Constrained Mixers solution.ipynb

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   "cell_type": "markdown",
   "id": "826047ba-aa6b-44d2-b43e-d924b59512d6",
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   "source": [
    "# Exercise 1: Max 4-Cut\n",
    "\n",
    "1. <u>Problem Definition</u>\n",
    "\n",
    "The Max 4-Cut problem is defined on a graph $ G = (V, E) $, with a corresponding problem Hamiltonian given by:\n",
    "\n",
    "$$\n",
    "H_P = \\sum_{e \\in E} w_{e} H_{e},\n",
    "$$\n",
    "\n",
    "where $ w_e $ represents the weight of edge $ e \\in E$, and $ H_e $ is the Hamiltonian associated with that edge.\n",
    "\n",
    "2. <u>Generic Graph Problem</u>\n",
    "\n",
    "In this exercise, the class `GraphProblem` from the `qaoa.problems` module is used to define the problem. The class requires two inputs:\n",
    "\n",
    "1. A networkx graph $G$,\n",
    "2. The number of qubits per vertex/node.\n",
    "\n",
    "The `GraphProblem` class includes a method to create a quantum circuit for implementing the phase separating Hamiltonian $e^{-i\\theta H_P}$. \n",
    "\n",
    "3. <u>Specific problem implementation</u>\n",
    "\n",
    "However, `GraphProblem` relies on an abstract method, `create_edge_circuit`, which must be implemented to define the phase separating Hamiltonian $ H_e $ for an edge.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7a02a36d-a236-4003-94f4-168a86bb563c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "\n",
    "from qaoa.problems import GraphProblem\n",
    "\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.circuit.library import PhaseGate\n",
    "\n",
    "class Max4Cut(GraphProblem):\n",
    "    def __init__(self, G: nx.Graph ) -> None:\n",
    "        \n",
    "        N_qubits_per_node = 2\n",
    "        super().__init__(G, N_qubits_per_node)\n",
    "\n",
    "        # each color is associated with a bitstring combination\n",
    "        self.colors = {\n",
    "            \"color1\": [\"00\"],\n",
    "            \"color2\": [\"01\"],\n",
    "            \"color3\": [\"10\"],\n",
    "            \"color4\": [\"11\"],\n",
    "        }\n",
    "        # Create a dictionary to map each index to its corresponding set\n",
    "        self.bitstring_to_color = {}\n",
    "        for key, indices in self.colors.items():\n",
    "            for index in indices:\n",
    "                self.bitstring_to_color[index] = key\n",
    "\n",
    "    def create_edge_circuit(self, theta):\n",
    "        qc = QuantumCircuit(2 * self.N_qubits_per_node)\n",
    "\n",
    "        qc.cx(0, 2)\n",
    "        qc.cx(1, 3)\n",
    "        qc.x([2, 3])\n",
    "        phase_gate = PhaseGate(-theta).control(1)\n",
    "        qc.append(phase_gate, [2, 3])\n",
    "        qc.x([2, 3])\n",
    "        qc.cx(1, 3)\n",
    "        qc.cx(0, 2)\n",
    "            \n",
    "        return qc\n",
    "\n",
    "        \n",
    "    def create_edge_circuit_fixed_node(self, theta):\n",
    "        # we will not use this function, so we can skip it\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a963bf0b-cc09-4a90-a596-e326084b50a4",
   "metadata": {},
   "source": [
    "Show the circuit for one edge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a5c3ebd0-1024-4641-bc13-4913d99d533d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph contains nodes with one or zero edges. These can be removed to reduce the size of the problem.\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 789.163x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test = Max4Cut(nx.Graph([(0, 1, {\"weight\": 1.0})]))\n",
    "test.create_edge_circuit(0.2).draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2760a972-782e-4e62-9b4c-df0336012175",
   "metadata": {},
   "source": [
    "4. <u>Graph instance</u>\n",
    "\n",
    "Let's start by defining a Graph with 10 nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4437afee-5817-472d-ae4a-c601521ff57a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "# Create a graph with 8 nodes\n",
    "G = nx.Graph()\n",
    "# Add nodes\n",
    "G.add_nodes_from(range(8))\n",
    "# Add edges (example connections)\n",
    "edges = [\n",
    "    (0, 1), (0, 2), (1, 3), (1, 4), (2, 4), (2, 5),\n",
    "    (3, 6), (4, 7), (5, 6), (6, 7), (7,3), (3,5)\n",
    "]\n",
    "G.add_edges_from(edges)\n",
    "\n",
    "# Draw the graph\n",
    "plt.figure(figsize=(3,3))\n",
    "nx.draw(G, with_labels=True, pos = nx.circular_layout(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75e31011-cf89-48a1-b7e6-aa56c45bfa51",
   "metadata": {},
   "source": [
    "5. <u>Problem instance</u>\n",
    "\n",
    "Now we can instantiate a Max4Cut problem with the graph and create and draw the resulting circuit for the phase separating Hamiltonian. Observe that there is one circuit per edge in the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "847155b6-6b3d-4fb6-bd58-00e2627be7cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1494.51x1371.22 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max4cut = Max4Cut(G)\n",
    "max4cut.create_circuit()\n",
    "max4cut.circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d49eaaff-8dfd-4eb2-851f-6d64b11d6453",
   "metadata": {},
   "source": [
    "5. <u>QAOA instance</u>\n",
    "\n",
    "We create a QAOA instance using\n",
    "- as initial state we use the $\\ket{+}$ state,\n",
    "- as mixing operator the $X$-mixer, and\n",
    "- as phase separation operator our newly created max4cut instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4522ed40-8b43-4436-aee9-f2d2788cb3a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qaoa import QAOA\n",
    "from qaoa.initialstates import Plus\n",
    "from qaoa.mixers import X\n",
    "from qiskit_algorithms.optimizers import COBYLA\n",
    "\n",
    "settings = {\"maxiter\": 100, \"tol\": 1e-3, \"rhobeg\": 0.05}\n",
    "optimizer = [COBYLA, settings.copy()]\n",
    "\n",
    "qaoa_k4 = QAOA(initialstate=Plus(), problem=max4cut, mixer=X(), optimizer=optimizer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e84c9d1-e1f2-41b2-a277-8563f730df4b",
   "metadata": {},
   "source": [
    "5. <u>Run QAOA</u>\n",
    "\n",
    "- Sample the cost landscape and plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "07fa0ec9-dbd2-4a1f-bc33-3307fb332a6a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2m2024-11-26 14:28:20\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mCalculating energy landscape for depth p=1...\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:20\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mExecuting sample_cost_landscape\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:20\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mparameters: 2                 \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:20\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mDone execute                  \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:27\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mDone measurement              \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:27\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mCalculating Energy landscape done\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot_functions import *\n",
    "qaoa_k4.sample_cost_landscape( angles={\"gamma\": [0, np.pi, 20], \"beta\": [0, np.pi/2, 10]} )\n",
    "plot_E(qaoa_k4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00153aed-f8d6-4aaa-a11e-ebc377a8c1e1",
   "metadata": {},
   "source": [
    "- Use a local optimizer to find the optimum for $p=1$. We converge quickly to the local optimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d0952185-a46a-4b44-a7d8-4ef85c7ff1e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2m2024-11-26 14:28:28\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 1 = -10.775390624999991\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qaoa_k4.optimize(depth=1)\n",
    "\n",
    "fig = plt.figure(figsize=(6, 6))\n",
    "gamma = []\n",
    "beta = []\n",
    "angles = qaoa_k4.optimization_results[1].angles\n",
    "for i in range(len(angles)):\n",
    "    gamma.append(angles[i][0])\n",
    "    beta.append(angles[i][1])\n",
    "plt.plot(gamma, beta, \"x-k\")\n",
    "plt.plot(gamma[0], beta[0], \"wo\")\n",
    "plt.plot(gamma[-1], beta[-1], \"or\")\n",
    "plot_E(qaoa_k4, fig=fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be6243e1-bae5-4b94-8faa-9e23f0df7e22",
   "metadata": {},
   "source": [
    "- Run QAOA up to depth $p=5$. We can see how the approximation ratio increases with $p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "00f0f797-f0a6-4cfc-9953-4ec89a9b7b71",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2m2024-11-26 14:28:32\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 2 = -11.375000000000007\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:36\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 3 = -11.568359375000005\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:43\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 4 = -11.631835937500007\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:49\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 5 = -11.710937500000004\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "maxdepth = 5\n",
    "qaoa_k4.optimize(depth=maxdepth)\n",
    "\n",
    "p = np.arange(1, len(np.array(qaoa_k4.get_Exp())) + 1)\n",
    "maxval=12\n",
    "plt.plot(p, -np.array(qaoa_k4.get_Exp()) / maxval, marker=\"x\")\n",
    "plt.xlabel(\"depth\")\n",
    "plt.ylabel(\"Approx. ratio\")\n",
    "plt.title(\"QAOA Max 4-Cut\")\n",
    "plt.ylim([0, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04d65a0c-9460-470b-b2de-a2f1ce8a4d79",
   "metadata": {},
   "source": [
    "# Exercise 2: Max 3-Cut using the full Hilbert space\n",
    "\n",
    "1. <u>Find the circuit with pen and paper</u>\n",
    "\n",
    "Given $\\operatorname{clr}^3_{< 3}$ we now want to devide the states into the following sets (containing power of two states),\n",
    "- set one consist of $\\ket{0000}, \\ket{0101}$, and\n",
    "- set two consists of $\\ket{1010}, \\ket{1111}, \\ket{1011}, \\ket{1110}$.\n",
    "  \n",
    "Apply Theorem 1 from [[1]](#1) and work out what the circuit for an edge should look like, using pen and paper. \n",
    "\n",
    "Are there any gates that cancel?\n",
    "\n",
    "2. <u>Specific problem implementation</ul>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e6e59cd9-23e5-4233-b570-3f8350197170",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Max3CutFullH(GraphProblem):\n",
    "    def __init__(self, G: nx.Graph ) -> None:\n",
    "\n",
    "        N_qubits_per_node = 2\n",
    "        super().__init__(G, N_qubits_per_node)\n",
    "\n",
    "        self.colors = {\n",
    "            \"color1\": [\"00\"],\n",
    "            \"color2\": [\"01\"],\n",
    "            \"color3\": [\"10\", \"11\"],\n",
    "        }\n",
    "        # Create a dictionary to map each index to its corresponding set\n",
    "        self.bitstring_to_color = {}\n",
    "        for key, indices in self.colors.items():\n",
    "            for index in indices:\n",
    "                self.bitstring_to_color[index] = key\n",
    "\n",
    "    def create_edge_circuit(self, theta):\n",
    "        qc = QuantumCircuit(2 * self.N_qubits_per_node)\n",
    "        \n",
    "        qc.cx(0, 2)\n",
    "        qc.cx(1, 3)\n",
    "        qc.x([2, 3])\n",
    "        phase_gate = PhaseGate(-theta).control(1)\n",
    "        qc.append(phase_gate, [2, 3])\n",
    "        qc.x([2, 3])\n",
    "        qc.cx(0, 2)\n",
    "        phase_gate = PhaseGate(-theta).control(2)\n",
    "        qc.append(phase_gate, [0, 2, 3])\n",
    "        qc.cx(1, 3)\n",
    "        \n",
    "        return qc\n",
    "\n",
    "    def create_edge_circuit_fixed_node(self, theta):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "027b569d-4de7-4a5f-9e2a-0c2d2d3b671d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph contains nodes with one or zero edges. These can be removed to reduce the size of the problem.\n"
     ]
    },
    {
     "data": {
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Wt26jpnKa/EUyN1aOJUeRkZHeLsctCgIHSKHX1qpv/0uGqkF53fhdAYA71IfzQF3WauF+mcx+KreXKzKy6ouOuHCFDeKlhjfWqu/Q4SMUaMtybUE1EBERoQ0bNtSqr88G+oiICB0/flybNm1SQkJCpWU5OTmaNWuWJCkuLs7tN75aLBYdPHjQrduosbByySzZy8vrTk2u1vSwFFq7rkctWVLpEdfWAwB1SX04D9RhrU4P7XQ4+Pm7U+M2UtW3UJ6X9fBBqcRYvxufDfTDhg1TWlqann32WQ0fPlwxMTGSpJSUFE2cOFFWq1WSZx4oFRER4fZt1FSOn5/sksx+fmrdtq23y3GLMr8iHZEkh0Ny4s2a2V6giBZBMsk3fy4AINWP80Cddvq8ZDKpLT9/t7GZi3VYcjoLmOzFimjuJ7MXssCF5EWfDfSJiYl6//33lZWVpR49eqhbt24qKSnRnj17dM011ygqKkpfffVVpfHz7lLbj0/cIXLYUh08UqTWEa2VvT3b2+W4zeBJK/TT5sNO9XloyiA9NX2GmyoCgLqhvpwH6qr+n0t2SX5mvzOTc8A9rrnnK3251rmf8fSJffXig/vcVJH7+OwdoJGRkUpOTtaIESMUFBSkzMxMNWvWTIsWLdLKlSuVnl4xLZEnAj087/5bejjVPijQT1PGdHVTNQAAwNOczQIB/mbdM66bm6pxL5+9Qi9J3bt314oVK856vaCgQJmZmTKbzbrooou8UBncbfTwjpp560V6Ycn287Y1m03699zL1aFN2HnbAgAAY7hqUKTm/Lm3/v7PzedtazJJbz4xWF07NnF/YW7g04G+Ojt27JDD4VBMTIxCQkLOWv7RRx9JklJTUyv9PyoqSn379vVcobggz8/sr6aNAvXEos0qLat6TtnwpkF6+8nBGnFZew9XBwAA3G3OPb3VOKyBZi/YUO1Dppo2aqB/zblUo4e7d9ZDd6qXgX7btm2Sqh9uM3bs2Cr/P2nSJL399tturQ2uYzKZ9Lcp8bp7bDe99Wm6/v1FhrbtzpXdLjUIMGvx3wdrzPAoBQXWy90AAACfZzKZ9MDEi3Tb9V30zme79e6KPdqy69iZLPDPRwfp5qs7KTjI2FnAZ8fQn8v5Ar3D4ajyizBvTOFNgzTr9jht+fBGtQ6v+ESmRdMg3XJdNGEeAIB6oGmjQN0/8SJtTLqhUha4/YYYw4d5iUDv5UoAAACAC2P8tyS1sHr1am+XAAAAALhEvbxCDwAAAPgKAj0AAABgYAR6AAAAwMAI9AAAAICBEegBAAAAAyPQAwAAAAZGoAcAAAAMjEAPAAAAGBiBHgAAADAwAj0AAABgYAR6AAAAwMAI9AAAAICBEegBAAAAAyPQAwAAAAZGoAcAAAAMjEAPAAAAGBiBHgAAADAwAj0AAABgYAR6AAAAwMAI9AAAAICBEegBAAAAAyPQAwAAAAZGoAcAAAAMjEAPAAAAGBiBHgAAADAwAj0AAABgYAR6AAAAwMAI9AAAAICBEegBAAAAAyPQAwAAAAZGoAcAAAAMzN/bBQA4m8PhUFGxzdtlOCUk2F8mk8nbZcBHsA8AQM0R6IE6qKjYpoYDl3i7DKcUrL9VoSEB3i4DPoJ9AABqjiE3AAAAgIER6AEAAAADI9ADAAAABkagBwAAAAyMQF+P2Gx22R0Ob5cBAPASu91x5jzg4HwA+AxmufFRDodDyRst+nrdQW3YYdXGtGOyHi85szznaJGu/vOX6tsjXFcmtNXgPhFMtwYAPiYj66SWfZupDalWbUy1KiMr/8yynKPFumTicvWJDdeg+Ja64YoOCgokFgBGxJ7rY4qKbXrrs3S9mpSm1Iy8atvZHdJX/z2or/57UE/961fFdm6ie8Z11x03xCgkmD8LADAqh8OhlT9m6ZUP0vTl2uzq20la9+sRrfv1iBYuTVXzJoGafGOMpt4cq/atG3quYAAXjCE3PiR5o0VxY5Zp2tPrzhnmq5Kakaf75q5T3JhlSt5ocU+BAAC3Oni4UNdN+1oj7/vmnGG+KsfyTum5t7Yp9oaP9coHqbLbGZIDGAWB3geUl9s164VfNOSOlZU+Tq2NjKx8Dbljpf4672eVl9tdVCEAwN0++nqfevxxmb5Idi7I/15hsU3Tnl6nYXet0pFjxS6qDoA7EegNzmaza8LD32veO9vkqvubHA7phSXbNeHh72WzEeoBoK57/aOdGjdrtU7kl7psnWtScjT4tpXKthS6bJ0A3INAb2AOh0OT5yQr6ct9bll/0pf7NHlOMjMhAEAd9u+Ve3T3E2tddlHnt9L3n9Dwu1dVmlQBQN1DoDewxcvStWT5HrduY8nyPXrzk3S3bgMAUDvpmSd05+M/uXUbO/ed+L83DFzcAeoqAr1BHcgp0F/m/ex0v5Slo5T1zc1KWTqqxn3+Mu9nZVkKnN4WAMB9ysvtuv2xH1VyqtypfrU5Dyz7LlP/+co9nwYDuHD1ItBbrVYlJiYqOjpaQUFBateunWbMmKHCwkJNnjxZJpNJCxcu9HaZTpnx7HrlF5Y53S8iPESRrUIVER5S4z4nC8o049n1Tm8LdcNT0/vIsXWybr+hS5XL1yy+ViUbblOP6KYerqx+KXdIW3Ol73Oknw5LWbxH9hhf3QfeWJau/2454nS/2pwHJGnq0/9VQZHz5x38j7WkYrpQqeLfEufeiwHV8vkJx7ds2aJrrrlGFotFoaGhio2N1aFDh7RgwQJlZGQoNzdXkhQfH+/dQp2wLztfn63Z79Ftfrp6vzIP5iuqbZhHt4sL9/irmzVySHv9468D9PW6gzp4uOjMsvtv6aHL+7XWQy+maMee416s0nedLJWW7a/4OlRUeVnfcGlMlPSH1hLPdXMfX9wHHA6HXvr3Do9u81jeKb3/RYamjOnm0e36gs3HpKR90pqcyoF+xNfSqPbSuI5Sa+feXwGV+PQVeqvVqpEjR8pisWjmzJnKycnRpk2bZLFY9Oyzz2rlypVKSUmRyWRSXFyct8utsX9+mOaWm5/OxeGQ/vnhTs9uFC5RZrNr0iM/KjQ4QIsfH3zm9Zioxnrqvr5av/WInn97mxcr9F3ZhdKkZGlh2tlhXpI2WKWHNkhzNktMKOU+vrgP/LDBorS9eR7f7isfpDGW3klv75buWit9e6jik7rfOlEmvZshjf+hIvQDteXTgX769OnKzs7WtGnTNG/ePIWF/e/qcmJionr16iWbzaaoqCg1atTIi5XWnMPh0LsrMryy7SXL93AgN6jNacc0d/GvumpQpO4a3VVms0lLnrpMJpM06ZEfeYCMG+Sekqauk7JqMOPfF9nS3K3y+Bv1+sTX9oF3V7h3QoTqbE3P1db0XK9s24g+2Fvxhv588sukGeulXSfcXxN8k88G+rS0NCUlJSk8PFxz586tsk2fPn0kSb169Trz2kcffaTRo0erQ4cOCgkJUbdu3fS3v/1NBQV1Y8DrwcNFyjlaxaU+D8g5WqRDR7yzbVy4J1/frC07j2nezP56+eEEDejZUn97eaPSMzmDuMNbu6WDTuwunx2QthtnxIch+dI+8Mu2o17bdsp2q9e2bSR5pdKC1Jq3LyqX5nt2FBV8iM8G+qVLl8put2vChAlq2LBhlW2Cg4MlVQ708+bNk5+fn55++mmtWrVK99xzj1577TVdffXVstu9/5n4xjTvHkg3pHIgNyqbzaFJj/yooEA/3XtTdyVvsujF97Z7uyyfVGyTlh9wvt+HmS4vBb/hK/tAYVGZUr0w3Oa0jZwHamT5AanUydiwwSrtu7AHvqOe8tmbYlevXi1JGjp0aLVtsrMrHo/920C/fPlytWjR4sz/hwwZohYtWmjChAn66aefdNlll7mp4prx9k1bO/Yc1/VDO3i1BtTeiYJSnSotV4MAP32RnMUQDzf5wSIV2Jzv980haXacFOSzR2bv84V9YFfmCa8OEdqRwUdJNbEiq/b97ot1bS3wfSaHjw6KbteunbKzs7V58+YqZ7Cx2Wxq3bq1rFarMjIy1KlTp2rXlZ6erq5du+r999/Xn/70J6dr6du3rywWi9P9qnIi+A8qCK76TUXK0lHnnYYsIjxY/n5m2crtsliLq21nsRap358+P+v1hsU/qnHxd84VXYfkNPmL7ObGMttPqHXeP7xdTrXsClBOs0dcvt7Vb1yjS+JbKSPrpDq0aai40Z9ob7ZrLge1zv1/Mosp7SQpdPg9Crvxb7Xqe+SRAbLnHnRxRcbDPlC9U/4dZG10R5XLPHEeCLAdUsuTi5wruh5qOW+HzCGNne5X/MsnOvH2fW6oCKfV1SwQERGhDRs21Kqvz14HKiysuBOtuLjqg1VSUpKsVqvCwsLUsWPHc65rzZo1kqTu3bvXqhaLxaKDB110gm6VLwVXvej03MI14e9nrnHb3yrIP6mCwwYOG2Hlklmyl5e77nfiDqYGUjPXrvK+8bEa2r+NZi/YoM/W7NempBv05hODdfkdX7hk/TmHDkmOUpesy+hanchTbSd4teTkqMxah/82PYV9oHohIVI18zh44jxQVlZWt4+fdUS43V6rcc1FRYX8fN3NKFnACT4b6CMiInT8+HFt2rRJCQkJlZbl5ORo1qxZkqS4uDiZzjEB9MGDB/Xoo4/q6quvrvVc9REREbXqV5X8oECdrGaZxXr+O/CcuTJTlUYNgxTm37YmpdZJOX5+sksy+/mpddu6+33YFaAcF64vun0jzZ3RV79sO6pn39wqu92hx1/bpLkz+um+8bF6+X0n7tyqRus2bbhC/3+CymswtU0VHGUlatmwgRRYd/82PYV9oHqlfo1U3S2xnjgPNPB3qEUdPn7WFY4TFqmh8w8rCzyVp7b8fN2qrmaBC8mLPjvkZvr06Xr55ZfVrl07ffvtt4qJiZEkpaSkaOLEidq7d6/Kyso0derUap8SW1BQoMsvv1wWi0UpKSlq3bq1J7+FKn2+Zr+un/FtrftnfXOzIluFKvtwodoN/8Dp/p+9NEyjDDyGPnLYUh08UqS2LUOU/a3zw6c8pbCoTA0HLnHJukwmKfnt69Qntrl6j/tUO/dVzOhhNpu0/r2Riu3cxCXDDgrW36rQkABXlGx4JTbp2m+kk05mu+vaSY/3dk9NRsM+UL2iYpvCEpbUehz9hZ4H7hnXTa8+MqhW265P3suQXqzFrDUfXSFFVT2XB1zEKFnAGT47y01iYqKaN2+urKws9ejRQz179lSXLl3Uv39/derUSVdccYWkyjfE/lZxcbFGjhypffv26euvv64TYV6S+sSG1+vtw3kzJ/XUoN6t9Nirm84EGUmy2x267dEf5e9n1ptPDD7HGuCsIH9pZDvn+42JcnkpkO/tAyHB/ort1MRr2+c8UDMj20mBTqas/uGEedSOzwb6yMhIJScna8SIEQoKClJmZqaaNWumRYsWaeXKlUpPT5dUdaAvKyvTmDFjtGHDBq1atUqxsXXndvM2LUPUpqV3ng/tzW2jdrp1bKwnp16sdb8e0QvvnD09X2pGnh5/bZOG9G2t+8bXnb9zX3B7F6m9E8OT/9hB6tHEbeXUW766Dwzo2eL8jdyk/0Xe27aRNG4gPXBRzduH+kt/caI98Fs+O4ZeqriJdcWKFWe9XlBQoMzMTJnNZl10UeW95/Tc9d99952++OIL9e/f31Pl1ojJZNKtI6P1zOKtHt/2pJFdznm/AeqenftOKLjfO+ds88zirV75e/J1TQKlhQnS9PVS5nmeSzeqvZTYs2JoCFzLV/eBW0dGa/En6R7fbny3Zrqoi/PjwuurMVFSSfn5h940DpD+MUCKNsZD61EH+ewV+nPZsWOHHA6HunTpopCQylecp06dqg8//FAPPPCAQkJCtH79+jNfR49678l8v3X3mG4eP/GbzSbdPbarZzcKGFybEOntwdL9PaR2VVytT2ghvdBferSX5F8vj8aorcF9ItSjcxOPb/fecd25sOOkWzpLb10qXd1W8v/dj65pg4pP896/XOrl4lmdUL/Uy1PItm3bJFU93GbVqlWSpGeeeUYJCQmVvlauXOnROqsT1TZMf/xDlEe3eeMVHdShTW0n4gPqr4YBFSf0j6+QllwmnT6fmyS9nCANieDKPJxnMpl0/y2eHZ/RommQxl/b2aPb9BU9m0n/r4/0xZWVjwErh0tTu0utqpmOGqgpAv3vZGZmyuFwVPl12223ebjS6r2YOFCNwxp4ZFuNwxropQcHemRbgK8ym6TYJpVP5sCFuOPGGF3Wx3XTIp/Pq3+7hJmsLlCzwMrHgAZ+3qwGvoRAb1CREaGaP2uA0/0s1iJlHy6s0VzFp72YOEBta/HwEQCA+5jNJr35xGAFBzmXCmtzHhh3VUeNufLcD2EE4D0+fVNsdVavXu3tElzituu76KfNh/WmEzdGVfUY73O548YYTRrVxdnSAAAe0LldI731xGX604NrVNOnyjh7Hojt3ESvMe88UKfVyyv0vsJkMmnRo4M0YYR7xjROGNFZrz82iBugAKAOu+nqTnrj8cFuuReje6cm+mbR1WrWOND1KwfgMgR6g/P3N2vJU0P00OQ4mc2uOZqbzSY9NDlOS54aIj8//kQAoK6748YYLZv/BzVt5Lp7q4YntNGPb41Qm5YMuQTqOtKaDzCbTZo7o59+emeEukY1vqB1dY1qrJ/eGaG5M/q57A0CAMD9brgiSqmfjtb1Q9tf0HrCQgP0+mOD9NU/r1Z40yAXVQfAnerlGHpfldCrlTb/5wa9u2KPXvkgTVvTc2vct1fXZrr3pu6aeF20goP4swAAI4oID9EnLw7T1/89qFc+SNOKHw/UeGx9y2ZBumt0V90zrjsTIQAGQ3LzMcFB/poyppvuGt1V6349om/WHdTG1GPamGZVztEiORwVc163bhGiPt3D1Se2ua68pK0GxrVkrDwA+ACTyaSrBkXqqkGRyjyYr09W79fGVKs2plq1+8BJlZdXJPxGDQMU37W5+sQ216D4Vhp5eXs1CGAeRcCICPQ+ymQy6ZL4VrokvtWZ1xwOh2w2h/z9TYR3AKgHotqG6YGJlR9AVVZml5+fiWGVgA8h0NcjJpNJAQEcwAGgPgsI4PY5wNewVwMAAAAGRqAHAAAADIxADwAAABgYgR4AAAAwMG6KBeqgkGB/Fay/1dtlOCUkmMMJXId9AABqjqMPUAeZTCaFhgR4uwzAa9gHAKDmGHIDAAAAGBiBHgDqqKioKHXt2lXx8fGKjY3VK6+8Um3bsWPHat26dTVe9+7du3XJJZcoJiZG/fr1044dO85qU1JSohtuuEExMTHq1auXhg8frj179pxZPnjwYO3bt8+5bwqAUzgOoCYI9ABQhyUlJWnLli1atWqVZs+era1bt57V5pdfflFubq4SEhJqvN67775bU6ZMUXp6uh588EHddtttVbabMmWKdu3apV9//VXXX3+97rzzzjPLZs6cqTlz5jj9PQFwDscBnA+BHgAMoEOHDuratavS09PPWrZo0SKNHz++xus6cuSINmzYoFtuuUWSNHr0aGVlZVW66iZJQUFBuvbaa2UyVTxheuDAgcrMzDyzfMSIEVq1apVOnDhRi+8IgLM4DqA6BHoAMIBt27Zp586d6tWr11nLvv/+ew0YMKDG68rKylLr1q3l718xL4LJZFL79u114MCBc/Z76aWXdP3115/5f0BAgHr27Knk5OQabxtA7XEcQHWY5QYA6rCbbrpJwcHBCgkJ0ZtvvqkuXbqc1SY7O1utWrU68/+EhATt3r27yvVt3ry5VnU8/fTT2rNnj7777rtKr0dERCg7O7tW6wRQMxwHcD4EegCow5KSkhQfH3/ONiEhISopKTnz//PdFBcYGKicnBzZbDb5+/vL4XDowIEDat++fZXt582bp2XLlunbb79VSEhIpWUlJSUKDg6u2TcDoFY4DuB8GHIDAAYXFxenXbt21bh9y5YtdfHFF+u9996TJH388ceKjIxUdHT0WW3/8Y9/aOnSpfrmm2/UpEmTs5anpaVV+fE/AM/iOFC/EegBwODGjBmjr776yqk+ixYt0qJFixQTE6NnnnlGb7311plld955pz7//HNlZ2dr5syZysvL09ChQxUfH19pjG5mZqbKy8s5kQN1AMeB+s3kcDgc3i4C8JTIYUt18EiR2rYMUfa3f/J2OaiH+n8u2VVxNeWXUa5ZZ0FBgS655BKtW7dOoaGhrllpDTz00EOKjo6uNIUdgHNzxzFA4jjgDF/MAlyhBwCDa9iwoebPn+/xh7u0adNGd9xxh0e3CaBqHAfqN26KBQAf8Ic//MHj25w+fbrHtwmgehwH6i+u0AMAAAAGRqAHAAAADIxADwAAABgYgR4AAAAwMAI9AAAAYGDMcgPUQQ6HQ0XFNm+X4ZSQYH+ZTCZvlwEfwT4AADVHoAfqoKJimxoOXOLtMpxSsP5WhYYEeLsM+Aj2AQCoOYbcAAAAAAZGoAcAAAAMjEAPAAAAGBiBHgAAADAwAj0AAABgYMxyA592/OQpbUo9po2pVu3af0K5J05JkvLyS/XqB6nqExuuuJhmCg5iVwAAwBedyC/VpjSrNqYe0859eWeywPGTpVq4NFV9YpurV0xzhQQbNwsYt3KgGuXldn25NluvfJCmL9dmy+E4u01hsU1Tn14nSQoO8tP4azrr3pu66+LYcA9XCwAAXM1ud+ibdQf1alKaVvyYJbv97DBQVGLTfXMrskBgAz/ddFVH3XtTd/Xv2cJwz5Qg0MOnfLv+oP785FplZOXXuE9xSbkWf5KuxZ+ka2i/1np9zqWKbt/IjVUCAAB3Sd5o0ZQnftLOfSdq3OdUabmWLN+jJcv3aFDvVvrXnEvVvVMT9xXpYoyhh0/ILyzVn59cq+FTvnQqzP/empQcxY1Zppfe217lu3kAAFA3FRXbNOOZdRpyx0qnwvzvrd18WL3Hfarn3tyq8nK7Cyt0HwI9DO/IsWJddvtKLfpwp0vWV1xSrvuf+1mTHvlBZWXG2JEBAKjPck+c0hV3fqEF76dWOdTWWadKy/Xgiyka99c1OlVafuErdDMCPQztWF6JrrjzC23Zmevydb+3IkO3/u0Hw7w7BwCgPjqRX6rhU1bp521HXb7uZd9latxfV8tmq9tZgEAPw7LbHRo7c7V2ZOS5bRsffLlXj7+22W3rBwAAtedwODTh4e+1Ke2Y27bx+fcHlDj/F7et3xUI9DCsV5PStCYlx6k+KUtHKeubm5WydFSN+8xd/Ks27HD9u34AAHBh3v5st1b+mOVUn9pkgRff26HkjRZny/OYehHorVarEhMTFR0draCgILVr104zZsxQYWGhJk+eLJPJpIULF3q7TDhhX3a+Hpyf4nS/iPAQRbYKVUR4SI37lJc7dPujySotq/tj6AAAqC8OHSnUA8//7HS/2mQBh0O6Y06yiktsTm/PE3w+0G/ZskU9e/bU888/L4vFotjYWJWVlWnBggW66aablJaWJkmKj4/3bqFwyrx3tqnIgzvV9j3H9cl3+z22PVd6anofObZO1u03dKly+ZrF16pkw23qEd3Uw5XVH0eKpUU7pdGrpdOjMO2SvsiSTvE+0e3YB+Btdoe09rD0wM+VjwHPbpUyTnqzMmN76d87dCK/1GPb23PgpJau2uux7TnDpwO91WrVyJEjZbFYNHPmTOXk5GjTpk2yWCx69tlntXLlSqWkpMhkMikuLs7b5aKG8gtLtWT5Ho9v99WkNI9v0xUef3Wztu3O1T/+OkBtW1W+GnH/LT10eb/WmvPqJu3Yc9xLFfouu0NakCqN/Fb6V7q0v6Dy8sc2SyO+kdYf8U599QX7ALxpX740do0042cp+XDlZR9mSjd9Lz2YIhXXzQu/dVbJKZsWf5Lu8e2+8kGqHK6YRsfFfDrQT58+XdnZ2Zo2bZrmzZunsLCwM8sSExPVq1cv2Ww2RUVFqVEjHiRkFEtX7VVBUZnHt/vjRovS9uZ5fLsXqsxm16RHflRocIAWPz74zOsxUY311H19tX7rET3/9jYvVuibHA7p6V+lJXuk8nMc+/NKK070Px2uvg0uDPsAvGVfvjT5p7PfzP/edznSfeulEj6xq7GPv83UsbxTHt/uprRj2rDD6vHtno/PBvq0tDQlJSUpPDxcc+fOrbJNnz59JEm9evU681pycrKGDRum1q1bKzAwUJGRkZWG5sD71vzi3I2wrvS9kzfh1hWb045p7uJfddWgSN01uqvMZpOWPHWZTCZp0iM/8hAtN1ieJX16oGZtyx3SwxukYyXurak+Yx+Ap5U7pJm/SCdreP1pS660MNW9NfkSskBl/t4uwF2WLl0qu92uCRMmqGHDhlW2CQ4OllQ50B8/flw9e/bU3XffrZYtWyo7O1tz585VQkKCtm/frsjISI/Uj+ptTPPeO+ONqXXvXXlNPfn6Zo26vL3mzeyv+G7NNaBnS/3l+Z+Vnln7p+mhag6HtNTJYZbF5dJnB6Q7YtxTE9gH4FnrjkgHCp3r8/kB6c/dpIYB7qnJl3g1C3hx29Xx2Sv0q1evliQNHTq02jbZ2dmSKgf6UaNGaf78+Ro7dqyGDBmiCRMmaNmyZTpx4oQ+/vhj9xaN8zpZUKrd+713B1Fd3IlrymZzaNIjPyoo0E/33tRdyZssevG97d4uyyf9mivtrsWf6cf7zz08BxeGfQCe9OE+5/sUlUursl1fi685VVqu7V6858Wdc97Xls9eod+/v2JGkg4dOlS53Gazae3atZIqB/qqNG/eXJLk71+7H1ffvn1lsdTduUuNxGZuIjV5oNrlKUtHnXMaqojw4DP/Zn1zc7XtLNYi9fvT52e9vm3HPo98SmNXgNTsEZev90RBqU6VlqtBgJ++SM5yyeOxT+sSEyOzPH9vQ10UMnSyGo39u9P9DhdLHXv0lv0kzz1gH4DRtXhms/watXC635xFH+iB9/7qhop8R7kpVLamidUud3cW2LPP4pYsEBERoQ0bNtSqr88G+sLCis+5iouLq1yelJQkq9WqsLAwdezY8azl5eXlstvt2r9/vx5++GFFRERo3LhxtarFYrHo4MGDteqL32lgk5pUv/j03LLn4+9nrlG73yu3mzzzuzQ1kJq5frVvPTFYDQL8lJpxXI9Midd/vtqnvdn5Lll3zqFDksNz04fVZRHFpartbfaHj59UqYXjBfsAjK5FQFCt+pV46jxjZP5NpHPMMuvuLOBwmOvc78hnA31ERISOHz+uTZs2KSEhodKynJwczZo1S5IUFxcnk8l0Vv8hQ4acuYIfHR2t1atXq0UL599pn64FrmEzN9a5JgOxWIvO2T8iPFj+fmbZyu2yWKt+s3eu9fiZ7Ypo27YmpV4QuwLk6ltu7hsfq6H922j2gg36bM1+bUq6QW8+MViX3/GFS9bfuk0brk7+n+AGZx9Taqplo2A5/Nz/N1bXsQ/A8EoKpOCw87f7nSBHmdp64DxjZOWmYJ1r3IO7s4DZVK7WbvgdXUheNDnq4mSaLjB9+nS9/PLLateunb799lvFxFTcaZaSkqKJEydq7969Kisr09SpU6t8SuyuXbuUl5enffv26fnnn9eRI0e0du1atW/f3tPfCn7jVGm5wgYuUZnNfv7GVcj65mZFtgpV9uFCtRv+gdP9B1/cSj++fV2ttu2MwqIyNRy4xGXri27fSFs+vEE79uQpYeJy2e0OPTQ5TnNn9NP0Z9bp5fcvfGqFgvW3KjSEO7kkKbtQuvE7ydmDa48m0juXuaMi42EfgNE99av0SS2eRzivn3R5a9fX40vKy+1qMui9Wk9hfaFZoHe35tr0nxtqtW138dmbYhMTE9W8eXNlZWWpR48e6tmzp7p06aL+/furU6dOuuKKKyRVP36+a9euGjBggG6++WZ99913ys/P13PPPefJbwFVCGzgp55dvPc0xz6x4V7bdm2ZTNLbT14mP7NJkx754cz0fM+9tU0p249q7oy+6hTp/FUkVC8yVEpo6Xy/sVEuLwViH4B3jIlyvk+rYOnSVi4vxef4+ZnVu5sbxuTVUJ/Y5l7bdnV8NtBHRkYqOTlZI0aMUFBQkDIzM9WsWTMtWrRIK1euVHp6xdPFzndDrCQ1adJE0dHR2rPH808nxdm8GaqNGOhnTuqpQb1b6bFXN2nnvv9Nz2e3O3Tboz/K38+sN58YfI41oDZu7yKZnRh50z5UGsan7G7BPgBv6NrY+XB+exfJ32eTmWuRBSrz6T+b7t27a8WKFcrPz1d+fr5+/vlnTZkyRYWFhcrMzJTZbNZFF1103vUcOXJEu3btUufOnT1QNc5n5BDvDHsK8DfrygRjJa5uHRvryakXa92vR/TCO2dPz5eakafHX9ukIX1b677xsV6o0Hf1bi491qtmB9lWQdKCgVKQn9vLqnfYB+BN/+/iiqF0NXFLZ2l01RPzoQreygJms0nXXFr3nknkszfFnsuOHTvkcDgUExOjkJDK0xrdcsstio6OVnx8vJo0aaLdu3dr/vz58vf31wMPVD9dIjzn2sGRat86VAdynHxixwUaMzxKLZsHe3SbF2rnvhMK7vfOOds8s3irnlm81UMV1S/XtZeaBEoLUqW9VUykYpY0OEJK7FnxUTtcj30A3tQwQPrnJdL8HdLKLOlUFbd/tQyS7ugijY6qGB6Gmhnav7W6RjXWLg8/GO66y9qpQ5u6N0SvXgb6bdu2Sap6uM3AgQO1ZMkSvfTSSyopKVG7du00dOhQzZ49u9o57eFZfn5m3T2mm/728kaPbveecd09uj34hktbSYNaSptzpW8OSrmnKj5Sbx8qXd9eiqh+qmQAPiDYX5rdS5rWXVqRJe08UfFk6LAAaXCrii+G2TjPZDLp3pu6a8az6z263bqaBQj0vzNt2jRNmzbN0yXBSfeNj9XrH+/S/kMFHtnejX/ooEsv5k4l1I7JJF3cvOILQP3UqIE0npG7LnXX6K56NSnNY1fpr7qkra4aVDeH3tbL94TnCvQwhrDQBnrz7565ia1Z40C99sigKp9XAAAAvCM4yF9vP3mZzM7MQFBLYaEB+tfjl9bZLFAvA/3q1avlcDg0YsQIb5eCC3DFgDZ6YGIPp/pYrEXKPlx43odO/NaiRweplcHGzgMAUB8M7NVSs+907gJtbbLAK7MT1C6iobPleUy9HHID3/H8X/rr8LESvf9FRo3a9/vT506tf+HsBI25smNtSgMAAB7wxNSLZbEW6Y1l6TVq72wWePb+fpo4skttSvOYenmFHr7Dz8+sJU9dpiljurp4vSb9a86lmnoz09gBAFCXmUwmLXrsUt1/i3Of2p+P2WzSgocGKvGOOJeu1x0I9DA8Pz+zFj12qf4z7wqFNw264PXFxTRTyvujdOdo175JAAAA7mE2mzQ/caA+e2mYIsIvfJhst46N9d8l1+m+8a59k+AuBHr4jLFXdtSOZX/U5BtjFBTo/BN6WjYL0pPTLlbK0lHq3b3uPQUOAACc26ihHbTjk9G6Z1w3hQQ5P7K8eZNAPXZ3b23+zw0aENfSDRW6h8nhcDi8XQTgarknTumtT9O1dNVebU3PVZmtiqd5SGoYEqABPVto8o0x+uOwKAU2qBuP6iwsKlPDgUu8XYZTCtbfqtCQAG+XAR/BPgDgQuWdPKUly/fo3ysztGXXMZWWVZ0FQoP91e+iFrr9+i4ad1VHBQUa7xZTAj183qnScm3bnatdmSdUVGyT2WxSo4YNFNelqbp0aOyR6a6cRZhBfcc+AMCVSsvKtWPPcaXuzTuTBRqGBCguppliOjSSn5+xB60Y7y0I4KTABn7q26OF+vZo4e1SAACAFzQI8FPv7uE+O6TW2G9HAAAAgHqOQA8AAAAYGIEeAAAAMDACPQAAAGBgzHID1EEOh0NFxTZvl+GUkGB/mUx1b8YgGBP7AADUHIEeAAAAMDCG3AAAAAAGRqAHAAAADIxADwAAABgYgR4AAAAwMAI9AAAAYGAEegAAAMDACPQAAACAgRHoAQAAAAMj0AMAAAAGRqAHAAAADIxADwAAABgYgR4AAAAwMAI9AAAAYGAEegAAAMDACPQAAACAgRHoAQAAAAMj0AMAAAAGRqAHAAAADIxADwAAABgYgR4AAAAwMAI9AAAAYGAEegAAAMDACPQAAACAgRHoAQAAAAMj0AMAAAAG9v8BJlcW46ZU7kwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 956.385x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test = Max3CutFullH(nx.Graph([(0, 1, {\"weight\": 1.0})]))\n",
    "test.create_edge_circuit(0.2).draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44943119-deb3-42f9-81f4-50b0394dc0a9",
   "metadata": {},
   "source": [
    "3. <u>Run QAOA</u>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "10dc164d-d510-4dc3-a571-9c51bb39bd26",
   "metadata": {},
   "outputs": [],
   "source": [
    "qaoa_k3_fullH = QAOA(initialstate=Plus(), problem=Max3CutFullH(G), mixer=X(), optimizer=optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cc3e014a-b85e-4fec-9f1a-5bbcefa4481c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2m2024-11-26 14:28:49\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mCalculating energy landscape for depth p=1...\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:49\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mExecuting sample_cost_landscape\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:49\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mparameters: 2                 \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:49\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mDone execute                  \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:56\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mDone measurement              \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:56\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mCalculating Energy landscape done\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:28:57\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 1 = -9.689453125000014\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qaoa_k3_fullH.optimize(depth=1, angles={\"gamma\": [0, np.pi, 20], \"beta\": [0, np.pi/2, 10]} )\n",
    "\n",
    "fig = plt.figure(figsize=(6, 6))\n",
    "gamma = []\n",
    "beta = []\n",
    "angles = qaoa_k3_fullH.optimization_results[1].angles\n",
    "for i in range(len(angles)):\n",
    "    gamma.append(angles[i][0])\n",
    "    beta.append(angles[i][1])\n",
    "plt.plot(gamma, beta, \"x-k\")\n",
    "plt.plot(gamma[0], beta[0], \"wo\")\n",
    "plt.plot(gamma[-1], beta[-1], \"or\")\n",
    "plot_E(qaoa_k3_fullH, fig=fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a27b3402-efb3-447c-a33f-b731c17affad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2m2024-11-26 14:28:59\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 2 = -10.17578125   \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:14\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 3 = -10.685546875000004\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:21\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 4 = -10.859375000000016\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:28\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 5 = -11.047851562499995\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "maxdepth = 5\n",
    "qaoa_k3_fullH.optimize(depth=maxdepth)\n",
    "\n",
    "p = np.arange(1, len(np.array(qaoa_k3_fullH.get_Exp())) + 1)\n",
    "maxval=12\n",
    "plt.plot(p, -np.array(qaoa_k3_fullH.get_Exp()) / maxval, marker=\"x\")\n",
    "plt.xlabel(\"depth\")\n",
    "plt.ylabel(\"Approx. ratio\")\n",
    "plt.title(\"QAOA Max 3-Cut using the full Hilber space\")\n",
    "plt.ylim([0, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7024434f-e325-49f3-8eba-1175c8eedab6",
   "metadata": {},
   "source": [
    "# Exercise 3: Max 3-Cut using subspaces\n",
    "\n",
    "1. <u>Show that the Grover mixer is valid using pen and paper</u>\n",
    "\n",
    "$$\n",
    "U_m(\\beta) = e^{-i\\beta \\ket{F}\\bra{F}}, \\quad \\text{where } U_S \\ket{0} = \\ket{F} := \\frac{1}{\\sqrt{|B|}} \\sum_{x \\in B} \\ket{x}\n",
    "$$\n",
    "\n",
    "2. <u>Create circuit for Grover mixer</u>\n",
    "\n",
    "Using the package `qaoa` create a Grover mixer for $\\ket{ltk3} = \\ket{00} + \\ket{01} + \\ket{11}$. For this we import the following:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "477e2b91-1f8f-4659-b445-87064988a4b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425.597x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qaoa.initialstates import LessThanK\n",
    "\n",
    "ltk3 = LessThanK(3)\n",
    "ltk3.create_circuit()\n",
    "ltk3.circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "916a788e-ff03-4241-955f-9026aeb0ac88",
   "metadata": {},
   "source": [
    "Create a circuit for $\\ket{ltk3}^{\\otimes 3}$. For this we can use the Tensor class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2ab2e08b-f5b5-459f-b64b-667ee1cd4c35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 426.001x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qaoa.initialstates import Tensor\n",
    "\n",
    "numNodes = 3\n",
    "phi0 = Tensor(ltk3, numNodes)\n",
    "phi0.create_circuit()\n",
    "phi0.circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20ca4185-8dd9-4563-94e9-d119743fe281",
   "metadata": {},
   "source": [
    "create the Grover mixer for $\\ket{ltk3}^{\\otimes 3}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6b649481-3f46-4888-920b-8c47f826b709",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1094.89x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qaoa.mixers import Grover\n",
    "\n",
    "grover = Grover(phi0)\n",
    "grover.create_circuit()\n",
    "grover.circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75367b7b-d8c0-4244-b24c-5a61e250fa7f",
   "metadata": {},
   "source": [
    "Alternatively, on can create a Grover mixer for $\\ket{ltk3}$ for 3 nodes using the box product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9b4649da-8553-43c0-bde1-9cbf88c58271",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1094.89x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numNodes = 3\n",
    "grover = Tensor(Grover(ltk3), numNodes)\n",
    "grover.create_circuit()\n",
    "grover.circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e3aff5d-6ad7-46ce-b4db-ff89944d1555",
   "metadata": {},
   "source": [
    "3. <u>Numerically test that the Grover mixer is valid</u>\n",
    "\n",
    "Show that we have a valid mixer by plotting the overlap $\\bra{z_1} U_M(\\beta) \\ket{z_2}$ depending on $\\beta$:\n",
    "\n",
    "- Pick two feasible computational basis states $\\ket{z_1} \\neq \\ket{z_2}$ and see that the overlap is nonzero for some values of $\\beta$\n",
    "- Pick a feasible and an infeasible state, and show that the overlap is always zero\n",
    "\n",
    "Let's start by importing the necessary things, before we can do some plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a4f3ed48-3557-41b5-b1f2-837bcd309f09",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as pl\n",
    "from tqdm import tqdm\n",
    "from qiskit_aer import Aer\n",
    "from qiskit import (\n",
    "    QuantumCircuit,\n",
    "    QuantumRegister,\n",
    "    ClassicalRegister,\n",
    "    transpile,\n",
    ")\n",
    "backend=Aer.get_backend(\"qasm_simulator\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8022ef9c-d28d-4eca-b5b0-b1d0f4beac65",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 50/50 [00:05<00:00,  9.79it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7984b970a600>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PvbndfbYQCwvRoOBPJCLy2MXt+Pvs1gkJUEnAgapmVDW1i45D5PdYWIgIANBmsaOs8iIATrjti5hwHXJHupZ9f3CQW/UTDTQWFiICABSXN8HmkJE0NBjDo0JEx/EJ7j1ZPuBqIaIBx8JCRACA3ae7ljOnRUOSJMFpfMO8CfHQqCQcu2DG6bpW0XGI/BoLCxEBuLT/yqxRnL/SV0NCtJ7jC7ZwWIhoQLGwEBHqzJ04UdsCSXKtEKK+W5DpHhaqgSzLgtMQ+S8WFiLyDAdNSDRgaKhWcBrf8p1xcdBqVDhT34bjxhbRcYj8FgsLEV0aDuLutl4L1wfhpjGuYTQOCxENHBYWogAny/KlCbdcznxVbu9aLbTl4AUOCxENEBYWogB3srYVdS0W6INUmJI6VHQcn3Tz2FhoNSqca2zHmXquFiIaCCwsRAFuV9d2/NkjoqDTqAWn8U0hWg2mX+earPzZ8TrBaYj8EwsLUYD7gsNB/WJO1zwWFhaigcHCQhTArHYn9pU3AeCE22s1Jz0OAFBScRHmTpvgNET+h4WFKICVVV5Eu9WB6DAd0uPDRcfxaSlRIRgZEwq7U8aukw2i4xD5HRYWogB2aXfbKG7H3w/mpMcC4LAQ0UBgYSEKYLu65q/M5PyVfnFTV2HZcaIOTieXNxP1JxYWogBV09yBg+ebAQDXp/H8oP4wLTUS4ToNGtusOND1vSWi/sHCQhSg3i07D1kGpl8XiXiDXnQcvxCkVuGG0a7yt53DQkT9ioWFKADJsoy3S88DAO6Zkiw4jX9xDwt9doKFhag/sbAQBaAvKy6iorEdoVo1bs2IFx3Hr9w4JgaSBByuNqPO3Ck6DpHfYGEhCkCbSqoAAPMnJiBEqxGcxr9Eh+kwMWkIAGA777IQ9RsWFqIA02ax48NDFwAA90zlcNBAmDOGy5uJ+hsLC1GA+fiwEe1WB0ZEh2LqcB52OBDc+7HsPtUAi90hOA2Rf2BhIQow7uGg701J4mZxA2R8YgRiw3VoszpQ3HX0ARFdGxYWogBS2diOfeVNkCTg7snDRMfxWyqVhJs4LETUr1hYiALI26WuuyuzRkUjwRAsOI1/cy9v5n4sRP2DhYUoQDidMt4pqwbAybaDYVZaNILUEioa23G2vlV0HCKfx8JCFCCKzjaiurkDEXoNbhkXJzqO3wvTaZAzIgoAh4WI+gMLC1GAcE+2vSMrEfogteA0gcEzLMT9WIiuGQsLUQAwd9rw8WEjAG7FP5jcy5uLy5vQ0mkTnIbIt7GwEAWALQcuwGJ3Ii02DBOTDKLjBIwR0aEYER0Km0PG7lMNouMQ+TQWFqIAsKlrddA9U7n3ymBz32XhPBaia8PCQuTnTte14qvKZqhVEhZO4t4rg22OZx5LPZxOWXAaIt/FwkLk594uPQ8AuGlMDGLD9YLTBJ5pqZEI02nQ0GrB4RqT6DhEPouFhciP2R1OvFvmKizf42RbIbQaFWaNigbAYSGia8HCQuTHdp1qQF2LBZGhWs/QBA2+Odz1luiasbAQ+TH3ZNs7sxKh1fCvuyg3pscAAA6cN6G+xSI4DZFvuqqfYOvWrUNqair0ej1ycnJQXFzc6/WbNm1Ceno69Ho9MjIy8NFHH33rmmPHjuGOO+6AwWBAaGgopk2bhsrKyquJR0QALrZZ8elR1//Rc+8VsWLD9cgY5lpOzk3kiK6O14Vl48aNWLlyJdasWYOysjJkZmZi7ty5qKvr+S/hnj17sHjxYjzwwAP46quvsHDhQixcuBCHDx/2XHPmzBnMmjUL6enp2LFjBw4ePIgnn3wSej0nCBJdrfcP1MDqcGJ8YgTGJUaIjhPwOCxEdG0kWZa9WmeXk5ODadOm4eWXXwYAOJ1OJCcn46GHHsLjjz/+resXLVqEtrY2bNmyxfPc9OnTkZWVhfXr1wMAvv/97yMoKAhvvvnmVb0Js9kMg8EAk8mEiAj+YCYCgNtf2oXD1WY8vWAcfjRzhOg4Ae9AVTPuXPcFwnQalD35HQ7REcG7399e/Y2xWq0oLS1FXl7epU+gUiEvLw9FRUU9vqaoqKjb9QAwd+5cz/VOpxMffvghRo8ejblz5yI2NhY5OTnYvHmzN9GI6GtO17XicLUZQWoJd2Zx7xUlyBhmQHSYFq0WO76qvCg6DpHP8aqwNDQ0wOFwIC6u+0mvcXFxMBqNPb7GaDT2en1dXR1aW1vx7LPPYt68efjkk09w11134e6778bOnTt7/JwWiwVms7nbg4guKTrj2gY+e0QkhoZqBachAFCpJMzsWt68+zS36SfylvB7kk6nEwBw55134he/+AWysrLw+OOP4/bbb/cMGX1Tfn4+DAaD55GczAmFRF+3t7wJAJAzIkpwEvo6934sn/NcISKveVVYoqOjoVarUVtb2+352tpaxMfH9/ia+Pj4Xq+Pjo6GRqPBuHHjul0zduzYy64SWrVqFUwmk+dRVVXlzdsg8muyLGPf2UYAwPTrWFiU5Po01/LmQ+ebYWrn6c1E3vCqsGi1WkyZMgWFhYWe55xOJwoLC5Gbm9vja3Jzc7tdDwDbtm3zXK/VajFt2jScOHGi2zUnT57E8OHDe/ycOp0OERER3R5E5HKmvg0NrVboNCpkJvNkZiWJN+gxKjYMThnYc4Z3WYi8ofH2BStXrsTSpUsxdepUZGdn44UXXkBbWxuWLVsGAFiyZAmGDRuG/Px8AMCKFSswe/ZsrF27FvPnz8dbb72FkpISvPrqq57P+eijj2LRokW44YYbcNNNN6GgoAAffPABduzY0T/vkiiA7Ct33V2ZlDIEOo1acBr6plmjonG6rhW7Tjfg1owE0XGIfIbXhWXRokWor6/HU089BaPRiKysLBQUFHgm1lZWVkKlunTjZsaMGdiwYQOeeOIJrF69Gmlpadi8eTMmTJjgueauu+7C+vXrkZ+fj4cffhhjxozBO++8g1mzZvXDWyQKLHvPuuavcDhIma5Pi8breyqwm/NYiLzi9T4sSsR9WIhcZFlGzjOFqGux4O8/mY7ckSwtStNqsSPrN5/A7pTx+aM3ISUqRHQkImEGbB8WIlK2isZ21LVYoFWrMClliOg41IMwnQaTU4YCAHadrhechsh3sLAQ+ZG9XauDslKGQB/E+StKNSutaz8WDgsR9RkLC5Ef8SxnHhEpOAn1xl1Y9pxphMPp86PyRIOChYXIT8iyjH3uDeM44VbRJg4zIFyvganDhkPVJtFxiHwCCwuRn6hsascFUyeC1JJnjgQpk0atwoyuCdG7T3EeC1FfsLAQ+Yl9XcuZM5OGIFjL+StKN6tr19tdnMdC1CcsLER+Ym/XhnE513H+ii+4vutcobLKi2iz2AWnIVI+FhYiP7GPG8b5lOFRIUgaGgybQ0Zx19wjIro8FhYiP1DV1I7q5g5oVBKmDOf8FV8gSRKu71otxGEhoitjYSHyA+7VQRlJBoRovT5xgwSZNco1j2U3N5AjuiIWFiI/4N4wjsNBvmXGyChIEnCythW15k7RcYgUjYWFyA+4T2jO4YZxPmVoqBYZwwwAuOst0ZWwsBD5uOrmDlQ1dUCtkjA1lYXF18zqWi20+zQLC1FvWFiIfJx7O/4JwwwI03H+iq/xnCt0ugGyzG36iS6HhYXIx3mWM3M4yCdNGT4UwUFq1LdYcKK2RXQcIsViYSHycfu4YZxP02nUyO4qm5zHQnR5LCxEPsxo6kRFYztUEjh/xYe592P5nIWF6LJYWIh8mPvuyvhEAyL0QYLT0NVyz2MpLm9Ep80hOA2RMrGwEPmwvV3zV7ic2beNiQtHTLgOnTYnys5dFB2HSJFYWIh82D5uGOcXJEnyLG/exeXNRD1iYSHyUXXmTpxtaIMkAdN4h8XnefZj4TwWoh6xsBD5KPf5QWPjI2AI5vwVX+eex3K4xoSLbVbBaYiUh4WFyEfx/CD/Ehehx5i4cMgy8MUZ3mUh+iYWFiIf5b7Dwv1X/Idn11sOCxF9CwsLkQ+qb7HgdF0rACCb+6/4DXdh2XWK2/QTfRMLC5EPKu66u5IeH46hoVrBaai/5IyIhFatQnVzByoa20XHIVIUFhYiH+TeMI7zV/xLiFaDycOHAAC+4PJmom5YWIh8kHvCLTeM8z+517mGhYq6/hsTkQsLC5GPaWqz4mRt1/wVFha/kzvSddds39lGzmMh+hoWFiIfU9w1HDQ6LgxRYTrBaai/ZSYboA9SoaHVilNdE6uJiIWFyOe4T/SdMTJacBIaCDqNGlOHu+6cFZ3hsBCRGwsLkQ+RZRk7T9QDAG4YzcLir9zDQiwsRJewsBD5kLMNbahu7oBWreIKIT82vWszwL3ljXA6OY+FCGBhIfIp7rsr00YMRYhWIzgNDZSJSUMQolWjud2G48YW0XGIFIGFhciHfH7KVVhmj44RnIQGUpBahaldOxjv5fJmIgAsLEQ+o9Pm8PzyuoGFxe/ldg35cT8WIhcWFiIf8WVFEzptTsRF6DAmLlx0HBpgX9+PxcF5LEQsLES+4vOTXauD0mIgSZLgNDTQJiRGIEyngbnTjmMXzKLjEAnHwkLkI3a6CwuHgwKCRq3y7GTM5c1ELCxEPuGCqQMna1shScCsUdx/JVBwHgvRJSwsRD7APRyUmTQEQ0O1gtPQYHHPYykub4Ld4RSchkgsFhYiH/D5Sdd2/BwOCixjEyIQodeg1WLH4RrOY6HAxsJCpHB2hxO7T7sKC/dfCSxqlYSc67hNPxHAwkKkeAfOm2DqsCFCr0FmkkF0HBpknMdC5MLCQqRw7vkrs9KioVHzr2ygcZ8ZVVLRBBvnsVAA408/IoVzL2fmcFBgSo8Px9CQILRbHTh4vll0HCJhWFiIFKy53er5JcUJt4FJpZKQM8J1l2Xv2SbBaYjEYWEhUrDdpxvglIHRcWFIMASLjkOCuJc3c+ItBTIWFiIF23ni0nb8FLjchaXkXBMsdofgNERisLAQKZQsy/j8FLfjJyAtNgzRYVp02pw4UGUSHYdICBYWIoU6UduCWrMF+qBLZ8pQYJIk7sdCxMJCpFDu5cw5I6KgD1ILTkOiXdqPpUFwEiIxWFiIFMq9HT+XMxNwaR5LWWUzOm2cx0KBh4WFSIHarXYUl7uWsHL+CgHAddGhiA3XwWp3oqzyoug4RIOOhYVIgfadbYLV4cSwIcEYGRMqOg4pgCRJnrssezmPhQIQCwuRArl3t71hdAwkSRKchpSC5wpRIGNhIVKgzz3b8UcLTkJK4j5XaH9VMzqsnMdCgYWFhUhhqpracbahDWqVhBmjWFjokuFRIUgw6GFzyCg5x236KbCwsBApjHs4aHLKEETogwSnISWRJMkzLLSXw0IUYFhYiBTGPRzE7fipJ9N5rhAFKBYWIgWxOZzY0/WLaPYYFhb6NvcdloPnTWiz2AWnIRo8LCxEClJ27iJaLXZEhmoxIdEgOg4pUHJkCJKGBsPulPFlBeexUOBgYSFSEPf8levToqFScTkz9cx9l2X3KW7TT4GDhYVIQT47XgeA2/FT7+akxwIAPjlaC1mWBachGhwsLEQKUd3cgePGFqgk4MYxsaLjkILNHhMDnUaFyqZ2HLvQIjoO0aBgYSFSiM+O1QIAJqcMRWSoVnAaUrIQrcZzF67giFFwGqLBwcJCpBCFXcNBN4+NE5yEfMG8CfEAgK2HWVgoMFxVYVm3bh1SU1Oh1+uRk5OD4uLiXq/ftGkT0tPTodfrkZGRgY8++uiy1/7sZz+DJEl44YUXriYakU9qt9o9y5lvHsvhILqym9PjoFFJOFHbgrP1raLjEA04rwvLxo0bsXLlSqxZswZlZWXIzMzE3LlzUVdX1+P1e/bsweLFi/HAAw/gq6++wsKFC7Fw4UIcPnz4W9e+99572Lt3LxITE71/J0Q+bPepBljtTiQNDUZabJjoOOQDDCFBntObtx6pFZyGaOB5XVief/55/OQnP8GyZcswbtw4rF+/HiEhIfjzn//c4/Uvvvgi5s2bh0cffRRjx47Fb3/7W0yePBkvv/xyt+uqq6vx0EMP4W9/+xuCgrgdOQUW9+qgvLFxPJ2Z+sw9LMR5LBQIvCosVqsVpaWlyMvLu/QJVCrk5eWhqKiox9cUFRV1ux4A5s6d2+16p9OJ+++/H48++ijGjx/vTSQin+d0yp7C4l6uStQX3xkXB0kCDlQ144KpQ3QcogHlVWFpaGiAw+FAXFz3SYFxcXEwGntu+Eaj8YrXP/fcc9BoNHj44Yf7lMNiscBsNnd7EPmqIzVm1LVYEKpVI+e6SNFxyIfEhusxJWUoAOATDguRnxO+Sqi0tBQvvvgiXn/99T7fCs/Pz4fBYPA8kpOTBzgl0cD5tGs58/VpMdBp1ILTkK/xDAtxtRD5Oa8KS3R0NNRqNWpruzf52tpaxMfH9/ia+Pj4Xq/ftWsX6urqkJKSAo1GA41Gg3PnzuGXv/wlUlNTe/ycq1atgslk8jyqqqq8eRtEiuIZDuLqILoKc8e7fpbuK29EU5tVcBqigeNVYdFqtZgyZQoKCws9zzmdThQWFiI3N7fH1+Tm5na7HgC2bdvmuf7+++/HwYMHsX//fs8jMTERjz76KLZu3drj59TpdIiIiOj2IPJFteZOHKo2AQBu4u62dBWSI0MwPjECThn49CiHhch/abx9wcqVK7F06VJMnToV2dnZeOGFF9DW1oZly5YBAJYsWYJhw4YhPz8fALBixQrMnj0ba9euxfz58/HWW2+hpKQEr776KgAgKioKUVFR3b5GUFAQ4uPjMWbMmGt9f0SK5r67kpk8BDHhOsFpyFfNGx+PIzVmFBwx4t5pHCIn/+R1YVm0aBHq6+vx1FNPwWg0IisrCwUFBZ6JtZWVlVCpLt24mTFjBjZs2IAnnngCq1evRlpaGjZv3owJEyb037sg8lGFx7qWM3N1EF2DeRPisXbbSew+1YBWix1hOq9/tBMpniT7wVGfZrMZBoMBJpOJw0PkMzptDkz6923osDnw4cOzMD7RIDoS+ShZlnHz2p0429CGlxZPwoJMbr5JvsGb39/CVwkRBaqis43osDmQYNBjXAKLNl09SZIwl5vIkZ9jYSESpLBrOfOc9FjubkvXbF7XaqHtx+vQaXMITkPU/1hYiASQZRmfHXOfzsz5K3TtJiYZkGDQo93qwO5TDaLjEPU7FhYiAY4bW1Bj6oQ+SIUZI6NFxyE/IEmSZ08WDguRP2JhIRLAPRw0a1Q09EHc3Zb6h3vX20+P1cLucApOQ9S/WFiIBCj0HHYYd4UrifpuWmokokK1aG63obi8SXQcon7FwkI0yBpaLdhf1QyApzNT/1KrJOSNdZVgDguRv2FhIRpkO07UQ5aB8YkRiDfoRcchP+MeFtp6xAin0+e32SLyYGEhGmTu+Ss3j+VwEPW/GaOiEKbToNZswf7zzaLjEPUbFhaiQWS1O/H5yXoAwM0cDqIBoNOoPUONWw9zWIj8BwsL0SAqLm9Cm9WBmHAdMoZxK34aGPO+tuutH5y+QgSAhYVoUBUe79rddkwsVCrubksDY/boGOg0KpxrbMeJ2hbRcYj6BQsL0SCRZdlzOvMc7m5LAyhUp8ENo2MAAAUcFiI/wcJCNEjO1LeisqkdWrUKs0Zxd1saWO5db90lmcjXsbAQDRL3L47ckVEI1WkEpyF/d0OaqxQfrjGhud0qOA3RtWNhIRokn3qWM3M4iAZebIQeabFhkGWg6Eyj6DhE14yFhWgQ1LV0ouTcRQDcf4UGz8yuocfdp3l6M/k+FhaiQbD1SC1kGchMHoJhQ4JFx6EA4Z4r9QULC/kBFhaiQVBw+AIA4Lau/TGIBkPOdZFQqyRUNLbj/MV20XGIrgkLC9EAa2qzYu9Z18m5t05IEJyGAkm4PgiZSa4NCvec5jwW8m0sLEQDbNtRIxxOGeMSIpASFSI6DgWYWZzHQn6ChYVogH3ctXHXbRkcDqLB5554u+dMA7fpJ5/GwkI0gEwdNs+Ex3kcDiIBJqUMRXCQGg2tVm7TTz6NhYVoABUeq4XNISMtNgyjYsNEx6EApNWokD0iEgCw+xSHhch3sbAQDSD3cNCtXB1EAnF5M/kDFhaiAdJqsWPnyXoAwK0ZHA4icdzzWPaVN8HmcApOQ3R1WFiIBsj243Ww2p1IjQpBeny46DgUwNLjwxEZqkW71YH9Vc2i4xBdFRYWogFS0DUcNG9CAiRJEpyGAplKJWHGyCgAnMdCvouFhWgAdFgd2H7CdTozlzOTEnAeC/k6FhaiAbDzZD3arQ4MGxKMjGEG0XGIPPNY9lc1o9ViF5yGyHssLEQDwH120LwJ8RwOIkVIjgxBSmQI7E4ZxeXcpp98DwsLUT+z2B0oPMbhIFIe912W3adYWMj3sLAQ9bMvTjegxWJHXIQOk5KHio5D5MF5LOTLWFiI+tnHh1yrg+aOj4dKxeEgUo7crpVCJ2pbUNfSKTgNkXdYWIj6kc3hxLZjtQBc81eIlCQyVIvxiREAgKIzHBYi38LCQtSP9p5tRHO7DVGhWmSnRoqOQ/QtszzzWDgsRL6FhYWoH7nPDrplfBw0av71IuWZ+bV5LLIsC05D1Hf8iUrUTxxOGZ8cubS7LZESTUuNhFatQo2pExWN7aLjEPUZCwtRP/myogkNrVYYgoM826ATKU2wVo3Jw4cAAHZztRD5EBYWon7iPjsob2wcgjgcRArmWd7MeSzkQ/hTlagfOJ2yp7DcytVBpHDueSxFZxvhcHIeC/kGFhaifvBVVTOM5k6E6TSYlRYtOg5RrzKGGRCu08DUYcORGpPoOER9wsJC1A/cZwfNSY+FPkgtOA1R7zRqFaZ3zbPiPBbyFSwsRNdIlmXPcmYOB5Gv4Db95GtYWIiu0ZEaM85f7IA+SIXZY2JExyHqk5mjXHdYvqy4iE6bQ3AaoitjYSG6Rlu79l65cXQsQrQawWmI+mZkTBjiInSw2p0oPXdRdByiK2JhIbpG7uEgnh1EvkSSJM9qIc5jIV/AwkJ0DU7XteB0XSuC1BJuSo8VHYfIKzxXiHwJCwvRNdh6xHUy84yR0TAEBwlOQ+SdWaOioZKAQ9UmnGtsEx2HqFcsLETXoIDDQeTDYiP0uD7NNVH87dLzgtMQ9Y6Fhegqnb/YjkPVJkgS8J1xcaLjEF2Ve6YmAXAVFu56S0rGwkJ0ldzDQdNSIxEdphOchujqfGdcHIaEBOGCqZOTb0nRWFiIrtJWbhZHfkCnUWNh1jAAwD9KqgSnIbo8Fhaiq1DfYsGX55oAAHPHs7CQb/veFNew0LYjtWhutwpOQ9QzFhaiq7DtaC1kGchMMiBxSLDoOETXZMIwA8YlRMDqcOKf+2tExyHqEQsL0VUo6Nrddi6Hg8hP3Ns1+ZbDQqRULCxEXjK127Cna3LiPA4HkZ+4M2sYtGoVjtSYcaTGJDoO0bewsBB5qfB4LexOGaPjwnBdTJjoOET9Ymio1rM8f1MJ92Qh5WFhIfKSZ7M43l0hP+Pek2Xz/mpY7DzBmZSFhYXIC+1WO3aerAfA+Svkf65Pi0F8hB7N7TZ8erROdByiblhYiLyw80Q9LHYnkiODMS4hQnQcon6lVkmeJc6cfEtKw8JC5AX36qB54+MhSZLgNET9z11Ydp2qxwVTh+A0RJewsBD1kcXuwGfHXLfJ501IEJyGaGCkRocie0QknDLwblm16DhEHiwsRH2050wjWix2xIbrMCl5iOg4RAPm3qnJAFzDQrLMAxFJGVhYiPrIfXbQ3PHxUKk4HET+67aMeIRq1TjX2I7i8ibRcYgAsLAQ9YnDKeOTo67TmedxdRD5uRCtBrdPTAQAbCrlniykDCwsRH1QXN6EpjYrhoQEIXtEpOg4RAPu3mmuybcfHryAVotdcBqiqyws69atQ2pqKvR6PXJyclBcXNzr9Zs2bUJ6ejr0ej0yMjLw0UcfeT5ms9nw2GOPISMjA6GhoUhMTMSSJUtQU8MDuEg5tnatDsobG4cgNXs++b/JKUNxXUwoOmwOfHiQP49JPK9/8m7cuBErV67EmjVrUFZWhszMTMydOxd1dT1vMrRnzx4sXrwYDzzwAL766issXLgQCxcuxOHDhwEA7e3tKCsrw5NPPomysjK8++67OHHiBO64445re2dE/cTplLm7LQUcSZK+NvmWw0IkniR7OQU8JycH06ZNw8svvwwAcDqdSE5OxkMPPYTHH3/8W9cvWrQIbW1t2LJli+e56dOnIysrC+vXr+/xa3z55ZfIzs7GuXPnkJKScsVMZrMZBoMBJpMJERHczIv61/6qZixc9wVCtGqUPfkd6IPUoiMRDYo6cydyn/0MDqeMwl/OxkienUX9zJvf317dYbFarSgtLUVeXt6lT6BSIS8vD0VFRT2+pqioqNv1ADB37tzLXg8AJpMJkiRhyJAhPX7cYrHAbDZ3exANFPfdlZvSY1lWKKDERuhx4+gYADwQkcTzqrA0NDTA4XAgLi6u2/NxcXEwGo09vsZoNHp1fWdnJx577DEsXrz4sm0rPz8fBoPB80hOTvbmbRD1mSzLKDh8AQCHgygw3dM1LPRO2XnYHU7BaSiQKWr2oM1mw7333gtZlvHKK69c9rpVq1bBZDJ5HlVVPPOCBsaRGjMqGtuh1ahwU3qs6DhEg25Oeiyiw7Sob7F4jqYgEsGrwhIdHQ21Wo3a2tpuz9fW1iI+vuf/+4yPj+/T9e6ycu7cOWzbtq3XsSydToeIiIhuD6KB8PqeCgDALePiEKbTiA1DJIBWo8J9OcMBAK/tKufOtySMV4VFq9ViypQpKCws9DzndDpRWFiI3NzcHl+Tm5vb7XoA2LZtW7fr3WXl1KlT+PTTTxEVFeVNLKIB0dBqwfv7Xcs5l80cITgNkTg/nD4cWo0KB6qaUVZ5UXQcClBeDwmtXLkSr732Gt544w0cO3YMP//5z9HW1oZly5YBAJYsWYJVq1Z5rl+xYgUKCgqwdu1aHD9+HE8//TRKSkqwfPlyAK6y8r3vfQ8lJSX429/+BofDAaPRCKPRCKvV2k9vk8h7G/ZVwupwIjPJgMkpQ0THIRImJlyHu7KGAQD+tKtccBoKVF7f4160aBHq6+vx1FNPwWg0IisrCwUFBZ6JtZWVlVCpLvWgGTNmYMOGDXjiiSewevVqpKWlYfPmzZgwYQIAoLq6Gu+//z4AICsrq9vX2r59O2688carfGtEV89qd+LNvecAuO6uSBLPDqLA9sD1I7CxpApbjxhR2diOlKgQ0ZEowHi9D4sScR8W6m+bv6rGIxv3IzZch92PzYFWo6j56URCLPlzMT4/WY9lM1OxZsF40XHIDwzYPixEgUCWZfzlC9dt7/u7xu6JCPjxLNdcrn98WQVTh01wGgo0/ElM9A1llc04cN4ErUaFH+RceadlokBxfVo0RseFoc3qwMYvK0XHoQDDwkL0DX/uurtyZ2YiosJ0gtMQKYckSfjxrOsAAK9/UQEbN5KjQcTCQvQ1Nc0dnq34uZSZ6NvuyEpEdJgWNaZOfHyYG8nR4GFhIfqaN/eeg8MpI2dEJMYlcgI30Tfpg9S4f3oqAOBPu85yIzkaNCwsRF06rA78vdg1Ls+7K0SX98PpKdBqVDh43oSSc9xIjgYHCwtRl837q9HcbkPS0GB8Z1zclV9AFKCiwnT47mT3RnJnBaehQMHCQoTuS5mX5qZCreJGcUS9+Zeuu5CfHK3FucY2wWkoELCwEAHYc6YRJ2tbEaJV495pyaLjECleWlw4bhwTA1kG/vJFheg4FABYWIgAz92V705OgiE4SHAaIt/gXuL8j5IqmNq5kRwNLBYWCnjnGttQeLwOAPCjmaliwxD5kJmjopAeH452qwN/50ZyNMBYWCjgvb6nArIMzB4dg5ExYaLjEPkMSZLwQNd2/dxIjgYaCwsFtJZOGzaVnAcALOPdFSKvuTaS08Fo7sRHhy6IjkN+jIWFAtrbpefRarFjZEwobkiLER2HyOfoNGoszR0OAHiNG8nRAGJhoYDldMp4Y08FAOBHM0dAxaXMRFflvunDodOocLjajH3lTaLjkJ9iYaGA9emxWlQ0tiNCr/FsgkVE3osM1eKeqUkAgHXbTwtOQ/6KhYUCkt3hxH9uPQEA+OH04QjRagQnIvJt/++GkVCrJOw61YADVc2i45AfYmGhgPSPkvM4XdeKoSFB+H+zR4qOQ+TzkiNDsDDLdafyZd5loQHAwkIBp9Vix/PbTgIAHr45jRvFEfWTf71pJCQJ2Ha0FseNZtFxyM+wsFDAefXzs2hotSA1KgT35QwXHYfIb4yMCcNtGQkAgHXbzwhOQ/6GhYUCSq25E6997jpd9tfz0qHV8K8AUX9aftMoAMCWgzU4U98qOA35E/60poDyX9tOosPmwOSUIbh1QrzoOER+Z2xCBPLGxkKWgVd28C4L9R8WFgoYJ2tb8I+SKgDAv80fC0nivitEA+HBrrssm7+qRlVTu+A05C9YWChg5H90DE4ZuHVCPKYMjxQdh8hvTUoZilmjomF3yvjj57zLQv2DhYUCwhenG7D9RD00Kgm/npcuOg6R31s+x3WX5R8l51Fr7hSchvwBCwv5PadTxjMfHQPg2iRuRHSo4ERE/i9nRCSmDh8Kq93pmehOdC1YWMjvbd5fjSM1ZoTrNHj45jTRcYgCgiRJnrssf9tXiaY2q+BE5OtYWMivddoc+EPXFvw/v2kkIkO1ghMRBY7Zo2OQMcyADpsDf95dLjoO+TgWFvJrf/miAjWmTiQa9PiXmSNExyEKKJIkeVYMvbGnAqYOm+BE5MtYWMhvNbZa8D9dZ5r8au4Y6IPUghMRBZ5bxsVhdFwYWix2vFlUIToO+TAWFvJbL312Gi0WO8YnRngOZSOiwaVSXbrL8r+7y9FutQtORL6KhYX8UnlDG/5v7zkAwOrbxkKl4iZxRKLMz0hAalQILrbbsGFfpeg45KNYWMjvyLKM3245CrtTxo1jYjBzVLToSEQBTaNW4ec3jgTgOny00+YQnIh8EQsL+Z0PD13AZ8froFWr8MT8saLjEBGAuyYlIdGgR12LBX/5okJ0HPJBLCzkV0ztNjz9/lEAwL/eNBKjYsMFJyIiANBqVFiR59oH6fdbj2PXqXrBicjXsLCQX3m24BgaWi0YGRPquQVNRMpw79RkfHdyEpwysHzDV6hoaBMdiXwICwv5jeLyJvy92HUac/7dE6HTcBkzkZJIkoTf3TUBk1KGwNRhw4//WoKWTu7NQn3DwkJ+wWJ3YNW7BwEAi7NTkD2CpzETKZE+SI0//nAK4iP0OF3XihVv7YfDKYuORT6AhYX8wis7zuBMfRuiw3R4nKcxEylabIQery6ZAp1Ghc+O1+EPn5wQHYl8AAsL+bzTdS34n+1nAABP3zEOhpAgwYmI6EomJg3Bf35vIgDX/3D8c3+14ESkdCws5NOcThmr3z0Mq8OJOemxmJ+RIDoSEfXRnVnDPJPjf/32QRyoahYbiBSNhYV82saSKhRXNCFEq8a/3zkeksQdbYl8ya9uGYOb02NhsTvx0zdLUGfuFB2JFIqFhXxWnbkTz3x0DADwy1vGIGloiOBEROQttUrCC9/PwqjYMNSaLfjpm6XcCZd6xMJCPus3W46ipdOOiUkG/GhGqug4RHSVwvVB+NOSqTAEB2F/VTNWv3cIssyVQ9QdCwv5pMJjtfjw4AWoVRKeuSsDah5uSOTTUqNDse4Hk6FWSXi3rBqv7TorOhIpDAsL+Zw2ix1P/fMIAODHs0ZgwjCD4ERE1B9mpUV7zv/K//g4Pj50QXAiUhIWFvIpsizjPz48hurmDiRHBnvOJiEi//CjGam4f/pwyDLwyMb9KD13UXQkUggWFvIZsizjdx8ew9+LKwEAv1uYgRCtRnAqIupPkiRhzYJxnpVDP/lrCc8cIgAsLOQj3HdW/rS7HADwzF0ZuGF0jOBURDQQNGoVXvrBJGQMM6CpzYof/aUYTW1W0bFIMBYWUjxZlvHbLcfwv18rKz/ISRGciogGUohWg//90VQMGxKMisZ2/OSvJVzuHOBYWEjRZFnGv285ij9/4Sor+XezrBAFithwPV5fNg3heg1Kz13EL/9xAE4elBiwWFhIsWRZxm8+OIq/fFEBAHj27gwszmZZIQokaXHh+OP9UxCklvDhoQt4ruC46EgkCAsLKZK7rLy+pwKSBDz33Qx8n2WFKCDNGBmN577rOijxj5+fxZt7zwlORCKwsJDiyLKMp98/cqms3D0Ri6axrBAFsrsnJ2Hld0YDANb88zAKj9UKTkSDjYWFFEWWZax5/wjeKDrXdWdlIu6dliw6FhEpwENzRuHeqUlwysDyDV/h0HmT6Eg0iFhYSDEsdgdWv3cIf+0qK//53Ym4dyrLChG5SJKE392VgevTotFhc+C+P+3Fp0d5pyVQsLCQIpyqbcHCdXvw9+IqSBLw++9l4h6WFSL6hiC1Cv9z32RMShkCc6cdP/5rCfI/Pgabwyk6Gg0wFhYSSpZlvFlUgdtf2o1jF8yIDNXiT0um4ntTkkRHIyKFCtcHYeNPc7FsZioA4I87z+IHr+2F0dQpNhgNKEn2gzO8zWYzDAYDTCYTIiIiRMehPmpoteCxtw+i8HgdAOCG0TH4wz0TERuuF5yMiHzFR4cu4NdvH0SrxY7IUC1eWJTFXbB9iDe/v3mHhYTYcaIO817YhcLjddBqVFizYBxe/9E0lhUi8sptGQnY8tAsjEuIQFObFUv/Uoznt52EgxvM+R3eYaFB1Wlz4NmPj+P1PRUAgDFx4XhxcRbS4/nfjYiuXqfNgd98cNRzOOrMUVF4YdEkxITrBCej3njz+5uFhQbNcaMZK/6+HydqWwC4jpF//NZ06IPUgpMRkb9476vzWP3uYXTYHIgJ1+HFRVmYMSpadCy6DBYWUowOqwOfHDXi7dLz+OJ0A5wyEB2mw+/vmYibxsSKjkdEfuhUbQv+9W9lOFXXCgDITB6CH2Qn4/aJiQjVaQSno69jYSGhnE4ZxRVNeKf0PD4+bESrxe752C3j4vDM3RmIDuNtWiIaOO1WO3675RjeLq2CzeH6NRem0+DOrEQszk7BhGEGwQkJYGERHSdglTe04d2y83i3rBrVzR2e55Mjg3H3pCTcPXkYhkeFCkxIRIGmodWCd0rP4+/FlahobPc8PzHJgMXZKViQmYgw3nURhoWFBoUsyzhubMH2E3XYdrQWX1U2ez4WrtNg/sQE3D05CdNSh0KSJHFBiSjgybKMorON+HtxFbYeNsLatdFcqFaNO7ISsWBiIrJHREKj5uLZwcTCQgOm1WLH7lMN2HGiDjtO1MNovrRRk0py7aVy9+Qk3DIujpNpiUiRGlsteLesGn8vrsTZhjbP81GhWtwyPh7zMxIw/TqWl8Ew4IVl3bp1+P3vfw+j0YjMzEy89NJLyM7Ovuz1mzZtwpNPPomKigqkpaXhueeew2233eb5uCzLWLNmDV577TU0Nzdj5syZeOWVV5CWltanPCwsA0eWZZyua8WOE/XYfqIOX1Y0ecaDAUAfpMLMkdG4cUwM5o6PR2wE91EhIt8gyzL2lTdh81fV2HrEiIvtNs/HhoYEYe74eNyWkYDckVEIYnkZEANaWDZu3IglS5Zg/fr1yMnJwQsvvIBNmzbhxIkTiI399qqPPXv24IYbbkB+fj5uv/12bNiwAc899xzKysowYcIEAMBzzz2H/Px8vPHGGxgxYgSefPJJHDp0CEePHoVef+VfgCws/cPmcOJ0XSuO1JhxpMaEozVmHL1gRkunvdt1qVEhuHFMLG5Kj0XOiEjeSSEin2dzOLHvbBM+PHQBW48Y0dRm9XxsSEgQ8sbGIS02DHEResRG6BAXoUdchJ7zX67RgBaWnJwcTJs2DS+//DIAwOl0Ijk5GQ899BAef/zxb12/aNEitLW1YcuWLZ7npk+fjqysLKxfvx6yLCMxMRG//OUv8atf/QoAYDKZEBcXh9dffx3f//73+/UNBxK7w4lOuxMdVgc6bQ502Lr+ab3073UtFhypdhWTE7UtsNq/fYCYVqPC9OuicNOYGNw4JhYjojlxloj8l93hRHH5pfLS0Gq97LUhWrWrxIS7SkxMuA7RYTpEhWkRE+b69+hwLaJCddBqeJfmm7z5/e1VNbRarSgtLcWqVas8z6lUKuTl5aGoqKjH1xQVFWHlypXdnps7dy42b94MACgvL4fRaEReXp7n4waDATk5OSgqKuqxsFgsFlgsFs+fzWazN2+jz+wOJ3730bEB+dyXI8uAU5bhcMpwyjLsDhkOWYbTKcMhAw6nEw6nDKvdiU6bExa7A502JzrtDli+/mebA/ar2Jo6XKfB2MQIjE+MwPhEA8YnRmBUbBhvhxJRwNCoVZgxKhozRkXj3++cgOLyJnx+qh5GUydqza5HndmCFosd7VYHyhvaUP61uTCXYwgOQlSYFuE6DdQqCRqVChq11PXvEjRqleefKglQSRIkAJAACRIkCZCArn92/bnrAklyzSPsfp1rsUN/rXnQqCT82/xx/fPJrubre3NxQ0MDHA4H4uLiuj0fFxeH48eP9/gao9HY4/VGo9Hzcfdzl7vmm/Lz8/Gb3/zGm+hXxSkDf/miYsC/zmAIDlIjWKtGcJAauiCV689BahiCgzA2wVVQxiVGIHloCFQqrughIgIAtUpC7sgo5I6M+tbH2ix21LVYupWYhlYL6lstaGi1oqHFgsY2CxpbrbA7ZZg6bDB12Hr4Kr5Bq1H5TmFRilWrVnW7a2M2m5GcnNzvX0clAQ/eNLLfP++VqCUJKpUEtSRBre76p0qCSpKgUbv+qdWooNOooA9Sux4aFXRBauiDVNBrXKVEr3GVFJ1GxWXFRET9LFSnwQid5orD5M6usuIuM502B2wO1510u1OG3eGE3dn156/9O+C64y7LgAx0/dP1Z8A1afjrH3PKMmTXB7pd31/UKrF32r0qLNHR0VCr1aitre32fG1tLeLj43t8TXx8fK/Xu/9ZW1uLhISEbtdkZWX1+Dl1Oh10uoHfKVWjVuHRuekD/nWIiMh/qVQShoZqMTRUi7S4cNFxfJZXdUmr1WLKlCkoLCz0POd0OlFYWIjc3NweX5Obm9vtegDYtm2b5/oRI0YgPj6+2zVmsxn79u277OckIiKiwOL1kNDKlSuxdOlSTJ06FdnZ2XjhhRfQ1taGZcuWAQCWLFmCYcOGIT8/HwCwYsUKzJ49G2vXrsX8+fPx1ltvoaSkBK+++ioA16SgRx55BP/xH/+BtLQ0z7LmxMRELFy4sP/eKREREfksrwvLokWLUF9fj6eeegpGoxFZWVkoKCjwTJqtrKyE6mvjXDNmzMCGDRvwxBNPYPXq1UhLS8PmzZs9e7AAwK9//Wu0tbXhpz/9KZqbmzFr1iwUFBT0aQ8WIiIi8n/cmp+IiIiE8Ob3NzfXICIiIsVjYSEiIiLFY2EhIiIixWNhISIiIsVjYSEiIiLFY2EhIiIixWNhISIiIsVjYSEiIiLFY2EhIiIixfN6a34lcm/WazabBSchIiKivnL/3u7Lpvt+UVhaWloAAMnJyYKTEBERkbdaWlpgMBh6vcYvzhJyOp2oqalBeHg4JEnq189tNpuRnJyMqqoqnlPUA35/esfvz+Xxe9M7fn96x+9P73zl+yPLMlpaWpCYmNjt4OSe+MUdFpVKhaSkpAH9GhEREYr+jy4avz+94/fn8vi96R2/P73j96d3vvD9udKdFTdOuiUiIiLFY2EhIiIixWNhuQKdToc1a9ZAp9OJjqJI/P70jt+fy+P3pnf8/vSO35/e+eP3xy8m3RIREZF/4x0WIiIiUjwWFiIiIlI8FhYiIiJSPBYWIiIiUjwWlitYt24dUlNTodfrkZOTg+LiYtGRFOHzzz/HggULkJiYCEmSsHnzZtGRFCM/Px/Tpk1DeHg4YmNjsXDhQpw4cUJ0LMV45ZVXMHHiRM+GVrm5ufj4449Fx1KkZ599FpIk4ZFHHhEdRTGefvppSJLU7ZGeni46lmJUV1fjhz/8IaKiohAcHIyMjAyUlJSIjtUvWFh6sXHjRqxcuRJr1qxBWVkZMjMzMXfuXNTV1YmOJlxbWxsyMzOxbt060VEUZ+fOnXjwwQexd+9ebNu2DTabDbfccgva2tpER1OEpKQkPPvssygtLUVJSQnmzJmDO++8E0eOHBEdTVG+/PJL/PGPf8TEiRNFR1Gc8ePH48KFC57H7t27RUdShIsXL2LmzJkICgrCxx9/jKNHj2Lt2rUYOnSo6Gj9Q6bLys7Olh988EHPnx0Oh5yYmCjn5+cLTKU8AOT33ntPdAzFqqurkwHIO3fuFB1FsYYOHSr/6U9/Eh1DMVpaWuS0tDR527Zt8uzZs+UVK1aIjqQYa9askTMzM0XHUKTHHntMnjVrlugYA4Z3WC7DarWitLQUeXl5nudUKhXy8vJQVFQkMBn5GpPJBACIjIwUnER5HA4H3nrrLbS1tSE3N1d0HMV48MEHMX/+/G4/f+iSU6dOITExEddddx3uu+8+VFZWio6kCO+//z6mTp2Ke+65B7GxsZg0aRJee+010bH6DQvLZTQ0NMDhcCAuLq7b83FxcTAajYJSka9xOp145JFHMHPmTEyYMEF0HMU4dOgQwsLCoNPp8LOf/Qzvvfcexo0bJzqWIrz11lsoKytDfn6+6CiKlJOTg9dffx0FBQV45ZVXUF5ejuuvvx4tLS2iowl39uxZvPLKK0hLS8PWrVvx85//HA8//DDeeOMN0dH6hV+c1kykVA8++CAOHz7MMfZvGDNmDPbv3w+TyYS3334bS5cuxc6dOwO+tFRVVWHFihXYtm0b9Hq96DiKdOutt3r+feLEicjJycHw4cPxj3/8Aw888IDAZOI5nU5MnToVzzzzDABg0qRJOHz4MNavX4+lS5cKTnfteIflMqKjo6FWq1FbW9vt+draWsTHxwtKRb5k+fLl2LJlC7Zv346kpCTRcRRFq9Vi1KhRmDJlCvLz85GZmYkXX3xRdCzhSktLUVdXh8mTJ0Oj0UCj0WDnzp347//+b2g0GjgcDtERFWfIkCEYPXo0Tp8+LTqKcAkJCd8q/WPHjvWbITMWlsvQarWYMmUKCgsLPc85nU4UFhZyrJ16Jcsyli9fjvfeew+fffYZRowYITqS4jmdTlgsFtExhLv55ptx6NAh7N+/3/OYOnUq7rvvPuzfvx9qtVp0RMVpbW3FmTNnkJCQIDqKcDNnzvzWFgonT57E8OHDBSXqXxwS6sXKlSuxdOlSTJ06FdnZ2XjhhRfQ1taGZcuWiY4mXGtra7f/oykvL8f+/fsRGRmJlJQUgcnEe/DBB7Fhwwb885//RHh4uGfOk8FgQHBwsOB04q1atQq33norUlJS0NLSgg0bNmDHjh3YunWr6GjChYeHf2uuU2hoKKKiojgHqsuvfvUrLFiwAMOHD0dNTQ3WrFkDtVqNxYsXi44m3C9+8QvMmDEDzzzzDO69914UFxfj1Vdfxauvvio6Wv8QvUxJ6V566SU5JSVF1mq1cnZ2trx3717RkRRh+/btMoBvPZYuXSo6mnA9fV8AyH/5y19ER1OEf/mXf5GHDx8ua7VaOSYmRr755pvlTz75RHQsxeKy5u4WLVokJyQkyFqtVh42bJi8aNEi+fTp06JjKcYHH3wgT5gwQdbpdHJ6err86quvio7UbyRZlmVBXYmIiIioTziHhYiIiBSPhYWIiIgUj4WFiIiIFI+FhYiIiBSPhYWIiIgUj4WFiIiIFI+FhYiIiBSPhYWIiIgUj4WFiIiIFI+FhYiIiBSPhYWIiIgUj4WFiIiIFO//A8GO8q0QKF1RAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "overlap = []\n",
    "betavalues = np.linspace(0,2*np.pi,50)\n",
    "shots=10**5\n",
    "for beta in tqdm(betavalues):\n",
    "    q = QuantumRegister(numNodes*2)\n",
    "    c = ClassicalRegister(numNodes*2)\n",
    "    circuit = QuantumCircuit(q, c)\n",
    "    for k in range(numNodes):\n",
    "        circuit.x(0+k*2)\n",
    "    circuit.barrier()\n",
    "    circuit.append(grover.circuit, q)\n",
    "    circuit.measure(q, c)\n",
    "    circuit = transpile(circuit, backend)\n",
    "    \n",
    "    # Assign float values to the parameters\n",
    "    parameters = list(circuit.parameters)\n",
    "    parameter_values = [beta]\n",
    "    bound_circuit = circuit.assign_parameters(dict(zip(parameters, parameter_values)))\n",
    "\n",
    "    \n",
    "    # Run the job\n",
    "    job = backend.run(bound_circuit, shots=shots)\n",
    "    counts = job.result().get_counts()\n",
    "    overlap.append(counts.get(\"10\"*numNodes,0.)/shots)\n",
    "    # overlap.append(counts.get(\"100100\",0.)/shots)\n",
    "    \n",
    "# bound_circuit.draw('mpl')\n",
    "\n",
    "pl.plot(betavalues, overlap)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eaea262-76aa-47a3-8b51-c5a3f65bb477",
   "metadata": {},
   "source": [
    "4. <u>Initial state class</u>\n",
    "\n",
    "To run QAOA we need to implement the `InitialState` class that creates a Tensor of $\\ket{ltk3}$ state, which can be done just as above\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5c678b40-60b7-4205-9206-960508f9ca9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qaoa.initialstates import InitialState\n",
    "class Max3CutInitialState(InitialState):\n",
    "    \n",
    "    def create_circuit(self) -> None:\n",
    "\n",
    "        numQubitsPerNode = 2\n",
    "        self.num_V = int(self.N_qubits/numQubitsPerNode)\n",
    "        \n",
    "        tg = Tensor(LessThanK(3), self.num_V)\n",
    "        tg.create_circuit()\n",
    "        self.circuit = tg.circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0678247c-b8be-4e2f-904d-a76777b6ecaf",
   "metadata": {},
   "source": [
    "5. <u>Mixer class</u>\n",
    "\n",
    "We also need to implement the `Mixer` class that creates a Tensor of Grover mixer, which can be done just as above\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "92935b26-ee63-46b8-a2a5-b20433ab0e94",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qaoa.mixers import Mixer\n",
    "class Max3CutGrover(Mixer):\n",
    "        \n",
    "    def create_circuit(self) -> None:\n",
    "\n",
    "        numQubitsPerNode = 2\n",
    "        self.num_V = int(self.N_qubits/numQubitsPerNode)\n",
    "        \n",
    "        gm = Tensor(Grover(LessThanK(3)), self.num_V)\n",
    "        gm.create_circuit()\n",
    "        self.circuit = gm.circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db85fd5a-f0fb-42dc-b70f-2d7a555be8e2",
   "metadata": {},
   "source": [
    "6. <u>Run QAOA</u>\n",
    "\n",
    "create an instance of QAOA and plot the resulting landscape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "436e1b9c-4312-4394-a980-0fa314c2152e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2m2024-11-26 14:29:35\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mCalculating energy landscape for depth p=1...\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:35\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mExecuting sample_cost_landscape\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:35\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mparameters: 2                 \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:35\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mDone execute                  \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:52\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mDone measurement              \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:52\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mCalculating Energy landscape done\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35msample_cost_landscape\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:53\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 1 = -9.953124999999998\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qaoa_k3_subH = QAOA(\n",
    "    initialstate=Max3CutInitialState(),\n",
    "    problem=Max4Cut(G),\n",
    "    mixer=Max3CutGrover(),\n",
    "    optimizer=optimizer)\n",
    "\n",
    "qaoa_k3_subH.optimize(depth=1, angles={\"gamma\": [0, 2*np.pi, 20], \"beta\": [0, 2*np.pi, 20]} )\n",
    "\n",
    "fig = plt.figure(figsize=(6, 6))\n",
    "gamma = []\n",
    "beta = []\n",
    "angles = qaoa_k3_subH.optimization_results[1].angles\n",
    "for i in range(len(angles)):\n",
    "    gamma.append(angles[i][0])\n",
    "    beta.append(angles[i][1])\n",
    "plt.plot(gamma, beta, \"x-k\")\n",
    "plt.plot(gamma[0], beta[0], \"wo\")\n",
    "plt.plot(gamma[-1], beta[-1], \"or\")\n",
    "plot_E(qaoa_k3_subH, fig=fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7869d14e-6138-4774-a809-87dd6a2b41ce",
   "metadata": {},
   "source": [
    "7. <u>Comparison for MAX 3-CUT</u>\n",
    "\n",
    "Compare the convergence for the method using the full Hilbert space and the subspace encoding up to depth $p=5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "97f29836-d369-4b30-b805-4994360ea206",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2m2024-11-26 14:29:55\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 2 = -10.501953124999996\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:29:59\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 3 = -10.691406250000005\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:30:05\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 4 = -10.971679687500007\u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n",
      "\u001b[2m2024-11-26 14:30:17\u001b[0m [\u001b[32m\u001b[1minfo     \u001b[0m] \u001b[1mcost(depth 5 = -11.1533203125 \u001b[0m \u001b[36mfile\u001b[0m=\u001b[35mqaoa.qaoa\u001b[0m \u001b[36mfunc\u001b[0m=\u001b[35moptimize\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "maxdepth = 5\n",
    "qaoa_k3_subH.optimize(depth=maxdepth)\n",
    "\n",
    "p = np.arange(1, len(np.array(qaoa_k3_subH.get_Exp())) + 1)\n",
    "maxval=12\n",
    "plt.plot(p, -np.array(qaoa_k3_fullH.get_Exp()) / maxval, marker=\"x\", label=\"full H\")\n",
    "plt.plot(p, -np.array(qaoa_k3_subH.get_Exp()) / maxval, marker=\"x\", label=\"sub H\")\n",
    "plt.xlabel(\"depth\")\n",
    "plt.ylabel(\"Approx. ratio\")\n",
    "plt.legend()\n",
    "plt.title(\"QAOA Max 3-Cut using the full Hilbert space\")\n",
    "plt.ylim([0, 1])\n",
    "plt.show()"
   ]
  },
  {
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   "source": [
    "For more info you can look into the following reference.\n",
    "\n",
    "# References\n",
    "<a id=\"1\">[1]</a>\n",
    "Fuchs, Franz G., Ruben P. Bassa, and Frida Lien.\n",
    "\"Encodings of the weighted MAX k-CUT on qubit systems.\"\n",
    "Preprint arXiv 2024.\n",
    "[arXiv:2411.08594](https://doi.org/10.48550/arXiv.2411.08594)\n",
    "\n",
    "<a id=\"2\">[2]</a>\n",
    "Fuchs, Franz G., Ruben P. Bassa.\n",
    "\"LX-mixers for QAOA: Optimal mixers restricted to subspaces and the stabilizer formalism.\"\n",
    "Quantum 8 (2024): 1535.\n",
    "[10.22331/q-2024-11-25-1535](https://doi.org/10.22331/q-2024-11-25-1535)\n",
    "\n",
    "<a id=\"3\">[3]</a>\n",
    "Bärtschi, Andreas, and Stephan Eidenbenz.\n",
    "\"Grover mixers for QAOA: Shifting complexity from mixer design to state preparation.\"\n",
    "In 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 72-82. IEEE, 2020.\n",
    "[10.1109/QCE49297.2020.00020](https://doi.org/10.1109/QCE49297.2020.00020)"
   ]
  }
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