{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c9cba238-94ae-4e05-94ff-17f5d5a7a45b",
   "metadata": {},
   "source": [
    "# Grover's Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fd1a79ee-2455-4bdd-ad86-fa00ddd60327",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This example is from:\n",
    "# https://quantum.cloud.ibm.com/docs/en/tutorials/grovers-algorithm\n",
    "\n",
    "# Modified for use with Quantum Rings SDK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4821da69-f459-4e32-a8b3-6a79f99bd13a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Built-in modules\n",
    "import os\n",
    "import math\n",
    "\n",
    "# Imports from Qiskit\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.circuit.library import grover_operator, MCMTGate, ZGate\n",
    "from qiskit.visualization import plot_distribution\n",
    "\n",
    "# Imports from Qiskit Runtime\n",
    "#from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "#from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
    "\n",
    "from quantumrings.toolkit.qiskit import QrRuntimeService\n",
    "from quantumrings.toolkit.qiskit import QrBackendV2\n",
    "from quantumrings.toolkit.qiskit import QrSamplerV2 as Sampler\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "17b8fc5d-242a-474c-bf12-a197e65db1bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'scarlet_quantum_rings'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To run on hardware, select the backend with the fewest number of jobs in the queue\n",
    "#service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "#backend = service.least_busy(operational=True, simulator=False)\n",
    "#backend.name\n",
    "\n",
    "my_token = os.environ[\"QR_TOKEN\"]\n",
    "my_account = os.environ[\"QR_ACCOUNT\"]\n",
    "my_backend = \"scarlet_quantum_rings\"\n",
    "\n",
    "qr_services = QrRuntimeService(name = my_account, token = my_token)\n",
    "qr_backend = qr_services.backend(name = my_backend, num_qubits=5)\n",
    "qr_backend.name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9535695f-2771-443c-8b4b-bc52e7b54c3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def grover_oracle(marked_states):\n",
    "    \"\"\"Build a Grover oracle for multiple marked states\n",
    "\n",
    "    Here we assume all input marked states have the same number of bits\n",
    "\n",
    "    Parameters:\n",
    "        marked_states (str or list): Marked states of oracle\n",
    "\n",
    "    Returns:\n",
    "        QuantumCircuit: Quantum circuit representing Grover oracle\n",
    "    \"\"\"\n",
    "    if not isinstance(marked_states, list):\n",
    "        marked_states = [marked_states]\n",
    "    # Compute the number of qubits in circuit\n",
    "    num_qubits = len(marked_states[0])\n",
    "\n",
    "    qc = QuantumCircuit(num_qubits)\n",
    "    # Mark each target state in the input list\n",
    "    for target in marked_states:\n",
    "        # Flip target bit-string to match Qiskit bit-ordering\n",
    "        rev_target = target[::-1]\n",
    "        # Find the indices of all the '0' elements in bit-string\n",
    "        zero_inds = [ind for ind in range(num_qubits) if rev_target.startswith(\"0\", ind)]\n",
    "        # Add a multi-controlled Z-gate with pre- and post-applied X-gates (open-controls)\n",
    "        # where the target bit-string has a '0' entry\n",
    "        qc.x(zero_inds)\n",
    "        qc.compose(MCMTGate(ZGate(), num_qubits - 1, 1), inplace=True)\n",
    "        qc.x(zero_inds)\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "858ed3bd-4bb4-435d-b0a9-d57226fdfbec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 538.33x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marked_states = [\"011\", \"100\"]\n",
    "\n",
    "oracle = grover_oracle(marked_states)\n",
    "oracle.draw(output=\"mpl\", style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ac0ba948-4ead-4dd3-ad52-890ac735af54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2126.94x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grover_op = grover_operator(oracle)\n",
    "grover_op.decompose().draw(output=\"mpl\", style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "427d257b-bdc7-4481-a123-b14febc6bed8",
   "metadata": {},
   "outputs": [],
   "source": [
    "optimal_num_iterations = math.floor(\n",
    "    math.pi / (4 * math.asin(math.sqrt(len(marked_states) / 2**grover_op.num_qubits)))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4698d640-82b3-4a72-9797-a8f8672e0af5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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So2UCgEf9/vvvMm3aNGnevLmUK1fO24cDN4eHb775RrZt2yb79++X5OTkS4sI5lqYq1atWlKnTh1p3bq1tGnTxtxWWJB4/vnnTQB58MEHpW3bth58JbgcWiY8QBP4I488IvXq1ZPIyEipWbOmjB07Vs6fPy+jR482q9y9+uqr3j5MAHDZOW/u3LkyZswYmTVrlnz99ddy5MiRPEHCvpjYgQMHZNWqVfLiiy/KfffdJ0uWLJELFy44DBIaTvQxK1euLPBc8C5aJtzsp59+Mv3D2qxXqlQpadKkiXlTvfLKK7Jv3z45ceKEuV+rVq0kEK1JOSY9v/lKpjRpIQ8mNHJ4n/Bli+SGynHyYYcu4k+a3zdQKjSvKxVa1JXY2lXkXNIxeb/9GKeeIywmShrf1Vdq92kvpevESVBIsHmepC83y7bXlkrq8TNuO37A1fQDXoPBv//97wKTkulqntoKUblyZfN9enq6ORf+9ttvOcFAz4eLFi0yYeHuu++Wli1b5gkSSlu0HnjgAZYa9zGECTen8/79+5sg8dBDD8nEiRMlNjbW7Js6dapMmDDBvKn0TdGiRQtvHy6c1PbxYZJ64qyc2LJfwktHO/340nXjpOeCJyWmRiU59Ol3sufdVZKdmSmV2jSQJnf1lfq3dJMVw6dIyo973HL8gCtpa8LLL78sP//8c85tYWFh0qlTJ+nWrZskJCQ4XB5cQ8L27dtNgPjhhx9MsDh+/LgJEO3bt5dffvklT5AYP368hIeHe/S14fIIE250//33y+HDh+Xee++V6dOn59mn3R7vvvuueeNpf2Hp0qW9dpwomfc7jJFzvx4z3w9Y/Q8JKxVZ7MeGRIVL97mPSnTV8rLy9ilyeOUPOft2/3uF7Jy7XP608GnpPneCfNTtwYBqoYiOjpYOHTqYLQLDuXPnZPLkyXLw4MGc26677joZNmxYzgVUYbTrV2sl9EsvvN58801TY6Fyry5LkPBt1Ey4yY4dO2ThwoVSsWJFk7AdsRcQaVOenT18aCKPiIigKc+H2YNESdQf2l3K1Ksu29/8JE+QsDv+8z7Z/Py7ElWprDQbM0ACiTZ1z5w502zh/9LS0mTKlCk5QULDg7a6/uUvf7lskMivatWq8sQTT0jfvn3z3F62bFl5+OGHCRI+jDDhJgsWLJDs7GyTzGNiYhzeJyoqqkCY2Lt3ryxevNi8qdq1ayeB4kJWlqSkpTn8uhLF97s6pxWiMHsXrZas9Ayp3ffSfQOFFtDplaxu4f/0oknPW/Y5RJ555hkzMqOk9uzZY7o8cjt16pR89913lo8V7kM3h5toEZLSvsLCaCtE/jBx7bXXmuFTSt+U69evd/uxesKzu7aZL1xStmEtST97Qc4ePFrofbIupsvpvUekfJPaEhodKZkXLvUb+zv9sLj99tvlnXfekUaNHBflwj9oceRnn32WUx/x+OOPS/Xq1S09X+5iSx35lpSUZL7X0SEMJ/ZdhAk3OXTokNnWrl3b4f7MzMycoJA7TAQHB2Zj0Z216kpitZoO9/X5do1cacJjo+TisVOXvV/GuUtD5MJiAidMIDBooeTs2bNzRmIMHjy40PNdcTgataE1Ejq0VM+VOpR+/vz5phsYvocw4Sb6h6/yD4/K3TSooz20T1ELMN3pqquuMoVNzogKDpbtrTq67BjqxcRI90pVxJ0aNGggF7OzXfJcYbZgmSjtxV3Sz16UsNioyx9HTLRkZ2WZUSOX06B+A8kIcs3rd8agQYOcuv+xY5dqTfSKtrizGQ4cOFD83cA7HpBSMaUl+Wiy1KhRo8DPvkbrEwqr91I6AsPealC3bt0CdQ6uCBJ6DCNHjjQjOs6ePWsmwLrttttMDUVh5wAdcoqS0e71TZs2leixhAk3/qfodME61Kljx7wfytqNoW8UpUNC3V1kqUFCx3I7I1pnofOzqS90zLrWZrhCeFCIiBuzz6ldv0rVjk0lNr5qoV0dOuKjTL1qcv5witgyL/+6jiQfkXRblteCc3HZA7Zui/tYZ/9+fZGGQvtWX0/+n32NFoAXZfny5Tnf6xD4kraqFhUklF5wXX/99fLRRx+ZOpvVq1cXGi71HKAFofA8woSb9OjRw4zoeOGFF6Rnz54mMauNGzfK8OHDTauEpyar0mDjLG2Z8DfVqlVzacuEuPEi/+DH35ow0eDW7rL5ufkO71Pv5uskJDxM9i1eW6znrBZXzSstEzoZmzPsAUILkIv7WCv98L4i+L/TROtWX0/+n31NUSMn9APb3qqkrQQlLRa/XJCw6969uyxdutR0qWiXR2FhQs8BtEx49rPCjjDhJvZ5JLQZsGnTpqbQTN8wWvWsM2LGx8ebZJ+7XsJdStJsZUtNlczBI8Sf7N69W4Iiiz/XQ1EyLqTK/ITbxF32LFgpje/oLU3u6SdHv9kmv63+Kc/+8s3rSJvHbpULR0/Izrc+L9Zz7t6zW8KiXfP6naEB2RlaL6RN13rF6WgSI0deeukl8XfP/XO+nDl3XuKqxpni6/w/+xr9f9KRZYXVhNlH4+gFUXH/H0sSJJTOmqn1GDr8VFtx9DE6P4Wjc0BJjgXW8a/uJtoHum7dOvPmWLNmjXkT6FTaWkx01113mdnglCfCBNyj7qBrzeyVKrJCaQkOC5UWDySan88d/kP2v7+2yJEaK0e+ID3ffUK6z3tMDn3ynRzdsE1sWVlSsVU9SRjUVdJPnzP3SU05LYFET/ZU5Ps3XbTLTusl3Bkkcv8ePY9q64RuGQnkWwgTbtS4cWP5+OOPC9yuY+z1zaB9jM2aNfPKscG6BkO7S9Vrmua5rc2EoWarwaCoMKHO7DsiS7s//N+1OTpIje6tJazUpaLMkzt/lc8GPCnpZ/IueBQI9Cp8xowZMm7cOJ8sPMTlaW2CnbMjOEoSJJS25tpp6wRhwrcQJrxAp4rVdK11FI6mFH7//fdzqqVz/6xvJh2Z4U+6Vqws6f0HF3mfy+33VZ8nTrT8HBnnLsovM943X0oX+rruzYdMuKh3y/Wy/Y2CYdTfaZjWVjttoYN/0noXnd1XlwN3ZpZLnWOkJEFC6ZIDOimW3lfntIBvIUx4wZYtW4rs4rj55psd/jxixAh5++23PXCE8BZbVrasuWeGdJszXtpPGilZqemy650vvH1YQB5Dhw41X86qUKGC6eLSEW3OrrVx9dVXmy/4JsKED4YJ+yQwuDJlZ2TKyuGFj+8H/FX58uXlqaeekiVLlphZUFlrI3AQJnwwTABAIAeKO++809uHARcjTHhx3Q7gSlSpUiUZO3as2QIIDIQJAB6l/ea6mi6AwOF/0xwC8GtnzpyRFStWmC2AwECYAODxOQp0qerccxUA8G+ECQAAYAlhAgAAWEKYAAAAlhAmAHhURESENGzY0GwBBAaGhgLwqDp16si8efO8fRgAXIiWCQAAYAlhAoBH6RLUnTp1MlsAgYEwAcCjdCE7XbqaBe2AwEGYAAAAllCACcciIiR00VzxK4wOAFwmJCREEhMTXfZ802YtlLPnz0tsqVIy/p4hBX521THDOwgTcCgoKEgkMtLbhwHAi+eA0FDXfURop1a27dJWnzf/z/Bv/A8C8Kj4+HhZsGCBVK9e3duHAsBFCBMAPCoyMlISEhK8fRgAXIgCTAAelZycLJMnTzZbAIGBMAHAo06fPi1Lly41WwCBgTABAAAsIUwAAABLCBMAAMASwgQAjypfvryMGDHCbAEEBsIEAI8KDg6WsLAwswUQGHg3A/ColJQUmT17ttkCCAyECQAAYAlhAgAAWEKYAAAAlhAmAHhUbGys9O7d22wBBAYW+gLgUbpa6LPPPuvtwwDgQrRMAPCotLQ0SUpKMlsAgYEwAcCjDhw4IImJiWYLIDDQzQGHbDabXkKKX4mIkKCgIG8fBYAAOg9mZWWJPwkJCfHKeZAwAcfS0iRz8AjxJ6GL5opERnr7MAAECA0SixcvFn+SmJgooaGe/2inmwMAAFhCmAAAAJbQzQHAoxo1aiTff/+9tw8DgAvRMgEAACwhTADwqEOHDsmoUaPMFkBgIEwA8KiLFy/K1q1bzRZAYCBMAAAASwgTAADAEsIEAACwhDABwKPi4uJk0qRJZgsgMBAmAHhUmTJlpE+fPmYLwDl//PGH+CImrQLgUSdPnpQVK1ZIjx49pFy5ct4+HMDti4X9+uuvsn//frNSbnJysqSnp0twcLDExMRI7dq1pU6dOlK/fn0pXbp0kc+1fPlymTdvnjzwwANy1VVXiS8hTADwqN9//12mTZsmzZs3J0wgYJ07d07Wrl0rX375pQkQhdm4caPZarjQgNCrVy9p2rRpgZU/NUi89dZb5vsZM2bI1KlTpXr16uIr6ObwkJSUFHnkkUekXr16EhkZKTVr1pSxY8fK+fPnZfTo0eYP59VXX5VAsyblmIQvWyT/2Lez0Pvo/hu/Wyf+pHTdOGk1foj0/fg5uWXr/5Nhe+bJn7+cJi3G3iShURHePjwAXpKdnS2ff/65/PWvf5V33nmnyCCR/3E6zfzkyZPliSeekKSkJIdBQvXv31+qVasmvoSWCQ/46aefTB/x0aNHpVSpUtKkSRM5cuSIvPLKK7Jv3z45ceKEuV+rVq28fagopvq3XC+N7ugtv36xSfYtWSe2zCypek1TafPorRLf/xr5pN/jkpWa7u3DBOBBx44dk9dee0127NiR53Y957du3Vrq1q0rtWrVkqioKBMe9NyvXR979+6V9evXy6lTp8z9tUvksccek0GDBpmLz7fffjvnuW688UYZMmRIgZYLbyNMeKBFQlOkBomHHnpIJk6cKLGxsWafNlNNmDDBrD2vfxgtWrTw9uGimA5+8q38MvMDyTh7Iee2Xe98IWcOJEvLBwZJ/aHXy863PvfqMQLwnIMHD8rzzz8vp0+fzrmtW7du0q9fv0K7I6pWrWq+OnbsKEOHDpVNmzbJokWLzMVmZmam/Oc//8lzf18NEopuDje7//775fDhw3LvvffK9OnTc4KE0m6Pli1bmj+a+Pj4yxbfwHcc/3lfniBhd+CjDWZbrlEtLxyVf4iOjpYOHTqYLRAIkpKSTPeEPUhUqlRJnnrqKbnnnnuKXdegF5VXX321TJkyxVyA5jdgwACfDRKKMOFG2tS1cOFCqVixokmsjrRt29ZsNVTYvf/++5KYmGiqfPWEq0s2ax+aFvT4qwtZWZKSlubwK5CUqlbBbC/+cam5EgVpM+/MmTPNFvB3qampppXZfn7WURl6vtciypIIDw83nxn5hYWF+WyQUHRzuNGCBQtMv9iwYcPMECBHtO8sf5jQFgw90T733HNSo0YNU3Ohk/ysWbPGVAdr1a+/eXbXNvMVyIKCg00XR3ZGpuz/4GtvH47PysrKMot86d9+SEiItw8HsGT+/Pk5cz9oTYTWOlhpdctfbGn3wQcfSLt27cxFpi8iTLjRqlWrcvrNCqNdIPnDxLJly0wzmV3Xrl3NzxpKvv76a7n22mvF39xZq64kVqvpcF+fb9dIIGj/7Eip3K6hbH5uvpzZd8Tbh+Oz9uzZI7fffrupdNdWN8Bfbd++3Qz9VBEREWaEniuDhNZI6DwVH330kQnhWtypF5m+eEFJmHCjQ4cOmW1hSVJrJbSCN3+YyB0k7OwTlPz2229OH4c+VgtAnREVHCzbW3UUV6kXEyPdK1URd2rQoIFczM52yXOF2YJlorQv9v1bP3KLNB59g+ya94VsmfmBeEOD+g0kI8g1r98ZWnHubMW7+uyzz2Tz5s3FeszAgQPF3w284wEpFVNako8mmxbH/D8HOn98/drlUFgXtdIPebuhQ4dKlSpVXBoktEZCPyf0faIXnlrk+fPPP5uRIUWdB3VSrJLQYlAtAi0JwoQb6RwSSpt0HdF6Ch3toUWZOgNaUVavXm22jRs3dvo4NEg4G0KitfnZz0aqagW01ma4QnhQiEgxzwutHhosLccNkj0LVsk3j7wh3nIk+Yik21zz+kvyd15c9veDbov72JKEaF+T/d+/Td3q68n/c6Dzx9evrQ1FnVf1g91+AdirVy+XBwmtkdBaiVtuucV0f6svvviiyDCh58E0L9SiESbcSFOeTh38ww8/mKE/uelEJuPHjzff65DQogpr9I2mlcG9e/cu0VwUehzO0pYJf6OTuLiyZUKyixckWj08WPYuXC3rH3pNvKlaXDWvtEzo3CnOsAcIrZko7mN9aaa/kgr+b32IbvX15P850Pnj69eWictd4KmePXuWuOuhqCBh16ZNG1OUqRefWkN3/PhxqVDhUrG3o/OglZaJkiJMuJGuPaAjOl544QXzx6bNT/bpU4cPH27+MFRRAUErhHVIkP5Rz5kzp0THUZJmK1tqqmQOHiH+ZPfu3RIUGemS58q4kCrzE24r8j7aGmGCxHtr5Otx/9JJ+MWbdu/ZLWHRrnn9zrBPB1xcO3fuNMXJOpFbcWsmXnrpJfF3z/1zvpw5d17iqsaZJuv8Pwc6f3z92sWwePHiQv+O7a4tYR1bcYKE0qDSpUsXU4SpNRR6rst/gWqn+3SYqacRJtxI55F49913zRhkHSakJ04dRqSznemJVOeW0D+m3PUSuWkzsI431hnS1q1bx5LNPqTRyN6mTuLc4T8ked0vUvemznn2X/zjtCSv/cVrx+fLdEp5/bvPPecK4E90lJ7WL6jKlStL2bJl3RYkcr9v7HSGzMLChLcQJtxIi4o0BGh3hg7r1D8+nVZ11qxZctddd0lCQoK5n6MwkZGRYQrbtFVh5cqV5nHwHRVbXfq/i6lRSbq8cl+B/Uc3bCNMFEKvmljgC/5Mu6ntdQmXq3dzRZCwDzu1swcZX0KYcDMtmPz4448ddl/oH4Q2XzVr1izPPvvcFBoiPv30U2nfvvijCnxN14qVJb3/4CLvc7n9vujrB/5pvuA8bdLWVQ/HjRvns1X8QFFyTyBYWO2CK4OE0gCunxf6+eBs0bMnECa8ZNu2babvS+so8o9L1tXm3nvvPXn00UfNvm+//TZnn7ZmOBo6CvjTiVhb7LR1DvBHuurz008/bVqQnQkT6enpJkyUdK0NbeXWlr3CJkH0JsKEl2zZsqXQLg4df690jnb9yk0T7ciRIz10lACA/PQiryRdz+Hh4fLkk0/K3/72N7M+jbNrbRQ1JNTbCBM+GCZ8sT8MAGBd+fLl5e9//7sZGu3La204izDhg2ECABC4ogNwxVzChJfX7QCuNFrzo2sYUPsDBA7CBACP0oI1Ha0EIHD435zJAPzamTNnZMWKFWYLIDAQJgB4lC5E9Pjjj5stgMBAmAAAAJYQJgAAgCWECQAAYAlhAoBHRURESMOGDc0WQGBgaCgAj9JVFufNm+ftwwDgQrRMAAAASwgTADxq165d0qlTJ7MFEBgIEwA8ymazmaWbdQsgMFAzAcciIiR00VzxKy4s6AuNipBh+/4t/kSPGYDrhISESGJiosueb9qshXL2/HmJLVVKxt8zpMDPrjpmbyBMwCGzNG5kpFzJrz8s+sp9/QAunQdCQ133MWkTkWzbpa0+b/6f/RndHAAAwBL/jkIA/E58fLwsWLBAqlev7u1DAeAihAkAHhUZGSkJCQnePgwALkQ3BwCPSk5OlsmTJ5stgMBAmADgUadPn5alS5eaLYDAQJgAAACWECYAAIAlhAkAAGAJozkAWNKuXTun7l+jRg2ZOHGi9OjRQ+Li4tx2XAA8hzABwKM0QDzzzDPePgwALkQ3BwAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEzDmzZsnbdu2lXLlyklUVJQ0btxY/vGPf4jNZvP2oQEoxKeffiqtWrWSiIgIiY+PN+/ZK8natWtlwIABUrt2bQkKCpLJkyfLlWTatGnSsWNHc94uW7asdO7cWT7//HOvHAsLfcGoXLmyPPXUU9KwYUNzYlq3bp2MGTNGQkJCZOzYsd4+PAD5bNq0yXyQPvzww7JgwQL57rvv5C9/+YtER0eb7ZXg3Llz0qRJE7n11lvlgQcekCvNqlWrZNSoUWblXv1/nz17tvTr10/WrFkjnTp18uixECZg/OlPf8rzc926deXDDz+Ur776ijAB+CBthdAPkeeff978rK2J27ZtkylTplwxYeKGG24wX2rChAlypfnss8/y/Dx16lTTMrFkyRKPhwm6OVCAdm18//33sn79eunWrZu3DweAA/r+7N27d57b9OdDhw7J4cOHvXZc8J7s7Gw5c+aMlCpVyuO/m5YJ5Dh9+rRUr15d0tPTzR/lxIkT5f777/f2YQF+5cLFVDl8NKXA7ZlZWTnb3QcOF/g5t2pVKkhMdFSRvyc5OVmqVq2a5zb7z7qvRo0a4i0HkpIlI/PS6yvJ64+JjpRqVSqKvzp+8owcP3WmwO3O/Bsk1KomISHOXe8/99xzcurUKbn77rvF0wgTyBEbGys//fSTXLhwQTZs2CCPPfaYVKtWTUaPHu3tQwP8RkR4uHyxdqMcPvpHoWFjzqJPC/25SsVycu+IgeLPjvx+XJat3FCi1x8kIncN7Sf+LCQkWN79aIWkpqWX6N+gbbMG0qCOc2HwX//6lwkTS5cu9UqQpJsDOYKDg6VevXrSokUL0+f6yCOPyBNPPOHtwwL87oNkcL9uEhoa4vxjgy89Niz08td5cXFxcvTo0Ty3/f777zn7vKlj26ZSr3b1Ej22c7sWUrdWNfFnZUvHyICenUr82P49rnHqMdOnT5fx48ebINGjRw/xBsIECqVdHampqd4+DMDvVK5QVm64roPTj+vRua1UL2bzvhbYLV++PM9tWnynwyS92cWhgoOC5OYbukpkRLhTj9NWmV7XXiWBoFWTetKiUV2nHqOtMhomnfl3e/rpp2XSpElmmLC3goSimwOG1kd06dLFjOLIyMgw47dfeOEFueOOO7x9aIBfurpNU9mx95DsOfhbse5fu3oV6dqhZbGff9y4cXLNNdeY1sPhw4eboaEzZ86UGTNmiC8oUzpGbuzVWf6zbFWxW2WG9L++WK0yuYeG7t2713yvtV7aUqNdtTExMaaV1ZuCgoLM6z9w+KicPXehWI/p0r6F1K1Z/FYlHQ47a9YsMzRYh/XbW6p0rqAyZcqIJwXZmJUI/z0xLVu2TH777TeJjIw0oULHL2t3h841AcB5p8+el5fmvC8XU9OKvF94WKiMvWOQVChX2qnn/+STT+Txxx+XnTt3muJLHcb94IMPii/R2oFfdu6/7P16d20v113dyqnn1qHrjkacde3a1ezzBbv3J8mc9/IO4XSkaqXycu/tA53qHtPA4siIESPk7bffFk8iTACAG/28fa8suMzV+U29r5X2LRtJINLiQg1UZ4q4Oo+vUVXuHtrP1G0Fog+/+Fq+/XF7kXU2GiTiKlcQfxWY/3Nw77C3ZMdV6gAKatmknrRsnFDo/sb1akm7Fg0lUEVHRcqgG64rdH94eJjc3Pe6gA0SSutnKpYvvNuhV5er/DpIqMD934NbrNu4RV595wP5ZNW33j4UwG8M6NVZSscUnEioVFSkaZUorLk6UOgwx45tmjrc1//6jlKhrHPdO/4mPDxMhvTtZgpTHbXKdGnXQvxdwIQJfTPa35Da96/FhKVLl5aKFSvKoEGDZN++fTn3/fjjj02fmi6MovfR+e337NlT6HOnpaXJyy+/bIqd9DFaU6DFLjoUJyWl4OQ0SouhdHpXne5W+zJ1vQudEGrw4MGycePGQn+XVuTq9LC6VkZYWJhUqFDBTJOr9Qs64503nb+YKhs2b815AwAonujICDO6IT8NErGlouVK0Oe6DlIp39V543q15aoAbpXJrWa1ytLtmtYFQsbgAGmVCZiaCXuQePXVV+Xee+81ky1VqVLFFCZdvHjRfJD/+OOPMn/+fFNsqOOw9UPevl+//+WXX6RSpUoFxm336dPHPFb/w2vWrGkCyO7du03IqFWrlqxevdoULOamlcQaYMqXL29+V3h4uPz6669y/PhxCQ0Nlf/85z+SmJhYYNKRv/71r+Z7DRE6xEuPLSkpyVQt33PPPfL666+Ltyxfu1FWf/OjaY67f+RNAX81Bbja0hXrZcPmbeb7ts0byM1FNP8HoqTkY/LavI8k22aTUtGRMm7UzRJTquiZPgNJVla2vPbvj3ImNBvUp2vghClbgNCXol/R0dG2uXPn5tx+/PhxW7t27cy+fv362aKiovLsT0lJsbVt29bsnzBhQp7nzM7OtnXt2tXs69u3r+3AgQM5+86ePWsbNWqU2dexY8cCx6O/Y8+ePXluy8rKsi1ZssQWExNjK1u2rHkOu4yMDFu5cuXM8/3rX/+yZWZm5jmONWvWmMd6y7kLF21P/2OObcKUWbatu/737wCg+NLSM2zT31hom/Lau7aLqWm2K9GX6zZdOo/svjLPI8dSTtqenD7bNnfx5+bcHigCrmXivvvuk1deeaXARC7aulDYfl15TbsWdObHn3/+OU+XQ9++faVZs2ama0K7N3LLysqS9u3byw8//CBff/11sVdp06W+J0+ebMYG33LLLeY2HR+sLRi6Lv2JEyfElWbOXSJnz1209Bxp6emSlp5hWmcut2YAgMLpeUNPuqFX6JBr/cjJyMg0TfxXqvSMTPP/HxzsW627sTFRct+Im0r02ICbtOrOO+8scFubNm2KtX///rxjoRcvXpwzZjd/kFA6/8Kf//xnEyZ0THP+MKF1GNqdoQFFuzd0Mih17Ngxs9XJVexhQrtX9HfoIi1ffvml9OzZU1xFg8SZc+ddtyqdi54LwJUrNd3xuhXwTwEXJhISCg7Byl0H4Wi/FjsqrUvITWso1FtvvSUffvihw99nnwtfJ3vK7cUXX5RHH31UMjMzCz1WDRi5g4lOOKOzTvbq1csEHJ0atXPnzqZYVOs0rKRNK2iVAIDAF2vhsyLgwoSjddxzFwpebn9u2kqgtm8vfLIRO11p005HXTz88MMmIGh3ho4WiY+PN79bf9ecOXPMSpz2lgo7XfFN59T/5z//aVo79Gvq1KlmJMitt95qFnPRgk5nlbTZyj6CY+rrC8z3wwb0kKYN4kv8XACAwBRwYcKVdH53pSux9e/fv9iPmzdvntk+9NBDDlfdzN0ikZte+etIFP06fPiwrFu3znR5LFq0yLSO6KgO/dmTNRO5WyU++nK9+QIABJ5Yaibco2nTpqauYevWrU6FiQMHDpitdlE48u23l5/wSVsohg4dar40lDRv3lxWrFhhnrtOnToer5mgVgIAUBjCRBF0siudl+KNN94wo0DsLRWXoyu2KfsKbvmLMnXSLGdDja4Ap90uR44ccTpMlLQfjFoJALhyxFqpr7MF2DwTrtyfe54JnUtiy5YtBeaN2LBhg+2ee+6x7du3L+f26dOnm8fUqVPHtnfv3pzbt27damvYsKEtMjLS7B8xYkTOvm3bttnuvPNO2zfffJNn7LHONzFjxgxzf33cyZMnbZ7AvBIAgCt2nonCXk5J9+t02VpAuWHDBvOzzkqps2XqzJQ6w+X585ea/nfs2CGNGl1a9e/s2bNmNMbevXvNlNg69bZ2E+h9dC6JMWPGyJNPPplnmVjtTmnd+tJUq7GxsWbUiRZwHjx4MKfGQmfI/L//+z/xBGa7BAAUl/9PCO5murbHmjVrzIe+zv2g4WHTpk2mdkGnzNbhnLq/QYMGOY/RMKCTWOl6GjoJ1a5du3Kmw9YRGjq1d376+NmzZ8uQIUNM4NA5L3R+Cp174uabbzbFmJ4KErnX4OjRqS1BAgBQpIBpmYDrHD91Rj5cvk7OXUilVQIAcFmECRQqNS1dIiPCvX0YAAAfR5gAAACWUDMBAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAECs+P/kIT9ReCq5CQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 663.998x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(grover_op.num_qubits)\n",
    "# Create even superposition of all basis states\n",
    "qc.h(range(grover_op.num_qubits))\n",
    "# Apply Grover operator the optimal number of times\n",
    "qc.compose(grover_op.power(optimal_num_iterations), inplace=True)\n",
    "# Measure all qubits\n",
    "qc.measure_all()\n",
    "qc.draw(output=\"mpl\", style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cbed4ccf-08f3-4c18-9e15-957ae5fa36c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2263.23x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "\n",
    "target = qr_backend.target\n",
    "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n",
    "\n",
    "circuit_isa = pm.run(qc)\n",
    "circuit_isa.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "78c951f2-ffc3-495b-b9ec-1b3509cd65e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# To run on local simulator:\n",
    "#   1. Use the SatetvectorSampler from qiskit.primitives instead\n",
    "sampler = Sampler(backend=qr_backend)\n",
    "sampler.options.default_shots = 10_000\n",
    "result = sampler.run([circuit_isa]).result()\n",
    "dist = result[0].data.meas.get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9e66a61b-2fba-4753-840d-3a01305d479f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_distribution(dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cdd32e59-2c26-4678-800f-3b7c2c95fc52",
   "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": "3.12.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}