{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9fb07d3a-5975-4222-95bc-44bdf9d16e9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, transpile\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "service = QiskitRuntimeService.save_account(channel=\"ibm_quantum\", token=\"HIER IHR TOKEN EINSETZEN\", set_as_default=True, overwrite=True)\n",
    "\n",
    "from qiskit.providers.basic_provider import BasicSimulator\n",
    "backend = BasicSimulator()\n",
    "\n",
    "from qiskit.visualization import plot_histogram\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4024bad1-00b6-4590-8e73-d98bbe45805f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def oracle(qubits):\n",
    "    # Bei welcher Qubit-Kombination von qubits[0], qubits[1] und qubits[2] schaltet das zentrale ccx(4,0,3) auf's qubits[3]?\n",
    "    # qubits[4] dient nur als Arbeitsqubit \n",
    "    qubits.cx(0,1)\n",
    "    qubits.cx(1,4)\n",
    "    qubits.x(0)\n",
    "    qubits.cx(1,2)\n",
    "    qubits.ccx(1,2,4)\n",
    "    # zentrales-Element: Auswirkung auf das Hilfsqubit qubits[3]\n",
    "    qubits.ccx(4,0,3) # auf's Hilfsqubit drauf\n",
    "    # \"Abbau\": die obigen Operationen wieder rückgängig machen \n",
    "    qubits.ccx(1,2,4) \n",
    "    qubits.cx(1,2)\n",
    "    qubits.cx(1,4)\n",
    "    qubits.x(0)\n",
    "    qubits.cx(0,1)\n",
    "    return qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2be6a348-657a-42ac-9bd9-64c65c36f306",
   "metadata": {},
   "outputs": [],
   "source": [
    "def grover_iteration(circuit):\n",
    "    # Aufruf des Quanten-Orakels\n",
    "    oracle(circuit)\n",
    "    circuit.barrier()  # nur für die Schaltkreis-Darstellung\n",
    "    # H-Gatter für alle x-Qubits\n",
    "    for i in range(3):\n",
    "        circuit.h(i)\n",
    "    circuit.barrier()  # nur für die Schaltkreis-Darstellung\n",
    "    # Beginn der Realisierung von D mit Schaltkreis von Übungsblatt 7, Aufgabe 3b);\n",
    "    # auf die Multiplikation mit (-1) wird verzichtet, da das alle Amplituden betrifft und \n",
    "    # daher insgesamt für den weiteren Verlauf und die abschließenden Messungen irrelevant ist.\n",
    "    for i in range(3):\n",
    "        circuit.x(i)   # P_x-Gatter für die drei Qubits\n",
    "    circuit.barrier()  # nur für die Schaltkreis-Darstellung\n",
    "    circuit.h(2)       # H-Gatter unten\n",
    "    circuit.ccx(0,1,2) # Toffoli-Gatter\n",
    "    circuit.h(2)       # H-Gatter unten\n",
    "    circuit.barrier()  # nur für die Schaltkreis-Darstellung\n",
    "    for i in range(3):\n",
    "        circuit.x(i)   # P_x-Gatter für die drei Qubits\n",
    "    # Ende der Realisierung von -D\n",
    "    circuit.barrier()  # nur für die Schaltkreis-Darstellung\n",
    "    # H-Gatter für alle x-Qubits\n",
    "    for i in range(3):\n",
    "        circuit.h(i)\n",
    "    circuit.barrier()  # nur für die Schaltkreis-Darstellung\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1b13d50a-12a0-4ed9-ba77-9bd727028f48",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3 x-Qubits, ein y-Qubit und ein Hilfqubit für's Orakel; Standard-Initialisierung mit 0\n",
    "circuit = QuantumCircuit(5,3) \n",
    "circuit.x(3)       # unterstes Qubit auf 1 setzen\n",
    "circuit.barrier()  # nur für die Schaltkreis-Darstellung\n",
    "# H-Gatter für alle Qubits\n",
    "for i in range(4):\n",
    "    circuit.h(i)    \n",
    "circuit.barrier()    # nur für die Schaltkreis-Darstellung\n",
    "# Grover-Iteration(en)\n",
    "grover_iteration(circuit)\n",
    "#grover_iteration(circuit)\n",
    "#grover_iteration(circuit)\n",
    "# Messungen\n",
    "for i in range(3):\n",
    "    circuit.measure(i, i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5ae6ebe3-8853-4e9f-9e79-e1d13d7584da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circ = transpile(circuit, backend)\n",
    "erg = backend.run(circ, shots=1024).result()\n",
    "plot_histogram(erg.get_counts(circuit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7d7f7570-d4aa-4369-8be9-5359be74372f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GlwMDFJdUKD2rUBnZhSorrzS6nICrrHQq+1Cx0jLylV9YZnQ5hsgrKFNaRr5+O1wc9Hcr/3a4WPc8s9rj7bydCzz52gZt28O3XgEAwS2/sEwVv88BXC6XwdUAAHzF9I2ujRs3qkuXLpo2bZqysrLUsWNHlZeX64UXXtBVV12l1NRUSVL37t2NLRTwgxWObIUvmKvn9mw/6XvCF8zVZWtWBbAq+MLLc1NVEMAP6ktKKzXjg20BO54vHTpSon++s1lth89TwsD31XzoXNU9+z2dOXa+3p2/SyWlFUaX6FeVlU4tWvmrLr5ziWr1e1fNLpyjxEEfqNF5s/XAv1O074B5nrtyMrt/zdN909eo4aD3lTR4tppeMEe1zpqlkX9dqq9/PCCnkwtcM3O5XPpufZau/vty1T5rlppc8KEaD/lQ9Qe8rzuf/kFbdvn+uUY1TeZvRXry1Q1qduEcNRz0gZoPnata/WZp8Pgv9NFXe02zJN3JlJc7Ne+rvRo0/gvVPmuWmg+dqwbnHv17eOq1DcpyFBldolfe+GSnjuQHrmFZUeHiDu8gxTUBnr6np1ybxuuGy9pU+frymRepZO316tS6boArAwKjosKpz5bt0wW3LlatfrN08FCJJCnrUIke+896pWfxXGqYG+cBWGE+aOpGl8Ph0PDhw5WVlaWJEycqMzNT69evV1ZWlqZOnapFixYpJSVFNptNXbt2NbpcAHBLWXmlXv94R8CP+9bnu4LuLphlazLU6qJ5uu+fP2nP/uMbOms2/6ZxD69U58s/0S4/PufMSDl5pTrv5sW65K6v9cWqdP35C4u/5ZTomZmb1PqSeXrto5NPdIKZy+XSv2ZtUdvh8/TPd7coJ++/Hwg7nS59tixNF9z6pS6+8yvL3t1idqVllRr7f99qwPWLNHvxLyr/052MBUXlemlOqrqM+lQPvbDWtN/o/eirvWp50Vw9+p/1OpB9fENneUqmrrxvmfqM/VwZ2eb8gCcju1B9xn6u0fct07cpmce9ln6wUI+8uF4ths3VJ0v3GVOglyornXplXmrAj/v+oj2WvSsaCGaTX9qgzbsO67n7+qpxw+Pv5vzrNZ10bu8kPfbSem314/P+AKNkHyrW2eMWauRfv9HXPx6/9L/T6dITr25Qy4vm6v1Fuw2qEPA/zgOwAlM3uu655x6lp6frrrvu0vTp0xUXF3fstUmTJqlbt26qqKhQ8+bNVatWLQMrRaBER0erb9++io72bKkWmIcZMrBwxX5lHy4J+HFz88v0yTf7An5cb61al6VhdyxRbsGpGxh79udr4I1f6NfMggBVFhiFReW68LYvtWJt1infV1np0q1PfK/XTdjs+tesLfrbtDU6Xf/iy+/Tdek9S1VaZr2l7MysstKpq//+rWYv/uW07/3HGz/r/573fDnYmu7Tb/Zp9P3LVFJ66mxv3H5Yg8Yv1qEjgT+3+NOhIyUaNH6xNm4/9V17JaWVuvK+Zfp8eVqAKqu+pasz9Gtm4JuTRSUVbv2bqsnMMBdE9VgxA+UVTo17eKViosI0c/KAY7/ftnltPX13L63elK1pb282sMLAsmIGrCo3v0zn3bxYazb/dsr3lVc4dc0DK/Th4j0BqgxGsuIYwHngeFbMgBWYttGVmpqqOXPmKD4+XlOmTKnyPT179pQkdevW7djv/dEY69OnjyIiImSz2QJSLwKjadOmmjFjhpo2bWp0KTCIGTLw/UbjHpb5w8Zsw47tiYoKp/7y9+Uqc3M5rszfinTbk9/7uarAevr1n5WyxeH2+29/+gdTLdmxY+8R3ffPn9x+/7cpmfrXrC1+rAiB9u6C3R415599a7O+32CehxHnFZTpuodWnLbR+4edabma9C9zNfvu++dP2unmHbtOp0vXPrgiaO7uNPJ8/MPPwf3vxAxzQVSPVTOwIfWQpsz8WRf2T9bNo9rJbrfp3afPkc0mjXt4paWWcrZqBqzo4RfXaYsHd6jc8Ogq033xByey6hjAeeC/rJoBszNto2v27NlyOp0aO3asYmNjq3xPVFSUpOMbXbt379bHH3+sxMRE9e7dOyC1InAqKytVUFCgykprfWu/qLJSjtLSKn9ZjRkysG6b+80Lnx871bhje2L+t7+esETX6Xz5fbr27M/zU0WBVVpWqdc/8Wx5y8pKlyFLYvrLK/O2u/0B/5+3qaw097OKrMLlcunF2Z4/V/ClOYFfCs5fZi3crYIiz55B+MEXe5RjkmXpDh0p8fjOo/zCcr2/KDi+yW3k+XjdtkOGHdsXzDAX9BbXBEdZOQNPvrZBG7cf0vSJfTTjgX7q26WBHpqxTjv3mXMZ75OxcgasJL+wTO/M3+XRNiWllXrrM8+2QfCx8hjAeeAoK2fAzPNB0za6li1bJkkaNGjQSd+Tnp4u6fhG1znnnKPMzEzNnz9fQ4YM8W+RCLhdu3Zp8ODB2rXLWhOXJ3ZsVaOvPq/yl9WYIQM/7zj1Ekz+tGlnTlB8y+dVL5bhc7mkNzxsDtVUny1LkyPH828ivvbx9qD4+Z5OaVml3vrc83/jaRkF+uqHA36oCIG2PvWQ1qd6/mH8vK/2muZbvK/O83wcLCmt1KwF5ng+xawFu71ajtSb84cRjJwLbN97RCWlnjVRaxIzzAW9xTXBUVbOQEWFS+MeXqnIiBDdcVUHrVqfpeffs94d7VbOgJV8uPgX5Rd6/ozpYJkLwHtWHgM4Dxxl5QyYeT4YanQB/pKWdnSN/WbNmlX5ekVFhb7//ugyVX9udNntvu/99erVS1lZp35GCrxzxRVXePT+7Oyjy7wsXrxY69atc2ubkSNHelxXdUXZ7drWvZ/P9ndT05Ya1ahJla8NW73CJ8do27atip2BvxPCrBk4GZekI3Ufk2xVj1Upsy9VYvzJ1xhOjI869r/7vx5z0vdlOYrU+y/zT/j90rJKNWnaQjbV7A+4smr/VQqp6/F2z7/8oWZNqzk/b2/lRZ4rRZ/8ix4nk+UoVnKz1rK7gvubPBX2WsqtM9Grbf9y/b2KLV3t44pqlsw6f5PstZWZlank5GSjy/GLovAuUqxn5wfp6Nr1HboNUHhlph+qChyXpIy6j0g2z6f6Dz7+gp79+yLfFxVgR6IvkSI9X53h59SsoPh3kVH3QckWUeVr/p4LuFxSi9YdFeLy7M5pf/JkPujNXFDimsBdwXBNEEwZcCpMqvewT/eZW1Cm0rJKhYeF6ItV+z2+A/502rRtK7s8by5URyCuCaWadV2I08uNukCK6u/xdrt/zVPj5CayKfi/AGglnAfcZ8bzgGTeDFhhPuj803vPPvtsbdiwwavjmrbRVVh49DkjxcXFVb4+Z84cORwOxcXFqUWLFn6tJSsrSwcO8A1xf/jj5+yuP/JQXFzs9rZG/OyiQ0Kk7r7bX+vYWJ2X0NB3O6xCRkaGigy45desGTg5m1Tv5A35xPhoJTeMOe1eQkPsbr2vKhmZWZKzhjdC4mxSiOeblZSU17Cft5caFklePlM1MzNbqizwbT2BFl4m1fFu09y8QuU6TJCBU4mrlOySs7LSHHmvSp1mUtUrV5/Wb47DUpEJ/l7qevflrcKiEhWaIReNS6RIzzdzKSQ4/l3UkXSSRwkHYi6QlXVQqqg5y/16Mh/0Zi4ocU3grmC4JgimDMgWLtXz7S7femKAwsNCtG1Pjh6+pbvmLtmrX9Lzfbb/zIwMyRXY5x0G4ppQqmnXhTitpBIpyrtNMzKyJFfN/nInjsd5wH1mPA9I5s2A1eaDBw96/zxg0za6EhMTlZOTo/Xr16tfv+O7npmZmbr//vslSV27dpXNdpKrRB/WAv+IifHs4vyPwSsqKsrtbRs3buxxXdUV5Yc7C/2tUaNGhnx706wZOJUDrnLJFlbla1mOU3+7OjE+SqEhdlVUOpXlqPqLAKfbT6OkBrKpZj/H6KCtxKt7zqIjKlW3hv28vVEQYZdXK2y7KtUosa5squ3rkgLKaYuQt/fj1IkLUUxE8GfgVDJDQuSUZA8JUZIJ8l6VkrBwebxwocsl2WxqWD9GoXWD/+8l01Ukp83zbl9slFTbBLnIjZK8adnbXUVB8e8iUxVyquo7ugIxF0hKjJfdFedesQHgyXzQm7mgxDWBu4LhmiCYMuBUmNdzmqrcfXVHDerTSA++sFafL0/T+jmX6c0nBujcG7/w2TGSGjUK+Df5A3FNKNW860KcWl6kTd58dG9zlahRI/9+CAzf4zzgHrOeByTzZsAK80Gn06nMzKNJb9jQ+/HXtI2uIUOGKDU1VVOnTtX555+vtm3bSpJSUlJ07bXXyuE4+gDn7t27+72WtWvX+v0YVpWSkuLR+7dv367Zs2dr2LBhat++vVvbPP/8815UVj2ukhJVjB4X8ONWx86dO2WL9OKr09Vk1gycSpfLP9GW3TlVvlbVEkN/tv/rMUpuGKMsR7GanP+hx8dumRynPZt+9Xi7QPvH6xv10Az3bz//wydvPqAL+//HDxUFVnpWoZoPm6PKSs/WIBg9tLXmTKv5P193DLt9ib78Pt2jbSLCQ7R7/UeqXyfwY1kgJQ+ZrQPZRUpKTFL6Fs/+joJFSWmFGg/5UIdzPbj71GbTGR3qa+2HP/v9S1CBcPeUH/Xi7G0eb/fdwufUrV19P1QUWOu3OdRzjOfrzN997Zl6/u81/99Fv2vma/Wm36p8zd9zgQb1InXg59016t+JJ/NBb+aCEtcE7gqGa4JgykBhUbliz3zXJ/tq3bSWpkzopZ82/6apb26S0+nS5JfXa8qE3rr76o6a8YHn54yq7Nq5UzHRVX8pz18CcU0o1bzrQpzajr1H1H7Exx5vN35UV70+uebPBXA8zgOnZ+bzgGTeDFhhPlhYWKjY2KNf0vzuu++8Pm7wtQTdNGnSJNWvX1/79+9Xp06d1KVLF7Vp00Z9+vRRy5YtNXjwYEnHP58L5te6dWstWbJErVu3NroUGMQMGejZMd6Sx/bE+MvbKSzUs1NcqyZxOr+fOb6lmZwYo+EDm3q83R1XdfBDNcbw5s8yZmhL0ze5rCIyIlTjR7b1eLs7rupQoz68r47bR7t/wfaHs7o3MEWTS5LO6Bivvl0SPN7Om783Ixg9FwjmfydmmAuieqyYAZtNevvJcxRit2ncwyvkdB79MtSzb21WypbfNGVCL7VMrjl3afqbFTNgRe1a1NF5fRt5vN3to81zTYSqWXEM4DxwPCtmwApM2+hKTk7WqlWrdPHFFysyMlL79u1TvXr19Oqrr2rRokXauXOnJBpdVhMaGqq6desqNNS0NzPiNMyQgV6djPxwKzg+AG1YP0qTbuji0TbPTOgtuz14P7j7X5Nv76HoSPdzfvE5TXROT/MstXvRgGSd2zvJ7ffXiQvXgzcxJzCTv17TSY0auP+wuu7t6+nqi1r5saLA6tiqrm70oNkXGmLT03f38mNFgTdlQi+Fhrg/rt90eVu1a1HHfwX5kJFzASOP7QtmmAuieqyYgYnjuqh/j4Z69KX12r73vwtcO50uXf/ISoWG2PXmEwMMrDCwrJgBq3ryrjMUEe7+R59jhrbUGUHy5U54z4pjAOeB41kxA1Zg2kaXJHXo0EELFy5Ufn6+8vPztWbNGt1yyy0qLCzUvn37ZLfb1blzZ6PLRAClp6dr4sSJSk/nNnSrMkMGRg5uphAPPrjzFZtNuuL8FgE/rreeuLOnbrmi3WnfZ7NJ/3mwn664IHj+bO7o1q6+Pvv3EMVEnX7iNqh3kj58dlBQf0P/f4WE2PXpv87TmV1Pf0dH7dhwLZhxvto2D+5nk+F4jRrEaPFLFyox/vRPIe/Uqo4WvXiBojxoDgeDlx8+SyPPa3ba94WF2vX+M+d61BwOBoP6NNKsfwx06w7fUUOa66WH+gegKt+45JymiggPMeTYo4P8fGmGuSCqx2oZaN+itp688wz9+HO2/vnOlhNe37bniCa/vF4DeyXp7qs7GlBh4FktA1bWr1tDzZk2WJERpz9nXjQgWW89aZ0P+q3MamMA54ETWS0DVmHqRtfJbN26VS6XS23atFF09Inf9P3oo4/00Ucfadu2bcf9N8/aCn4FBQVatWqVCgq8eTx58BkY30Blw0frb61OvgxP2fDR+qyvdSZzZshA44YxGjn49B9c+trQ/slq1aRWwI/rLbvdplce6a83nxigLm3qVvmewX2StOSVobpjjDknc+f3a6wfZg3X6AtbVHlXQ5PEGD19d099+cqFijVgDW1/q1MrQsveuEiP3dZDSQknnu/Dw+y65pJWWv3+cJ19hnnuZsN/dW1bT2vev1Q3j2pX5R2O9WpH6L5xXfTdO5eoUQPPHmQfDMLDQjRv+mA9P6mvWjc9cfy22aThA5tq5VsXa/SFLQ2o0P/GDGulFW9dpEvOaaKqevltmtXSC/93puZOH6ywsOC5NIqvG6kxQwP/MzunZ6I6t6kX8OP6khnmgp7imuB4VsvA9r25iur9js66dsGxpar+1zMzN8nWdabPns9S01ktA1Y3YlAzrXr7Yo08r1mVK3i0aBynaX/ro8//fb4iI8z1pSdUzWpjAOeBE1ktA5I15oOWHME3b94s6eTLFl555ZVV/ve4ceP09ttv+7U2AHDHXX/pqI++3hfQY945JvjWKrfZbLrhsra6fkQb/bAxWxfduUR5BeWqHRum1e9fqvZBskRVdXRtW09zpg1W5m9F+nx5mib9K0X5heWqVztCv3wxWqEePsss2ERFhmryHWfooZu7a9GqXzXuoZXKKyxXnbhw7VxwhRLqnf5uHwS3pkmxeu2xs/Xsvb312fI0TXhmtfIKy1W3VrgOLB1j+g80QkLsmnBNZ919dSct+ylDo/72zbFxcOO8kWre2Pxr8ffr1lALXrxA+w7ka9Gq/Xrg32uVX1iu+nUitP3zK4J22do7x3TQO/N3BfyYAAAEm16dEvTJv4Zof1aBFnz7q/7vj7lA7QjtXnRl0M4FAAD/Ze5Pt07idI0ul8tV5S+aXABqioG9kgL6Te7hA5vqogFNAnY8X7PZbOrfo6Hifr9rKTY6zBJNrj9LSojWbaM7qFbM0b+DqIgQ0ze5/iwszK7LBjdX3O9//pioUJpcFlOnVoSuH9H2WAaiI0NN3+T6M7vdpiFnNj5uHLRCk+vPmjeO051jOh4bByPDQ4L6g63enRM03oPnsFXXeX0b6cogX7YQAGBtTRJjdcef5wIRwT0XAAD8l3U+4fqT0zW6ACAYzHignxrUi/T7cerEhevVR/ub6vlNAACYwT/v66vkhv5fdjM2OkxvTD6buQAAAACAGsmSja5ly5bJ5XLp4osvNroUBFhCQoImTJighIQEo0uBQcyUgfi6kXrnqYEKDXX/Q6csR5HSDxYqy1Hk1vvtdpvefGJAlc83AgAAxqodF673pgxUuAfPF/N0LiBJrzxylmnuADTTXBDeIQMgA4C1MQaADJiTddZrASTVr19fY8eONboMGMhsGRh6drJmPT1Q1zy4QpWVVT9U9M96/2W+2/u22aTXHztbI89rXo0KAQCAPw3slaS50wfryonLVF7hPO37PZkLSNKLD/bT2Itbe1tejWO2uSA8RwZABgBrYwwAGTAnS97RBevKy8vT0qVLlZeXZ3QpMIgZMzBmWCt98tx5qhUb5rN9xkSF6sNnB+nGAD77AwAAeGfEoGZa+OL5qlsr3Gf7jIwI0dtPnqM7x3T02T5rAjPOBeEZMgAyAFgbYwDIgDnR6IKlZGRk6MEHH1RGRobRpcAgZs3ApYOaacsnl+vCsxpXe1/n9k7S5o8v1+gLW/qgMgAAEAgXnJWsrZ+O0qXnNq32vs7q3kAb516mcSPa+KCymsWsc0G4jwyADADWxhgAMmBONLoAwCSaJMZq8csX6v0p56p353iPt+/evp7efvIcffP6MLVINsdzOAAAsJKkhGh99u8hmjd9sM7q3sDj7Tu3rqtXH+2vlW9drHYt6vi+QAAAAADwA57RBQAmYrPZdPXFrXT1xa20dutvemf+bv20+Tf9vPOwSssqj3tveJhdXdvWU+9O8bpueBv17Zogm81mUOUAAMAXbDabrrigha64oIU2bj+ktz/fpTWbs7Vxx2GVlB4/FwgLtatLm7rq3TlBYy9qpbPPaMhcAAAAAEDQodEFACbVq1OCenVKkCSVlzu1e3+eCovL5XIdfQZX66a1FB4WYnCVAADAX7q3r6/n29eXJFVUOLVnf57yi/47F2jVpJYiwpkLAAAAAAhuNLpgKREREWrXrp0iIiKMLgUGsWoGwsLs6tCyjtFlAAAAg4SG2lmOUNadC+K/yADIAGBtjAEgA+ZEowuW0qJFC82aNcvoMmAgMgAAAGBdzAVBBkAGAGtjDAAZMCe70QUAAAAAAAAAAAAA3qDRBUvZsWOH+vfvrx07dhhdCgxCBgAAAKyLuSDIAMgAYG2MASAD5kSjC5bicrlUXl4ul8tldCkwCBkAAACwLuaCIAMgA4C1MQaADJgTz+gCaqKICIXOfcfoKjzDAxwBAAAA3+GawPKio0JVsPo6o8vwSHQUHzMBgK9wHgDzQfeRPKAGstlsUmSk0WUAAAAAMAjXBLDZbIqJDjO6DACAQTgPgPmg+1i6EAAAAAAAAAAAAEGJO7pgKc2bN9fs2bPVuHFjo0uBQcgAAACAdTEXBBkAGQCsjTEAZMCcaHTBUiIjI9WqVSujy4CByAAAAIB1MRcEGQAZAKyNMQBkwJxYuhCWkpmZqaeeekqZmZlGlwKDkAEAAADrYi4IMgAyAFgbYwDIgDnR6IKl5Obmav78+crNzTW6FBiEDAAAAFgXc0GQAZABwNoYA0AGzIlGFwAAAAAAAAAAAIISjS4AAAAAAAAAAAAEJRpdAAAAAAAAAAAACEo0umApdrtdPXr0kN1O9K2KDAAAAFgXc0GQAZABwNoYA0AGzImfJizF6XRqw4YNcjqdRpcCg5ABAAAA62IuCDIAMgBYG2MAyIA50egCAAAAAAAAAABAUKLRBQAAAAAAAAAAgKBEowsAAAAAAAAAAABBiUYXLCUuLk5Dhw5VXFyc0aXAIGQAAADAupgLggyADADWxhgAMmBOoUYXAARS48aN9cQTTxhdBgxEBgAAAKyLuSDIAMgAYG2MASAD5sQdXbCU0tJS7d+/X6WlpUaXAoOQAQAAAOtiLggyADIAWBtjAMiAOdHogqXs3btXo0aN0t69e40uBQYhAwAAANbFXBBkAGQAsDbGAJABc6LRBQAAAAAAAAAAgKDEM7qAGsjlcknBdvtsRIRsNpvRVQAAAACmwDUBXC6XioorjC7DI9FRoWTARxgDQAbAeQCMA+6j0QXURKWlqhg9zugqPBI69x0pMtLoMgAAAABz4JrA8oqKKxR75rtGl+GRgtXXKSY6zOgyzIExAGTA8jgPgHHAfSxdCAAAAAAAAAAAgKDEHV2wlPbt2+unn34yugwYiAwAAABYF3NBkAGQAcDaGANABsyJO7oAAAAAAAAAAAAQlGh0wVLS0tJ04403Ki0tzehSYBAyAAAAYF3MBUEGQAYAa2MMABkwJ5YuhKUUFxdry5YtKi4uNroUGIQMwIqyDxVr3TaHdv2ap/zCcklSYXGF1m1zqHPruooIDzG4QgD+VF7u1LZfcrRh+yHlFx0dAwqKyjV/eZp6doxXowbRstlsBlcJBAZzQZABkAFryvytSOu2ObRn//HXRBu3H1KnVnUVFsa9AFbBGAAyYE40ugAAMKGd+3L1yrxUffT1Pu3PKjzh9SP5Zeo15nOFhdrVu3O8bh7VTldd2FJRkUwNADMoK6/UZ8vS9Oq87frh52yVlFYe93puQblGTFgqSUqMj9Jlg5rpjqs6qEvbekaUCwAA4HPb9uTo5bnb9ck3+5SRXXTC60fyy9Rj9GeKCA/RmV0TdMuo9hp1fnO+CAgAQYhPswAAMJHUX47o3mdXa8kPB9x6f3mFUz9szNYPG7M1cfpPmjC2k/5vfFeFh3FxBwSjykqnZnywTVPf2qQsh3vfUMxyFOuVedv1yrztOrtHQ/1rUl/16pTg50oBAAD8Y+P2Q/rbtDVanpLp1vtLyyq1Ym2WVqzN0l+fjdR947rob9d1Vmgod3kBQLBgxAYAwAQqKpya+ubP6jH6M7ebXP/rcG6pHntpvXr/Zb42pDp8XCEAf9ux94jOuWGR7p22xu0m1//6bsNBnXnNAj30wlqVllWefgMAAIAaoqy8Uo+/vF69r/7c7SbX//otp0R/fz5FZ123QFt35/i4QgCAv9DogqUkJSXp8ccfV1JSktGlwCBkAGaUX1imobcv0f8975sPpjftPKw+Y+dr1oJdPqgOQCAsXPGrelz1mX7YmF3tfVVWuvSPN37W2eMWypFT4oPqgJqDuSDIAMiAOeXklWrwTYs1+eUNqqhwVXt/KVscOuOqz/Tx13t9UB1qEsYAkAFzotEFS6ldu7aGDRum2rVrG10KDEIGYDaFReUaevsSfbMmw6f7rahw6bqHVurNT3f6dL8AfO/z5Wkaee9SFZf49g6stVsdOvfGRTp0hGYXzIO5IMgAyID5HMkr1Xk3Ldb3Gw76dL9l5U6Nvn+55i75xaf7hbEYA0AGzIlGFywlJydH8+bNU04Ot59bFRmAmbhcLo2ZtNwnd3CczM2Pf6cvv0v32/4BVM9Pm3/T6PuW+eSby1XZuueIht/9tSoqnH7ZPxBozAVBBkAGzKWy0qmR936jDdsP+WX/TqdL1zywQqvWZfll/wg8xgCQAXOi0QVLOXjwoKZNm6aDB337LR8EDzIAM5n5yU4tXLnfo21SZl+q/V+PUcrsS916v9Pp0vjJq5STV+pNiQD8qKS0QuMeXqGycvebUJ6OAZL048/ZevatTd6UCNQ4zAVBBkAGzOXf72/Vtx4+j8vT+VB5hVPXP7JShUXl3pSIGoYxAGTAnGh0AQAQhH7NLNDfpq/xeLvE+GglN4xRYny029tkZBfp3mc9PxYA/3rspfXavjfXo228GQMkafLLG7R552GPtgEAAPCnnfty9dCMdR5v58186Jf0fD3wwlqPjwUACAxLNLocDocmTZqk1q1bKzIyUk2aNNGECRNUWFio8ePHy2az6cUXXzS6TMDnVjiyFb5grp7bs/2k7wlfMFeXrVkVwKoA+MLTr29UfmHgvlH4zvxd2ro7eG/r37LrsCY886Mcvz9r6HBuqeYvT1NlJcuxWYHT6dLS1Qc07qEVcuQczcCR/DKt3fqbwZV5L/O3Ij03a0vAjlde4dQj//H8gyQAxuOaAE/f01OuTeN1w2Vtqnx9+cyLVLL2enVqXTfAlSEQzDwGPPbSepWU+vYZpafy4uxt2ncgP2DH8xUzZwDu4TwAK4wDpm90bdy4UV26dNG0adOUlZWljh07qry8XC+88IKuuuoqpaamSpK6d+9ubKEAALgpN79M7y3cE/Djvjw3NeDHrK7dv+bp3BsXqcuoT/XCB9tUWna0sVVcWqkRE5aq5UVzNedLHi5tZl9+l64OIz7W+bd8qXcX7Fbp78v8FRZXqPdf5qvP1Z9ro5+e6eBPr3+8w2/P5TqZBSv2a39WQUCPCQCovskvbdDmXYf13H191bjh8Xew/PWaTjq3d5Iee2l9UH+pCdaT5SjSx0v3BfSYLpf02kc7AnpMwBc4D8AKTN3ocjgcGj58uLKysjRx4kRlZmZq/fr1ysrK0tSpU7Vo0SKlpKTIZrOpa9euRpeLAIiOjlbfvn0VHe3Zcj0wDzIAM3h3wS4VlVQYcNzdyi8sC/hxvbVl12H1u3aBVqw9+YOjf80s1JhJy/Xi7G0BrAyB8uHiPbrk7q+0M+3ky/ulbHFowPUL9f2G4FmfvaLCqdc+Ovk38fzF6XTx4Q6CHnNBWDED5RVOjXt4pWKiwjRz8oBjv9+2eW09fXcvrd6UrWlvbzawwsCyYgbMaOYnO1VeEfjVGd74ZIdKywJ3Fxl8z4pjAOeB41kxA1Zg6kbXPffco/T0dN11112aPn264uLijr02adIkdevWTRUVFWrevLlq1aplYKUIlKZNm2rGjBlq2rSp0aXAIGQAZrD4u3RDjptfWK4fNmYbcmxPFRSV66I7vzq2TN3p3PPMj1q6+oCfq0Igrd/m0HUPrVRl5enveiooqtCl93ytLEdRACqrvs27DutAtjG1GjX+AL7CXBBWzcCG1EOaMvNnXdg/WTePaie73aZ3nz5HNps07uGVcjoDe5ewkayaAbNZ/L0xc5Lfckq0PtVhyLHhG1YdAzgP/JdVM2B2pm10paamas6cOYqPj9eUKVOqfE/Pnj0lSd26dTv2ex999JFGjRqlZs2aKTo6Wu3bt9dDDz2kggKWaTGDyspKFRQUqLLSWt++KaqslKO0tMpfVmPVDMA8XC6X1m0z7sLKyGN74v1Fe7Q/q9Dt97tc0rNvbfJjRQi052Zt8ehbvodzS/X6x8Fxt9K6bcYttbhp52G+xYygZuW5INcER1k5A0++tkEbtx/S9Il9NOOBfurbpYEemrFOO/ed/M5nM7JqBsw0BlRWOrUh1bj5kJFzseowUwaqw6pjgMR54A9WzoCZx4FQowvwl9mzZ8vpdGrs2LGKjY2t8j1RUVGSjm90TZ8+XU2bNtU//vEPJScna+PGjXr88ce1YsUKrVy5Una7aXuDlrBr1y5dd911evfdd9W+fXujywmYJ3Zs1RM7thpdRo1g1QzAPNIPFir7sHt3KflDMFzUuVwuvTTH8+eJff1jhnbuy1Xb5rX9UBUCKftQseZ9tdfj7V6dt10PjO+m0NCaPd8zsuFcXuHUlt056tkx3rAagOqw8lyQa4KjrJyBigqXxj28UimzL9UdV3XQqvVZev69LUaXFXBWzYCZxoAd+3INWcr9D2u3BseX//6XmTJQHVYdAyTOA3+wcgbMPA6YttG1bNkySdKgQYNO+p709KO3Of+50bVgwQIlJCQc+++BAwcqISFBY8eO1XfffadzzjnHTxUD/nNT05Ya1ahJla8NW70iwNUAqI70g+7fpWTG47vjt8Ml2rTzsFfbLl19gEaXCaxan6Wycs+f2XAgu0ipvxxRl7b1/FCV7xj97zD9YCGNLiAIcU0AScotKFNpWaXCw0L0xar9cllnpSrLM9MYYPRc6EB2zb8mqoqZMgDvcR6wNjOPA6ZtdKWlpUmSmjVrVuXrFRUV+v777yUd3+j6c5PrD7169ZIkHTjg3bM7evXqpaysLK+2xaldccUVHr0/O/vos2UWL16sdevWubXNyJEjPa6ruqLsdm3r3s9n+2sdG6vzEhr6bH9Vadu2rYqdgX8QrFkzAP/IrPM3yV5bmVmZSk5ONrocr5SGNpdq3VDlaymzL1Vi/KkfppoYH3Xsf/d/Peak78tyFKn3X+af8PsbNm5ScvId7hdsgAp7PanOBK+2feDhJ/SP+77zcUU1ixn+HZxOYXh3Kda7sXvwBRcromK/bwvyMUfctVJY6ypfO9044O4YIJ18HLhh/C2KLgvebwFa4d+A1XgyH/RmLihxTeCuYLgmCKYMOBUm1XvYp/t864kBCg8L0bY9OXr4lu6au2SvfknP99n+27RtK7vKfbY/dwTimlAKfAYYA06uOKytFDe2ytcCcU20ctUPSk6+2YOKvUMG3Md5wH1mPA9I5s2AFcYB55/ee/bZZ2vDhg1eHde0ja7CwqPfriguLq7y9Tlz5sjhcCguLk4tWrQ45b6WL18uSerQoYNXtWRlZXndJMOp/fFzdtcfeSguLnZ7WyN+dtEhIVL3gB+2WjIyMlRkwNq2Zs0A/CSuUrJLzsrK4P25RkdKtap+KTE+WskNY9zaTWiI3e33/ll5WUnN/7sLLZDqeLdp3pFs5R2q4X++6jLDv4PTqZ0kVb1y9Wk5DqZLJTX876VZoRRW9UvujgPejgGSlHMoWzl5Nfzv6FSs8G/AYjyZD3ozF5S4JnBXMFwTBFMGZAuXfHiT8d1Xd9SgPo304Atr9fnyNK2fc5nefGKAzr3xC58dIzMjQ3KV+Wx/7gjENaEU+AwwBpxCbB0pruqXAnFNVFZaFJA8kAH3cR5wj1nPA5J5M2C1ceDgwYNeH9e0ja7ExETl5ORo/fr16tfv+K5nZmam7r//fklS165dZbPZTrqfAwcO6JFHHtHQoUPVvXt3r2uBf8TEeDYh+WPwioqKcnvbxo0be1xXdUUF4bPgGjVqZMi3dsyaAfhHZkiInJLsISFKCtKfa4U9Sic77Wc5ik67fWJ8lEJD7KqodCrLUfWXQU61r8jQMtWv4X93Ltl0sPKwKkM8uCJwuSSbTQkx+QqPrNl/vuoyw7+D06mwF+ng7z9TT9icRUqqHyKbavbfS05EpU72r/1044C7Y8Cp9hVfN0IRcTX77+hUrPBvwGo8mQ96MxeUuCZwVzBcEwRTBpwKU6aP9tW6aS1NmdBLP23+TVPf3CSn06XJL6/XlAm9dffVHTXjg20+OU5So0YB/yZ/IK4JpcBngDHg5MpCIvXbSV4LxDVRVFiF6gUgD2TAfZwHTs/M5wHJvBmwwjjgdDqVmXk06Q0ben+3mWkbXUOGDFFqaqqmTp2q888/X23btpUkpaSk6Nprr5XDcfTBkadqXhUUFGjEiBEKDw/Xm2++6XUta9eu9XpbnFpKSopH76+oqND111+vuLg4hYa6F//nn3/ei8qqx1VSoorR4wJ+3OrYuXOnbJGRAT+uWTMA/0geMlsHsouUlJik9C3pRpfjFZfLpXpnv6cj+Sd+Q6qqZTX+1/6vxyi5YYyyHMVqcv6HHh9/0t1j9Pidz3q8XaBNe2uTJv3Lg/HBZlPfLgla/b5nY0owMsO/A3dcevfXWrDiV4+2mXhDX02buM8/BfnQfz7cprv+8WOVr51uHKjuGGC325SW+p2io4L3MsIq/wasxJP5oDdzQYlrAncFwzVBMGWgsKhcsWe+W+392GzS20+eoxC7TeMeXiGn8+gDWZ59a7MuP6+5pkzopUUr9/tk6apdO3cqJvoktx37SSCuCaXAZ4Ax4OTKyisVd+a7VT6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      "text/plain": [
       "<Figure size 2210.55x1120.39 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "22538f79-9b8e-4ce8-b822-049fb74ec8d4",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}