKnT8+HFYWlqiQYMGEAqFcHFx4TukStWrVw9BQUFYt24dIiIi+A5HpXl7e9OEpYY09p7u4sWL0bBhQ2zatInvUFRORkYG5s+fD5FIhP379+OTTyp+Q4AyOnHiBL755htERUXByMiI73BUzuvXr9G+fXs8evQIjRs35jsclaORM93CwkL4+vrSA93VxBiDj48PrK2t0alTJ8TGxqpcwgWAsWPHwtXVFVOnTqXCODXg5+eH4cOHU8KtIY1MumfOnIGVlRXat2/PdygqIyUlBZ9++il27tyJixcvYuvWrdDT0+M7rBr74Ycf8PbtW2zevJnvUFSOl5cXLaDVgkYmXbofVXUymQy7d++Gvb09nJ2dERERoRaLJ7q6uggMDMQff/yBS5cu8R2OyoiJicGbN28wcGDlb/olFdO4e7qpqamwtbVFWloa9PX1+Q5HqSUmJsLDwwNaWlrYv38/OnfuzHdIchcaGgo3Nzfcu3cPrVq14jscpTd//nyYmJhg3bp1fIeisjRupltS3IYSbsUkEgm2bt2Kvn37YvLkyQgLC1PLhAsAAwYMwJIlSzB+/HgqjPMRBQUF8Pf3x/Tp0/kORaVpVNKlB7o/Ljo6Go6Ojrh+/TqioqIwb948aGmp95/JihUrYGZmhmXLlvEdilI7deoUevToQcVtakm9r6YPhIaGomHDhlV+S4EmKSgowKpVqzBs2DAsWbIE58+f15iLSyAQ4ODBgzh37hwCAgL4Dkdp0WYi+dCogjdU3KZ8N2/ehLu7O6ytrREfHw8zMzO+Q+KcoaEhgoKCMHToUNjY2Ci83q+qSUlJQWxsLBW3kQONWUgrKW7z8OFDeiD+v3Jzc7Fq1SqcPHkSv/32Gz7//HO+Q+Kdl5cXtm3bhoiICCqM855169bhzZs32LVrF9+hqDyNub3g7++PoUOHUsL9r/Pnz8PS0hIFBQUQiUSUcP/L3d0dPXv2xKxZs6gwzn9JpVIcOHCAbi3IicYkXbof9a9Xr17hyy+/xNy5c+Hl5QUvLy/aWfQBT09PJCYmwtPTk+9QlEJISAhMTExgY2PDdyhqQSOSblxcHF68eIHBgwfzHQpvGGM4duwYLC0t0aRJEwiFQo3+fVRGX18fQUFB2LhxI+7cucN3OLyjzUTypRH3dBctWgQDAwNs3LiR71B4kZ6ejrlz5+LBgwfw8vJCr169+A5JJZw+fRoLFy5EVFSUxtZcfvXqFTp06EDFbeRI7We6hYWF8PPz08gHuhlj8Pb2ho2NDSwtLRETE0MJtxpGjx4NNzc3TJkyBVKplO9weOHn54cRI0ZQwpUjtU+6p0+fhrW1tcYVt0lOTsbQoUOxZ88eXL58GZs2bULdunX5DkvlbNmyBYWFhRpZApQxRsVtFEDtk66m3Y+SSqXYsWMHHB0dMXToUNy5c4cWQGpBR0cHAQEB2LdvHy5cuMB3OJyKiYlBdnY2nJ2d+Q5Fraj15ognT57g3r17OHnyJN+hcOKvv/6Cu7s76tSpg/DwcHTq1InvkNRC06ZN4e/vjwkTJiAiIgKtW7fmOyROeHl5YcaMGWq/DZxrav3b9PHxgZubm9oXtykqKsKmTZvQv39/TJs2DdeuXaOEK2f9+vXD0qVLMX78eBQWFvIdjsIVFBQgICBAI9dCFE1tk66mFLeJjIyEg4MDbt++jejoaMyZM4dmJgqybNkyNG/eHEuXLuU7FIU7efIkHBwcNGZWzyW1vTqvXbsGAwMD2NnZ8R2KQuTn52PFihUYMWIEVqxYgXPnzlE9WAUTCAQ4cOAALly4AD8/P77DUShaQFMctU266lzcJiwsDDY2NkhNTYVQKMSUKVPU8t+pjAwNDXH8+HEsWrQICQkJfIejEI8ePUJ8fDxGjx7NdyhqSS03R7x58wbt2rVTu+I2OTk5WLlyJc6ePYs9e/Zg1KhRfIeksXx8fPDjjz/i3r17aNiwId/hyNXatWuRnZ2NnTt38h2KWlLLma6/vz9cXFzUKuGeO3cOlpaWkEqlEIlElHB5Nn36dPTt2xceHh5qVRhHKpXCx8eHbi0okFomXXUqbvPy5UtMnToVCxcuhI+PD/7v//4PhoaGfIdFAOzevRv//PMPdu/ezXcocnPlyhWYmprSs90KpHZJNzY2FpmZmRg0aBDfodQKYwwBAQGwtLSEmZkZ4uPj6Q2sSkZPTw9BQUHYvHkzbt++zXc4cqFpm4n4oHb3dBcuXIjGjRtjw4YNfIdSY0+fPsXcuXPx8OFDeHl5wcnJie+QSCXOnj2LefPmISoqCiYmJnyHU2MlxW1SUlLo05QCqdVMVywWq3RxG8YY9u3bB1tbW3Tv3h3R0dGUcFXAyJEjMWXKFEyePFmlC+P4+vris88+o4SrYGqVdE+fPg1bW1u0a9eO71Cq7eHDhxg0aBD27duHq1evYv369ahTpw7fYZEq2rRpE6RSqcp+wiopbkO3FhRPrZKuKv7RSKVS/Prrr3BycsKIESNw+/ZtWFlZ8R0WqSYdHR34+/vD29sb58+f5zucaouKikJubi769+/PdyhqT20K3jx+/BhRUVE4ffo036FUmUgkgru7O+rVq4c7d+7A3Nyc75BILZiZmcHf3x+urq6IiIhQqVfYl2wmoi3kiqc2v2EfHx9MmjRJJYrbFBUVYcOGDXB2doa7uztCQkIo4aqJvn37YsWKFXB1dVWZwjgFBQUIDAzEtGnT+A5FI6hF0lWl4jYRERHo0aMHIiMjERMTg9mzZ9PsQs188803aN26NZYsWcJ3KFVy4sQJODo6Uu0OjqjF1X716lU0btxYqYvb5OfnY+nSpRg1ahRWr16NM2fOoGXLlnyHRRSgpDDOlStXcOTIEb7D+SgqbsMttUi6JfejlNW1a9dgZWWFjIwMiEQiuLm5UYEaNdeoUSMcP34cS5YsgUgk4jucCiUnJ0MoFNK2cg6p/OaIkuI2ycnJaNKkCd/hlJKdnY3ly5fj/Pnz+P333/HZZ5/xHRLh2KFDh7Blyxbcu3cPjRo14jucMtasWYPc3Fzs2LGD71A0hsrPdP38/PDpp58qXcI9e/YsLC0toaWlBZFIRAlXQ3355ZcYMGAA3N3dla4wTklxG1V7zFLVqXzSVbZnczMzMzFp0iQsWbIEhw8fxt69e2FgYMB3WIRHO3fuRHJystKVSrx8+TKaNWtGz4VzTKWTbkxMDF69eqUUxW0YY/D19YWVlRVatWqF+Ph4DBgwgO+wiBIoKYzzww8/4NatW3yH846yr4WoK5W+p7tgwQIYGRlh/fr1vMaRmpqKr7/+Gk+ePIG3tzfs7e15jYcop3PnzmHOnDmIioqCqakpr7G8fPkS5ubmePz4MX0S45jKznTFYjH8/f0xY8YM3mKQyWTYu3cv7Ozs4OTkhMjISEq4pEIjRozAl19+qRSFcXx9fTFy5EhKuDxQ2aR76tQpdO/enbetlv/88w8GDhwIHx8fhIaGYs2aNVSghnzUxo0bwRjDunXreIuBitvwS2WTLl9/NMXFxfjll1/Qq1cvjBkzBrdu3UK3bt04j4OoJm1tbfj7++PgwYM4d+4cLzFERkbi7du36NevHy/9azqVLHiTkpKCmJgYjBkzhtN+4+Pj4e7uDgMDA0RERKB9+/ac9k/Ug6mpKQIDA/H555/j7t27aNu2Laf9U3Ebfqnkb72kuI2enh4n/RUWFmLt2rUYPHgw5syZg8uXL1PCJbXSu3dvrFq1Cq6urhCLxZz1m5+fT8VteKZySZfr4ja3b99G9+7dER8fj9jYWLi7u9MWXiIXixYtQvv27bF48WLO+jxx4gR69uxJdT94pHJJNyQkBEZGRujevbtC+3n79i0WL16MsWPHYsOGDTh58iSaN2+u0D6JZhEIBNi/fz+uXbuGQ4cOcdInFbfhn8olXS4e6L5y5QqsrKzw+vVriEQijB8/nma3RCFKCuMsXboUQqFQoX09fPgQCQkJVNyGZyq1OeL169do3769worbZGVlYenSpbhy5Qr27t2LYcOGyb0PQspz5MgRbNy4Effu3VPYs7Pff/898vPz8euvvyqkfVI1KjXT9fPzw7BhwxSScE+dOoVu3bpBT08PQqGQEi7h1NSpUzFo0CDMnDlTIYVxSorb0K0F/qlU0lXEs7nPnz/HhAkTsGLFCvj7+8PT01MpS/AR9bdjxw48efIE27dvl3vbly5dQosWLWBpaSn3tkn1qEzSjYmJwZs3bzBw4EC5tMcYw6FDh2BtbY0OHTogLi6OHhYnvKpbty6OHTuGn376CTdv3pRr21TcRnmozD3d+fPnw8TERC7bJ588eYKvvvoK6enp8PLyQo8ePeQQISHycf78ecyaNQtRUVEwMzOrdXuZmZno2LEjFbdREiox0xWLxQgICMD06dNr1Y5MJoOnpyfs7OzQt29f3Lt3jxIuUTrDhg3DzJkzMWnSJBQXF9e6PV9fX4waNYoSrpJQiaR78uRJ2NnZ1aq4zYMHD9C/f3/4+vrixo0b+O6776CrqyvHKAmRn3Xr1kFHRwdr166tVTtU3Eb5qETSrc0fjUQiwY8//og+ffpgwoQJuHHjBrp06SLnCAmRL21tbfj6+uLIkSM4e/Zsjdu5d+8eCgoKaL1CiSh9wZuUlBTExsZi9OjR1T43JiYG7u7uMDY2RmRkJOeFRQipDRMTEwQGBmLMmDG4fft2jep9lCyg0eYe5aH0M90DBw5g8uTJ1SpuIxaLsXr1ari4uGDhwoW4ePEiJVyiknr16oXVq1dj/Pjx1S6Mk5+fj6NHj1JxGyWj1ElXKpVWu7jNrVu3YGtri/v37yM+Ph7Tp0+n/8sTlbZgwQKYm5tj4cKF1Trv+PHj6NWrF1q0aKGgyEhNKHXSDQkJgYmJCWxtbT96bF5eHhYuXIjx48djy5YtOH78OJo2bar4IAlRsJLCODdu3ICPj0+Vz6MFNOWk1Em3qg90X7p0CZaWlsjJyYFIJMK4ceM4iI4Q7jRs2BBBQUFYvnw54uLiPnp8UlISEhMT8dlnn3EQHakOpVhIe5lXiKCoNNzPyEGOuBiN9HTQupEOLobewu+//17hea9fv8bSpUtx7do1/PHHH3BxceEwakK41a1bN+zcuROurq6IjIx899xteddPSmw4xk+dQe/tU0K87kiLS82CZ2gSwv7OBAAUFsve/UwHMkhlDEOtmmNuf3PYtDIsde7x48exYMECuLq6YuvWrWjQoAGXoRPCm/nz5+Pp06dYt8sbe0Iflnv9sOIi1KlTBwO7mJV7/RD+8JZ0j9xJwZbg+xAXS1FZBAIBoKejjdXDLTC1Z1ukp6dj/vz5SEhIgJeXF/r06cNd0IQogcLCQti7LUaBxXBIBVrVun4I/3i5p/tvwk1EgaTyhAsAjAEFEim2BCdi3vYA2NjYwMLCArGxsZRwiUY6FpOOIsuRKEblCRcoff0cuZPCSXykcpzPdONSs+C27w4KJNJS35cW5OJV8E6IU2Kgpd8IjftPQ/1uA0qfLC3Cfz5tAdeBjtwFTIgSqej6AYC3f4Uh65Y/pDmZ0K7fGEYjFkOv1f9KOerraiNwdk9YtzTkMGLyIc4X0jxDkyAuLvsH8/rS7xBo66LlgiMoep6MF0EboGvaDnVM/ldvQaBTB1eeacGVy4AJUSIVXT8Fj2LwJtQHJqNXok7zTpDmvS5zjLhYij2hSdg71Z6LUEkFOL298DKvEGF/Z5b5SCQrEiP/QTgM+02FVh196LXqhnrmTnibcK3UcYwB1x5k4lVeIYdRE6IcKrp+ACD7pi8M+kxC3RYWEAi0oNPQGDoNjUsdQ9ePcuA06QZFpZX7/eLXTyHQ0oJuk//tnNE1bQdJ5uMyxwoABEWX3w4h6qyi64fJpChMT4IsPxtP985Cmuc0vL70O2SSssmVrh/+cZp072fklHqspYRMUgBB3XqlvqdVtx5kRQVljhUXy3A/PVdhMRKirCq6fqRvswBZMfIf3ILZ1J/QbMYuFD1PRnZ4YJlj6frhH6dJN0dcfkFmLV19sMLSCZYV5kOrjn4F7UjkHhshyq6i60egWxcA0LDHSOg0aALtegZo6DAGBQ8jK2iHrh8+cZp0G+mVv26n06QFmEwKyeun775X9OIRdE3KL1reSI+KjxPNU9H1o63XANof3L+tvB26fvjEadK1aNoIdXXKdqlVRw/1OvdC1g1fyIrEEKf9hfyku6jfzbnMsXo6WrBo1pCLcAlRKhVdPwDQwGowcqP+hPRtFqTiPORGnkY9c4cyx9H1wz9On9N9mVeIPj9dLf++VFWe0wVQV0cL4SsHwqhBXQ4iJkR5VHb9MGkxXl/5P7z9KwwCHV3Ut+iLxs4zINApXXuBrh/+cb45YvbhSFxOfP7RnTTlEQgAl65m9Jwh0Vh0/ag+zrcBzxtgDj0d7Rqdq6ejjbkDzOUcESGqg64f1cd50rVpZYjVwy2gr1u9rvV1tbB6uAVtYSQaja4f1cdLPd2Sakc1qTJGiKaj60e18VpPNz4tC3tCk3DtQSYE+PfB7RJ6OlpgAJw7m2DuAHP6PzQhH6DrRzXxmnRLvMorRFB0Gu6n5yJHLEEjPV1YNGsIV7uWtMpKyEfQ9aNalCLpEkKIplDqF1MSQoi6oaRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEcoqRLCCEc+n9T1tN10ETM0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "pos = {ii: (ii/atoms_w,ii%atoms_w) for ii in graph.nodes()}\n",
    "nx.draw(graph, pos=pos, ax=ax, with_labels=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can define our loss function. For this problem, we'll use the Quantum Adiabatic Algorithm to train variational parameters. These parameters encode the shape of the global detuning waveform `Delta`. We'll train 3 variational parameters. As these parameters change, so too does the shape of the global detuning waveform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [],
   "source": [
    "def loss_piecewise_linear(atoms: AtomArrangement, x: list):\n",
    "    assert len(x) == 3\n",
    "    Delta_start = -13 * 2 * np.pi * 1e6\n",
    "    Delta_0 = 11 * 2 * np.pi * 1e6\n",
    "    Delta_end =  11 * 2 * np.pi * 1e6\n",
    "\n",
    "    Omega_max = 2.5e7 # 4 * 2 * np.pi * 1e6\n",
    "    T_max = 0.6 * 1e-6\n",
    "\n",
    "    Deltas = TimeSeries()\n",
    "    Deltas.put(0.0, Delta_start)\n",
    "    Deltas.put(0.05 * 1e-6, Delta_start)\n",
    "    Deltas.put(0.2 * 1e-6, Delta_0 * x[0])\n",
    "    Deltas.put(0.3 * 1e-6, Delta_0 * x[1])\n",
    "    Deltas.put(0.4 * 1e-6, Delta_0 * x[2])\n",
    "    Deltas.put(0.55 * 1e-6, Delta_end)\n",
    "    Deltas.put(T_max, Delta_end)\n",
    "    \n",
    "    # keep amplitude (Rabi frequency) constant once we turn it on\n",
    "    Omegas = TimeSeries()\n",
    "    Omegas.put(0.0, 0.0)\n",
    "    Omegas.put(0.05 * 1e-6, 0.0)\n",
    "    Omegas.put(0.1 * 1e-6, Omega_max)\n",
    "    Omegas.put(0.5 * 1e-6, Omega_max)\n",
    "    Omegas.put(0.55 * 1e-6, 0.0)\n",
    "    Omegas.put(T_max, 0.0)\n",
    "\n",
    "    # do not use the phase parameter\n",
    "    Phi = TimeSeries().put(0.0, 0.0).put(T_max, 0.0)\n",
    "\n",
    "    # for this problem, our Hamiltonian has no local detuning\n",
    "    H = DrivingField(amplitude=Omegas, phase=Phi, detuning=Deltas)\n",
    "\n",
    "    \n",
    "    program = AnalogHamiltonianSimulation(hamiltonian=H, register=atoms)\n",
    "    device = LocalSimulator(\"braket_ahs\")\n",
    "    \n",
    "    # if you want to use Aquila, uncomment these lines\n",
    "    # keep in mind that you may have to modify the fields\n",
    "    # device = AwsDevice(Devices.QuEra.Aquila)\n",
    "    # program = program.discretize(device)\n",
    "    \n",
    "    # run the AHS program and extract measurements\n",
    "    results = device.run(program, shots=1000, steps=100).result()\n",
    "    \n",
    "    \n",
    "    r_counts = []\n",
    "    \n",
    "    # states are one of:\n",
    "    # 'e' - empty\n",
    "    # 'r' - Rydberg\n",
    "    # 'g' - groundstate\n",
    "    states = ['e', 'r', 'g']\n",
    "    for shot in results.measurements:\n",
    "        pre = shot.pre_sequence\n",
    "        post = shot.post_sequence\n",
    "        state_idx = np.array(pre) * (1 + np.array(post))\n",
    "        state_labels = [states[s_idx] for s_idx in state_idx]\n",
    "        r_count = np.count_nonzero([sl == 'r' for sl in state_labels])/len(atoms)\n",
    "        r_counts.append(r_count)\n",
    "\n",
    "    # the mean density of Rydberg states - this will be our cost\n",
    "    # higher is better, as it corresponds to a larger independent set\n",
    "    density_sum = np.mean(r_counts)\n",
    "    \n",
    "    return -density_sum, results, Deltas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial density: -0.3674285714285714\n",
      "Final density: -0.37371428571428567\n",
      "Final values: [0.10333333 0.76       0.82666667]\n",
      "Time to run AHS with local simulator: 19.06173086166382\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "# initial waveform parameters\n",
    "x0 = [0.1, 0.8, 0.8]\n",
    "initial_rydberg_density, initial_registers, initial_Deltas = loss_piecewise_linear(atoms, x0)\n",
    "print(f\"Initial density: {initial_rydberg_density}\")\n",
    "# perform optimization\n",
    "optresult = optimize.minimize(lambda x: loss_piecewise_linear(atoms, x)[0], x0, method='Nelder-Mead', options={'maxiter': 10})\n",
    "final_rydberg_density, final_registers, final_Deltas = loss_piecewise_linear(atoms, optresult.x)\n",
    "print(f\"Final density: {final_rydberg_density}\")\n",
    "print(f\"Final values: {optresult.x}\")\n",
    "stop = time.time()\n",
    "print(f\"Time to run AHS with local simulator: {stop-start}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's visualize the solutions generated by the AHS program, to verify that they are independent sets and to see how large they are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false,
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent set of 0-th most likely outcome\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent set of 1-th most likely outcome\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent set of 2-th most likely outcome\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent set of 3-th most likely outcome\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent set of 4-th most likely outcome\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "\n",
    "states = ['e', 'r', 'g']\n",
    "state_labels = []\n",
    "for shot in final_registers.measurements:\n",
    "    pre = shot.pre_sequence\n",
    "    post = shot.post_sequence\n",
    "    state_idx = np.array(pre) * (1 + np.array(post))\n",
    "    state_labels.append(\"\".join([states[s_idx] for s_idx in state_idx]))\n",
    "\n",
    "occurence_count = Counter(state_labels)\n",
    "\n",
    "most_frequent_regs = occurence_count.most_common(5)\n",
    "for ii in range(len(most_frequent_regs)):\n",
    "    fig, ax = plt.subplots()\n",
    "    vert_colors = ['red' if (most_frequent_regs[ii][0][i] == 'r') else 'blue' for i in range(len(most_frequent_regs[ii][0]))]\n",
    "    print(f'Independent set of {ii}-th most likely outcome')\n",
    "    nx.draw(graph, pos = {ii: (ii/atoms_w,ii%atoms_w) for ii in graph.nodes()}, ax=ax, with_labels=True, node_color=vert_colors)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, the most likely solution is the maximum independent set. Other solutions are either missing vertices or invalid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize the initial and final waveforms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "vscode": {
     "languageId": "python"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(initial_Deltas.times(), initial_Deltas.values())\n",
    "ax.plot(final_Deltas.times(), final_Deltas.values())\n",
    "ax.set_xlabel(\"Time (s)\")\n",
    "ax.set_ylabel(\"Delta/2*pi (MHz)\")\n",
    "ax.legend([\"initial\", \"optimized\"], loc=\"lower right\")\n",
    "plt.show()"
   ]
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    "## Conclusion\n",
    "\n",
    "In this example, we generated a unit disk graph and found its maximum independent set. Because we are using the Amazon Braket local AHS simulator, we are restricted to relatively small graphs of fewer than 15 vertices. QuEra's Aquila device, by contrast, can handle far larger graphs of up to 256 vertices. See the [Braket Developer Guide](https://docs.aws.amazon.com/braket/latest/developerguide/braket-get-started-hello-ahs.html) to learn more about working with Aquila and analog Hamiltonian simulation in general."
   ]
  }
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