23_HybridApproaches-VariationalClassification(-).ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 23: Hybrid Approaches - Variational Classification \n",
    "\n",
    "We use the parameterized $qiskit4 quantum circuit over two qubits $U_{\\phi(\\textbf{x})}=ZZFeatureMap$ with repetition two where the parameter are defined by the data by the command $bind\\_parameters$ with the two dimensional vector $\\textbf{x}$.\n",
    "The variational quantum circuits that represents the free parameter $\\textbf{w}$ that will adapt during  training is the $qiskit$ quantum circuit  $U_{W(\\textbf{w})}=TwoLocal$.\n",
    "The $TwoLocal$ circuit is a parameterized circuit consisting of alternating rotation layers and entanglement layers. The rotation layers are single qubit gates applied on all qubits. The entanglement layer uses two-qubit gates to entangle the qubits according to the definition. In our example we will use the rotation gates $RX$ and $RZ$ and the  entanglement  gate  \n",
    "controlled $Z$ rotation, $CZ$. with two repetitions resulting in $12$ free parameters. The twelve dimensional vector  $\\textbf{w}$  defines the parameters by the  $bind\\_parameters$  command. After the operations we measure the two qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌────────┐                                 ┌───┐┌────────┐                                  ░ ┌────────────────┐»\n",
       "q_0: ┤ H ├┤ P(0.2) ├──■───────────────────────────■──┤ H ├┤ P(0.2) ├──■───────────────────────────■───░─┤ Ry(3.28559355) ├»\n",
       "     ├───┤├────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐├───┤├────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐ ░ ├────────────────┤»\n",
       "q_1: ┤ H ├┤ P(0.2) ├┤ X ├┤ P(18.5025717407428) ├┤ X ├┤ H ├┤ P(0.2) ├┤ X ├┤ P(18.5025717407428) ├┤ X ├─░─┤ Ry(5.48514978) ├»\n",
       "     └───┘└────────┘└───┘└─────────────────────┘└───┘└───┘└────────┘└───┘└─────────────────────┘└───┘ ░ └────────────────┘»\n",
       "c: 2/═════════════════════════════════════════════════════════════════════════════════════════════════════════════════════»\n",
       "                                                                                                                          »\n",
       "«     ┌────────────────┐   ┌────────────────┐┌────────────────┐   ┌────────────────┐┌────────────────┐ ░ ┌─┐   \n",
       "«q_0: ┤ Rz(5.13099949) ├─■─┤ Ry(4.08885928) ├┤ Rz(4.92364593) ├─■─┤ Ry(3.66837805) ├┤ Rz(3.60713748) ├─░─┤M├───\n",
       "«     ├────────────────┤ │ ├────────────────┤├────────────────┤ │ ├────────────────┤└┬─────────────┬─┘ ░ └╥┘┌─┐\n",
       "«q_1: ┤ Rz(0.88372228) ├─■─┤ Ry(2.45568528) ├┤ Rz(5.59032015) ├─■─┤ Ry(4.84632313) ├─┤ Rz(2.43546) ├───░──╫─┤M├\n",
       "«     └────────────────┘   └────────────────┘└────────────────┘   └────────────────┘ └─────────────┘   ░  ║ └╥┘\n",
       "«c: 2/════════════════════════════════════════════════════════════════════════════════════════════════════╩══╩═\n",
       "«                                                                                                         0  1 </pre>"
      ],
      "text/plain": [
       "     ┌───┐┌────────┐                                 ┌───┐┌────────┐                                  ░ ┌────────────────┐»\n",
       "q_0: ┤ H ├┤ P(0.2) ├──■───────────────────────────■──┤ H ├┤ P(0.2) ├──■───────────────────────────■───░─┤ Ry(3.28559355) ├»\n",
       "     ├───┤├────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐├───┤├────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐ ░ ├────────────────┤»\n",
       "q_1: ┤ H ├┤ P(0.2) ├┤ X ├┤ P(18.5025717407428) ├┤ X ├┤ H ├┤ P(0.2) ├┤ X ├┤ P(18.5025717407428) ├┤ X ├─░─┤ Ry(5.48514978) ├»\n",
       "     └───┘└────────┘└───┘└─────────────────────┘└───┘└───┘└────────┘└───┘└─────────────────────┘└───┘ ░ └────────────────┘»\n",
       "c: 2/═════════════════════════════════════════════════════════════════════════════════════════════════════════════════════»\n",
       "                                                                                                                          »\n",
       "«     ┌────────────────┐   ┌────────────────┐┌────────────────┐   ┌────────────────┐┌────────────────┐ ░ ┌─┐   \n",
       "«q_0: ┤ Rz(5.13099949) ├─■─┤ Ry(4.08885928) ├┤ Rz(4.92364593) ├─■─┤ Ry(3.66837805) ├┤ Rz(3.60713748) ├─░─┤M├───\n",
       "«     ├────────────────┤ │ ├────────────────┤├────────────────┤ │ ├────────────────┤└┬─────────────┬─┘ ░ └╥┘┌─┐\n",
       "«q_1: ┤ Rz(0.88372228) ├─■─┤ Ry(2.45568528) ├┤ Rz(5.59032015) ├─■─┤ Ry(4.84632313) ├─┤ Rz(2.43546) ├───░──╫─┤M├\n",
       "«     └────────────────┘   └────────────────┘└────────────────┘   └────────────────┘ └─────────────┘   ░  ║ └╥┘\n",
       "«c: 2/════════════════════════════════════════════════════════════════════════════════════════════════════╩══╩═\n",
       "«                                                                                                         0  1 "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit,QuantumRegister, Aer,execute\n",
    "from qiskit.visualization import plot_histogram\n",
    "import numpy as np\n",
    "from qiskit.circuit.library import ZZFeatureMap, TwoLocal\n",
    "\n",
    "x = [0.1, 0.1]\n",
    "feature_map = ZZFeatureMap(feature_dimension=2, reps=2)\n",
    "feature_map = feature_map.bind_parameters(x)\n",
    "\n",
    "weights =np.array([3.28559355, 5.48514978, 5.13099949,\n",
    "                          0.88372228, 4.08885928, 2.45568528,\n",
    "                          4.92364593, 5.59032015, 3.66837805,\n",
    "                          4.84632313, 3.60713748, 2.43546])\n",
    "two_local = TwoLocal(2, ['ry', 'rz'],'cz', reps=2)\n",
    "two_local = two_local.bind_parameters(weights)\n",
    "\n",
    "\n",
    "\n",
    "qc = QuantumCircuit(2,2)\n",
    "qc.compose(feature_map, inplace=True)\n",
    "qc.barrier()\n",
    "qc.compose(two_local, inplace=True)\n",
    "qc.barrier()\n",
    "qc.measure(0,0)\n",
    "qc.measure(1,1)\n",
    "qc.decompose().draw(fold=130)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Total count are: {'01': 5580, '00': 725, '10': 1785, '11': 1910}\n"
     ]
    },
    {
     "data": {
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kUwozuEG31t6LiIh0NQpBERGRkMJe0wxF1zRFRKQzC3tNMwxd0xQRkU4tpmuaIiIiXZkCUUREJCTdpykiIhKS7tMUEREJSfdpioiIhKQQFBERCSnm0DSzIjN7wswqI685LZ63KSIi0inFFJpmdgnwDnAy8LvIayCwzMz+Kf7liYiIpI6wz9M86B7g++5+b3Sjmf0rcDfwZLwKExERSTWxnp49CXimlfb5wIBjL0dERCR1xRqabwJntdJ+FrDoWIsRERFJZbEO2P4K8GMzKwbejrSdDnwTuDPu1YmIiKSQox2wfXrkFe1nwCPHXJGIiEiK0oDtIiIiISkQRUREQor1lhPMLBP4OjAU6B49zd3vilNdIiIiKSem0DSz04GXgQaC20/qCQY6aADWAwpNERHptGI9PXs/8BQwBNgPfJXgiLMS+Lf4liYiIpJaYg3NscBMd3egCchw9y3ALYS85cTMrjWzWjPbb2bLzezMduadYGZLzWy7me0zsw/M7OZW5rvAzGrMrCHy9fwYt0tEROSIYg3NA1HvtwCnRN7vBQYfaWEzmwI8BNwLnAosBV4xs6FtLLIXeBgYD+QRDNX3QzO7NmqdpcDTBEfAhZGv882sJPRWiYiIhBBraFYB4yLvFwJ3m9llBMH2bojlbwJmu/ssd3/f3a8HNgHXtDazuy9393nuvsrda939SeD3QPTR6Q3Am+5+T2Sd90RquyHGbRMREWlXrKF5G/CXyPvbgY8IBjXI5PDBDg5hZt2B04BXW0x6FTgjzDc3s1Mj80YP2Vfayjp/H3adIiIiYcXUe9bdK6Pef0Rw60lYJwJpBKd1o20BzmlvQTOrI+itmw780N1/ETV5UBvrHNTGuppHMxo8eDALFy4EICcnhz59+lBdXQ1A//79yc/PZ/HixQCkp6dTVlZGVVUVu3fvBqC4uJgtW7awceNGAEaMGEFGRgYrV64EYMCAAYwcOZIlS5YAkJGRQWlpKZWVlezduxeAkpIS6urqqK+vB2DUqFGkpaVRU1MTbNygQQwfPpzy8nIAevbsSUlJCRUVFezbtw+A0tJSamtr2bx5MwB5eXk0NTWxevVqAIYMGUJWVhYVFRUA9O7dm+LiYsrLy2loaACgrKyMNWvWsHXrVgDGjBlDQ0MDa9euBSA7O5uBAwdSWRn8F+jbty9FRUUsWbKExsZGAMaPH8+qVavYvn07AAUFBezZs4d169YBMGzYMPr160dVVRUAmZmZFBQUsGjRItwdM2PChAlUV1ezc+dOAIqKitixYwfr16+PaT91Jp15P+nnSfspFfdTeyzo0xMbM/siMDryscbd14VYZjDBLSoT3H1xVPsdwCXuPqqdZYcDvQnGuf034F/cfU5k2gHgu+7+RNT8lwKz3D2jvZqKi4v94H9a6VyufDDZFcTPrBuSXYFI12Jmy929uLVpsd6n2R/4NTAZ+Ox/m+23wOXuvr2dxbcR9Lgd2KJ9ILC5ve/r7rWRt++Z2UCCnrpzIm2bj2adIiIisYr1muajQC5BR5wekdd4YDgwq70F3f0AsBw4t8Wkcwl60YbVDYg+giyPwzpFRESOKNZh9CYCX3P38qi2t8zsKuAPIZZ/AJhjZsuAt4CrCW5V+QWAmT0B4O6XRj5fD9QCqyPLjwdu5tCnqTwELDazW4HngfOBs4HOdWFLRESSLtbQ/Aj4ayvtnwDtnZoFwN2fjpzivZ1g+L2VwCR33xCZpeX9mmkE1zCHAY3An4BbiYRsZJ1LzWwqwT2cd0XmmeLuFeE3S0RE5MhiDc27gAfN7J/dvR7AzIYA/0HIcWfd/RHaeO6mu5/V4vODwIMh1vksrT/3U0REJG6OGJpm9h4Q3cV2OLDezOojnw+OQzuA4JqniIhIpxTmSFNHcCIiIoQITXf/YSIKERERSXUxP4QawMy+SjCAugOr3H1hPIsSERFJRbEObjAE+B+CMWQPjkE72MwqgfPd/S9tLiwiInKci3Vwg4cJRvXJdfdsd88GRkTaHo53cSIiIqkk1tOz5wJnRQ1rh7uvM7MZwOtxrUxERCTFxHqkCYfeftJem4iISKcSa2i+DvzMzLIPNpjZUIIBCHSkKSIinVqsoTkDOAFYZ2YbzGwDwbB1J0SmiYiIdFqxXtPcDvwNcBbwpUjb++4eZrB2ERGR41ro0DSzNGAXUODurwGvdVhVIiIiKSj06Vl3bwI2AN07rhwREZHUFes1zR8B95nZiR1RjIiISCqL9ZrmzQRPOak3szpaPFvT3cfGqzAREZFUE2toPktwT6Z1QC0iIiIpLVRomlkv4H7gH4HPEdyTeb27b+u40kRERFJL2GuaPwS+DbwMzAXOAf6zg2oSERFJSWFPz34TuMLd5wGY2VPAW2aWFulVKyIi0umFPdLMBv7fwQ/uvgxoBAZ3RFEiIiKpKGxopgEHWrQ1cpQPsRYRETkehQ09A540s4aoth7ALDP75GCDu0+OZ3EiIiKpJGxoPt5K25PxLERERCTVhQpNd/9ORxciIiKS6o7mIdQiItKFLViwgFGjRpGbm8t999132PTFixdTVFREeno6zz777CHTbrnlFsaMGcOYMWN4+umnm9tnzpxJbm4uZsa2bak7BIBCU0REQmtqauK6667jlVdeoaamhrlz51JTU3PIPEOHDmX27NlcfPHFh7S//PLLVFVVsWLFCioqKvjJT37C7t27AfjKV77CH/7wB0455ZSEbcvRUGiKiEhoy5YtIzc3l5ycHLp3787UqVN54YUXDpln2LBhjB07lm7dDo2Ympoaxo8fT3p6OieccAJjx45lwYIFAJx66qkMGzYsUZtx1BSaIiISWn19PdnZ2c2fs7KyqK+vD7VsQUEBCxYs4JNPPmHbtm28+eabbNy4saNK7RC6z1JERBLivPPO45133uGMM87gpJNOorS0lLS0tGSXFRMdaYpISjvaTidvvvkmhYWFza8ePXrw/PPPA/D6669TVFREYWEhZWVlfPjhh4nanOPekCFDDjk6rKurY8iQIaGXv+2221ixYgWvvfYa7s7IkSM7oswOo9AUkZR1LJ1Ozj77bFasWMGKFSt444036NWrF+eddx4A11xzDU899RQrVqzg4osv5u67707YNh3vxo0bx9q1a6mtreXAgQPMmzePyZPDjWvT1NTE9u3bAXj33Xd59913m/fJ8UKhKSIp61g6nUR79tln+frXv06vXr0AMLPmXpu7du1i8GANox1Weno6M2fOZOLEiYwePZqLLrqI/Px87rjjDl588UUA3nnnHbKyspg/fz5XXXUV+fn5AHz66aeceeaZ5OXlMX36dJ588knS04OrhA8//DBZWVnU1dUxduxYvvvd7yZtG9uja5oikrJa63RSUVER83rmzZvHTTfd1Pz50UcfZdKkSfTs2ZO+ffvy9ttvx6XermLSpElMmjTpkLa77rqr+f24ceOoq6s7bLkePXocdqbgoBkzZjBjxoz4FtoBdKQpIp3apk2beO+995g4cWJz209/+lN+97vfUVdXx3e+851DAlWkPQpNEUlZx9rpBOCZZ57h/PPP53Of+xwAH330EdXV1ZSUlAAwZcoUli5dGr+ipVNTaIpIyjqWTicHzZ07l2nTpjV/zszMZNeuXaxZswaA1157jdGjR8e1bum8dE1TRFJWdKeTpqYmLr/88uZOJ8XFxUyePJl33nmH888/n507d/LSSy/xgx/8gFWrVgGwfv16Nm7cyIQJEw5Z56xZs7jgggvo1q0bmZmZ/OY3v0nWJspxxtw92TUkTXFxsVdWVia7DOkAVz6Y7AriZ9YNya5AOjP9rBzOzJa7e3Fr03R6VkREJCSFpoiISEgKTRERkZAUmiIiIiGp96yIJIw6ncjxTkeaIiIiISk0RUREQlJoioiIhKTQFBERCUmhKSIiEpJCU0REJCSFpoiISEgJD00zu9bMas1sv5ktN7Mz25n3ZDP7LzP7wMyazGx2K/N828y8lVePDt0QERHpchIammY2BXgIuBc4FVgKvGJmQ9tYJAPYBtwHVLSz6k+Ak6Nf7r4/XnWLiIhA4o80bwJmu/ssd3/f3a8HNgHXtDazu6939xnuPhvY0c563d03R7/iX7qIiHR1CRtGz8y6A6cBP2kx6VXgjGNcfU8z2wCkASuA77v7H9uoYzowHWDw4MEsXLgQgJycHPr06UN1dTUA/fv3Jz8/n8WLFwPBg2vLysqoqqpi9+7dABQXF7NlyxY2btwIwIgRI8jIyGDlypUADBgwgJEjR7JkyRIAMjIyKC0tpbKykr179wJQUlJCXV0d9fX1AIwaNYq0tDRqamoAGDRoEMOHD6e8vDzY0J49KSkpoaKign379gFQWlpKbW0tmzcHfyvk5eXR1NTE6tWrARgyZAhZWVlUVAQH671796a4uJjy8nIaGhoAKCsrY82aNWzduhWAMWPG0NDQwNq1awHIzs5m4MCBHHz+aN++fSkqKmLJkiU0NjYCMH78eFatWsX27dsBKCgoYM+ePaxbtw6AYcOG0a9fP6qqqgDIzMykoKCARYsW4e6YGRMmTKC6upqdO3cCUFRUxI4dO1i/fn1M+6kz6Uz7qTN1ozj4u+N4/3mCtk70HX82bdoUl9977UnYQ6jNbDBQD0xw98VR7XcAl7j7qCMs/1tgm7t/u0V7KTASqAb6AP8CTAIK3H1te+vUQ6g7L41xmpq0X1KP9snh2nsI9XE/YLu7lwPlBz+b2VKCo83rgRlJKktERDqhRJ4r2QY0AQNbtA8E4nYN0t2bgEpgRLzWKSIiAgkMTXc/ACwHzm0x6VyCXrRxYWYGjCXoYCQiIhI3iT49+wAwx8yWAW8BVwODgV8AmNkTAO5+6cEFzKww8rYv8Fnk8wF3r4lM/wHwNrA2Ms8MgtBstUeuiIjI0UpoaLr702bWH7id4H7KlcAkd98QmaW1blwte8H+PbABGBb5/AXgV8AgYFdk/vHuviyuxYuISJeX8I5A7v4I8Egb085qpc2OsL4bgRvjUpyIiEg7Os9NUyIiIh1MoSkiIhKSQlNERCQkhaaIiEhICk0REZGQFJoiIiIhKTRFRERCUmiKiIiEpNAUEREJSaEpIiISkkJTREQkJIWmiIhISApNERGRkBSaSbJgwQJGjRpFbm4u991332HTGxoamDJlCrm5uZSUlLB+/XoAnnrqKQoLC5tf3bp1Y8WKFXzyySd84xvf4Etf+hL5+fnceuutCd4iEZHOT6GZBE1NTVx33XW88sor1NTUMHfuXGpqag6Z59e//jWZmZl8+OGH3Hjjjdxyyy0AXHLJJaxYsYIVK1YwZ84chg8fTmFhIQA333wzH3zwAX/84x956623eOWVVxK9aSIinZpCMwmWLVtGbm4uOTk5dO/enalTp/LCCy8cMs8LL7zAZZddBsCFF17I66+/jrsfMs/cuXOZOnUqAL169eLss88GoHv37hQVFVFXV5eArRER6ToUmklQX19PdnZ28+esrCzq6+vbnCc9PZ3Pf/7zbN++/ZB5nn76aaZNm3bY+j/++GNeeuklvva1r3VA9SIiXZdC8zhVUVFBr169GDNmzCHtjY2NTJs2jRkzZpCTk5Ok6kREOieFZhIMGTKEjRs3Nn+uq6tjyJAhbc7T2NjIrl276N+/f/P0efPmtXqUOX36dEaMGMENN9zQMcWLiHRhCs0kGDduHGvXrqW2tpYDBw4wb948Jk+efMg8kydP5vHHHwfg2Wef5atf/SpmBsBnn33GM88803w986Dbb7+dXbt28eCDDyZkO0REuhqFZhKkp6czc+ZMJk6cyOjRo7nooovIz8/njjvu4MUXXwTgiiuuYPv27eTm5vLAAw8cclvK4sWLyc7OPuT0a11dHffccw81NTUUFRVRWFjIo48+mvBtExHpzNKTXUBXNWnSJCZNmnRI21133dX8vkePHsyfP7/VZc866yzefvvtQ9qysrIO610rIiLxpSNNERGRkBSaIiIiIen0bBxc+WCyK4ifWTckuwIRkdSlI00REZGQFJoiIiIhKTRFRERCUmiKiIiEpNAUEREJSaEpIiISkkJTREQkJIWmiIhISApNERGRkBSaIiIiISk0RUREQlJoioiIhKTQFBERCUmhKSIiEpJCU0REJCSFpoiISEgKTRERkZAUmiIiIiEpNEVEREJSaIqIiISk0BQREQlJoSkiIhKSQlNERCQkhaaIiEhICk0REZGQEh6aZnatmdWa2X4zW25mZx5h/gmR+fab2Tozu/pY1ykiInI0EhqaZjYFeAi4FzgVWAq8YmZD25h/OPC7yHynAj8GfmZmFxztOkVERI5Woo80bwJmu/ssd3/f3a8HNgHXtDH/1cBf3P36yPyzgMeBm49hnSIiIkfF3D0x38isO/AJMM3d50e1/xwY4+4TWllmMfCeu18X1fYt4L+AXoAdxTqnA9MjH0cBq+OweYlwIrAt2UXIYbRfUo/2SWo6nvbLKe5+UmsT0hNYxIlAGrClRfsW4Jw2lhkE/KGV+dMj67NY1+nuvwJ+FbrqFGFmle5enOw65FDaL6lH+yQ1dZb9ot6zIiIiISXySHMb0AQMbNE+ENjcxjKb25i/MbI+O4p1ioiIHJWEHWm6+wFgOXBui0nnEvR4bU15G/NXuvunR7nO49Vxd0q5i9B+ST3aJ6mpU+yXhHUEgubbQ+YA1wJvEfSOvQLId/cNZvYEgLtfGpl/OLASmAX8EvgK8AhBx5/nwqwzYRsnIiKdXiJPz+LuT5tZf+B24GSCQJwUFW5DW8xfa2aTgJ8S3ELyF2DGwcAMuU4REZG4SOiRpoiIyPFMvWdFRERCUmiKiIiEpNAUkU7DzCz6q0i86ZpmCjOzLCCX4H7Uz4DV7q77T0VCOhierl90EicKzRRlZtcAlwMFwF+BD4E64G3geXdfbWbd3P2zJJbZpZhZT3ffl+w65HBm1g34B+AkgnGp64FF7r41qYVJp6PQTEGRW2g+BP4D+E+CXwTnAGcBownC80Z3rzEz01/RHc/MMoFq4GXgSWDpwX/36H1gZl8ieDLP7qQV28WYWR/g18DZBGdk6gAH9gOLgDnu/oF+VhLHzD4HDAc2uHtDsuuJJ13TTE0XA2vc/W533+7uH7j7THe/ELiK4C/p35rZifolkDD/RDA842nAYuBDM7vLzEZFBWY2MJfgYQKSODMInlg0yd0HApcADwLvAecB/25mJ+lnJaGuA/4I/MLM/t7MBplZWvQMZtbXzL4eCdjjhkIzNR0A+pjZGAAzy4g8Wg13X0LwS2E/wS8ESYyxwGPA3xE87PwZYBpQY2ZvRx4590/ACHdfl7wyu6S/BR5393cAIn9kPgl8D/g/BGdn5iSxvq5oCrCMoE/G8wRDot5vZmVm9vnIPBcDP3D3T5NT4tFRaKamZwlOM91gZn3cvcHdD0Su2+DufwY+BrKSWGOXYWYZQA2w0d23uvu77v6vQDEwMTLtTuAe4N+SVmgXZGbpBKOAXWBmJ0Xa0iLX+5vcfTHB0JpZZlaQzFq7ish++BSY5e5nAqcQnD7/O4KzNG+Y2S3ADUBFsuo8WrqmmWKiusr/A/AQ0I/gqOYRgtMdWcB4gmudX3b39Ukos8uJBGemu2+OnGby6E5YZnYW8AYw1N3rklNl12RmpwNPEfyx+YC7b2kxPRt4Hxjl7vVJKLFLMbOTgalAjbv/vsW0U4HvRqZnAtnH2z5RaKYoM/sCwVi8ZwDnEwxWD8Ejz4ygc8OdSSmuiznYgcTMcoC/Rv9Sjpp2B/Btd89JXqVdT+TsSzfgO8C9BONpPwc8DfyZ4LT63wF57j4uWXV2NWbWk+APy/3R98xGXf+/h+Aa9KnJqvFoKTRTiJkNAP6Z4DrMNmAfwWnYJQS3mnyO4BrBAndfk6Qyu5SofXITsJXgWa6bgPnAf7v7XyO/FK4k6DX726QV28VF/tD8NsG1skJgD8G1/3eAH7v7cXcq8HjWVm9lM+sFVAGPuftxdzlDoZlCzGw2kA+8BOwgODX7ZWAkwS/s2/WDn1ht7JNTgS8R3Npwv7u/mrQCuzAz6wvsif7FHDny7AH0BsYQnBnQz0yCtLZPWpmnB0FHobmRZyIfVxSaKSJytLKH4JTF4qi2oUAJwXWAHOAid69KWqFdSDv7JAs4neDo8hSC57tqnySYmf2SoIfmMoL7AQ+7N9bMMt19p+7RTIyQ++QL7v5xomuLF/WeTR15QC3B7SZAcP7f3Te4+zPA3xOcqv1WcsrrktraJxvdfT7BtbI9aJ8knJlNI/ij5T+AFwhuZ/immeVGrqdhZr2Bx8zsywrMjtfGPjnfzL4YtU96Ao8fvJ3ueKQjzRQR+c/0W4KBCy4F/tRyiDwzux64wt0LE19h16N9krrMbBbQBPw78E3gMuCLwGrgd8DrBAMePOTu3ZNVZ1fSVfaJjjRTRGRM09uAnsATwKVmlh35a/ngxfMJBPekSQJon6SmyL2ZtcDH7r7O3X/i7l8GxhEMm3cZwW1aP0ODGiREV9onOtJMMZHTFt8HJhMM1F4OfEQw9uwm4Lvu/l7yKux6tE9ST2Qs4IGRMWW7A5+26BA0hWBIwyJ3X5GkMruUrrJPFJopKnKrwzeAfyToNr8SmO/uHySzrq5M+yS1RXrOmrs3mdmVBKcBeyW7rq6sM+4TheZxwPQIsJSjfZLazOwmIM3d7092LRLoLPtEoSkinU7kyRlN+sMmdXSWfaLQFBERCUm9Z0VEREJSaIqIiISk0BQREQlJoSkiIhKSQlNERCQkhaaIiEhI/x8nluktUcgZDgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result=execute(qc,simulator,shots=10000).result()\n",
    "counts = result.get_counts()\n",
    "print(\"\\nTotal count are:\",counts)\n",
    "\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We perform 1$0000$ shots.\n",
    " The string $01$ appears (approximately) $5483$ times and the string $10$ appears  (approximately)  $1892$. \n",
    " We define the binary output from the binary string by a parity function,  $p(1)=o_k=(5483+1892)/1000=0.7375$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $Qiskit$ Variational Quantum Classifier\n",
    "\n",
    "In this simple $qiskit$  example we create $10$ two dimensional training data points and $5$ testing data points  for two classes each.\n",
    " We use  the same classification circuit as before.\n",
    "We one hot encode our labels, as required by the algorithm using cross entropy.\n",
    "Then, we set up our classical optimizer and the VQC algorithm  using the callback function.\n",
    "We plot the cost function with respect to optimization step,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.utils import algorithm_globals\n",
    "algorithm_globals.random_seed = 3142\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(algorithm_globals.random_seed)\n",
    "\n",
    "from qiskit_machine_learning.datasets import ad_hoc_data\n",
    "TRAIN_DATA, TRAIN_LABELS, TEST_DATA, TEST_LABELS = (\n",
    "    ad_hoc_data(training_size=10,\n",
    "                test_size=5,\n",
    "                n=2,\n",
    "                gap=0.3,\n",
    "                one_hot=False)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.circuit.library import ZZFeatureMap, TwoLocal\n",
    "FEATURE_MAP = ZZFeatureMap(feature_dimension=2, reps=2)\n",
    "VAR_FORM = TwoLocal(2, ['ry', 'rz'], 'cz', reps=2)\n",
    "AD_HOC_CIRCUIT = FEATURE_MAP.compose(VAR_FORM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder\n",
    "encoder = OneHotEncoder()\n",
    "train_labels_oh = encoder.fit_transform(TRAIN_LABELS.reshape(-1, 1)\n",
    "                                       ).toarray()\n",
    "test_labels_oh = encoder.fit_transform(TEST_LABELS.reshape(-1, 1)\n",
    "                                      ).toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit_machine_learning.algorithms.classifiers.vqc.VQC at 0x7ff48d43be50>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit,QuantumRegister, Aer,execute\n",
    "from qiskit.algorithms.optimizers import SPSA\n",
    "\n",
    "class OptimizerLog:\n",
    "    \"\"\"Log to store optimizer's intermediate results\"\"\"\n",
    "    def __init__(self):\n",
    "        self.evaluations = []\n",
    "        self.parameters = []\n",
    "        self.costs = []\n",
    "    def update(self, evaluation, parameter, cost, _stepsize, _accept):\n",
    "        \"\"\"Save intermediate results. Optimizer passes five values\n",
    "        but we ignore the last two.\"\"\"\n",
    "        self.evaluations.append(evaluation)\n",
    "        self.parameters.append(parameter)\n",
    "        self.costs.append(cost)\n",
    "\n",
    "#initial_point = np.random.random(VAR_FORM.num_parameters)\n",
    "initial_point = np.array([0.3200227 , 0.6503638 , 0.55995053,\n",
    "                          0.96566328, 0.38243769, 0.90403094,\n",
    "                          0.82271449, 0.26810137, 0.61076489,\n",
    "                          0.82301609, 0.11789148, 0.29667125])\n",
    "\n",
    "from qiskit_machine_learning.algorithms.classifiers import VQC\n",
    "log = OptimizerLog()\n",
    "vqc = VQC(feature_map=FEATURE_MAP,\n",
    "          ansatz=VAR_FORM,\n",
    "          loss='cross_entropy',\n",
    "          optimizer=SPSA(callback=log.update),\n",
    "          initial_point=initial_point,\n",
    "          quantum_instance=Aer.get_backend('qasm_simulator'))\n",
    "\n",
    "vqc.fit(TRAIN_DATA, train_labels_oh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure()\n",
    "plt.plot(log.evaluations, log.costs)\n",
    "plt.xlabel('Steps')\n",
    "plt.ylabel('Cost')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the cost function with respect to optimization step, we can see it starts to converge to a minimum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we test our trained VQC classifier by score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# score == accuracy\n",
    "vqc.score(TEST_DATA, test_labels_oh)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.7.11"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}