QSP_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "670c95a8",
   "metadata": {},
   "source": [
    "# LCU + QSP solution of a tridiagonal system\n",
    "\n",
    "We are interested in solving the Laplacian problem.\n",
    "\n",
    "The Laplacian problem, in 1D, is a tridiagonal system.\n",
    "\n",
    "A tridiagonal system can be decomposed into a gate-efficient set of unitaries.\n",
    "\n",
    "An LCU of these unitaries will create a block-encoding of the system.\n",
    "\n",
    "The block-encoding of the system will be used in QSP to solve the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d3a5c57d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit\n",
    "from qiskit import QuantumCircuit, QuantumRegister"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e531fbc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of qubits in work register\n",
    "n = 4\n",
    "\n",
    "workRegister = QuantumRegister(n)\n",
    "\n",
    "circ = QuantumCircuit(workRegister)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "284fa6d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 287.496x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Circuit that creates L1_1 unitary\n",
    "L1_1 = QuantumCircuit(n)\n",
    "\n",
    "# Apply -ve sign to one side\n",
    "L1_1.z(0)\n",
    "L1_1.x(0)\n",
    "\n",
    "L1_1.draw('mpl',style='iqp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0a0dd1da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 203.885x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Circuit that creates L1_2 unitary\n",
    "L1_2 = QuantumCircuit(n)\n",
    "\n",
    "L1_2.x(0)\n",
    "\n",
    "L1_2.draw('mpl',style='iqp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bcc757f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_22951/1249342728.py:10: DeprecationWarning: The method ``qiskit.circuit.quantumcircuit.QuantumCircuit.cnot()`` is deprecated as of qiskit 0.45.0. It will be removed no earlier than 3 months after the release date. Use QuantumCircuit.cx as direct replacement.\n",
      "  [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in range(1,i+1)]\n",
      "/tmp/ipykernel_22951/1249342728.py:13: DeprecationWarning: The method ``qiskit.circuit.quantumcircuit.QuantumCircuit.cnot()`` is deprecated as of qiskit 0.45.0. It will be removed no earlier than 3 months after the release date. Use QuantumCircuit.cx as direct replacement.\n",
      "  [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in reversed(range(1,i+1))]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1643.3x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Circuit that creates L2_1 unitary\n",
    "\n",
    "# First need a function to create the Ci circuits\n",
    "def C_i(i,workRegister):\n",
    "    n = workRegister.size\n",
    "    if i<1 or i>(n-1):\n",
    "        print('WRONG VALUE FOR i !!!!')\n",
    "        return\n",
    "    Ci = QuantumCircuit(workRegister, name='C_{}'.format(i))\n",
    "    [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in range(1,i+1)]\n",
    "    Ci.append(qiskit.circuit.library.MCXGate(num_ctrl_qubits=i, ctrl_state='0'*i),workRegister[:i+1])\n",
    "#     Ci.mcx(control_qubits=workRegister[:i-1],target_qubit=workRegister[i-1])\n",
    "    [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in reversed(range(1,i+1))]\n",
    "    return Ci\n",
    "\n",
    "\n",
    "\n",
    "L2_1 = QuantumCircuit(workRegister)\n",
    "\n",
    "\n",
    "# Apply -ve to sign to alternating bits\n",
    "L2_1.x(0)\n",
    "L2_1.z(0)\n",
    "L2_1.x(0)\n",
    "\n",
    "for j in range(1,n):\n",
    "    L2_1 = L2_1.compose(C_i(j,workRegister))\n",
    "    \n",
    "    \n",
    "    \n",
    "L2_1.draw('mpl',style='iqp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a950e51b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_22951/2674443748.py:10: DeprecationWarning: The method ``qiskit.circuit.quantumcircuit.QuantumCircuit.cnot()`` is deprecated as of qiskit 0.45.0. It will be removed no earlier than 3 months after the release date. Use QuantumCircuit.cx as direct replacement.\n",
      "  [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in range(1,i+1)]\n",
      "/tmp/ipykernel_22951/2674443748.py:13: DeprecationWarning: The method ``qiskit.circuit.quantumcircuit.QuantumCircuit.cnot()`` is deprecated as of qiskit 0.45.0. It will be removed no earlier than 3 months after the release date. Use QuantumCircuit.cx as direct replacement.\n",
      "  [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in reversed(range(1,i+1))]\n"
     ]
    },
    {
     "data": {
      "image/png": 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ve9XXZdIVXfUDeQUy3IziFGIiXdNlX3z+huEsvTP543NISM6Hf0N73Ng2GJ+82RJedW0hFgtR28kSs8YF4q8dQ9CtdR3k5ksxcs5Jg1lSgveDRFQZpVKJMR+cQlYV1wVPTi/E+PlnNBwVaYrRJgVnzJiB+Ph4TJ8+HcuWLYOtrW3pa3PmzEHz5s0hk8ng5eUFOzs7AEBGRgYAwMHBodzjPn3taVlDcTVcd08ws3KKER2n/1NGCotkWPP3KJqfFnRCcIBzmeVEIiF+mNceLf2dUFQsxzodjcBUlS7PAV22Tf+4Gq67pIwu21bFr/vuIydPCr8GtbDuky4wMyv7MtnUxxEbP+sCANiw+x5yDWBdqcSUfCRU8rRXkwzlHCAyZrr8HF6LSDWIxNm92CwcvvAYAgGw65secHe1LrOcrbUEO7/uDjsbM9yLzcaxS4+1HGn18H6QiCpz/voT/BWVrlKds9dUr0P6wSiTghEREdiyZQucnZ2xaNGiMssEBwcDAJo3b176s8LCkl2xJBJJucc2NzcHABQUPDs67OHDhxg4cCBsbW3h4OCAV199FWlp+vMF6LqOF3k3hEXmdx6PRWpGITxqW2PIC54VlhWJhHhrTACAkjVSDIEuz4Gk1AI8MdDNWYxFTl4x7j/S3bD+G3f1vw8AgNV/r706fXRAuQnBp3p39ICvZy3k5Emx6UC0NsKrEV33w7q+DhGRbvuB7FwpHj7W/4fEa3aUPCB+sXM9+HrVqrCsvZ05xg30AaCbtbtVVSyV4/Z93Q1suB7JhAGRIVi9vXr92WoD6AfpeWXPkTVwmzZtgkKhwNixY2FjY1NmGUtLSwDPJgUtLCwAAMXF5Q+TLSoqeqY+ULJBSUhICBwdHbFp0yYUFBRgzpw56N+/P86fPw+hsHq511atWiEpST3T/dKthwDmQWW+FrppINycrcqt6+ZsWfrvuKOjKmwnKTUfrUc/vwnL5Klv4+0i/Z5il235AmDZFf271INYXPnfbHCIJybgLGISclHXwwsC6Pd6WUm13gZEZY+C1cY50KxFe5gp+IRYV+QCO8BhVrmvq+scKO/vH/0wER4eHipErH1KCJDg8BEgEGJQt4ofDACAUCjAoJD6WLrhFt6ZtwyfvH1IC1FWX76kKWAzvMzXKvv7AzU/B/7YsguH145WIWIiUrcndtMAce0yX9PGvUD7Tt0hkWt/TUNVpNqMBSS+GNStfpXKDw7xxPd/hGPvkTB4eIzXbHA1pBBYQO4wt9zXNX0vkJScqff3AkQEJNtNAcTuKtf7+bcD2L1qhAYiosq4ubkhLCysWnWNMil44sQJAEBISEi5ZeLj4wE8mxSsytTgsqYY//TTT3j8+DHOnDmD+vVLbiA8PDzQoUMH7NmzB4MHD67W+0hKSsLjx2qailCvEDAv+yU3Zyt41C57asS/iUXCKpUrS2ZmNjLT9XxahVsBYAlYWoiqVNzS4p+PT0JiCqDQ8x12bRRAOW9NG+dAcnIKUMQFpnXGrBAof2UEjZ8DCiXU159pjAhwLHkgUOV+wLykH8jLK0Regp6/P/t6QNnPyar89weqfw4UFhYbwDlAZOSsFOXe/WvjXiAlJQ0o0PN+oIEMkDx7n1eRp9cLmdwArnMiG53eCyiVQv3/HRERYKWsVqaouFjOz7gBMsqkYGxsLICSDUPKIpPJcP78eQDPJgV9fX1L68tksjI3G4mOjn6mLADs27cPnTp1Kk0IAkD79u3RsGFD7N27t9pJQTc3t2rVK0uGpQTlpaySUitOZrk5W0IsEkImVyApteIpoOUdy76WNawt61YlVJ3JsRAhG0B4dGaVyt95Ov1CKYN7HUcIKrrL0gNJIiXK23dWG+dAbVdHiBWCqoRKGiAXWKOiccfqOgfKO45QIEeduvrdBwBAgqIQSqEFwqMz0Tm48j74TnRJP2BrJYCdnr+/AjNblDdxq7K/P1Dzc8DSXAxHPf8dERm7ZLES5a2Aqo17AVcXB5jJ9XvH9nQzOQqgyv1gSTkzYTFc9byPU0CCisZpavpeQAAZ3PX8d0REQIpIiur01BZmMjjxM64TNckdGWVSMC8vD8Dz6/49tWXLFqSmpsLW1hYNGjQo/XmLFi0gkUhQVFSEsLAwtGvX7rm6586dAwC0bdu29Gfh4eEYPvz5KVlNmjRBeHh4td9HdYd/lmXRzzcx77uyj1fW8P5/izs6Ch61rZGUWoB6PTdXq/29239Gp5bqS3Jqwr3YLPgO2I4jFx/jQXw2GnrYVVj+6VoLI/v6YPOXcdoIsUZenHYYB8/Fl/maps8BiZkQj6JvQGJWtdFXpH4KhRL2HX9FTl7ZXwc1fQ50bOWDMxvKPv/0yaQFZ7FuZxR+3BZZaVIwMSUfu0+VPIQ6u+8bNG/spI0Qq+1GZBpajNhV5muV/f2Bmp8D704fi8/e+lrlekSkPsNnHcf2ozFlvqbp64BAAERHXIKNlZnKdbVp+5GHGP7eCazbFYWPp7Wo9N7l6f3gwvcG4f2JH2kjxGpTKpWo88Kmctd51vQ50KJJXVzdov/3AkSm7vs/7mDG4ksq11v95et4deBSDUREmmSUG408zZJeu3btudcSExMxe/ZsAECzZs0gEPwzcsnW1hY9e/YEAKxZs+a5umfOnEFUVBQkEgkGDRpU+vOMjAzY29s/V97R0RHp6fqxoG5wgO6+rAoEQJCffn9ZBgAfz1ro3aEulErg3aWXIZcryi0bejsFv+y9DwCYNsJfWyHWSHm7KWtDoI8jE4I6JhQK0NJfd59DXZ5/qnhzZMnneeuRBzgTVv54CoVCifeWX4FMpkTHFrX1PiEIAE28HWAu0d3n0FDOASJjpsvPYWOvWnqfEASAQSGeqONihSdpBfhizc0Ky/669x7C7qRCYibExMG+FZbVBwKBQKffCXgdIDIMrw7wgVUVl1B4ysneHCN6N6i8IOkdo0wK9ujRAwCwZMkSREVFlf48NDQUISEhSE0t2ewgKCjoubrz58+HQCDA+vXrsXHjxtKfR0dHY9KkSQCAKVOmwNXVVYPvQP10eRH2a2BvEDeBAPDx1JaQmAmx++QjDHv3OKLjnt2tVSpVYNOBaPSccgiFRXL06ehRpSmG+qBVE92dA7q8AaV/tNJhP2AoXwRaBjhjeK8GkMmUePHNI9i4+x6Kpc9OvI9NyMGYD07ijwPREIsFWPhmSx1FqxozMyGa+zrqrH1DOQeIjJlu7wUMow8wMxPis+nBAIBPfryOWcsuIzWj8JkyOXnF+HLdXxj/4VkAwHvjAuHiaPncsfRRqwAXnbVtKOcAkamrZSvBvNeaV17wXz6e2hIW5kY5EdXoGeVfbc6cOfjjjz8QFxeHJk2awM/PD4WFhbh//z769u0LLy8vHD58+Jn1BJ9q164dFi9ejPfffx/jx4/HggUL4ODggNu3b0Mmk6Ft27ZYvHjxM3UcHByQmZn53LHS09Ph6Ki7L2D/5mRvgZDWdXAyVPs7vg3vaThPDNo1d8XmL0Mwas5J7D75CLtPPkLP9u5o4u2AvAIZ9p2JQ2JKyTopnVrUxtZlIc+MNtVnPdq6w87GDNm55a0mpDnDexnOOWDMXurZAMt/ua31di0tROjXpZ7W262ujZ91QUZ2EY5dSsD4D89gztdXMKBrfdham+FuTBYOnY+HUgmIxQJsXNgVIW1U351NV17q6YUrt1O03m6bpi6oX6ecXU6ISGs6t3SDi4MFUv6T5NIGQ7oXmDjEFwkpefhwxTV89cttrNgUjoHd6qOemzVSMgqx++Sj0uU4Jg7xxcK/k4iGYFhPL3y6+rrW2xWLBRgUUrUdnYlI9+ZNbo7E1Hz8sDmi8rKvNcf00QFaiIo0wShHCnp4eODs2bPo168fLCwsEBMTA0dHR6xevRr79+8vHT1YVlIQKEkqHjp0CD179kRWVhYiIyPh6+uLzz//HKdPn4aVldUz5f39/ctcOzA8PBz+/voztXTaSO3HIhIJMHlYY623WxNDunvh9Lp+6NPRAwBw9GICvvntDtbsuIvElHy4Olpg/utBOPpTH9haS3QcbdVZW5lh/EAfrbfr61kLLxhQ0sSYtW3mghY6mMo/uq83HOzK2f5cD1laiLH/h15YOL0l3F2tkJxeiLU7o/DNb3dw8FxJQrBHO3cc/6kvxvTz1nW4Kpkw2FcnU4h1cf0houeZS0R4baj278vquVmjX2fDeTgEAPNfb4Hty19AcIAziqUKbD8ag69/vYPf9kUjJ08KX89aWDW/A37+uBOEQsN4QAwAzXwd0alFba23O6yHF9ycrSovSER6QSAQ4Pu57bH2k84I8LYvs0zzxo74Y3E3fD6jlXaDI7UyypGCQEmibt++fc/9PDc3FzExMRAKhWjatGm59Xv37o3evXtXqa3+/ftj3rx5iI+Ph4dHSSLp8uXLiI6OxtKl+rPQ5qAQT9R1tcLj5Mp3mVSXwSGe8HCz1lp76tKuuSsOruqN6Lhs/HksBp+uvo7cfBkc7CSIOzrKYNfHmzrSH99vCodSqb02p430M6ibZWMmEAjw5ih/vPbxOa22a4gJIYmZCPNfb4H3JzTH3tOPMH7+aeTky2BnbYYrfwxE4wb2ug6xWpwdLDCqT0Ns3HNPa21yjRki/TJleGN8ueEvyOXauxl4Y7gfxGLDG4swrGcDDOvZAKG3U3DkwmMsXncTufkyONmbI3LPMIOZLfJfb47yx7nrT7Tb5kiOIiIyNAKBABOH+GLCYB+cDkvCwBlHkZMnha21GQ6t6o32zV0Nth+kfxje1bmG7ty5A6VSCR8fn+dG/FXX66+/jjp16mDQoEHYt28ftm/fjtGjR6NNmzbPbEiia2ZmQnz3QXuttWdtKcbSd9torT1N8K5nh9kTmqGWTcmIQCsLscEmBIGS9R1njm2itfYCfRww1QATQsZs3EAftGmqvfWEXhvqa9BrCJmZCTG0hxfs/u4DbK3NDDYh+NTnbwWjlq32Rjl/9V5bWKq4WDURaY6nuy0+mNhMa+35eNrh7ZfLfxBvCFo3dcH/Xg8qvR+0kIgM+ovwiN4N0bWV9tbEHt23ocGswU1EzxMIBOjWug7srEv2CbCzNkOHoNoG3Q/SP0wuKXjr1i0A5U8drg47OzucOHECderUwahRo/Daa6+hQ4cO2LdvH4RC/foVD+3hhZF9tDNiY8k7rdHAw1YrbVHVff5WKzSqb6fxdkQiAdYv7GLQSVRjJBYLsX5hZ0jMNN83edS2xrJZbTXeDqmmbm1rfDunnVba6t+lHl4Z0EgrbRFR1X04pQWaNnLQeDsCAbD+0y6wsuSDAX0iFAqw7tPOKu8uWh2ujhZaHZRARESq0a+MlRZoIikIAN7e3ti3bx9yc3ORmZmJ3377DS4uutvdqyIr5nZAQxWSdUmp+Yh/koek1KpPO+7fpR6mjuAIMX1kZSnGb190haVF1ZN11TkHPn8r2KBHiBmzAG8HfD1btWSdqueAxEyIX7/oqtURaVR1rw5shFF9GqpUR9VzwKO2NX5a0IlPkYn0kLlEhF+/6AobK7Mq16nOvcD814PQUQfr11HlGnrY4Yf/qZasU/UcEIkE2LCwC5wdLKoTIhERaYHJPbbTVFLQkDg7WODYT33RdeJ+xCXlVVq+9eg9Kh0/pHUdbF32AteR02Ntm7lix/LuGPLOcRQVyystr+o5MHt8IOZM0N7UJFLdtFEBSMsqwkc/XKtSeVXOAbFYgE1LQtCtdZ3qhkcaJhAIsPHzLsjOK8aBs/FVqqPKOeDmbImjP/VBHRcuKk+kr4L8nLDnux7oP/0o8gtllZZX9V7gzVH++GRay+qGR1owfpAv0jKL8N7yK1Uqr8o5IBQKsPGzLuhrYBvMEBGZGpMbKXjixAkolUr069dP16HoVAMPW5zb2F/tU0eG9fDC/h96cf0oA9C3cz0c+KEXHGupb1dYoVCAz98KxpJ3WnN0kAH4cEoLfD27LUQi9f2t7GzMsPvbnhjaw0ttxyTNkJiJsPObHni5v3p3UPbxtMPZDf3hZ+BrLxKZgpA27jj6Ux+4Oqp3JNf/JjfH93Pb817AAMwaF4gfP+wIMzVuBGNtKca2ZS9gbD8uH0FEpO9MLilI/6hfxwahmwbig0nNajyqz95Wgl8+74Jty19gQtCAvNDWHXd2DsWgkPo1PlZjr1o4v7E/5k0O4pcAA/L2K01x5feBCPSp+QOCPh09cOfPYXiRowIMhsRMhF+/6IYtS0NqPL1LIADeeaUJbmwdopV1S4lIPToE1cadncNUXlKgLA09bHFq3Yv47K1WvBcwIFOG++Hq5kFo6e9U42OFtK6DWzuG8uEgEZGBYFLQxFmYi7FoZmtc/n0ABr/gqXJy0MbKDFNH+OHOzqF4ZYAPbwANkJuzFXZ+0wPblr2AtoGqr4NZ19UKn00PxvWtg9GuuasGIiRNaxngjLDNg/DlO63h6W6jcv0Wfk74bVFXHFjZCx5u1hqIkDRtRO+GuPPnUMwYEwA7m6qvMQaUJAP7damHcxv746vZ7bihAJEBcnawwKYvQ7D72x7VWgPQzdkSC95ogb+2D0HXVlw6whAF+jri0m8D8c2ctvCup/pGgYE+Dlj3aWccW9OXGw0SERkQgVKpVOo6CNIfcUm5WLPjLk6FJuJ6ZDpy86XPlXF1tEBwgDP6damHV/o3gp2N8W8k4NFjEx4n56OuqxXij43WdTgadTU8Fet2RuHizWTcup8Omez5LqKhhy1aNXHGqD4NMaBrfYjVOOWEdEsuV+DguXj8vj8aYeGpuP8o+7kyIpEATbwd0K6ZCyYM8kXbZi5G/0DAlPqA3Hwp/jgQjT2nHuFqeCqSUgueK2NlIUaQnyO6BtfB5GGN+QWQyMjcvJuGtTujcOFGMv6KSodUpniujJe7DYIDnDGidwMMecELZlrY1V7XTOVaoFAocfTiY/y2/z5Cb6fibkzWc2WEQgECGtqjbaALxg/yQccWtY3+XoDI1JlKH2hqmBSkcsnlCtx/lI1O4/YhNbMIzg7muL5lCOrWtjK5i76pdoCFRTJEPsxCz9cPIjWzCC4O5ri7dzgc7NS3DiHpt8zsIkTFZqPfm4f/PgcsEHt4pMktE2CqfQAAJCTnISYhF4NmHEVqZhFcHS2QcHw0RCLjTwAQEVAslSPyYRa6v3ag9F4gYvdLcLI3vR1lTfVakJ1bjLsxWXhx2j/3AjGHRnJkOJGJMdU+0NixJ6dyiURCNG5gD3OJCABgbibi1EATY2EuRpCfU+k5IDETMSFoYuztzNEm0OVf54DQ5BKCps7d1Rrurtal54CZWMiEIJEJkZiJ0MzX8Zl7AVNMCJoyOxsJWjd99l6ACUEiIuPAu3oiIiIiIiIiIiITw6QgERERERERERGRiWFSkIiIiIiIiIiIyMQwKUhERERERERERGRimBQkIiIiIiIiIiIyMUwKEhERERERERERmRgmBYmIiIiIiIiIiEwMk4JEREREREREREQmhklBIiIiIiIiIiIiE8OkIBERERERERERkYlhUpCIiIiIiIiIiMjEMClIRERERERERERkYpgUJCIiIiIiIiIiMjFMChIREREREREREZkYJgWJiIiIiIiIiIhMDJOCREREREREREREJoZJQSIiIiIiIiIiIhPDpCAREREREREREZGJYVKQiIiIiIiIiIjIxDApSEREREREREREZGKYFCQiIiIiIiIiIjIxTAoSERERERERERGZGCYFiYiIiIiIiIiITAyTgkRERERERERERCaGSUEiIiIiIiIiIiITw6QgERERERERERGRiWFSkIiIiIiIiIiIyMQwKUhERERERERERGRimBQkIiIiIiIiIiIyMUwKEhERERERERERmRixrgMg0lfZucW4HpmG6Lgc5OZLAQD5hTLcfZgJH89aEAoFOo6QNC0pNR9Xw1ORkJyPYpkCErEQbs5WCA5wgrurta7DIyINk0oVuBOdgdv3M5CTJ4VSqYS1pRkCvO0R6OMAC3PeRhm73Hwprkek4X5cNvILZRAJBbC3laB5Yyf4etpBJOLzdSJjplQq8fBxDq5HpCE1swgyuQLmZiJ41bVBcIAzHOzMdR0iEVGN8G6W6F8eJeZi9bZI7DgWg7sxWc+9npFdDL9BO2BrbYYOzV0xeVhjDOzmCTMzfikwFmF3UrBySwQOX3iMhOT8csu5OVuiZ7u6mDrSD+2auUIgYJKYyBjk5kvx+/5obNxzD9ci0lBULC+znFgsQDMfR7zcvxHGD/LhF0Mj8vhJHtbsuIutRx4i8mEmlMqyy1lbitG+uSteG9oYQ7p7QmIm0m6gRKQRCoUSh8/HY/X2SJy5moSM7OJyyzaoa4tBIfUxdYQ/fL1qaTFKIiL1YFKQCMD9R9l4b/ll7D0dB4WinLv/f8nJk+Lwhcc4fOEx3F2tMHtcIN4aE8ARAwbs+KUEzP0uFKG3U6tUPim1AL/uu49f991HkJ8jPpsejH5d6ms4SiLSlNx8KT5ZdR2rt0ciJ09aaXmZTIlrEWm4FpGG/30fhnEDfPD5jFZwrMXkoKGKeZyDOV+H4s/jMZDLK78XyCuQ4dilBBy7lIDaTpZ495WmePfVphCLeS9AZIiUSiXW77qHz9fcwIP4nCrVefg4B9/8dgff/HYHPdu7Y+m7bdC8sZOGIyUiUh/etZBJUyiU+Pa322j20p/YffJRlRKC/5WQnI93ll5G5/H7cfdhpvqDJI3KySvGGwvPo8frB6ucEPyvG5Hp6D/9KMbPP4OM7CI1R0hEmnYqNBHNhu3Eso23qpQQ/K+CQjl+3BaJJkN2YM/JWA1ESJqkVCrx49YIBA7biW1HHlYpIfhfT9IK8P43oWj38l7cvpeugSiJSJMeJeaiz9TDmLTgbJUTgv919GICWo3ejU9WXYNUqlBzhEREmsGkIJmsvHwp+k8/gre/vIyCwrKnh6ni4s1kBI3YhV0nYmoeHGnFg/hstBixC6u3RarleBv33EPzl3YikslhIoOgVCqx6OebCJl0AA8fV+9L4L8lpRZg0MxjeHfppWo9ZCLtKyySYdi7xzH1swul6wfXxNXwVLQcuRubDkSrIToi0obTYYkIHPYnjlx4XONjyWRKfLzqOrpO3I/0LD4oJiL9x6QgmaT8AhlefPMIDp6LV+txC4vkeGnWCWw/8lCtxyX1i47LRufx+xEdV/NEwL/FJeWh8/j9iHiQqdbjEpH6LVh5DfO+C1P7cb/+9Q6mfnYeyvIWoyO9UFQsx+CZx7DzuHpHd0plCoydewq/7Lmn1uMSkfqduJyAPlMPIzu35g8F/u3izWSETDrAGSREpPeYFCzHkSNH0KdPHzg5OcHKygqBgYFYtGgRiovLX2iWDINSqcSYD07izNUkjRxfLldizAencFZDx6eay8wuQs/XD1W4kUhNpGYUoufrB5GSXqCR4xNRzf24NQILV9/Q2PF/2n4Xn/54XWPHp5pRKpWY+NFZHFbDyKCyjw9M+OgsjlxQ78NHIlKf2/fSMXDGURQW1XzGUFn+ikrHgLeOQibjVGIi0l9MCpZh+fLl6N27Nw4fPgxbW1s0btwYkZGRmDdvHkJCQlBQwC/6hmz9rnvYffKRSnVCNw1E3NFRCN00sErlpTIFxn94BnlqmIpE6vfO0ssqTxVU9Rx4nJyPN7+4WJ3wiEjD7j/KxrvLLqtUR9U+AAAW/nQDYXdSVA2PtGDr4Yf4Q8UpvqqeAwpFSeIxkyOFiPSOVKrAuPlnkFcgq3Kd6lwHzl9/gqUbblUnRCIirWBS8D+uXLmC2bNnQyAQYMOGDYiJicH169cRGRmJRo0a4cKFC5g7d66uw6RqikvKxTtLL6lcz83ZCh61reHmbFXlOg/iczBXA9PSqGb2n3mEDbtVn9JVnXNg25GH2Map5ER6pSRRc0bltWSr0wfI5UqMn38GRcWaGYVC1ZOcVoA3v7igcr3qnAOPk/NVTkATkeYtWX8T1yLSVKpTnT4AAD5edQ137meoVIeISFuYFPyPhQsXQqlUYsKECRg3blzpz729vbF27VoAwKpVq5CcnKyrELUmPasIyzfeKl0kNz2rCH/sjzboLzcLV99Q+5ohFVmxKRwP4rO11p663X+UjbnfhiLt73MgI7sIJ68kGOw6WUqlErO/CtVqm7O/ugK5nNNGDFViSj4+++l6aT+YkV2EXSdiOBXIgO0+GYuz155orb070ZlYvytKa+1R5Ravu4m0TO2N3lu/6x53JDZgBYUybNx9Dy/PPVV63uTmSzkC1IClZRbi8zU3tdZesVShkfVribQlJ68Yq7ZEPJMX+HnHXeSrMNKW9JfRJwVTU1MxZ84cNGrUCBYWFqhXrx5mzpyJvLw8TJo0CQKBACtWrAAA5OTk4MiRIwCAyZMnP3esLl26wNfXF8XFxdizZ49W34c25eVL8cbC86jbYxPeW34FBX+vs1FQJMfYuadQv9dmLN94y+ASQ5nZRfh9v3Z3A1QqobadbbXpYXwO+rxxCD79t2Hx2r9K11rJL5TjhdcOosmQP3HgbJyOo1TdqdBErW8AEpuQq/YNbUjz0rOKMOb9k6jfezM+XHGttB/ML5RjyNvH0fDFrVi3k4keQ7RyS4RO2jS0a6axyi+QYf0u7W8Asmqr4d0LmDqFQonPfroOj56bMf7DM/h9fzQK/34wnpUrRd0emzFz8UWDflhuqjbsvqexdQTLs+9MHB4l5mq1TaKaKpbKMXv5Fbh334Rpn194Ji8w+ZNzqNtjEz764SoHQBg4sa4D0KQbN26gb9++SEpKgrW1NQICApCQkIDvvvsO0dHRSE8veWobFBQEALh+/TqKi4thbm6OVq1alXnMTp06ISoqCpcuXcJrr72mrbeiNTl5xej5+iFcvlWyBlKQnyNG9WkIBztzxCbkYsOee0hIzsd7y6/g/qNsrJzfAQKBQMdRV80ve+8jv1D7TzPW7ozCJ9NawsLcMD5uEQ8y0W3ifiSnF0IgAPp09EDfTh4wEwtxPTINv++PRsSDTAx46yjWf9oZrw700XXIVaaLZAAA/LA5Av271tdJ26S6J2kF6DZxPyIfZgEAOgS5YlgPL9hYmeFuTBY27rmHuKQ8TFpwFnFJuVgwtaWOI6aquvswE8cuJWi93Vv3MnDu2hN0DnbTetv0rM2HHiAzR/ubxv2y9z4Wv90KttYSrbdNqlMolHj1f6dLHybXr2ONcQN94FHbGmmZRfh9/33cic7Ed3+E4697GTjwQy9YWhjGfZ6pUyiUWLVV+/eDCoUSq7dF4vMZZX/HJNI3RcVyDJpxtMINuTJzirFw9Q2ER2diy9IQiERGP+bMKBnt1Ss1NRUDBgxAUlISZs2ahQULFsDW1hYA8OWXX+L999+HWCyGQCBAs2bNAABRUSWjPjw9PSEWl/2r8fb2fqassRk3/wwu30qBYy1zbP4yBD3auT+T9Pt4akv8uC0Cb395GT9ui4SPpx3efTVQhxFX3b4zqm0uoi5pmUW4fCsFXVvV0Un7qsjJK0bfaYeRnF6I5o0dsW3ZC/DxrPVMmaXvtsE7Sy9j3c4oTPr4LBrVt0OHoNo6irjq5HIFDpzVzYi9Y5cfo7BIZjCJYVOmVCoxeOZRRD7Mgkdta+z4qjvaBLo8U+bzt4KxeO1f+OTH6/h41XX4etbC6Be9dRQxqeKADkft7j8bx6SgHtDVvUBuvhRnriahXxc+IDIEC1dfx+/7oyEWC7Dqfx0xYbDPM192P5jUDPvPxGHs3FM4FZqIKZ+exy9fdNVhxFRVd2OyEB2n2mZz6rL/bByTgmQwZi65VGFC8N92HIvBvO/CsOSdNhqOijTBaFO5M2bMQHx8PKZPn45ly5aVJgQBYM6cOWjevDlkMhm8vLxgZ2cHAMjIKFkA1sHBodzjPn3taVljcvteOnYej4VIJMDBlb3Rs33d50YBmpkJ8daYJvh6dlsAwJfrb6FYqv/TJpRKJa6Gq7aYsDpdDU/VWduq+H1/NGITclG/jjWO/dT3uYQgANjZSPDzx50wvFcDyGRKLFn3lw4iVd3dmCydjBQFAJlMiVv3jK/PMEbHLyfg0l8psLEyw/E1fZ9LCAKAhbkYH09riQ8mlTxQ+mzNDU4NNRC67IsN5Tpg7HR7DujuPoSqLi9fiq9+vQ0A+OmjTnhtWOPnRr8IBAL071ofe77rCQD4bf99PIzXTaKJVKPLPuBOdAYKi7gGG+m/hOQ8rP3zrkp1VmyK4FqrBsook4IRERHYsmULnJ2dsWjRojLLBAcHAwCaN29e+rPCwkIAgERS/tQOc3NzAEBBQUHpz54mH9u0aQNzc3ODmU77X0/XuxnUzbPML8L/NnWEP9xdrfAkrQB/HovRQnQ18ygxt3RhVF0whC8CSqWydHrtOy83hbODRbllBQIBPn2zZMrkvjNxiE3Q/xthVXeYUzcmBAzD08/AuIGN4Ov1fFL83z6Y2BzWlmKER2fizNUkbYRHNaTrpCCTx7qVmlGIR4l5Omuf1wHD8MeBaGTnStGovh3GVbJEStdWddCzvXvJGtLbuW6kIbgWobvPoUymxF9RfEhM+u/nP6Mgk6t2z5JfKMPGPdpfs5dqziiTgps2bYJCocDYsWNhY2NTZhlLS0sAzyYFLSxKkiDFxeWvNVNUVPRMfQC4f/8+duzYATc3N7Ru3brG8evKofMl06omDfWttKyZmRDjBpTcKBnCJgq6/BJQ0r7+LyycmJKPW/cyIBQKMH5Q5esE+jWwR8cWtaFQKHH0ovbX6FKVrv8Guj4HqWpK+8EhlfeDtWwlGN6rAQDD6AdJt5/DjOxi7tKnY7q+DsQl8TpgCA7+fR2YMMgHQmHlD/onDWlcUo/XAYOg6/sxXfdDRFVx8Fz1NpRkP2iYjHKBqxMnTgAAQkJCyi0TH19ywv47KViVqcFlTTHu0qULEhMTAQAff/wxzp8/X83In9WqVSskJWlv9Emi/RxAaA3POmUnUv/L072k3NYde3F841hNhlZjheKGgN24Ml8L3TQQbs5WFdZ3c7Ys/Xfc0VHllktKzUfr0c/vTH059Bo8PN5QIWLtkwqdAfu3UMvGDPZ25lWq41nHBuevP8Gs9z/ExzMvaDjCmsm2DAEsu5X5mjbOge9XrMIvSw9XPWA9k2j/LiCshcSkRHh4eOg6HI1QQogCxwUAAE9320pKl3jaX65YuRa/LRuisdj0gTGcA/kOHwECUZmvVdYP1LQPAIBGjQMgUhaU+RppXpHYA7CbXOZr2rgO3LoTAQ+P6SpErF+MoQ+oilTbcYBZw9L73Mo8vQ7ciYg26t8LYBznQJrNGEDSuMzX1HUdAMrvB15/4028XWwYS++Q6XpS601A5KpyvRNnLsHDw/g2YzUEbm5uCAsLq1Zdo0wKxsbGAijZMKQsMpmsNHH376Sgr69vaX2ZTFbmZiPR0dHPlAUAoVAzAy6TkpLw+HHVFvdUC5tCQGKNjCquBfB0Om5hfpZ246wOa2vAruyX3Jyt4FHbukqHEYuEVS77b9KiAv3/HZkVAPZAXoEMxVI5JGZlf3H+t6fnQHZGMrLT9fz9uWQAlmW/pI1zIDcnE7lP9Px3VBFbOSAEFHK5/p/LNeEgAwRiZGQXwbFW5cnx9L/7y7ycdOQlGfHvBTCOc8BeVm5SsKr9QHX7AABISogDFFxvR2csxTq9F5AVFxruZwcwjj6gKjyzAbOS0b1V8fQ6IJfmG/fvBTCOc6B+HlDOSlHauA5kpKcgI8tAf3dkOizygIqfk5VJWphjuH2DCTPKpGBeXsmw8H+v+/dvW7ZsQWpqKmxtbdGgQYPSn7do0QISiQRFRUUICwtDu3btnqt77tw5AEDbtm01EPmz3Ny0u0thGpJQCCdsOvgAnVpW3LZSqcSmgyUJ0lpmGbCpW1cbIVabVGiF5HJeS0rNr7S+m7MlxCIhZHIFklLLH+VR3rEszKRw0vPfkRJCJCmyUSy1w5/HYjCqb8W7qT5JK8DxyyXThl1s8iCx1O/3l2cuRmY5r2njHLCzEcFWrN+/o4okikRQABCKRKij5+dyTaTIElBsVh+bDkZj/ustKiwrlSqw7chDAICDZRasjPj3AhjHOZCkLIAcZSd7K+sHatoHCJTFqFPHBQJwXUFdkQmt8aSc17RxHTAXS+FsoJ8dwDj6gKrIFqchB8Cmg9GYPjqg0vJP74etBMlwMOLfC2Ac50CGuQLlfdrVdR2o6FjO9uYwtzHM3x2ZjkxhCvLQoPKC/2EjSkUtA+0bDF1NckdGmRR0c3NDRkYGrl27hvbt2z/zWmJiImbPng0AaNas2TObgtja2qJnz57Yv38/1qxZ81xS8MyZM4iKioJEIsGgQYM0/j6qO/yzuk5cTkD3yQfxy977mP96EOq4lP944PD5x7h1LwOWFiLEnPu9ytNNdUUuV8Cu/a9l7j5b3jSvf4s7Ogoeta2RlFqAej03q9z+vHfG4sMpy1Sup20fr7yGT368jq9+vY1hPRrAzKz8UbDf/X4HUpkCbQNdcOn3UC1GWT2ht1PQZkzZf2ttnAO7N32Lbq3rqFxPX3j02ITHyfmo41YH8beNd72Q3/ffx8tzT+PHrZF4a3QT1LItf+Op3/bfR1JqAdycLRF79UCVRtcaMmM4B4a8fQy7TsSW+Vpl/UBN+4B2QR648Gv11ugh9VAqlXDp+jvSMp8framN68DM1wdjyTtfqFxPXxhDH1AVSan5qNdrMy7cSMb560/QsUXtcsvGPM7B1sMlD4dO7ViA1k1XaCtMnTCGc2D1tki8sbDspZ40fR0AgHt/Hdf7701Et++lI3DYTpXqCATA7dMrqrwED+kPo9xopEePHgCAJUuWICoqqvTnoaGhCAkJQWpqya5TQUFBz9WdP38+BAIB1q9fj40bN5b+PDo6GpMmTQIATJkyBa6uqs+x13chbeqgma8jcvOl6DP1MBJTyn7CdelmMsZ8cBIAMGGQr0Fc2EQiIYL8HHXWfnCAs87aVsXkYY1hZSFG6O1UjJt/GkXF8jLLrdkeiS9+vgkAePvlJtoMsdoCfRwgFutuZ/AWfk46a5uq7qWeDVDX1QqPk/MxcMZRZJaznMLBs3GY9nnJOppvjvI3+oSgsQgO0N3n0FCuA8ZMIBDo9O/Ac8AwuDlbYVSfhgCAoe8cw/VydquNTchBn6mHUSxVoEOQK1o3ddFmmFRNurwONKpvZxDfm4ia+jiie1t3leoM7e7FhKCBMsqk4Jw5c+Dk5IS4uDg0adIEgYGB8PHxQZs2bdCwYUO88MILAJ5dT/Cpdu3aYfHixVAqlRg/fjy8vLzQokUL+Pn54f79+2jbti0WL16s7bekFQKBAH9+3R2ujhb4KyodvgO2Y+rC8zgTlohbUenYe+oRBs88io7j9iEjuxgdglyxbFYbXYddZSE6GqVlLhGhXTPDSCLXrW2NzV+GQCQSYNPBB/B+cSs+/fE6Qm+n4ObdNGzYHYW2Y/bg9U9LnrDOGBOAkX/fOOs7C3MxOjQv/2m/JgUHOFc44oz0h7lEhD3f9YSttRnOXE1Cwxe3Ytayy7hw4wn+ikrH9iMP0WvKQbz45hEUFskxoGt9fDDx+WsJ6aeQ1qrd4Kq3bcMdKWxMdPV3EIkE6FzJ0iykP36Y1wFBfo5ITi9Em7F7MHzWcRw8G4dbUek4eSUBry04C//BO3A3Jgseta2x5csXdB0yVVEzX8cqrRmsCbwOkCH5bVFXNKhbtSRfgLc91nzcScMRkaYYZVLQw8MDZ8+eRb9+/WBhYYGYmBg4Ojpi9erV2L9/f+nowbKSgkBJUvHQoUPo2bMnsrKyEBkZCV9fX3z++ec4ffo0rKyqseqmgfCuZ4cLvw5A88YlIwZ/3BaJrhMPoNlLOzFwxlHsPvkICoUSL/X0wuEf+8DSwnBmoE8e1hhCofZHio3s3UBnNx/VMaBbfexf0QsuDhZ4nJyPBSuvoc2YPQgavgsTPjyLK7dTIDET4uOpLfDN++2emYKv794Y7mdS7VL1tAxwxpn1/eBdzxYZ2cX46pfb6PjqPjR/aSeGv3cCRy8mQCAo6VO2f/UCxGKjvJQapQ5BrmjayEHr7bq7WmFA1/pab5eeN2GwL8x08Jkd1M2zwmVZSL/Y2Uhw8ucX0a9LPchkSmw/GoMX3zyCZi/txAuvHcTanVEoKJSjdVNnXPi1PzzcqrfpBGmfxEyEiYN9Ky+oAbwfJEPi5myF87/0r3AJBQDo2d4dZ9b3gwNHwRosw8noqMjf3x/79u177ue5ubmIiYmBUChE06ZNy63fu3dv9O7dW5Mh6i3vena4vnUwToclYeWWCITeTkFugQz2thK82MkDb4zwh39De12HqTJPd1v071IPe0490mq700b6a7U9dejd0QNxR0dhx9EYrPnzLu4/yoZUpkBtJ0uM7tsQEwf7wtWpnK189diwnl5w/dICyemFWmuzlq0EY16seNMW0j9Bfk64u+clHL7wGKu2RODguXjIFUqIRQK8Nz4QU17yg1cVn56S/hAIBHhzlD+mfnZBq+2+PqxxhWu0kvbUdrLESz29sOngA622++Yow7sXMHX2dubYt6IXbkWlY9XWCBy5+BgP43OgUAKW5iIc/akvOgS5GtTDUSrxxgg/LP/lFpRa3PepbaALWnIJATIwdVyscHZDP1y5lYKVWyLw+/5oyBVKiIQCTBjsg2kj/dHCn+e1oTPapGB57ty5A6VSCV9fX7WO+Nu+fTsAIDw8/Jn/9/LyQqtWrdTWjrYIBAJ0a13HoDdGKMv814Ow70wcFArt3AX07lAXbQINc40Zc4kIY/p5Y0w/40loScxE+N/kIMxccklrbc4ZHwgrS5Prao2CSCTEi53r4cXO9UoXV6/tZIlFM1vrOjSqgVf6N8KX62/h4eMcrbTn7GBhkA+HjNncSc2x/WgMpDKFVtrr3LI2QtoY1/2UKQn0dcTK+R0B/LPRhmMt80pHz5D+8q5nh1cH+GDjnntaa3PBGy201haROgkEArRt5oq2zVxx/HICHifnw83ZEms+7qzr0EhNTO6x9a1btwCUP3W4uoYPH47hw4dj27Ztz/z/ihXGvQuZoWnd1AWzxwdqpS07GzOs+bgTnyDrmemjA9BJSzfywQHOmDOhmVbaIqKqsbYyw7pPtXcj+8O89nBxNLyR1cYs0NcRH04J0kpblhYirPu0C+8FiPTM13Paam1K//hBPujbuZ5W2iIiUhWTgmqiVCrL/GfDhg1qbYdq7uOpLdDE216lOkmp+Yh/koek1LJ3ZC7LN3PaoZ6bjYrRkaYJhQKsX9gF1iqO3lP1HDCXiLBhYWeuN0ekh7q1roO3xgSoVKc614HhvRpgRG/D2IzJ1HwwsTlaNVFtylN1zoElb7dGo/p2qoZHRBrmYGeOnz7qqFKd6vQBHrWt8fXstqqGR0SkNSY3p01TSUEyHBbmYhxY2Rudxu1DXFJeleq0Hr1HpTbmTmqOCTpaxJgq16i+HXZ92wP93jyCYmnVpo+pcg6IRAJsW/YCmvo4VjdEItKw5bPa4mF8DvadiatSeVWvAx1b1MZ6LY5IJNWYmQmx57ue6Dx+H6LjqjaVXNVzYMaYAEwfrVrymYi0p3/X+vhmTlu8/eXlKpVXtQ9wrGWOQ6t6w54bMBCRHjO5ISwnTpyAUqlEv379dB0K6VD9OjY4va4fGnqof6OA+a8H4fMZwWo/LqlXj3Z1sff7nrBS8w7a5hIRdnzVHQO6cadRIn1mZibE9q+6Y0h3T7Ufu1vrOjjwQy9YW5mp/dikPnVcrHBqbT/4Nail9mO/80oTfD2nHacNE+m5mS83xbfvt1P7cd2cLXFq7YtoooMd74mIVGFySUGipxp42OLy7wMxqo96pnY5O1hgy9IQLJwezC8BBqJXBw9c/n0AgtW0G1ygjwMu/NIfg0LUn2QgIvUzl4iwbdkLWPJ2a5hLRDU+nlAowNxJzXFoVW/Y2UjUECFpmoebNS7+OgDjB/mo5Xj2thL88nkXLH+vLYRC3gsQGYIZY5vg0Kre8KhtrZbj9enogdA/BiHQlzNGiEj/MSlIJs3ZwQKbvgzBjq+6o65r9RYbFgiAkX0a4M6fQ7l2lAFq6uOIi78OwGfTg1VeZ/ApC3MR5r8ehLDNg9BSTQlGItIOkUiIOROb4dqWQTXaTbR5Y0dc+m0AvpjZSi0JRtIeeztzrF/YBftW9ISne/XXAh78gifu7ByKVwb48OEgkYHp3dEDt/8cisnDGkMkqt7n19nBAus+7YwDK3vBw009CUYiIk0zuTUFicoytIcXBnStj72nH2Hllggcv5xQaR3HWuaYNMQXU4b7wbseFxE3ZGZmQvzv9SBMHx2A3/bfx8otEQiPzqy0no+nHaaN8Me4QT5w4HoxRAYtwNsB5zb2R+jtFKzaGoFNBx+gsEheYR2xWIBhPbwwbYQ/Oge7MRFk4Pp1qY8+HT2w/0wcVm2NxKHz8ZXWsbeVYMJgH7wx3B++XuqfhkxE2lPLVoKfFnTCgjdaYM2Ou/hpx10kplS+qUi7Zi54c1QAXurpBQtzfr0mIsPCXovob2ZmQgzt4YWhPbyQkV2Ea+FpCAtPwf1H2SgslkMsEsLeVoIWfk4IDnCGX4NaEIk42NaY1LKV4M1RAZg20h+Pn+QjLDwFV8PTkJCSj00HolFQJIeNlRgbP+uK4AAn1K9jwyQAkZFp3dQFrZu6YOX/OuDWvQxcDU/FrXsZWL87CgWFclhbirFoZiu0auKM5r5OsKrmCGPSTyKREANDPDEwxBOZ2UW4HpmGq+FpiIrNwm/77qOgqOQcWDGvPYL9neHf0J67zBMZmbq1rfHxtJb46I0WuP8oG2F3UnE9Mg0rt4Qjv1AOKwsR5r0WhOAAZwQHOMHF0VLXIRMRVRvvZInK4GBnju7t3NG9nbuuQyEdEAgE8HCzhoebNQa/4AUAOHw+Ho+T81HLRoKhPbx0Gh8RaZ6Fubg0QQgAu0/G4nFhPuxtJXhrTBMdR0faYG9njpA27ghpU3IvcOBsHB4nl5wD4wf56jg6ItI0oVAAX69a8PWqhTH9vLHpYDTyC/PhYGeO/70epOvwiIjUgo82iYiIiIiIiIiITAyTgkRERERERERERCaGSUEiIiIiIiIiIiITw6QgERERERERERGRiWFSkIiIiIiIiIiIyMQwKUhERERERERERGRimBQkIiIiIiIiIiIyMUwKEhERERERERERmRgmBYmIiIiIiIiIiEwMk4JEREREREREREQmhklBIiIiIiIiIiIiE8OkIBERERERERERkYlhUpCIiIiIiIiIiMjEMClIRERERERERERkYpgUJCIiIiIiIiIiMjFMChIREREREREREZkYJgWJiIiIiIiIiIhMDJOCREREREREREREJoZJQSIiIiIiIiIiIhPDpCAREREREREREZGJYVKQiIiIiIiIiIjIxDApSEREREREREREZGKYFCQiIiIiIiIiIjIxTAoSERERERERERGZGCYFiYiIiIiIiIiITAyTgkRERERERERERCaGSUEiIiIiIiIiIiITw6QgERERERERERGRiWFSkIiIiIiIiIiIyMQwKUhERERERERERGRimBQkIiKqgFKphFKpLP1vIlMklSqQly+FTKbQdShERKQDcrkC+QUyFEvlvB8iMiJiXQdARESkT4qlcuw7HYez15IQdicV1yPTkFcgAwAkpBTAq88WBPs7o1UTZwx+wRP+De11GzCRmikUShy/nIDjlxNwNTwVV8NTkZFdXPq6m7MlggOcEezvjBc7e6BNoAsEAoEOIyYiInWLeJCJXSdiEXYnFVcjUhGbkFv6mo2VGVr4OSI4wBldgt3Qv0t9mJlxvBGRIWJSkIiICEBSaj5WbonAmh13kZRaUG652IRcxCbk4s/jMZj3XRhCWtfBtJH+GNrDC0IhEyNkuLJzi7Fmx12s2hqB6LiccsslpRZg/5k47D8Th09XX0dLfydMHeGPVwY0grlEpMWIiYhInRQKJXYci8HKLRE4FZpYbrncfCnOXnuCs9ee4Jvf7qCOixUmD22MqSP94OZspcWIiaimmM4nIiKTplQqsWF3FPwG7cDC1TcqTAiW5WRoIoa/dwLdJx/Eg/hsDUVJpFmHz8ejyZA/8d7yKxUmBMtyLSINkz85h1ajduNaeKqGIiQiIk16EJ+NF147gBHvnagwIViWxJR8fLr6OvwH7cAve+5xejGRAWFSkIiITFZmdhEGvnUUEz48i6yc4sorVOBUaCKaDduJDbuj1BQdkeYVS+WY8uk59Jl6GPFP8mp0rNv3M9Bm7B4sXH2dXwiJiAzIup1RCBy6E6fDkmp0nMycYoybfwaDZhyr8X0VEWkHk4JERGSSUjMKEfLaAew7E6e2Y+YVyDDhw7NYuv4vtR2TSFMKi2QYNOMYftp+V23HlMuV+OiHa5j22QUoFEwMEhHpuyXrbmLSgrPIL5Sp7Zh7Tz9Ct0n7kZpRqLZjEpFmMClYjiNHjqBPnz5wcnKClZUVAgMDsWjRIhQX84kHEZGhy8krRp+ph3EjMl0jx5/zdSh+2ByukWMTqYNMpsCI907i0Pl4jRz/x22RmLXsskaOTURE6vH9H3fwwTdhGjn2jch09J12GDl5/P5MpM+YFCzD8uXL0bt3bxw+fBi2trZo3LgxIiMjMW/ePISEhKCgQLX1poiISL+8u/Qyrmp47bOZSy5xfTXSW8t/uYW9px9ptI1vfruDncdjNNoGERFVz9XwVLyzVLMPb8LupOK95Vc02gYR1QyTgv9x5coVzJ49GwKBABs2bEBMTAyuX7+OyMhINGrUCBcuXMDcuXN1HSYREVXT4fPx+PlP1db9C900EHFHRyF008Aq15HLlZjw0VkUS+WqhkikUeHRGfjoh2sq1anOZwAA3lh4ntPHiIj0TFGxHOPnn4FcrtoyD9W5Fvy0/S6OXnysaohEpCVMCv7HwoULoVQqMWHCBIwbN670597e3li7di0AYNWqVUhOTtZViESkRVk5xTh26TEKikrWWTG1NbKUSiVCb6eUvn+pTKHjiGpGKlXg9U/PqVzPzdkKHrWt4eZspVK9v6LS8fWvt1VuT58UFslwOiyx9ByQyw37HKiO2/fSUVBUktwtlioMfhONNxaeR7FUtb9jdT8DyemF+OCbUJXqEOmb3HwpTlxO+KcfNLF7ATI+X/1yG7fvZ6hcr7rXgsmfnINUxesO6ZeM7CIUFpfcCxUWy5Gdy2nhxsLok4KpqamYM2cOGjVqBAsLC9SrVw8zZ85EXl4eJk2aBIFAgBUrVgAAcnJycOTIEQDA5MmTnztWly5d4Ovri+LiYuzZs0er74OItCs8OgNvLDyPuj02oefrh5CeVXLhS0otwKQFZ3HzbpqOI9Ss3Hwpvvn1NvwG7kCbMXtK339yeiE6vLIXv+27b5DJoV0nY/EosWY7rKpqxaYIyAwwmRqXlIv3v74Cj56b0W3igX8+A2mFeOnd4zgdlqjjCDVLKlVg/a4otB69G4HDdiI9qwgAkJJRiMChf+KHzeEoUOOi7NpyLTwVZ6890Wqbv+2P5mhBMkhRMVmY/sUFuHffhO6TDz5zL/DqvNMIu5Oi4wiJVCeVKrBCy+sexybkYs+pWK22SepxIzINEz86A/fum5CWWXIvlJZZBPfum/DGwvMIj1Y9uUz6xaiTgjdu3EBgYCCWLl2KpKQkBAQEQCqV4rvvvsPIkSMREREBAAgKCgIAXL9+HcXFxTA3N0erVq3KPGanTp0AAJcuXdLKeyAi7dt+5CFajtyN1dsikVcgg5e7Ddo3d0VDD1soAazbGYVWo3fj1733dB2qRiQk56Hjq/vwztLLiIrNgo2VGdo0dUFLfyeIRQJcvJmMV+adxrB3jxtcUkQXm3/EP8nT+Npt6nbhxhMEDd+FL9ffQlpmEdycLdGumQsCvO0BADuOxaDbxANYuPq6wY+aK0tuvhT93zqCiR+dRdidVEjMhGjVxBmtmzrDykKMO9GZmP7FRXSbeAAp6Ya1zvDKLRFab7OoWI71u1Sbsk+ka/vPPEKLEbvww+YI5ORJUc/NGu2aucDH0w4A8Ou++2g7di9+2h6p40iJVLPnVCwSkvO13u4Pm7V//aGa2bj7HlqP3o31u+6hsOjZ5XDyCmRYvS0SLUfuwo6jD3UUIamDWNcBaEpqaioGDBiApKQkzJo1CwsWLICtrS0A4Msvv8T7778PsVgMgUCAZs2aAQCiokpuWD09PSEWl/2r8fb2fqYsERmXIxfiMer9k5DLleje1h3zXw9C11ZuEAgEUCqVuHAjGV/8fAMHzsZj3PwzsLEyw5DuXroOW22yckp25b11LwOujhb4ZFpLjO3nDVtrCQAgKTUfP22/iy9+vondJx/h5bmnsW35CxAKBTqOvHKPEnNxOixJJ23/sve+wZwnt6JKdgvMzpWihZ8TFkxtgX6d60EsLnmOePteOpb/chsbdt/DRz9cg7WlGO++GqjjqNVHJlNg+KwTOHLhMawsxPhwShAmDfGFi6MlgJLPyMY99/DJj9dx5XYK+k8/ipNrX4SVpf7fUkmlCmw6+EAnbf+y9z5mT2imk7aJVHUmLBFD3zmOYqkCXYLd8OGUILzQxr30WnflVgoWr7uJncdjMeXT87CxNMOYft46jpqoan7dd18n7Z4MTUR8Uh483Kx10j6p5s9jMZjw0RlU9uy3qFiBUXNO4sBKCXq2r6ud4EitjHak4IwZMxAfH4/p06dj2bJlpQlBAJgzZw6aN28OmUwGLy8v2NmVPPHLyCgZ+urg4FDucZ++9rQsERkPhUKJqZ9dgFyuxNh+3jj8Y290a10HAkHJlwCBQICOLWpj7/e9MHlYYyiVwJtfXDSqNVK+++MObt3LgJuzJS7+NgBvjPAvTQgCJWvJfPRGCxxc2QsSMyH+PB6Dg+fidBhx1YXe1t00L122rapZyy8jO1eKLsFuOLexPwaFeJYmBAGgqY8j1i/sgiVvtwYAzP02DMlphjVariLbjz7EofPxsLIQ4/iavvhgUvPShCAA1LKVYMbYJji3sT8ca5njyu0UrNlhGCOFwh9kIF9Ho3vDH2QiN1+qk7aJVKFUKvHmFxdRLFVgaHcvHPupL3q0q/vMw682gS7Y8VV3vP1yEwDAW4svGtzIeTJdV26n6qztUE65NwjFUjne/OJCpQnBp2RyJaZ9fsHk1l43FkaZFIyIiMCWLVvg7OyMRYsWlVkmODgYANC8efPSnxUWlqx3I5FIyqwDAObm5gCAgoJ/vgBt374dw4YNg6enJ6ysrODn54f//e9/yM3NrfF7ISLtOXLhMR7E56CWrQSrP+wIkajsLlIoFGDFvPZwdbRAYko+dp80jjVSZDIFVm8rSW4sm9UGDT3syi0b0sYdb40OAKCb6YjVERauu5vgx8n5SErV/lQdVd2LzcLRiwkQCIANC7tUOPpt9oRAtGnqgmKpAuuMaGro0/N59vhAtGvuWm45/4b2+Pyt4L/rRBrENOqr4bpbC1WhUOJGpHGvxUrG4dy1J7h9PwNWFmKs/aQTzMzKvhcQCARYNqsNPN1tkJ5VhK2HOX2O9F9Cch4SU3R3P3JVh/diVHW7TsQiKVW1B773H2Xj2CXuMm2IjDIpuGnTJigUCowdOxY2NjZllrG0LHnq/++koIWFBQCguLj8nXSKioqeqQ8Ay5Ytg0gkwhdffIGDBw9i6tSpWLVqFfr06QOFwnhGEBEZuw17ShIb4wf6wNrKrMKyEjMRJg9rDADYuMc41hY8cSUBj5Pz4exggZd6Nqi0/Bsj/AEAB8/FG0TC6879TJNuvyp+2VsypejFzvXQwMO2wrICgQBTR/oBMJ7PwIP4bJy99gQikQCvv9S40vIlU+vNEBWbhUt/JWshwpq5o+PFwO9EZ+q0faKqeNqfjXmxIeztzCssKxIJMeWlkn5wg5H0g2TcdN0P67p9qprq3tdt2M1+0BDp/wI41XDixAkAQEhISLll4uPjATybFKzK1OCyphjv3bsXLi4upf/ftWtXuLi4YOzYsTh37hy6dOlSjXcBtGrVCklJuln/isgUpdhOAszqo3PL2lUq37mlG4CbOHziCjw8Jmo2OC3Ik7QEbAahbaALzCWiSss3qm+HOi5WSEzJR7PgrpDI9Xs32lTbcYBZwzJfC900EG7OVuXWdXO2LP133NFRFbaTlJqP1qOf36F+xOhXYCm9q0LE2pdhPRgwb6HiZwC4+yAFHh4eGoxMO4rEnoDdRDSqZwd318rXPLK1lqCFnxPOXE1CvyGvwqr4jhairL4MqwGARdkbqWnjMzBn7kdY+M4FFSLWL4n27wLCWkhMSjSK811VpvL+U21fAcwalfZvlXnaX569dBseHq9rMjSdM5VzoDzG8P4LzPwA29FlvlbZdQCo+rWgvOvAwcMn4OExvuoBk048sZsKiKvWB/7bjj0n4fH7KxqIiCrj5uaGsLCwatU1yqRgbGzJVD5PT88yX5fJZDh//jyAZ5OCvr6+pfVlMlmZm41ER0c/UxbAMwnBp57uXvz4cfWH0CYlJdWoPhGpqGERYIYqr5/xtJxUKjWOz6pDA8AGKk2DfFo2JfkJUKjnv4MGhUA5A0DdnK3gUbvyJJBYJKxSubKkp6UBOXr+O/LIB8xV/wwoFQrj+AxYWQF2VX//wD+fgYy0NGRk6/nvwD0XsCj7JW18BrKzMpGdque/o4rYygEhoJDLjeN8V5WpvH+vwmrdC8hlMuP+vQCmcw6Uxxjev60LUM5EgKpeB4DqXwuKCgsN93dnSixl1coUFRcX8e9rgIwyKZiXlwfg2XX//m3Lli1ITU2Fra0tGjT4Z4pcixYtIJFIUFRUhLCwMLRr1+65uufOnQMAtG3btsIYTp48CQDw9/ev1nsASrK9RKQ96eJCFAA4ey0JL/WqfPrsmaslI3ktRPlwqmv4u20VigVIQ8kC1IVFMliYV3yJiIrJKllvRKmEm7MlREr9/h2kSYQoLOe1yqY/uzlbQiwSQiZXVLrGSnnHcnK0hYWdfv+Osi2kyEHJZ+CDSc0rLX/2WslnQIwc1DaCz4BMKMETANHx2VXaITE7txjX/14nz8VeDImtfv8OsizNUN5qx9r4DNjbWcHaXL9/RxVJFImgACAUiVDHCM53VZnK+88wK0I+Svq3cYN8Ki3/tB+UCPPgYsS/F8B0zoHyGMP7LxTborzVXauyFExVrwXlHcvCXGgU98zGLlWUh6Jq1LMUF8KRf1+dqEnuSKA0hJWxVRQQEICIiAisWLECb7755jOvJSYmIjg4GImJiejYsWNpku+p/v37Y//+/Zg4cSLWrl37zGtnzpxB165dIZFIEBcXB1fXshcgf/z4MVq0aIHg4GAcPHhQvW+OiDTmyIV49H7jMOxszPD42GjYVLCuYFGxHPV6bkZKRiF2fNUdQ3t4aS9QDZHJFGj44lbEJeXhl8+74JUBFX8ZeufLS/jmtzvo36Ue9q7opaUoq2/et2FYtPZmterGHR0Fj9rWiH+Sh3o9N1frGEknx6C2k2XlBXXo/qNs+PTfBoEAuL9/eIWbzSiVSrQZswdhd1Kx5O3WmDOxmRYj1ZxuE/fjdFgSPpwShE/fDK6w7A+bwzH9i4vwa1AL4buGle5Urq/W74rCxI/OVquuOj4D5zb2R8cWVZuaro88emzC4+R81HW1QvyxsqffGTNTef/nrz9Bp3H7YGkhwuNjo+FQwbqCMpkC3v224lFi1a6bhs5UzoHyGMP7T0zJh3v3TdWuX9NrwfzXg7BwesXXVtK97UceYvh7J1Sud/SnPujRjklBQ2OUG4306NEDALBkyRJERf2zI2JoaChCQkKQmlqy61FQUNBzdefPnw+BQID169dj48aNpT+Pjo7GpEmTAABTpkwpNyGYm5uLQYMGQSKRYN26dep6S0SkBT3a1UWj+nbIzpXitY/PQiYre6MghUKJqZ+dR0pGIdxdrTCwW30tR6oZYvE/C6a/t/wK7sVmlVv26MXH+GFzyS6t00ZWf0S0NgUHOOms7bquVnqfEARK1ons3aEulErglXmnkZsvLbfsF2tuIuxOKswlIkwc4ltuOUPz9HxeuuEWzl0rf13f2/fSMf/7q6V19D0hCADBAc46a1soFCCosaPO2ieqqg5Brmjm64iCQjnGzz+DYqm8zHJKpRJvf3kJjxLz4GRvjuFVmGFApGt1XKxQx6XidQM1SZf3YlR1g0I8VT5PfD1r4YU27hqKiDTJKJOCc+bMgZOTE+Li4tCkSRMEBgbCx8cHbdq0QcOGDfHCCy8AeHY9wafatWuHxYsXQ6lUYvz48fDy8kKLFi3g5+eH+/fvo23btli8eHGZ7RYUFGDAgAF4+PAhjhw5gjp16mj0fRKRegmFAvw4vyPEYgG2HHqInlMO4ejFx1AoSgZUK5VKnApNRN9ph7F+1z0IhQKs/rAjxGLj6UpnjA1AkJ8jktML0fHVffj+jzvIyvlnR/b4pDx8uOIq+k8/AqlMgRG9G6B3R8NYbLtN4PPrv5pC26r6anZb1LKV4MKNZHR8dR+2H3kIqfSfBPm18FS8PPcU5q8oSYgtfbc1nB3KWajOAA3t7oV+XeqhsEiOXm8cwsLV15+ZBpWeVYTlG2+h8/j9yMwpRvvmrnhtaOU7FeuDgIb2sLbUzcoxTbztK93VnUgfCAQCrJrfAeYSEfaceoSQSQdw4Gwc5PKSflCpVOL89ScYNONY6cOxlf/rUOmSG0T6oq0O70laNzGc+yFTZmYmxI/zO0AorNoDTzOxEKtUKE/6xSivXh4eHjh79ixmz56N06dPIyYmBgEBAVi9ejUmT54Mb29vAGUnBYGSpGLz5s2xfPlyhIaG4smTJ/D19cXYsWMxa9YsmJs/P41AKpXipZdeQlhYGI4fP46AgACNvkci0ozu7dyxfXl3jJpzEqdCE3EqNBF1Xa3g5myF5PQCxCWVrFkqMRNi42dd0L+rcYwSfMrWWoKDK3uj35tHcC0iDTMWX8IH34TB18sOcrkS4Q8yIZeXJEmH9fDCxs+6GMwNQD03G4S0roOTodrfJXncQMOZUhbg7YDDq3qj/1tH8VdUOoa/dwLODhbwrGODrNxi3H+UXVp28dut8NaYJjqMVv3EYiG2fBmCEbNP4MDZeHz0wzV8uvo6Aho6QCAA7sZkobCoZORQhyBX7PmuJywtDON2SiwWYsyL3lizQ/u7YBvSZ4CoQ1Bt7P62B16adQIXbiSj35tHUMfFCu4uVkjNLERsQsnqnCKRAD991Akjepe9sz2RPnp1QCPsOhGr9Xa7t3VH3WpuVEXaNzDEE79+3hXjPzwDaTmzpwDA0lyEzV+G4IW2HCVoqAzjLrYa/P39sW/fvud+npubi5iYGAiFQjRt2rTc+r1790bv3r2r1JZCocDYsWNx/PhxHDhwAG3atKl23ESke4NCPHFz2xB8vykcG/fcw+PkfDxOLhkpZG0pxsv9G+Gt0QFo0shBx5FqhpuzFc6s74eNe+7hhy0RCI/OxI3I9NLXu7Zyw9QR/hjeq4HBJASfmjbSX+tJwXpu1ujXuZ5W26ypts1ccXPbYKzcEoE1O+4iOb0QqRkl27SYiYUY1sMLb40JQIcgw10friLWVmbY/W1PbDn8AD9sjsDFm8n4K+qfz0Dzxo54c6Q/XhnQyOBGB00b6a/1pKCFuQjjq7BhA5E+6d3RAze2DcYPm8Oxftc9JKbkIzGl5F5AAGDiEF9MHx2AID9OhyTDMqBr/dJ1AbXJUJaboX+M6eeNZr4OWLE5Ar/tu4+8Alnpa3Y2Zhg30AfTRwXA16uWDqOkmjKsO1k1uHPnDpRKJXx9fWFlpZ71FN58801s27YNH3zwAaysrHDp0qXS17y9veHiwmHSRIbG16sWvp/bHotmtsLV8FTk5Elha22GoMZOqGUr0XV4GmdtZYZpowIwdaQ/bt5NR2JKPkQiARrUtYWPp+Fe+AeFeMLL3QYxCeXtwap+b40OMMgp5u6u1vjsrVb46I0WCL2diozsIlhZiNGkkYNBrI9YU2KxEGP7NcLYfo0Q+TATsQm5UCoBd1crBPo4GMQagmUJ8nNCt9Z1cEqLyfFXBzSCk73xTDEn0+Fdzw5fzW6Hz6a3QtidFAx55zjSs4rg5myJnz/prOvwiKpFLBbirdEBeP+bUK212aCurdGswW1qmvo44scPO2LJ263RqN9WpGYWwdneHA8PjaxwU0YyHCaXFLx16xaA8qcOV8fTHYYXL1783HqD69evx/jx49XWFhFpl42VGbq2Mt31QQUCAYL8nIxmJISZmRBrPu6Enq8f0kp7QX6OePvl8kelGwKJmcigd4xVB78G9vBrYK/rMNRm1fwOCBq+C0XFZW+goE5uzpZYNLO1xtsh0iQrSzG6tKoDS3MRABjcKHmi/3r7lSb442A0bt5Nr7ywGvz8cSeDfEBK/6hlK4G5pKQPNJeImBA0Iib3ydREUjAmJgZKpbLMf5gQJCLSLz3a1cWU4X4q1UlKzUf8k7xnNpyojFgswIaFXWBmZnKXWtJzfg3s8dn0YJXqVOczAAA/fdQJjrWeX4uZiIh0R2ImwoaFXSAWq5bgrs61YOoIP643R6THOFKQiIhMzrJZbXA9Ig1XbqdUqXzr0XtUbmPF3A5o3tg4RliS8XnnlSa4cPMJdh6v2mLz1fkMzB4fiAGcLkZEpJeC/Jzw/QftMfWzC1Wuo+q1oG2gC5a+y/X2ifSZyQ1fOHHiBJRKJfr166frUIiISEdsrMxwYGUvBAc4a+T4X81uq/JoRCJtEomE2LQkBP26aGYTnDdH+WPJO5w2TESkz94Y4Y9lszSTtGvVxBkHVvaGNaeZEuk1k0sKEhERAYCTvQVO/NwXg1/wVNsxba3N8OsXXfHOK4a9jiCZBnOJCDu/7qHWHSHFYgG+mNEK389tb7CbsRARmZJZ4wKx8bMual0jbkh3Txxf05fLRxAZACYFiYjIZNnZSPDn193x+6JuNb5x7dneHbf/HIqX+zdSU3REmmdmJsQP/+uAYz/1hae7TY2OFeTniLBNgzD3teZMCBIRGZBXB/rg1o4h6F7Dtf8ca5njj8XdsOOr7rCzkagpOiLSJJNbU5CIiOjfBAIBxvTzRo927li9PRKrt0XicXLVF9Du1aEupo30x8Bu9ZkIIYPVvV1JUnv9riis3BKByIdZVa7bNtAFU0f4Y8yL3txYh4jIQHnVtcXRn/pgz6lHWLklAkcuPK5yXY/a1pgyvDGmvOQHF0dLDUZJROrGpCAREREAVydLfDilBeZOao6D5+Jx9loSroan4npkGjKyiwEAQqEA3vVsEezvjOAAZwwKqQ8fz1o6jpxIPWyszPDWmCaYPjoAp0ITceJKIq6Gp+JaRBqepBWUlqvnZo3gAGcEBzihb6d6Glubk4iItEsgEGBQiCcGhXjiXmwWdp2IxdWIVFwNT8OD+BwoFMq/ywEhresgOMAZnVu6oW8nD4jFfChEZIiYFCQiIvoXsViIAd3qP7NrqkKhhFyu5CgoMgkCgQAhbdwR0uafaWR1u/+BhJQCuLtY4tGRUTqMjoiItMHHsxZmT2j2zM/+uRZY4fjPL+ooMiJSJyYFiYiIKiEUCiAUcmowma6nU+M5RZ6IyHTxGkBkfDjkgYiIiIiIiIiIyMQwKUhERERERERERGRimBQkIiIiIiIiIiIyMUwKEhERERERERERmRgmBYmIiIiIiIiIiEwMk4JEREREREREREQmhklBIiIiIiIiIiIiE8OkIBERERERERERkYlhUpCIiIiIiIiIiMjEMClIRERERERERERkYpgUJCIiIiIiIiIiMjFMChIREREREREREZkYJgWJiIiIiIiIiIhMDJOCREREREREREREJoZJQSIiIiIiIiIiIhPDpCAREREREREREZGJYVKQiIiIiIiIiIjIxDApSEREREREREREZGKYFCQiIiIiIiIiIjIxTAoSERERERERERGZGCYFiYiIiIiIiIiITAyTgkRERERERERERCaGSUEiIiIiIiIiIiITI9Z1AERERERERERE6qBUKoGiIl2HoRpzcwgEAl1HYTR4DlQdk4JEREREREREZByKiiAbMU7XUahEvHUjYGGh6zCMB8+BKuP0YSIiIiIiIiIiIhPDpCAREREREREREZGJYVKQiIiIiIiIiIjIxDApSEREREREREREZGKYFCQiIiIiIiIiIjIx3H2YiIiIiIjoX5RKJWITcnE1PBVXw9MQ/yQP6VlFAICsnGL8sT8awQFO8PGsBaFQoONoiYjUT6FQIjouG1fDU3EtIg3p2SV9YHp2EeZ+G4qW/s4IDnBCg7q2EAjYDxoqJgWJiIiIiIhQkvD7Ze89rNoaiYgHmWWWyS2QYezcUwCAem7WmPKSH14b1hi1nSy1FygRkYakpBdg3a4o/Lg1EjEJuc+9XlAox+K1f5X+v4+nHaaO8Mf4QT5wsDPXZqikBpw+TEREREREJk0mU2Dx2puo22MTZiy+VG5C8L/ikvIwf8VV1Ou5Ge8uvYT8AplmAyUi0pDCIhk++CYUHj0344NvwspMCJblXmw23l16GXV7bMKnP16HVKrQcKSkTkwKEhERERGRyQqPzkCHV/di7rdhyKtmUk8qU+DrX++g+fCdOHctSc0REhFp1pVbKWg5cjeWrPsLxdVM6hUUyrFg5TW0GbsbN++mqTlC0hQmBYmIiIiIyCSduJyANmP2IPR2qlqOd/9RNrpNOoDf9t1Xy/GIiDRt25GH6DRuX5VHSFfmRmQ62r+yFwfPxqnleKRZTAoSEREREZHJOR2WiH7Tj1R7dGB55HIlXv3fafy+n4lBItJvfx6Lwag5JyGVqXfKb0GhHINmHsPh8/FqPS6pH5OC5Thy5Aj69OkDJycnWFlZITAwEIsWLUJxcbGuQyMiIiIiohqITcjBwBlHUVgk18jxlUpg3PwzuHQzWSPHJyKqqRuRaRj9/kkoFEqNHF8qU2DoO8dxLzZLI8cn9WBSsAzLly9H7969cfjwYdja2qJx48aIjIzEvHnzEBISgoKCAl2HSERERERE1aBUKvHax+eQnStVqV7opoGIOzoKoZsGVqm8XK7EhI/OoLCIm48QkX4plsox/sMzKq0fqGofCAD5hTJM+Ogs5HJuPqKvmBT8jytXrmD27NkQCATYsGEDYmJicP36dURGRqJRo0a4cOEC5s6dq+swiYiIiIioGtbsuItjlxJUrufmbAWP2tZwc7aqcp3Ih1lYsPKaym0REWnSop9v4ubddJXqVKcPBIDz15/g+z/CVapD2sOk4H8sXLgQSqUSEyZMwLhx40p/7u3tjbVr1wIAVq1aheRkTgUgIiIi46VUKnHySgKGzzqOxNSSWRJJqQV4bcFZXI9Qz6YM+i4uKRcfrriKxgO2IyElHwCQklGIP/ZHo6hYM9NO9UlRsRx/7I9G1wn7kZha8v6fpBXgox+uIj4pT8fRVY9MpsBnP93Qapvf/RGOjOwirbapLmmZhVi24Raav7QTiX9/BpLTC7FqSwRy8ox/WSW5XIF9px+h35uHn+kHZy6+iMiHmboNTkvuxWZh1rLL8H5xa2k/mJpZiF0nYiBT8zp0+uZ0ajIke7fiq+jIcstI9m7F4MtntRhVzeXkFWP5L7e12uaitTdRLDW866axngP/ZvRJwdTUVMyZMweNGjWChYUF6tWrh5kzZyIvLw+TJk2CQCDAihUrAAA5OTk4cuQIAGDy5MnPHatLly7w9fVFcXEx9uzZo9X3QURERKQtMY9zEDxyN1547SC2H40pXW9IrlBi7c4otBy5G33eOGSwiY7KyOUKvLv0Erz6bMVnP91AVGwWlH8vuVQsVWDs3FPw7L0FJ6+oPtrMUJy4nID6vTZj7NxTOHM1CYq/v/vL5EosXH0DXn23YNayywY3JWz/2TjEaTmhWVgkx4bd97TaZk0plUp8/ettePTcjNlfXcFfUel4uuyYVKbAtM8voG6PzUa9mcrte+nwG7QDA946igNn45/pB7/7Ixz+g3Zg9JyTKCg0zunhRcVyjJ9/Br4DtuOrX27jQXxOaT9YVKzAkLePw6f/NlwLN42HRMbk9/3RyMlTbfmEmkpOL8Sfx2K02iZVjVjXAWjSjRs30LdvXyQlJcHa2hoBAQFISEjAd999h+joaKSnlwyXDQoKAgBcv34dxcXFMDc3R6tWrco8ZqdOnRAVFYVLly7htdde09ZbISIiItKK2IQcdBy3DwnJ+bCxMsPL/bwxtp83nB0sEJeUh/W7orD9aAwOX3iMkEkHcHpdP9Syleg6bLVRKpWY8OFZ/LqvJNnRrXUdvDHcD818HVFYJMPe03FYvT0SCcn56P3GYexb0RO9OnjoOGr1Onw+HgPeOgqpTIG6rlaYMtwP/bvUg4W5GDfvpuHHbZE4HZaEr365jbTMIqxf2BkCgUDXYVfJ6m3lj/bQpFVbI/DOK0110nZ1LFx9o3Tac5CfI6aN8Ef75q5QKoETVxKwckskomKz8PLc0ygolOO1YY11HLF63YpKR+cJ+5GVUwwHOwkmDvbF8F4NUMtWgvuPsrFmx13sOxOHzYceICmtAIdW9Ya5RKTrsNVGKlVg8MxjOHQ+HgIB0LeTB15/yQ+NvWohJ0+KHcdi8POfdxGTkIuuEw/g5Nq+aNXERddhUxWt3q6rfjASo/p666RtKp/RJgVTU1MxYMAAJCUlYdasWViwYAFsbW0BAF9++SXef/99iMViCAQCNGvWDAAQFRUFAPD09IRYXPavxtvb+5myRERERMZCqVRixHsnkZCcjwBvexxe1Qcebtalr/s1sEfP9nXxwaR09JpyCDfvpmP6ogv49YtuugtazVZvi8Sv++5DJBLgj8XdMKJ3w2deb+HvjDkTAjH2g9P483gMXpp1Ag8PjoCTvYWOIlav1IxCvDTrBKQyBYb18MJvi7rCwvyf+2L/hvYY1dcbmw9G4+V5p7Fxzz10CHLF6y/56TDqqpHLFTgdlqSTtu/FZiMhOQ/urtaVF9axY5celyYEl7zdGrMnBD6T9A30dcRbY5pg1rLL+Oa3O3jjs/NoG+iCQF9HXYWsVjKZAoNmHkNWTjHaN3fFvhW94FjLvPR1vwb26N+1Ps5eTUK/6UdwKjQRH664ii/fbaPDqNXrs59u4ND5eFhZiLHr2x7o2b7uM6+3buqCuZOaY/Dbx3AqNBGDZh7DgwMjjCoxaqwysotwI1K1tQTV5eLNZBQVy3me6BmjnT48Y8YMxMfHY/r06Vi2bFlpQhAA5syZg+bNm0Mmk8HLywt2dnYAgIyMDACAg4NDucd9+trTskRERETG4tJfybhyOwUW5iIcWtX7mYTgvzXzdcSfX3cHgJKRMn+vN2folEolvv39DgDgi7daPZcQfMrCXIw/lnRDoI8DcvKkWL/LsKaGVmTdzijk5kvRzNcRfyzp9kxC8N9G9fXG528FAwC+/f0OlE/nFeqxuzFZyNfhVM+r4Wk6a1sV3/5W8hmYPKwx5kxsVuYoUKFQgK9mt0W/LvUglyvxw5YIbYepMXtOPcLDxzlwcbDA/h+eTQj+W+dgN6z/tDMA4Kcdd5GXr93pmJpSVCzHqq0lf88fP+zwXELwqVq2Euz+tgfqulohITkf248+1GaYWpUvlyO1qKjMfwzNNR32Q1KZArfu6SYhWVPGdA78l1EmBSMiIrBlyxY4Oztj0aJFZZYJDi65iWnevHnpzwoLCwEAEkn5U2DMzUsuCgUFBaU/O3v2LHr06IE6derA3NwcHh4eGDlyJCIijOfiSERERMZv5d9f7Ef1aYh6bjYVlu0QVBsdglwhkynx8593tRGexp0KTUTkwyzYWJnhjREVj3wzl4gwY0wTACVTQ5+uN2bIFAolfvx7eu3MsU0gMat4NMcbw/1hbSlGeHQmzlzVzQg8VVyL0G1S7poBbNAT8zgH+8/GAQDeGxdYYVmBQIDZ40vK/LbvPrJzjWPjkaf94GtDG8PBruyE4FNDunuhoYctsnKKsfnQA22Ep3E7jsYgJaMQdV2tMLqSqZ52NhJMGV7SV640osTwf3169w7cj+wu8x9Do+t+SNf9cHUZ0znwX0Y5fXjTpk1QKBQYO3YsbGzKvqG1tLQE8GxS0MKiZNpHcXH5F7SivzPBT+sDJaMGAwMDMWXKFLi6uiI+Ph6LFi1C+/btcfv2bXh4VG+dmVatWiEpSf9vsIiIiMg4PKk1HRC5YFSfskfI/deoPg1x4UYyPv/qd/z46QANR6d5ORYdAate6NfFA3Y2la+TOKpvQ0z+5BwexOfAw9MXQmVBpXX0mVxghSSH9wEAI3s3qLR8LVsJXuxcD9uOPMTAUTNhW3hB0yHWSK55e8C6T5mvhW4aCDdnqwrruzlblv477uiocsslpeaj9ejnNyVc+vWPWPP5ARUi1r4CMz8obUcjOMAZvl61Ki3fJdgNdVyskJiSj0ZNOkMif6yFKDUrwf4DQGiJUX0r7weFQgFG9m6IRWtvYuYHX2PBjH1aiFCzMq16AxYdMLxXA4jFlY8hGt3XGx/9cA0XriegrocH9GF1UUuhEOFB7dV2vNfqN8Qw93plvtb30mm1tOHr64sCheY3bsqy7AlYdirztcr6war2gUD5/eDsDz7Bp29rfqdeUzsH3NzcEBYWVq26RpkUPHHiBAAgJCSk3DLx8fEAnk0KVmVqcFlTjAcOHIiBAwc+U65169Zo3LgxduzYgZkzZ6r4DkokJSXh8WPDv7ASERGRgbARAiLAvoobhzwdRVNYpDSOexbXAsAKsLeteHTQU9aWYojFAshkSiQ+SQOkBr68jJkj4ABIzISwtjKrUhUHu5JzJTunANnJen4OOOcC5Szp5+ZsBY/aVVvvTywSVrnsv+XlFSIvQc9/R/YegG3V+wCBQAB7WwkSU/KRkpYF5On5+6sK+5Jzv+r9YEm5vAIp8oyhH3QvBiyq/v5LywnESHicCED3O5JbiURAkPqO18jGBt1daqvvgGVISEhAvlyu0TYAAHUKAMuyX6pqP1jdPhAAsnPytXKt4DlQdUaZFIyNjQVQsmFIWWQyGc6fPw/g2aSgr69vaX2ZTFbmZiPR0dHPlC2Pk5MTAJS7YUlVuLm5VbsuERERkaqeCKWQAYhJyEXbZq6Vlo9JyAEAWJgr4VS37HWnDEmuuQRZKJlCWRUJyfmQyUqmDddxdYAQFY8003cKgTkSARRLFVXeFCMmIRcAUMtGAhsz/T4Hcs2tkVXOa1VZF9PN2RJikRAyuQJJqeWPCi3vWNbW5rDX889JgZkV0lHy2VYqlZXuKl1ULEdCSsn7dXGygcRev99fVSSiCAqIEfM4B/XrVLyMAvDPZ8DaUqj3f9+qyLIUIxf/vK/KPL0OCJRFcK9bR4ORVZ2l0PBWSXN3d9fSSEELlPeXrawfrGofWNGx7GwtYauFa4WpnQM1yR0ZZVIwLy8PwLPr/v3bli1bkJqaCltbWzRo8M/UiBYtWkAikaCoqAhhYWFo167dc3XPnTsHAGjbtu1zr8nlcigUCsTGxmLu3Llwc3PDiBEjqv0+qjv8k4iIiKg6PvgmFEvW/YW1O+9iZCVTiOVyBdbtLNlgY+XiNzBh8FfaCFGj7j7MhN+gHTh6KQGxCTnwdLetsPzTtRQ7taiNsxujtRGixnV8dS8u3EjG2p1R+HBKiwrLPozPwdGLJSM+rhxfV6Xpprq060QMhrx9vMzXyprm9l9xR0fBo7Y1klILUK/nZpXb/+R/MzBr3BqV62lTVk4x6vbYhOi4HJwOS0K31hUnebYffVhSx9UKMdeuVGm6qb4b97/T+GXvfazdGYUurSp+/3n5Uvx+oOSzv33dAvTppN9/36o4HZaIbhMPYNuRh/hmTjvUqmTE4M9/RgEAXurth63L4rURYqWUhYWQjRin6zBUEhUVBYGF5nexX7UlAtM+L3uph8r6wZr2gQCw6tvPMaZfxWtVqgPPgaoz/F67DE+zpNeuXXvutcTERMyePRsA0KzZs7tp2draomfPngCANWue79DPnDmDqKgoSCQSDBo06LnXu3btColEAh8fH9y4cQMnTpyAi4uLWt4TERERkaZNeckPAgFw9GICTlxOqLDs2p1RePg4Bw52EowsZ5deQ9O4gT26t3WHQqHEhyuuVbijbnxSHn7YXLKw/rSR/toKUeOevpcVm8Lx+EleueWUSiU+/OEqlEqgZ3t3vU8IAkBwgLNJt18VtWwleLl/IwDAgpXXUCwtfypbTl4xvvj5JgBgynA/o0gIAv98BrYcfogbkRVvirBs4y1k5RSjoYctenUw/FGCQMk6kQHe9sgrkOGLn29UWDY8OgO/7r0PwLj6QWOm634oOMBJp+3T84yj5/6PHj16AACWLFmCqKio0p+HhoYiJCQEqaklO+4EBQU9V3f+/PkQCARYv349Nm7cWPrz6OhoTJo0CQBKNxT5r7Vr1+LSpUvYtGkT7Ozs0KtXLzx69Eidb42IiIhIYxp42OKVvxMCg2Yew87jMc8lxqRSBVZuDi8daTDr1UBYWRrP5JO5k5pDKBTg1333Me2zC2XuqHrzbhpemHwAKRmF8G9oj6E9vLQfqIa81LMB/BrUQnJ6IUJeO4C/otKfK5OVU4w3Fp7H7/ujIRQKMHdS8zKOpH88alvDxUH7ozCeauFnGF+G33m5CawtxThzNQnD3jmOJ2nPz76KTchBn6mHER6dCVdHC7z+UsW7dRuSNoEu6NneHUXFcvSacggnLic81w8WFsnw2U/X8fGq6wCA/00OglCoD1ts1JxAIMD8yUEAgC/X38L878OQXyB7rty5a0no8foh5BfK0KlFbXRtxaWvDEEzXweIxbo5V22tzeDjqf8PkEyN8dzB/cucOXPwxx9/IC4uDk2aNIGfnx8KCwtx//599O3bF15eXjh8+PAz6wk+1a5dOyxevBjvv/8+xo8fjwULFsDBwQG3b9+GTCZD27ZtsXjx4jLbbdy4MYCSqcV9+vSBl5cXvvzyS6xYsUKj75eIiIhIXVZ/1BGPk/Nx/HIChr5zHI29amHMi95wtjdH3JM8/LL3PhKSS9YKmjDYB/MmG0ZCqKq6t3PHj/M7YMrC8/hxWyR+3XcfY/t5I9DHEUXFcuw9/Qinw5IAAPXrWOPAD71gLhHpOGr1MZeIcHBlb3SduB/3YrPR/KWd6NrKDQO61oe5RIS/otLxx4Fo5BXIIBAAqz/siJA27roOu0oEAgEGdKuPdTujKi+sZl2C3SqdhqkvGjewx/bl3THknWPYdyYO9XpuxrAeXmjf3BVKpRInriRi35k4KBRK2NtKsG9FL9R2KmfnAgMkEAiwdekL6D75IK5FpKH75IMI8nPEiF4NYWdjhui4bPyy9z7SMosAlDxImDik4vXmDc3oF70RHZ+ND1dcw+drbmLllgi80r8RfL1qITdfiu1HYxB2p2SgTdNGDtj5TY9K158k/WBhLkbPdnVx8Jz2p3q/2NnDaJLnxkSgrGhehAGLiIjA7Nmzcfp0yfbQAQEBmDRpEiZPngxvb288fPgQly9fRps2bcqsf/jwYSxfvhyhoaEoLCxEw4YNMXbsWMyaNQvm5lXbka5Vq1ZwdnbGoUOH1Pa+iIiIiDStqFiOed+F4aftd5GbL33udRcHC7w3LhCzJwQa7RfB3SdjMffbMEQ8yHzuNZFIgEHdPLFiXnvUcTHszUXKk5Cch+mLLmL3yUdQKJ7/uuDf0B6LZ7bCwJCyN/bTV2F3Uqq0fmBZnq6nFf8kT+X1tLYsDcEIA5tmf+lmMt5ZegmX/kop8/Xubd3x3QftEODtoOXItCMnrxjvLr2M3/ZHo7Do+WnU9dysMf/1IKMaJflfG3ffw8errpW56YjETIhRfRri2/fbwd6uat+PtcUQ15MTb92otfXk9p56hIEzjqpcryZ9IACcWd8PnYO1M6KU50DVGW1SsDy5ubmws7ODQCBATk4OrKw0cyOXnJwMb29vvPrqq/jhhx800gYRERGRJuXkFeO3fdG49FcycvNlsLMxQ6/2dTG0h5dRjY4rj1KpxOmwJGw9/AApGYWQmInQ2KsWJg72hYdb5TvzGoO4pFys2xmFqNhsFEvlcHGwwIjeDdG1lZvBJoTbjNmN0NupKter7hdiN2dLxB4eCYmZYX5mroWn4td995GQkg+BAPCsY4MJg33h18Be16FpRVpmITbsvocbd9NQUCiHva0EA7rVR7/O9YxmHcWKyOUKHDofj90nHyE9qwgW5iI083HEhME+cHHUzxGiTAhVTC5XwLvfNsRWcYfpp2qSFGzayAF/7RiitesGzwEV2tV6izp2584dKJVK+Pr6qi0h+PLLL6NRo0YICgqCvb097t27h6+//hpisRjvvPOOWtogIiIi0jZbawmmjvTHVBNdQF4gEKBb6zqV7sBqzOq52WDB1Ja6DkOtlr3bBl0nHtBae0vebm2wCUEAaBngjJYGsEmKpjjZW2DWuEBdh6EzIpEQ/brUR78u9XUdCqmJSCTE0nfbYMR7J7TW5vL32hjsgyRjZ/yPNv7j1q1bAFDmeoLV1a5dOxw4cAATJkxA3759sXTpUnTu3Bk3btxAo0aN1NYOERERERHVTJdWdTBjTIBW2urfpR5eGcDvA0SkX4b3aoDhvRpopa3JwxqjVwcPrbRFqjO5kYKaSApOnz4d06dPV9vxiIiIiIhIc76Y0QrHLyfgTnRmleskpeY/8+/K1HayxOqPOnJ0DBHppR/mtcfFm8mIf5JXpfKq9oEA0Ki+HZbNKnsfB9IPTAoSEREREZFJsbYyw+Ef+6DLhP14EJ9TpTqqbFDiWMscR1f3gburaaw9SUSGx8XREsd+KukHk9MLKy2v6iZN9dysceynPrCzMYyd102VyU0fPnHiBJRKJfr166frUIiIiIiISEfq1rbG2Q39EOij3t1z67pa4cz6fgj0dVTrcYmI1K1xA3uc3dAfnu426j2uVy2c29gfnu62aj0uqZ/JJQWJiIiIiIgAwN3VGpd/H4j3xgVCKKz5NN9XBzTCrT+Hokkj9SYaiYg0xderFm5uG4LXhvqq5XgzxgTg6uZBqF9HvYlG0gwmBYmIiIiIyGRZWoixdFYbnNvYD11buVXrGC38nLD3+57Y+HlXONiZqzlCIiLNqmUrwZqPO+PQqt5o3bR6u413alEbp9e9iG8/aA9rKzM1R0iaYnJrChIREREREf1X++a1cWpdP9y5n4FVWyNw8Fx8hesN1nW1Qve27pg6wh9tm7lwQxEiMni9O3qgd0cPhN5OwaqtETh2KQFxSeVvROLlboPeHT0wbaQ/mnHJBIPEpCAREREREdHfmjRywIp5HQAA6VlFuBaRisdP8lEklUNiJoSroyWCA5xR28lSx5ESEWlG66YuaN3UBQCQnFaAq+GpeJJegGKpAuZmIri7WqGlvxOc7C10HCnVFJOCREREREREZXCsZY4e7erqOgwiIp1xdbJE3871dB0GaQjXFCQiIiIiIiIiIjIxTAoSERERERERERGZGCYFiYiIiIiIiIiITAyTgkRERERERERERCZGoFQqlboOgoiIiIiIiIioppRKJVBUpOswVGNuDoFAoOsojAbPgapjUpCIiIiIiIiIiMjEcPowERERERERERGRiWFSkIiIiIiIiIiIyMQwKUhERERERERERGRimBQkIiIiIiIiIiIyMUwKEhERERERERERmRgmBYmIiIiIiIiIiEwMk4JEREREREREREQmhklBIiIiIiIiIiIiE8OkIBERERERERERkYlhUpCIiIiIiIiIiMjEMClIRERERERERERkYpgUJCIiIiIiIiIiMjFMChIREREREREREZkYJgWJiIiIiIiIiIhMDJOCREREREREREREJoZJQSIiIiIiIiIiIhPDpCAREREREREREZGJYVKQiIiIiIiIiIjIxDApSEREREREREREZGKYFCQiIiIiIiIiIjIxTAoSERERERERERGZGCYFiYiIiIiIiIiITAyTgkRERERERERERCaGSUEiIiIiIiIiIiITw6QgERERERERERGRifk/VK6F72nSiUsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1643.3x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Circuit that creates L2_2 unitary\n",
    "\n",
    "# First need a function to create the Ci circuits\n",
    "def C_i(i,workRegister):\n",
    "    n = workRegister.size\n",
    "    if i<1 or i>(n-1):\n",
    "        print('WRONG VALUE FOR i !!!!')\n",
    "        return\n",
    "    Ci = QuantumCircuit(workRegister, name='C_{}'.format(i))\n",
    "    [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in range(1,i+1)]\n",
    "    Ci.append(qiskit.circuit.library.MCXGate(num_ctrl_qubits=i, ctrl_state='0'*i),workRegister[:i+1])\n",
    "#     Ci.mcx(control_qubits=workRegister[:i-1],target_qubit=workRegister[i-1])\n",
    "    [Ci.cnot(control_qubit=i, target_qubit=(i-j), ctrl_state='0') for j in reversed(range(1,i+1))]\n",
    "    return Ci\n",
    "\n",
    "L2_2 = QuantumCircuit(workRegister)\n",
    "\n",
    "for j in range(1,n):\n",
    "    L2_2 = L2_2.compose(C_i(j,workRegister))\n",
    "    \n",
    "# Apply -ve sign to final piece\n",
    "L2_2.h(n-1)\n",
    "L2_2.append(qiskit.circuit.library.MCXGate(num_ctrl_qubits=n-1, ctrl_state='1'*(n-1)),workRegister)\n",
    "L2_2.h(n-1)\n",
    "    \n",
    "L2_2.draw('mpl',style='iqp')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c23d1f0",
   "metadata": {},
   "source": [
    "# Test all these circuits individually to make sure they are forming the unitaries we want"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1169625e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import numpy\n",
    "numpy.set_printoptions(threshold=sys.maxsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "531a159c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import Aer, execute\n",
    "import numpy as np\n",
    "\n",
    "backend = Aer.get_backend('unitary_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a1e14df1",
   "metadata": {},
   "outputs": [],
   "source": [
    "L1_1_result = execute(L1_1,backend,shots=0).result()\n",
    "L1_2_result = execute(L1_2,backend,shots=0).result()\n",
    "L2_1_result = execute(L2_1,backend,shots=0).result()\n",
    "L2_2_result = execute(L2_2,backend,shots=0).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6566e4ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "L1_1_matrix = np.array(L1_1_result.get_unitary().data)\n",
    "L1_2_matrix = np.array(L1_2_result.get_unitary().data)\n",
    "L2_1_matrix = np.array(L2_1_result.get_unitary().data)\n",
    "L2_2_matrix = np.array(L2_2_result.get_unitary().data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "df484a13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.0\n",
      "0.0\n",
      "2.0906028553828477e-16\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.norm(L1_1_matrix.imag,2))\n",
    "print(np.linalg.norm(L1_2_matrix.imag,2))\n",
    "print(np.linalg.norm(L2_1_matrix.imag,2))\n",
    "print(np.linalg.norm(L2_2_matrix.imag,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8a43ffba",
   "metadata": {},
   "outputs": [],
   "source": [
    "summed_matrix = (np.eye(L1_1_matrix.shape[0]) + 0.5*L1_1_matrix + 0.5*L1_2_matrix + 0.5*L2_1_matrix + 0.5*L2_2_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fe54bcbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "expected_matrix = np.eye(L1_1_matrix.shape[0])\n",
    "for j in range(expected_matrix.shape[0]-1):\n",
    "    expected_matrix[j+1,j] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e3e8e8c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "23451664",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8039882590205613e-16"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(expected_matrix - summed_matrix,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "239a33df",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c9ef050",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "267af5d7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "15862ee2",
   "metadata": {},
   "source": [
    "# Create the prepare and prepare+ operations for LCU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8b68fb27",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prepare the state [1, 0.5, 0.5, 0.5, 0.5]/normalizatoin in order to do a linear combination of the unitaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "97e1fee1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the Select circuit\n",
    "# alphas = np.array([np.sqrt(1+0j), np.sqrt(0.5+0j), np.sqrt(0.5+0j), np.sqrt(0.5+0j), np.sqrt(0.5+0j)])\n",
    "alphas = np.array([np.sqrt(1.0+0j), np.sqrt(0.5+0j), np.sqrt(0.5+0j), np.sqrt(0.5+0j), np.sqrt(0.5+0j)])\n",
    "\n",
    "# alphas = np.array([np.sqrt(1+0j), np.sqrt(-0.5+0j), 0, 0])\n",
    "# alphas = np.array([np.sqrt(1), -np.sqrt(0.5), 0, 0])\n",
    "alphas = alphas/np.linalg.norm(alphas,2)\n",
    "lcu_size = int(np.ceil(np.log2(alphas.size)))\n",
    "alphas = np.pad(alphas, (0,2**lcu_size - alphas.size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "880623b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8,)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7cedb0c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "lcuRegister = QuantumRegister(lcu_size)\n",
    "prep = QuantumCircuit(lcuRegister)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "764218cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7f4725f51810>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prep.prepare_state(alphas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "bbac99fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 491.382x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prep.draw('mpl',style='iqp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6d57c7f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 491.382x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prep.inverse().draw('mpl',style='iqp')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3cd2bb3",
   "metadata": {},
   "source": [
    "# Check if the prepare operation is properly creating alphas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "83b355e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import Aer, execute\n",
    "import numpy as np\n",
    "\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "\n",
    "prep_result = execute(prep,backend,shots=0).result()\n",
    "\n",
    "prep_vector = np.array(prep_result.get_statevector().data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5658ffd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.77350269e-01+0.j,  4.08248290e-01+0.j,  4.08248290e-01+0.j,\n",
       "        4.08248290e-01+0.j,  4.08248290e-01+0.j, -2.77555756e-17+0.j,\n",
       "       -1.06546085e-17+0.j,  1.12792092e-17+0.j])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prep_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d041f8eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.901918103915613e-16"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(prep_vector - alphas,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db50b7ce",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "152a3eda",
   "metadata": {},
   "source": [
    "# Now create the block encoding using LCU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "3eebd3f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#blockEncoded = QuantumCircuit(lcuRegister,workRegister)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7f3a55b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "blockEncoded = QuantumCircuit(workRegister,lcuRegister)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1be9d454",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Apply the PREP operation\n",
    "blockEncoded = blockEncoded.compose(prep,lcuRegister)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "707ae89f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7f4782ac86d0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Apply the SELECT operation using contolled versions of the circuits L1-L3\n",
    "blockEncoded.append(L1_1.control(num_ctrl_qubits=3,ctrl_state='001'), lcuRegister[:] + workRegister[:])\n",
    "blockEncoded.append(L1_2.control(num_ctrl_qubits=3,ctrl_state='010'), lcuRegister[:] + workRegister[:])\n",
    "blockEncoded.append(L2_1.control(num_ctrl_qubits=3,ctrl_state='011'), lcuRegister[:] + workRegister[:])\n",
    "blockEncoded.append(L2_2.control(num_ctrl_qubits=3,ctrl_state='100'), lcuRegister[:] + workRegister[:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a728a4cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Apply the PREP+ operation\n",
    "blockEncoded = blockEncoded.compose(prep.inverse(),lcuRegister)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7104ab70",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "2b009ec3",
   "metadata": {},
   "source": [
    "# Check if the block encoding is produced correctly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "59c9701b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "73188ba1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/lore/raisuo/conda_envs/qiskit/lib/python3.11/site-packages/qiskit/visualization/circuit/matplotlib.py:266: FutureWarning: The default matplotlib drawer scheme will be changed to \"iqp\" in a following release. To silence this warning, specify the current default explicitly as style=\"clifford\", or the new default as style=\"iqp\".\n",
      "  self._style, def_font_ratio = load_style(self._style)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1829.16x618.722 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blockEncoded.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8652ab1a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04c14db7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "36924790",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import Aer, execute\n",
    "import numpy as np\n",
    "\n",
    "backend = Aer.get_backend('unitary_simulator',precision='double')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "c542841c",
   "metadata": {},
   "outputs": [],
   "source": [
    "blockEncoded_result = execute(blockEncoded,backend,shots=0).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "9f3cff72",
   "metadata": {},
   "outputs": [],
   "source": [
    "blockEncoded_matrix = np.array(blockEncoded_result.get_unitary().data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "1dbce200",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3440458587812923e-14\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.norm(blockEncoded_matrix.imag,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ff21fb44",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1. -0.  0. -0.  0.  0. -0. -0. -0. -0.  0.  0.  0. -0. -0. -0.]\n",
      " [ 1.  1.  0. -0. -0. -0. -0.  0. -0. -0. -0.  0.  0. -0.  0.  0.]\n",
      " [ 0.  1.  1.  0. -0.  0.  0.  0.  0. -0. -0. -0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  1.  1.  0. -0. -0. -0. -0. -0.  0. -0. -0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  1.  1. -0.  0.  0. -0. -0. -0. -0. -0. -0.  0.  0.]\n",
      " [-0.  0.  0. -0.  1.  1.  0.  0. -0. -0.  0. -0.  0. -0. -0.  0.]\n",
      " [ 0. -0.  0.  0.  0.  1.  1.  0. -0.  0. -0. -0.  0. -0. -0. -0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  1.  1.  0. -0.  0. -0.  0.  0.  0. -0.]\n",
      " [ 0. -0.  0.  0.  0.  0. -0.  1.  1.  0.  0. -0.  0.  0. -0.  0.]\n",
      " [ 0.  0.  0.  0.  0. -0.  0.  0.  1.  1.  0. -0. -0. -0.  0. -0.]\n",
      " [ 0.  0.  0.  0.  0.  0. -0.  0.  0.  1.  1.  0. -0.  0.  0.  0.]\n",
      " [ 0.  0.  0. -0. -0.  0.  0. -0.  0.  0.  1.  1.  0.  0.  0. -0.]\n",
      " [ 0. -0. -0.  0.  0.  0.  0.  0.  0.  0. -0.  1.  1. -0.  0.  0.]\n",
      " [ 0. -0.  0.  0. -0.  0. -0.  0. -0.  0.  0. -0.  1.  1.  0.  0.]\n",
      " [ 0.  0. -0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  1.  1. -0.]\n",
      " [-0. -0.  0.  0. -0.  0. -0.  0.  0.  0.  0.  0. -0.  0.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.round(blockEncoded_matrix[0:2**n,0:2**n].real/np.abs(blockEncoded_matrix[0,0].real),5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "c9931914",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1. -0.  0. -0.  0.  0. -0. -0. -0. -0.  0.  0.  0. -0. -0. -0.]\n",
      " [ 1.  1.  0. -0. -0. -0. -0.  0. -0. -0. -0.  0.  0. -0.  0.  0.]\n",
      " [ 0.  1.  1.  0. -0.  0.  0.  0.  0. -0. -0. -0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  1.  1.  0. -0. -0. -0. -0. -0.  0. -0. -0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  1.  1. -0.  0.  0. -0. -0. -0. -0. -0. -0.  0.  0.]\n",
      " [-0.  0.  0. -0.  1.  1.  0.  0. -0. -0.  0. -0.  0. -0. -0.  0.]\n",
      " [ 0. -0.  0.  0.  0.  1.  1.  0. -0.  0. -0. -0.  0. -0. -0. -0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  1.  1.  0. -0.  0. -0.  0.  0.  0. -0.]\n",
      " [ 0. -0.  0.  0.  0.  0. -0.  1.  1.  0.  0. -0.  0.  0. -0.  0.]\n",
      " [ 0.  0.  0.  0.  0. -0.  0.  0.  1.  1.  0. -0. -0. -0.  0. -0.]\n",
      " [ 0.  0.  0.  0.  0.  0. -0.  0.  0.  1.  1.  0. -0.  0.  0.  0.]\n",
      " [ 0.  0.  0. -0. -0.  0.  0. -0.  0.  0.  1.  1.  0.  0.  0. -0.]\n",
      " [ 0. -0. -0.  0.  0.  0.  0.  0.  0.  0. -0.  1.  1. -0.  0.  0.]\n",
      " [ 0. -0.  0.  0. -0.  0. -0.  0. -0.  0.  0. -0.  1.  1.  0.  0.]\n",
      " [ 0.  0. -0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  1.  1. -0.]\n",
      " [-0. -0.  0.  0. -0.  0. -0.  0.  0.  0.  0.  0. -0.  0.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.round(blockEncoded_matrix[0:2**n,0:2**n].real/np.abs(blockEncoded_matrix[1,0].real),5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "c009a549",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.33333333333333354-1.143505040328834e-15j)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blockEncoded_matrix[1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2fe8fddc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "8cc68595-c553-4b51-af4d-37892b7813d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ideally this function should take a list of the block-encoding qubits + the rotation qubit\n",
    "\n",
    "\n",
    "def CR_phi_d(d,phi,circuit,m):\n",
    "    circuit.append( qiskit.circuit.library.MCXGate(num_ctrl_qubits=m , ctrl_state='0'*m), circuit.qubits[circuit.num_qubits-m-1:]  )\n",
    "    circuit.rz(2*phi,circuit.num_qubits-1)\n",
    "    circuit.z(circuit.num_qubits-1)\n",
    "    circuit.append( qiskit.circuit.library.MCXGate(num_ctrl_qubits=m , ctrl_state='0'*m), circuit.qubits[circuit.num_qubits-m-1:]  )\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b755f66-d6f0-461c-8e08-4518f9dd4269",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "e90e6431-1a4d-4afb-8387-68b34de4b207",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Qubit(QuantumRegister(4, 'q0'), 0),\n",
       " Qubit(QuantumRegister(4, 'q0'), 1),\n",
       " Qubit(QuantumRegister(4, 'q0'), 2),\n",
       " Qubit(QuantumRegister(4, 'q0'), 3),\n",
       " Qubit(QuantumRegister(3, 'q15'), 0),\n",
       " Qubit(QuantumRegister(3, 'q15'), 1),\n",
       " Qubit(QuantumRegister(3, 'q15'), 2)]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blockEncoded.qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "3da8a507-bfe9-46dc-b825-f3038d8e8de9",
   "metadata": {},
   "outputs": [],
   "source": [
    "QSP_circuit = QuantumCircuit(blockEncoded.qubits, QuantumRegister(1,name='rotation'), name='QSP')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f68b8f2-ba24-4540-88b1-bf78eb40c9a2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "4ddbbb8e-a6a0-4884-bb77-708d9f797f95",
   "metadata": {},
   "outputs": [],
   "source": [
    "blockEncoded_i = blockEncoded.inverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "731f8b09-171d-46f3-8a13-403ff7c6728c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# CR_phi_d(1,2,blockEncoded,3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "6b4441dc-a1f6-499b-8217-f19a2e263591",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.io import loadmat\n",
    "phi_angles = np.array( loadmat('phi_kappa_50_pts_5000_deg_999_crit_14.mat') ).item()['phi_proc']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "e76266fb-ab4d-4ca1-ac89-4db128fb8c00",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 7.85398162e-01]\n",
      " [ 2.54245076e-09]\n",
      " [-3.34684048e-09]\n",
      " [ 4.28672448e-09]\n",
      " [-5.37569787e-09]\n",
      " [ 6.63071164e-09]\n",
      " [-8.06766550e-09]\n",
      " [ 9.70594904e-09]\n",
      " [-1.15640391e-08]\n",
      " [ 1.36640265e-08]\n",
      " [-1.60272262e-08]\n",
      " [ 1.86787162e-08]\n",
      " [-2.16429552e-08]\n",
      " [ 2.49483113e-08]\n",
      " [-2.86226905e-08]\n",
      " [ 3.26980778e-08]\n",
      " [-3.72061683e-08]\n",
      " [ 4.21829120e-08]\n",
      " [-4.76641401e-08]\n",
      " [ 5.36901313e-08]\n",
      " [-6.03012455e-08]\n",
      " [ 6.75424795e-08]\n",
      " [-7.54591093e-08]\n",
      " [ 8.41012647e-08]\n",
      " [-9.35195734e-08]\n",
      " [ 1.03769733e-07]\n",
      " [-1.14908159e-07]\n",
      " [ 1.26996573e-07]\n",
      " [-1.40097662e-07]\n",
      " [ 1.54279660e-07]\n",
      " [-1.69612006e-07]\n",
      " [ 1.86169950e-07]\n",
      " [-2.04030217e-07]\n",
      " [ 2.23275605e-07]\n",
      " [-2.43990654e-07]\n",
      " [ 2.66266267e-07]\n",
      " [-2.90195381e-07]\n",
      " [ 3.15877582e-07]\n",
      " [-3.43414785e-07]\n",
      " [ 3.72915861e-07]\n",
      " [-4.04492334e-07]\n",
      " [ 4.38262989e-07]\n",
      " [-4.74349583e-07]\n",
      " [ 5.12881471e-07]\n",
      " [-5.53991319e-07]\n",
      " [ 5.97819725e-07]\n",
      " [-6.44510938e-07]\n",
      " [ 6.94217498e-07]\n",
      " [-7.47095959e-07]\n",
      " [ 8.03311527e-07]\n",
      " [-8.63033776e-07]\n",
      " [ 9.26441313e-07]\n",
      " [-9.93717507e-07]\n",
      " [ 1.06505512e-06]\n",
      " [-1.14065208e-06]\n",
      " [ 1.22071609e-06]\n",
      " [-1.30546043e-06]\n",
      " [ 1.39510854e-06]\n",
      " [-1.48988985e-06]\n",
      " [ 1.59004437e-06]\n",
      " [-1.69581850e-06]\n",
      " [ 1.80746964e-06]\n",
      " [-1.92526201e-06]\n",
      " [ 2.04947125e-06]\n",
      " [-2.18038023e-06]\n",
      " [ 2.31828369e-06]\n",
      " [-2.46348404e-06]\n",
      " [ 2.61629596e-06]\n",
      " [-2.77704225e-06]\n",
      " [ 2.94605846e-06]\n",
      " [-3.12368863e-06]\n",
      " [ 3.31029001e-06]\n",
      " [-3.50622883e-06]\n",
      " [ 3.71188493e-06]\n",
      " [-3.92764754e-06]\n",
      " [ 4.15392000e-06]\n",
      " [-4.39111546e-06]\n",
      " [ 4.63966160e-06]\n",
      " [-4.89999637e-06]\n",
      " [ 5.17257267e-06]\n",
      " [-5.45785412e-06]\n",
      " [ 5.75631970e-06]\n",
      " [-6.06845955e-06]\n",
      " [ 6.39477960e-06]\n",
      " [-6.73579734e-06]\n",
      " [ 7.09204649e-06]\n",
      " [-7.46407273e-06]\n",
      " [ 7.85243836e-06]\n",
      " [-8.25771805e-06]\n",
      " [ 8.68050351e-06]\n",
      " [-9.12139917e-06]\n",
      " [ 9.58102688e-06]\n",
      " [-1.00600216e-05]\n",
      " [ 1.05590361e-05]\n",
      " [-1.10787365e-05]\n",
      " [ 1.16198071e-05]\n",
      " [-1.21829462e-05]\n",
      " [ 1.27688701e-05]\n",
      " [-1.33783096e-05]\n",
      " [ 1.40120141e-05]\n",
      " [-1.46707474e-05]\n",
      " [ 1.53552923e-05]\n",
      " [-1.60664463e-05]\n",
      " [ 1.68050260e-05]\n",
      " [-1.75718631e-05]\n",
      " [ 1.83678087e-05]\n",
      " [-1.91937290e-05]\n",
      " [ 2.00505098e-05]\n",
      " [-2.09390522e-05]\n",
      " [ 2.18602772e-05]\n",
      " [-2.28151208e-05]\n",
      " [ 2.38045395e-05]\n",
      " [-2.48295048e-05]\n",
      " [ 2.58910084e-05]\n",
      " [-2.69900574e-05]\n",
      " [ 2.81276790e-05]\n",
      " [-2.93049159e-05]\n",
      " [ 3.05228307e-05]\n",
      " [-3.17825017e-05]\n",
      " [ 3.30850268e-05]\n",
      " [-3.44315195e-05]\n",
      " [ 3.58231130e-05]\n",
      " [-3.72609557e-05]\n",
      " [ 3.87462158e-05]\n",
      " [-4.02800762e-05]\n",
      " [ 4.18637394e-05]\n",
      " [-4.34984227e-05]\n",
      " [ 4.51853624e-05]\n",
      " [-4.69258091e-05]\n",
      " [ 4.87210323e-05]\n",
      " [-5.05723156e-05]\n",
      " [ 5.24809607e-05]\n",
      " [-5.44482830e-05]\n",
      " [ 5.64756157e-05]\n",
      " [-5.85643051e-05]\n",
      " [ 6.07157147e-05]\n",
      " [-6.29312205e-05]\n",
      " [ 6.52122152e-05]\n",
      " [-6.75601031e-05]\n",
      " [ 6.99763046e-05]\n",
      " [-7.24622511e-05]\n",
      " [ 7.50193890e-05]\n",
      " [-7.76491752e-05]\n",
      " [ 8.03530807e-05]\n",
      " [-8.31325859e-05]\n",
      " [ 8.59891844e-05]\n",
      " [-8.89243783e-05]\n",
      " [ 9.19396818e-05]\n",
      " [-9.50366167e-05]\n",
      " [ 9.82167157e-05]\n",
      " [-1.01481518e-04]\n",
      " [ 1.04832572e-04]\n",
      " [-1.08271431e-04]\n",
      " [ 1.11799659e-04]\n",
      " [-1.15418821e-04]\n",
      " [ 1.19130491e-04]\n",
      " [-1.22936244e-04]\n",
      " [ 1.26837661e-04]\n",
      " [-1.30836325e-04]\n",
      " [ 1.34933822e-04]\n",
      " [-1.39131736e-04]\n",
      " [ 1.43431657e-04]\n",
      " [-1.47835169e-04]\n",
      " [ 1.52343859e-04]\n",
      " [-1.56959308e-04]\n",
      " [ 1.61683097e-04]\n",
      " [-1.66516800e-04]\n",
      " [ 1.71461990e-04]\n",
      " [-1.76520230e-04]\n",
      " [ 1.81693077e-04]\n",
      " [-1.86982081e-04]\n",
      " [ 1.92388782e-04]\n",
      " [-1.97914709e-04]\n",
      " [ 2.03561381e-04]\n",
      " [-2.09330303e-04]\n",
      " [ 2.15222968e-04]\n",
      " [-2.21240852e-04]\n",
      " [ 2.27385417e-04]\n",
      " [-2.33658106e-04]\n",
      " [ 2.40060345e-04]\n",
      " [-2.46593539e-04]\n",
      " [ 2.53259073e-04]\n",
      " [-2.60058307e-04]\n",
      " [ 2.66992581e-04]\n",
      " [-2.74063206e-04]\n",
      " [ 2.81271471e-04]\n",
      " [-2.88618633e-04]\n",
      " [ 2.96105922e-04]\n",
      " [-3.03734535e-04]\n",
      " [ 3.11505641e-04]\n",
      " [-3.19420371e-04]\n",
      " [ 3.27479824e-04]\n",
      " [-3.35685060e-04]\n",
      " [ 3.44037104e-04]\n",
      " [-3.52536936e-04]\n",
      " [ 3.61185501e-04]\n",
      " [-3.69983697e-04]\n",
      " [ 3.78932380e-04]\n",
      " [-3.88032358e-04]\n",
      " [ 3.97284394e-04]\n",
      " [-4.06689198e-04]\n",
      " [ 4.16247433e-04]\n",
      " [-4.25959707e-04]\n",
      " [ 4.35826576e-04]\n",
      " [-4.45848538e-04]\n",
      " [ 4.56026036e-04]\n",
      " [-4.66359450e-04]\n",
      " [ 4.76849104e-04]\n",
      " [-4.87495255e-04]\n",
      " [ 4.98298099e-04]\n",
      " [-5.09257764e-04]\n",
      " [ 5.20374312e-04]\n",
      " [-5.31647732e-04]\n",
      " [ 5.43077948e-04]\n",
      " [-5.54664805e-04]\n",
      " [ 5.66408077e-04]\n",
      " [-5.78307459e-04]\n",
      " [ 5.90362571e-04]\n",
      " [-6.02572951e-04]\n",
      " [ 6.14938057e-04]\n",
      " [-6.27457261e-04]\n",
      " [ 6.40129853e-04]\n",
      " [-6.52955035e-04]\n",
      " [ 6.65931920e-04]\n",
      " [-6.79059533e-04]\n",
      " [ 6.92336804e-04]\n",
      " [-7.05762573e-04]\n",
      " [ 7.19335582e-04]\n",
      " [-7.33054477e-04]\n",
      " [ 7.46917807e-04]\n",
      " [-7.60924019e-04]\n",
      " [ 7.75071460e-04]\n",
      " [-7.89358371e-04]\n",
      " [ 8.03782891e-04]\n",
      " [-8.18343051e-04]\n",
      " [ 8.33036776e-04]\n",
      " [-8.47861877e-04]\n",
      " [ 8.62816060e-04]\n",
      " [-8.77896913e-04]\n",
      " [ 8.93101914e-04]\n",
      " [-9.08428423e-04]\n",
      " [ 9.23873687e-04]\n",
      " [-9.39434830e-04]\n",
      " [ 9.55108861e-04]\n",
      " [-9.70892666e-04]\n",
      " [ 9.86783009e-04]\n",
      " [-1.00277653e-03]\n",
      " [ 1.01886975e-03]\n",
      " [-1.03505906e-03]\n",
      " [ 1.05134072e-03]\n",
      " [-1.06771088e-03]\n",
      " [ 1.08416553e-03]\n",
      " [-1.10070057e-03]\n",
      " [ 1.11731173e-03]\n",
      " [-1.13399464e-03]\n",
      " [ 1.15074479e-03]\n",
      " [-1.16755751e-03]\n",
      " [ 1.18442804e-03]\n",
      " [-1.20135146e-03]\n",
      " [ 1.21832271e-03]\n",
      " [-1.23533662e-03]\n",
      " [ 1.25238785e-03]\n",
      " [-1.26947095e-03]\n",
      " [ 1.28658032e-03]\n",
      " [-1.30371024e-03]\n",
      " [ 1.32085483e-03]\n",
      " [-1.33800808e-03]\n",
      " [ 1.35516385e-03]\n",
      " [-1.37231586e-03]\n",
      " [ 1.38945769e-03]\n",
      " [-1.40658277e-03]\n",
      " [ 1.42368442e-03]\n",
      " [-1.44075580e-03]\n",
      " [ 1.45778994e-03]\n",
      " [-1.47477974e-03]\n",
      " [ 1.49171796e-03]\n",
      " [-1.50859721e-03]\n",
      " [ 1.52541000e-03]\n",
      " [-1.54214867e-03]\n",
      " [ 1.55880545e-03]\n",
      " [-1.57537242e-03]\n",
      " [ 1.59184155e-03]\n",
      " [-1.60820466e-03]\n",
      " [ 1.62445346e-03]\n",
      " [-1.64057951e-03]\n",
      " [ 1.65657427e-03]\n",
      " [-1.67242905e-03]\n",
      " [ 1.68813505e-03]\n",
      " [-1.70368334e-03]\n",
      " [ 1.71906489e-03]\n",
      " [-1.73427052e-03]\n",
      " [ 1.74929097e-03]\n",
      " [-1.76411684e-03]\n",
      " [ 1.77873861e-03]\n",
      " [-1.79314669e-03]\n",
      " [ 1.80733133e-03]\n",
      " [-1.82128272e-03]\n",
      " [ 1.83499092e-03]\n",
      " [-1.84844590e-03]\n",
      " [ 1.86163753e-03]\n",
      " [-1.87455557e-03]\n",
      " [ 1.88718973e-03]\n",
      " [-1.89952957e-03]\n",
      " [ 1.91156462e-03]\n",
      " [-1.92328429e-03]\n",
      " [ 1.93467793e-03]\n",
      " [-1.94573480e-03]\n",
      " [ 1.95644410e-03]\n",
      " [-1.96679493e-03]\n",
      " [ 1.97677636e-03]\n",
      " [-1.98637739e-03]\n",
      " [ 1.99558693e-03]\n",
      " [-2.00439387e-03]\n",
      " [ 2.01278703e-03]\n",
      " [-2.02075519e-03]\n",
      " [ 2.02828708e-03]\n",
      " [-2.03537138e-03]\n",
      " [ 2.04199676e-03]\n",
      " [-2.04815184e-03]\n",
      " [ 2.05382522e-03]\n",
      " [-2.05900546e-03]\n",
      " [ 2.06368112e-03]\n",
      " [-2.06784074e-03]\n",
      " [ 2.07147284e-03]\n",
      " [-2.07456595e-03]\n",
      " [ 2.07710859e-03]\n",
      " [-2.07908928e-03]\n",
      " [ 2.08049655e-03]\n",
      " [-2.08131895e-03]\n",
      " [ 2.08154503e-03]\n",
      " [-2.08116338e-03]\n",
      " [ 2.08016260e-03]\n",
      " [-2.07853133e-03]\n",
      " [ 2.07625825e-03]\n",
      " [-2.07333206e-03]\n",
      " [ 2.06974153e-03]\n",
      " [-2.06547546e-03]\n",
      " [ 2.06052271e-03]\n",
      " [-2.05487221e-03]\n",
      " [ 2.04851294e-03]\n",
      " [-2.04143395e-03]\n",
      " [ 2.03362437e-03]\n",
      " [-2.02507339e-03]\n",
      " [ 2.01577030e-03]\n",
      " [-2.00570447e-03]\n",
      " [ 1.99486536e-03]\n",
      " [-1.98324253e-03]\n",
      " [ 1.97082564e-03]\n",
      " [-1.95760443e-03]\n",
      " [ 1.94356879e-03]\n",
      " [-1.92870869e-03]\n",
      " [ 1.91301423e-03]\n",
      " [-1.89647564e-03]\n",
      " [ 1.87908325e-03]\n",
      " [-1.86082754e-03]\n",
      " [ 1.84169911e-03]\n",
      " [-1.82168872e-03]\n",
      " [ 1.80078725e-03]\n",
      " [-1.77898572e-03]\n",
      " [ 1.75627532e-03]\n",
      " [-1.73264738e-03]\n",
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      " [-8.31325859e-05]\n",
      " [ 8.03530807e-05]\n",
      " [-7.76491752e-05]\n",
      " [ 7.50193890e-05]\n",
      " [-7.24622511e-05]\n",
      " [ 6.99763046e-05]\n",
      " [-6.75601031e-05]\n",
      " [ 6.52122152e-05]\n",
      " [-6.29312205e-05]\n",
      " [ 6.07157147e-05]\n",
      " [-5.85643051e-05]\n",
      " [ 5.64756157e-05]\n",
      " [-5.44482830e-05]\n",
      " [ 5.24809607e-05]\n",
      " [-5.05723156e-05]\n",
      " [ 4.87210323e-05]\n",
      " [-4.69258091e-05]\n",
      " [ 4.51853624e-05]\n",
      " [-4.34984227e-05]\n",
      " [ 4.18637394e-05]\n",
      " [-4.02800762e-05]\n",
      " [ 3.87462158e-05]\n",
      " [-3.72609557e-05]\n",
      " [ 3.58231130e-05]\n",
      " [-3.44315195e-05]\n",
      " [ 3.30850268e-05]\n",
      " [-3.17825017e-05]\n",
      " [ 3.05228307e-05]\n",
      " [-2.93049159e-05]\n",
      " [ 2.81276790e-05]\n",
      " [-2.69900574e-05]\n",
      " [ 2.58910084e-05]\n",
      " [-2.48295048e-05]\n",
      " [ 2.38045395e-05]\n",
      " [-2.28151208e-05]\n",
      " [ 2.18602772e-05]\n",
      " [-2.09390522e-05]\n",
      " [ 2.00505098e-05]\n",
      " [-1.91937290e-05]\n",
      " [ 1.83678087e-05]\n",
      " [-1.75718631e-05]\n",
      " [ 1.68050260e-05]\n",
      " [-1.60664463e-05]\n",
      " [ 1.53552923e-05]\n",
      " [-1.46707474e-05]\n",
      " [ 1.40120141e-05]\n",
      " [-1.33783096e-05]\n",
      " [ 1.27688701e-05]\n",
      " [-1.21829462e-05]\n",
      " [ 1.16198071e-05]\n",
      " [-1.10787365e-05]\n",
      " [ 1.05590361e-05]\n",
      " [-1.00600216e-05]\n",
      " [ 9.58102688e-06]\n",
      " [-9.12139917e-06]\n",
      " [ 8.68050351e-06]\n",
      " [-8.25771805e-06]\n",
      " [ 7.85243836e-06]\n",
      " [-7.46407273e-06]\n",
      " [ 7.09204649e-06]\n",
      " [-6.73579734e-06]\n",
      " [ 6.39477960e-06]\n",
      " [-6.06845955e-06]\n",
      " [ 5.75631970e-06]\n",
      " [-5.45785412e-06]\n",
      " [ 5.17257267e-06]\n",
      " [-4.89999637e-06]\n",
      " [ 4.63966160e-06]\n",
      " [-4.39111546e-06]\n",
      " [ 4.15392000e-06]\n",
      " [-3.92764754e-06]\n",
      " [ 3.71188493e-06]\n",
      " [-3.50622883e-06]\n",
      " [ 3.31029001e-06]\n",
      " [-3.12368863e-06]\n",
      " [ 2.94605846e-06]\n",
      " [-2.77704225e-06]\n",
      " [ 2.61629596e-06]\n",
      " [-2.46348404e-06]\n",
      " [ 2.31828369e-06]\n",
      " [-2.18038023e-06]\n",
      " [ 2.04947125e-06]\n",
      " [-1.92526201e-06]\n",
      " [ 1.80746964e-06]\n",
      " [-1.69581850e-06]\n",
      " [ 1.59004437e-06]\n",
      " [-1.48988985e-06]\n",
      " [ 1.39510854e-06]\n",
      " [-1.30546043e-06]\n",
      " [ 1.22071609e-06]\n",
      " [-1.14065208e-06]\n",
      " [ 1.06505512e-06]\n",
      " [-9.93717507e-07]\n",
      " [ 9.26441313e-07]\n",
      " [-8.63033776e-07]\n",
      " [ 8.03311527e-07]\n",
      " [-7.47095959e-07]\n",
      " [ 6.94217498e-07]\n",
      " [-6.44510938e-07]\n",
      " [ 5.97819725e-07]\n",
      " [-5.53991319e-07]\n",
      " [ 5.12881471e-07]\n",
      " [-4.74349583e-07]\n",
      " [ 4.38262989e-07]\n",
      " [-4.04492334e-07]\n",
      " [ 3.72915861e-07]\n",
      " [-3.43414785e-07]\n",
      " [ 3.15877582e-07]\n",
      " [-2.90195381e-07]\n",
      " [ 2.66266267e-07]\n",
      " [-2.43990654e-07]\n",
      " [ 2.23275605e-07]\n",
      " [-2.04030217e-07]\n",
      " [ 1.86169950e-07]\n",
      " [-1.69612006e-07]\n",
      " [ 1.54279660e-07]\n",
      " [-1.40097662e-07]\n",
      " [ 1.26996573e-07]\n",
      " [-1.14908159e-07]\n",
      " [ 1.03769733e-07]\n",
      " [-9.35195734e-08]\n",
      " [ 8.41012647e-08]\n",
      " [-7.54591093e-08]\n",
      " [ 6.75424795e-08]\n",
      " [-6.03012455e-08]\n",
      " [ 5.36901313e-08]\n",
      " [-4.76641401e-08]\n",
      " [ 4.21829120e-08]\n",
      " [-3.72061683e-08]\n",
      " [ 3.26980778e-08]\n",
      " [-2.86226905e-08]\n",
      " [ 2.49483113e-08]\n",
      " [-2.16429552e-08]\n",
      " [ 1.86787162e-08]\n",
      " [-1.60272262e-08]\n",
      " [ 1.36640265e-08]\n",
      " [-1.15640391e-08]\n",
      " [ 9.70594904e-09]\n",
      " [-8.06766550e-09]\n",
      " [ 6.63071164e-09]\n",
      " [-5.37569787e-09]\n",
      " [ 4.28672448e-09]\n",
      " [-3.34684048e-09]\n",
      " [ 2.54245076e-09]\n",
      " [ 7.85398162e-01]]\n"
     ]
    }
   ],
   "source": [
    "print(phi_angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "d2d822b4-1da5-4eaf-9d85-23a4cfa7c63b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # phi_W to phi\n",
    "# phi_angles[0] -= np.pi/4\n",
    "# phi_angles[-1:] += np.pi/4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "eae655fb-a232-445e-abc6-db6058e24170",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# print(phi_angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "6318aa11-8dd7-4ddb-9a2e-cc049242018f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # phi to phi_tilde\n",
    "# phi_angles[1:] += np.pi/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "a1882727-26f9-44a0-9c10-835d50e670da",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# print(phi_angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "52435d92-c4c6-46ee-a586-131b903b83c2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_d: 999     phi: 0.7853981615386494\n",
      "_d: 998     phi: 2.5424507621540607e-09\n",
      "_d: 997     phi: -3.3468404847946574e-09\n",
      "_d: 996     phi: 4.2867244787078545e-09\n",
      "_d: 995     phi: -5.375697869421365e-09\n",
      "_d: 994     phi: 6.6307116411175285e-09\n",
      "_d: 993     phi: -8.067665504570867e-09\n",
      "_d: 992     phi: 9.705949039630519e-09\n",
      "_d: 991     phi: -1.1564039091491138e-08\n",
      "_d: 990     phi: 1.3664026520037937e-08\n",
      "_d: 989     phi: -1.6027226240866234e-08\n",
      "_d: 988     phi: 1.8678716220256254e-08\n",
      "_d: 987     phi: -2.1642955241294434e-08\n",
      "_d: 986     phi: 2.4948311301469504e-08\n",
      "_d: 985     phi: -2.862269054478244e-08\n",
      "_d: 984     phi: 3.2698077762541153e-08\n",
      "_d: 983     phi: -3.7206168292673736e-08\n",
      "_d: 982     phi: 4.218291200531334e-08\n",
      "_d: 981     phi: -4.766414012641698e-08\n",
      "_d: 980     phi: 5.369013132174657e-08\n",
      "_d: 979     phi: -6.030124547348857e-08\n",
      "_d: 978     phi: 6.754247951471221e-08\n",
      "_d: 977     phi: -7.545910925902256e-08\n",
      "_d: 976     phi: 8.410126471922766e-08\n",
      "_d: 975     phi: -9.351957339400534e-08\n",
      "_d: 974     phi: 1.0376973293873245e-07\n",
      "_d: 973     phi: -1.1490815864264026e-07\n",
      "_d: 972     phi: 1.269965726735201e-07\n",
      "_d: 971     phi: -1.4009766215148883e-07\n",
      "_d: 970     phi: 1.5427966022438153e-07\n",
      "_d: 969     phi: -1.696120063655594e-07\n",
      "_d: 968     phi: 1.8616995018981186e-07\n",
      "_d: 967     phi: -2.0403021714992716e-07\n",
      "_d: 966     phi: 2.2327560450630512e-07\n",
      "_d: 965     phi: -2.439906541734609e-07\n",
      "_d: 964     phi: 2.6626626664514685e-07\n",
      "_d: 963     phi: -2.901953813604596e-07\n",
      "_d: 962     phi: 3.158775823496051e-07\n",
      "_d: 961     phi: -3.43414784966682e-07\n",
      "_d: 960     phi: 3.729158606873987e-07\n",
      "_d: 959     phi: -4.0449233360558915e-07\n",
      "_d: 958     phi: 4.382629893651567e-07\n",
      "_d: 957     phi: -4.743495833186276e-07\n",
      "_d: 956     phi: 5.128814711977543e-07\n",
      "_d: 955     phi: -5.539913185649455e-07\n",
      "_d: 954     phi: 5.978197245474981e-07\n",
      "_d: 953     phi: -6.445109376431976e-07\n",
      "_d: 952     phi: 6.942174982519782e-07\n",
      "_d: 951     phi: -7.470959593124806e-07\n",
      "_d: 950     phi: 8.033115272805191e-07\n",
      "_d: 949     phi: -8.630337762191802e-07\n",
      "_d: 948     phi: 9.264413134628403e-07\n",
      "_d: 947     phi: -9.937175069362673e-07\n",
      "_d: 946     phi: 1.0650551248557439e-06\n",
      "_d: 945     phi: -1.1406520801084034e-06\n",
      "_d: 944     phi: 1.22071609439434e-06\n",
      "_d: 943     phi: -1.3054604269580568e-06\n",
      "_d: 942     phi: 1.3951085418647683e-06\n",
      "_d: 941     phi: -1.489889847671059e-06\n",
      "_d: 940     phi: 1.5900443680102692e-06\n",
      "_d: 939     phi: -1.695818495958286e-06\n",
      "_d: 938     phi: 1.8074696423656513e-06\n",
      "_d: 937     phi: -1.925262007281232e-06\n",
      "_d: 936     phi: 2.049471247833528e-06\n",
      "_d: 935     phi: -2.180380228898072e-06\n",
      "_d: 934     phi: 2.3182836946557787e-06\n",
      "_d: 933     phi: -2.4634840373830493e-06\n",
      "_d: 932     phi: 2.6162959600776674e-06\n",
      "_d: 931     phi: -2.7770422517551514e-06\n",
      "_d: 930     phi: 2.9460584559474595e-06\n",
      "_d: 929     phi: -3.1236886252488955e-06\n",
      "_d: 928     phi: 3.3102900129757926e-06\n",
      "_d: 927     phi: -3.50622883014879e-06\n",
      "_d: 926     phi: 3.711884928730937e-06\n",
      "_d: 925     phi: -3.927647543806197e-06\n",
      "_d: 924     phi: 4.153920000913926e-06\n",
      "_d: 923     phi: -4.39111546217434e-06\n",
      "_d: 922     phi: 4.6396616029462706e-06\n",
      "_d: 921     phi: -4.899996371645927e-06\n",
      "_d: 920     phi: 5.172572674562133e-06\n",
      "_d: 919     phi: -5.457854116910001e-06\n",
      "_d: 918     phi: 5.756319700494699e-06\n",
      "_d: 917     phi: -6.068459549314927e-06\n",
      "_d: 916     phi: 6.394779596595259e-06\n",
      "_d: 915     phi: -6.735797341149111e-06\n",
      "_d: 914     phi: 7.092046492116092e-06\n",
      "_d: 913     phi: -7.4640727253516604e-06\n",
      "_d: 912     phi: 7.85243835774908e-06\n",
      "_d: 911     phi: -8.257718051978905e-06\n",
      "_d: 910     phi: 8.680503510590787e-06\n",
      "_d: 909     phi: -9.121399168858193e-06\n",
      "_d: 908     phi: 9.58102687621065e-06\n",
      "_d: 907     phi: -1.0060021595044146e-05\n",
      "_d: 906     phi: 1.0559036058093338e-05\n",
      "_d: 905     phi: -1.1078736462828855e-05\n",
      "_d: 904     phi: 1.1619807123154314e-05\n",
      "_d: 903     phi: -1.2182946154914946e-05\n",
      "_d: 902     phi: 1.2768870106145209e-05\n",
      "_d: 901     phi: -1.3378309636836666e-05\n",
      "_d: 900     phi: 1.4012014143814665e-05\n",
      "_d: 899     phi: -1.4670747439206021e-05\n",
      "_d: 898     phi: 1.5355292322601578e-05\n",
      "_d: 897     phi: -1.6066446262228463e-05\n",
      "_d: 896     phi: 1.6805025980498713e-05\n",
      "_d: 895     phi: -1.7571863116667044e-05\n",
      "_d: 894     phi: 1.8367808732555536e-05\n",
      "_d: 893     phi: -1.9193729032043377e-05\n",
      "_d: 892     phi: 2.00505098342327e-05\n",
      "_d: 891     phi: -2.093905224669841e-05\n",
      "_d: 890     phi: 2.186027715592763e-05\n",
      "_d: 889     phi: -2.2815120844030496e-05\n",
      "_d: 888     phi: 2.380453949530865e-05\n",
      "_d: 887     phi: -2.482950479461529e-05\n",
      "_d: 886     phi: 2.5891008361973528e-05\n",
      "_d: 885     phi: -2.699005736224524e-05\n",
      "_d: 884     phi: 2.8127678977642038e-05\n",
      "_d: 883     phi: -2.9304915871072443e-05\n",
      "_d: 882     phi: 3.052283072793932e-05\n",
      "_d: 881     phi: -3.1782501683910447e-05\n",
      "_d: 880     phi: 3.308502679511827e-05\n",
      "_d: 879     phi: -3.443151948244782e-05\n",
      "_d: 878     phi: 3.582311297378931e-05\n",
      "_d: 877     phi: -3.726095571771337e-05\n",
      "_d: 876     phi: 3.8746215751713036e-05\n",
      "_d: 875     phi: -4.0280076159882004e-05\n",
      "_d: 874     phi: 4.186373941289424e-05\n",
      "_d: 873     phi: -4.349842273221741e-05\n",
      "_d: 872     phi: 4.518536236616059e-05\n",
      "_d: 871     phi: -4.6925809085138495e-05\n",
      "_d: 870     phi: 4.872103232286141e-05\n",
      "_d: 869     phi: -5.057231558855342e-05\n",
      "_d: 868     phi: 5.2480960669538215e-05\n",
      "_d: 867     phi: -5.444828297026926e-05\n",
      "_d: 866     phi: 5.647561568227295e-05\n",
      "_d: 865     phi: -5.8564305103703875e-05\n",
      "_d: 864     phi: 6.0715714714226045e-05\n",
      "_d: 863     phi: -6.293122054264159e-05\n",
      "_d: 862     phi: 6.521221520052034e-05\n",
      "_d: 861     phi: -6.75601031112239e-05\n",
      "_d: 860     phi: 6.997630458733582e-05\n",
      "_d: 859     phi: -7.246225105229916e-05\n",
      "_d: 858     phi: 7.501938900870609e-05\n",
      "_d: 857     phi: -7.76491752339054e-05\n",
      "_d: 856     phi: 8.0353080735137e-05\n",
      "_d: 855     phi: -8.31325858955301e-05\n",
      "_d: 854     phi: 8.598918440654554e-05\n",
      "_d: 853     phi: -8.892437826652066e-05\n",
      "_d: 852     phi: 9.193968183574538e-05\n",
      "_d: 851     phi: -9.503661670796795e-05\n",
      "_d: 850     phi: 9.82167156802407e-05\n",
      "_d: 849     phi: -0.00010148151769521157\n",
      "_d: 848     phi: 0.00010483257162628372\n",
      "_d: 847     phi: -0.00010827143127515096\n",
      "_d: 846     phi: 0.00011179965914853639\n",
      "_d: 845     phi: -0.00011541882126544915\n",
      "_d: 844     phi: 0.00011913049102084458\n",
      "_d: 843     phi: -0.0001229362438941907\n",
      "_d: 842     phi: 0.00012683766126081897\n",
      "_d: 841     phi: -0.00013083632510804268\n",
      "_d: 840     phi: 0.00013493382172770558\n",
      "_d: 839     phi: -0.000139131736404506\n",
      "_d: 838     phi: 0.00014343165715418775\n",
      "_d: 837     phi: -0.00014783516921770083\n",
      "_d: 836     phi: 0.00015234385884825262\n",
      "_d: 835     phi: -0.0001569593077415331\n",
      "_d: 834     phi: 0.00016168309676688298\n",
      "_d: 833     phi: -0.0001665168004155009\n",
      "_d: 832     phi: 0.00017146199031254644\n",
      "_d: 831     phi: -0.00017652022977800665\n",
      "_d: 830     phi: 0.0001816930772885154\n",
      "_d: 829     phi: -0.00018698208096790562\n",
      "_d: 828     phi: 0.0001923887819018929\n",
      "_d: 827     phi: -0.00019791470866771006\n",
      "_d: 826     phi: 0.00020356138070589901\n",
      "_d: 825     phi: -0.0002093303025899991\n",
      "_d: 824     phi: 0.0002152229675185715\n",
      "_d: 823     phi: -0.0002212408515234343\n",
      "_d: 822     phi: 0.00022738541675308466\n",
      "_d: 821     phi: -0.00023365810587980618\n",
      "_d: 820     phi: 0.00024006034522549728\n",
      "_d: 819     phi: -0.00024659353903509106\n",
      "_d: 818     phi: 0.0002532590726758664\n",
      "_d: 817     phi: -0.0002600583068896678\n",
      "_d: 816     phi: 0.00026699258085828505\n",
      "_d: 815     phi: -0.0002740632064386219\n",
      "_d: 814     phi: 0.00028127147127490315\n",
      "_d: 813     phi: -0.00028861863288510986\n",
      "_d: 812     phi: 0.0002961059217109127\n",
      "_d: 811     phi: -0.00030373453527498417\n",
      "_d: 810     phi: 0.0003115056412223596\n",
      "_d: 809     phi: -0.00031942037128254226\n",
      "_d: 808     phi: 0.00032747982429927444\n",
      "_d: 807     phi: -0.0003356850603501184\n",
      "_d: 806     phi: 0.00034403710354566293\n",
      "_d: 805     phi: -0.00035253693610959574\n",
      "_d: 804     phi: 0.0003611855013192561\n",
      "_d: 803     phi: -0.00036998369738186384\n",
      "_d: 802     phi: 0.00037893238044635705\n",
      "_d: 801     phi: -0.0003880323583610518\n",
      "_d: 800     phi: 0.0003972843937374332\n",
      "_d: 799     phi: -0.00040668919773385355\n",
      "_d: 798     phi: 0.0004162474328989556\n",
      "_d: 797     phi: -0.0004259597070771051\n",
      "_d: 796     phi: 0.00043582657619949697\n",
      "_d: 795     phi: -0.0004458485381718352\n",
      "_d: 794     phi: 0.0004560260357351031\n",
      "_d: 793     phi: -0.0004663594500541787\n",
      "_d: 792     phi: 0.00047684910387999846\n",
      "_d: 791     phi: -0.00048749525492672237\n",
      "_d: 790     phi: 0.0004982980991123892\n",
      "_d: 789     phi: -0.0005092577639935082\n",
      "_d: 788     phi: 0.0005203743115960593\n",
      "_d: 787     phi: -0.0005316477324869297\n",
      "_d: 786     phi: 0.0005430779480434842\n",
      "_d: 785     phi: -0.000554664804720017\n",
      "_d: 784     phi: 0.0005664080765260877\n",
      "_d: 783     phi: -0.0005783074588022858\n",
      "_d: 782     phi: 0.0005903625711084264\n",
      "_d: 781     phi: -0.0006025729509812578\n",
      "_d: 780     phi: 0.0006149380565788384\n",
      "_d: 779     phi: -0.000627457260555622\n",
      "_d: 778     phi: 0.0006401298529290026\n",
      "_d: 777     phi: -0.0006529550345489877\n",
      "_d: 776     phi: 0.0006659319202961935\n",
      "_d: 775     phi: -0.0006790595326214882\n",
      "_d: 774     phi: 0.0006923368043695338\n",
      "_d: 773     phi: -0.0007057625727384701\n",
      "_d: 772     phi: 0.0007193355819475381\n",
      "_d: 771     phi: -0.000733054477219125\n",
      "_d: 770     phi: 0.0007469178074332037\n",
      "_d: 769     phi: -0.0007609240192634097\n",
      "_d: 768     phi: 0.000775071459902291\n",
      "_d: 767     phi: -0.0007893583708988497\n",
      "_d: 766     phi: 0.0008037828913225586\n",
      "_d: 765     phi: -0.0008183430513823369\n",
      "_d: 764     phi: 0.0008330367756978751\n",
      "_d: 763     phi: -0.0008478618770364104\n",
      "_d: 762     phi: 0.0008628160595263372\n",
      "_d: 761     phi: -0.0008778969125019749\n",
      "_d: 760     phi: 0.0008931019137020168\n",
      "_d: 759     phi: -0.0009084284232787567\n",
      "_d: 758     phi: 0.0009238736870058605\n",
      "_d: 757     phi: -0.0009394348302400606\n",
      "_d: 756     phi: 0.0009551088613736254\n",
      "_d: 755     phi: -0.000970892665731418\n",
      "_d: 754     phi: 0.0009867830091276606\n",
      "_d: 753     phi: -0.0010027765318546015\n",
      "_d: 752     phi: 0.0010188697522918976\n",
      "_d: 751     phi: -0.0010350590609995915\n",
      "_d: 750     phi: 0.0010513407243313586\n",
      "_d: 749     phi: -0.0010677108787687764\n",
      "_d: 748     phi: 0.0010841655343995704\n",
      "_d: 747     phi: -0.0011007005694739478\n",
      "_d: 746     phi: 0.0011173117340169448\n",
      "_d: 745     phi: -0.001133994644438902\n",
      "_d: 744     phi: 0.0011507447872078878\n",
      "_d: 743     phi: -0.0011675575134815679\n",
      "_d: 742     phi: 0.0011844280430755238\n",
      "_d: 741     phi: -0.0012013514591717464\n",
      "_d: 740     phi: 0.001218322712259663\n",
      "_d: 739     phi: -0.0012353366150300602\n",
      "_d: 738     phi: 0.0012523878464627105\n",
      "_d: 737     phi: -0.0012694709468682075\n",
      "_d: 736     phi: 0.0012865803219124965\n",
      "_d: 735     phi: -0.0013037102380145217\n",
      "_d: 734     phi: 0.0013208548264756511\n",
      "_d: 733     phi: -0.0013380080788317965\n",
      "_d: 732     phi: 0.001355163851196516\n",
      "_d: 731     phi: -0.0013723158598703366\n",
      "_d: 730     phi: 0.0013894576856531191\n",
      "_d: 729     phi: -0.0014065827697332914\n",
      "_d: 728     phi: 0.0014236844181427545\n",
      "_d: 727     phi: -0.00144075579759927\n",
      "_d: 726     phi: 0.0014577899403532644\n",
      "_d: 725     phi: -0.0014747797400422936\n",
      "_d: 724     phi: 0.00149171795678102\n",
      "_d: 723     phi: -0.0015085972130952144\n",
      "_d: 722     phi: 0.0015254099992280251\n",
      "_d: 721     phi: -0.0015421486692945264\n",
      "_d: 720     phi: 0.0015588054464986802\n",
      "_d: 719     phi: -0.0015753724197749802\n",
      "_d: 718     phi: 0.001591841548986492\n",
      "_d: 717     phi: -0.001608204661911573\n",
      "_d: 716     phi: 0.001624453459423325\n",
      "_d: 715     phi: -0.0016405795125226585\n",
      "_d: 714     phi: 0.0016565742682815986\n",
      "_d: 713     phi: -0.0016724290463832486\n",
      "_d: 712     phi: 0.0016881350456391937\n",
      "_d: 711     phi: -0.001703683340605324\n",
      "_d: 710     phi: 0.0017190648882618193\n",
      "_d: 709     phi: -0.0017342705248694673\n",
      "_d: 708     phi: 0.0017492909728007155\n",
      "_d: 707     phi: -0.0017641168375467453\n",
      "_d: 706     phi: 0.0017787386146950789\n",
      "_d: 705     phi: -0.0017931466874040226\n",
      "_d: 704     phi: 0.0018073313332102163\n",
      "_d: 703     phi: -0.001821282721794638\n",
      "_d: 702     phi: 0.0018349909221500999\n",
      "_d: 701     phi: -0.001848445900298421\n",
      "_d: 700     phi: 0.0018616375267035382\n",
      "_d: 699     phi: -0.0018745555743536128\n",
      "_d: 698     phi: 0.0018871897261083623\n",
      "_d: 697     phi: -0.0018995295730674586\n",
      "_d: 696     phi: 0.0019115646221554902\n",
      "_d: 695     phi: -0.0019232842945444842\n",
      "_d: 694     phi: 0.0019346779334430692\n",
      "_d: 693     phi: -0.0019457348027861682\n",
      "_d: 692     phi: 0.0019564440951554615\n",
      "_d: 691     phi: -0.0019667949305309327\n",
      "_d: 690     phi: 0.0019767763644368912\n",
      "_d: 689     phi: -0.0019863773870139223\n",
      "_d: 688     phi: 0.0019955869310900806\n",
      "_d: 687     phi: -0.0020043938714099474\n",
      "_d: 686     phi: 0.002012787033062832\n",
      "_d: 685     phi: -0.002020755190719557\n",
      "_d: 684     phi: 0.0020282870771872186\n",
      "_d: 683     phi: -0.0020353713828015862\n",
      "_d: 682     phi: 0.002041996764138886\n",
      "_d: 681     phi: -0.002048151843541458\n",
      "_d: 680     phi: 0.0020538252178982515\n",
      "_d: 679     phi: -0.0020590054582459425\n",
      "_d: 678     phi: 0.0020636811188624285\n",
      "_d: 677     phi: -0.0020678407367243573\n",
      "_d: 676     phi: 0.002071472840866492\n",
      "_d: 675     phi: -0.002074565951825522\n",
      "_d: 674     phi: 0.0020771085911174556\n",
      "_d: 673     phi: -0.0020790892808359323\n",
      "_d: 672     phi: 0.0020804965529824674\n",
      "_d: 671     phi: -0.002081318949474263\n",
      "_d: 670     phi: 0.0020815450311762263\n",
      "_d: 669     phi: -0.0020811633781391216\n",
      "_d: 668     phi: 0.002080162598646627\n",
      "_d: 667     phi: -0.002078531329492089\n",
      "_d: 666     phi: 0.0020762582450430007\n",
      "_d: 665     phi: -0.0020733320575286648\n",
      "_d: 664     phi: 0.0020697415260581583\n",
      "_d: 663     phi: -0.0020654754570165515\n",
      "_d: 662     phi: 0.002060522713088052\n",
      "_d: 661     phi: -0.00205487221346158\n",
      "_d: 660     phi: 0.0020485129429721567\n",
      "_d: 659     phi: -0.0020414339523514274\n",
      "_d: 658     phi: 0.002033624367169131\n",
      "_d: 657     phi: -0.0020250733880495557\n",
      "_d: 656     phi: 0.002015770299719388\n",
      "_d: 655     phi: -0.002005704470994689\n",
      "_d: 654     phi: 0.0019948653638466036\n",
      "_d: 653     phi: -0.001983242533335577\n",
      "_d: 652     phi: 0.0019708256365391103\n",
      "_d: 651     phi: -0.001957604432419487\n",
      "_d: 650     phi: 0.0019435687906995318\n",
      "_d: 649     phi: -0.001928708691548223\n",
      "_d: 648     phi: 0.0019130142344151075\n",
      "_d: 647     phi: -0.0018964756376672039\n",
      "_d: 646     phi: 0.001879083247154989\n",
      "_d: 645     phi: -0.0018608275358771378\n",
      "_d: 644     phi: 0.0018416991123435993\n",
      "_d: 643     phi: -0.0018216887201212804\n",
      "_d: 642     phi: 0.0018007872461657253\n",
      "_d: 641     phi: -0.0017789857200642843\n",
      "_d: 640     phi: 0.001756275322404892\n",
      "_d: 639     phi: -0.001732647383795955\n",
      "_d: 638     phi: 0.0017080933930609151\n",
      "_d: 637     phi: -0.001682604996277841\n",
      "_d: 636     phi: 0.0016561740046870312\n",
      "_d: 635     phi: -0.0016287923936373642\n",
      "_d: 634     phi: 0.001600452310429104\n",
      "_d: 633     phi: -0.0015711460730531092\n",
      "_d: 632     phi: 0.001540866177923982\n",
      "_d: 631     phi: -0.0015096052985259702\n",
      "_d: 630     phi: 0.0014773562930009065\n",
      "_d: 629     phi: -0.0014441122026873096\n",
      "_d: 628     phi: 0.0014098662595994583\n",
      "_d: 627     phi: -0.0013746118848539013\n",
      "_d: 626     phi: 0.0013383426960958855\n",
      "_d: 625     phi: -0.001301052505794439\n",
      "_d: 624     phi: 0.001262735328585526\n",
      "_d: 623     phi: -0.0012233853795651723\n",
      "_d: 622     phi: 0.0011829970814857317\n",
      "_d: 621     phi: -0.0011415650630861415\n",
      "_d: 620     phi: 0.0010990841662142003\n",
      "_d: 619     phi: -0.0010555494440872347\n",
      "_d: 618     phi: 0.0010109561685199982\n",
      "_d: 617     phi: -0.0009652998280955037\n",
      "_d: 616     phi: 0.000918576135457312\n",
      "_d: 615     phi: -0.0008707810254951428\n",
      "_d: 614     phi: 0.0008219106626934378\n",
      "_d: 613     phi: -0.0007719614394439842\n",
      "_d: 612     phi: 0.0007209299833806357\n",
      "_d: 611     phi: -0.0006688131558790232\n",
      "_d: 610     phi: 0.0006156080595031514\n",
      "_d: 609     phi: -0.0005613120365930765\n",
      "_d: 608     phi: 0.0005059226769928859\n",
      "_d: 607     phi: -0.0004494378167900089\n",
      "_d: 606     phi: 0.0003918555460959938\n",
      "_d: 605     phi: -0.00033317420823998937\n",
      "_d: 604     phi: 0.0002733924077263696\n",
      "_d: 603     phi: -0.0002125090096422458\n",
      "_d: 602     phi: 0.0001505231480232837\n",
      "_d: 601     phi: -8.743422550039023e-05\n",
      "_d: 600     phi: 2.3241922052208643e-05\n",
      "_d: 599     phi: 4.205380494059119e-05\n",
      "_d: 598     phi: -0.00010845271158176753\n",
      "_d: 597     phi: 0.00017595426703430957\n",
      "_d: 596     phi: -0.0002445576437917965\n",
      "_d: 595     phi: 0.0003142617168811202\n",
      "_d: 594     phi: -0.0003850650537778386\n",
      "_d: 593     phi: 0.0004569659127614129\n",
      "_d: 592     phi: -0.0005299622324582018\n",
      "_d: 591     phi: 0.0006040516297105761\n",
      "_d: 590     phi: -0.0006792313883388717\n",
      "_d: 589     phi: 0.0007554984565314642\n",
      "_d: 588     phi: -0.0008328494348479421\n",
      "_d: 587     phi: 0.0009112805729644725\n",
      "_d: 586     phi: -0.0009907877570266318\n",
      "_d: 585     phi: 0.0010713665056504588\n",
      "_d: 584     phi: -0.001153011956570323\n",
      "_d: 583     phi: 0.001235718861875391\n",
      "_d: 582     phi: -0.0013194815738191558\n",
      "_d: 581     phi: 0.0014042940393152303\n",
      "_d: 580     phi: -0.0014901497851151503\n",
      "_d: 579     phi: 0.0015770419111808091\n",
      "_d: 578     phi: -0.0016649630751646\n",
      "_d: 577     phi: 0.0017539054850709466\n",
      "_d: 576     phi: -0.0018438608827586738\n",
      "_d: 575     phi: 0.0019348205357565653\n",
      "_d: 574     phi: -0.002026775219911786\n",
      "_d: 573     phi: 0.0021197152105615577\n",
      "_d: 572     phi: -0.002213630263993807\n",
      "_d: 571     phi: 0.0023085096078919246\n",
      "_d: 570     phi: -0.002404341922248183\n",
      "_d: 569     phi: 0.002501115328571058\n",
      "_d: 568     phi: -0.002598817370207394\n",
      "_d: 567     phi: 0.0026974350008309857\n",
      "_d: 566     phi: -0.0027969545637785823\n",
      "_d: 565     phi: 0.0028973617800357194\n",
      "_d: 564     phi: -0.0029986417268096275\n",
      "_d: 563     phi: 0.0031007788247742517\n",
      "_d: 562     phi: -0.0032037568160118435\n",
      "_d: 561     phi: 0.0033075587509900717\n",
      "_d: 560     phi: -0.0034121669656493572\n",
      "_d: 559     phi: 0.003517563067883333\n",
      "_d: 558     phi: -0.0036237279146190374\n",
      "_d: 557     phi: 0.0037306415976458415\n",
      "_d: 556     phi: -0.0038382834205870826\n",
      "_d: 555     phi: 0.003946631884531762\n",
      "_d: 554     phi: -0.004055664664996725\n",
      "_d: 553     phi: 0.004165358597547566\n",
      "_d: 552     phi: -0.004275689654841207\n",
      "_d: 551     phi: 0.004386632932567635\n",
      "_d: 550     phi: -0.004498162626891811\n",
      "_d: 549     phi: 0.004610252020819019\n",
      "_d: 548     phi: -0.0047228734622778235\n",
      "_d: 547     phi: 0.004835998351313836\n",
      "_d: 546     phi: -0.004949597118981236\n",
      "_d: 545     phi: 0.0050636392157250845\n",
      "_d: 544     phi: -0.005178093091461523\n",
      "_d: 543     phi: 0.0052929261853724135\n",
      "_d: 542     phi: -0.00540810490749637\n",
      "_d: 541     phi: 0.0055235946304997355\n",
      "_d: 540     phi: -0.005639359673088371\n",
      "_d: 539     phi: 0.005755363293896814\n",
      "_d: 538     phi: -0.0058715676774855705\n",
      "_d: 537     phi: 0.00598793393056175\n",
      "_d: 536     phi: -0.0061044220709607685\n",
      "_d: 535     phi: 0.006220991026731433\n",
      "_d: 534     phi: -0.0063375986285319425\n",
      "_d: 533     phi: 0.006454201612208456\n",
      "_d: 532     phi: -0.0065707556146523015\n",
      "_d: 531     phi: 0.006687215180481378\n",
      "_d: 530     phi: -0.006803533762122959\n",
      "_d: 529     phi: 0.006919663730842109\n",
      "_d: 528     phi: -0.007035556381425908\n",
      "_d: 527     phi: 0.0071511619481345046\n",
      "_d: 526     phi: -0.007266429614453308\n",
      "_d: 525     phi: 0.0073813075344530705\n",
      "_d: 524     phi: -0.0074957428479481125\n",
      "_d: 523     phi: 0.0076096817076541454\n",
      "_d: 522     phi: -0.007723069300378954\n",
      "_d: 521     phi: 0.007835849880169377\n",
      "_d: 520     phi: -0.007947966795874546\n",
      "_d: 519     phi: 0.008059362530858448\n",
      "_d: 518     phi: -0.008169978737019475\n",
      "_d: 517     phi: 0.008279756281377046\n",
      "_d: 516     phi: -0.008388635286895076\n",
      "_d: 515     phi: 0.008496555186000733\n",
      "_d: 514     phi: -0.00860345476854696\n",
      "_d: 513     phi: 0.008709272242207862\n",
      "_d: 512     phi: -0.008813945287642544\n",
      "_d: 511     phi: 0.008917411125952703\n",
      "_d: 510     phi: -0.009019606580837261\n",
      "_d: 509     phi: 0.009120468153004664\n",
      "_d: 508     phi: -0.00921993208921106\n",
      "_d: 507     phi: 0.009317934463383672\n",
      "_d: 506     phi: -0.00941441125217898\n",
      "_d: 505     phi: 0.009509298422516011\n",
      "_d: 504     phi: -0.009602532013180638\n",
      "_d: 503     phi: 0.009694048228214663\n",
      "_d: 502     phi: -0.009783783524030783\n",
      "_d: 501     phi: 0.009871674707979852\n",
      "_d: 500     phi: -0.009957659030228116\n",
      "_d: 499     phi: -0.009957659030228116\n",
      "_d: 498     phi: 0.009871674707979852\n",
      "_d: 497     phi: -0.009783783524030783\n",
      "_d: 496     phi: 0.009694048228214663\n",
      "_d: 495     phi: -0.009602532013180638\n",
      "_d: 494     phi: 0.009509298422516011\n",
      "_d: 493     phi: -0.00941441125217898\n",
      "_d: 492     phi: 0.009317934463383672\n",
      "_d: 491     phi: -0.00921993208921106\n",
      "_d: 490     phi: 0.009120468153004664\n",
      "_d: 489     phi: -0.009019606580837261\n",
      "_d: 488     phi: 0.008917411125952703\n",
      "_d: 487     phi: -0.008813945287642544\n",
      "_d: 486     phi: 0.008709272242207862\n",
      "_d: 485     phi: -0.00860345476854696\n",
      "_d: 484     phi: 0.008496555186000733\n",
      "_d: 483     phi: -0.008388635286895076\n",
      "_d: 482     phi: 0.008279756281377046\n",
      "_d: 481     phi: -0.008169978737019475\n",
      "_d: 480     phi: 0.008059362530858448\n",
      "_d: 479     phi: -0.007947966795874546\n",
      "_d: 478     phi: 0.007835849880169377\n",
      "_d: 477     phi: -0.007723069300378954\n",
      "_d: 476     phi: 0.0076096817076541454\n",
      "_d: 475     phi: -0.0074957428479481125\n",
      "_d: 474     phi: 0.0073813075344530705\n",
      "_d: 473     phi: -0.007266429614453308\n",
      "_d: 472     phi: 0.0071511619481345046\n",
      "_d: 471     phi: -0.007035556381425908\n",
      "_d: 470     phi: 0.006919663730842109\n",
      "_d: 469     phi: -0.006803533762122959\n",
      "_d: 468     phi: 0.006687215180481378\n",
      "_d: 467     phi: -0.0065707556146523015\n",
      "_d: 466     phi: 0.006454201612208456\n",
      "_d: 465     phi: -0.0063375986285319425\n",
      "_d: 464     phi: 0.006220991026731433\n",
      "_d: 463     phi: -0.0061044220709607685\n",
      "_d: 462     phi: 0.00598793393056175\n",
      "_d: 461     phi: -0.0058715676774855705\n",
      "_d: 460     phi: 0.005755363293896814\n",
      "_d: 459     phi: -0.005639359673088371\n",
      "_d: 458     phi: 0.0055235946304997355\n",
      "_d: 457     phi: -0.00540810490749637\n",
      "_d: 456     phi: 0.0052929261853724135\n",
      "_d: 455     phi: -0.005178093091461523\n",
      "_d: 454     phi: 0.0050636392157250845\n",
      "_d: 453     phi: -0.004949597118981236\n",
      "_d: 452     phi: 0.004835998351313836\n",
      "_d: 451     phi: -0.0047228734622778235\n",
      "_d: 450     phi: 0.004610252020819019\n",
      "_d: 449     phi: -0.004498162626891811\n",
      "_d: 448     phi: 0.004386632932567635\n",
      "_d: 447     phi: -0.004275689654841207\n",
      "_d: 446     phi: 0.004165358597547566\n",
      "_d: 445     phi: -0.004055664664996725\n",
      "_d: 444     phi: 0.003946631884531762\n",
      "_d: 443     phi: -0.0038382834205870826\n",
      "_d: 442     phi: 0.0037306415976458415\n",
      "_d: 441     phi: -0.0036237279146190374\n",
      "_d: 440     phi: 0.003517563067883333\n",
      "_d: 439     phi: -0.0034121669656493572\n",
      "_d: 438     phi: 0.0033075587509900717\n",
      "_d: 437     phi: -0.0032037568160118435\n",
      "_d: 436     phi: 0.0031007788247742517\n",
      "_d: 435     phi: -0.0029986417268096275\n",
      "_d: 434     phi: 0.0028973617800357194\n",
      "_d: 433     phi: -0.0027969545637785823\n",
      "_d: 432     phi: 0.0026974350008309857\n",
      "_d: 431     phi: -0.002598817370207394\n",
      "_d: 430     phi: 0.002501115328571058\n",
      "_d: 429     phi: -0.002404341922248183\n",
      "_d: 428     phi: 0.0023085096078919246\n",
      "_d: 427     phi: -0.002213630263993807\n",
      "_d: 426     phi: 0.0021197152105615577\n",
      "_d: 425     phi: -0.002026775219911786\n",
      "_d: 424     phi: 0.0019348205357565653\n",
      "_d: 423     phi: -0.0018438608827586738\n",
      "_d: 422     phi: 0.0017539054850709466\n",
      "_d: 421     phi: -0.0016649630751646\n",
      "_d: 420     phi: 0.0015770419111808091\n",
      "_d: 419     phi: -0.0014901497851151503\n",
      "_d: 418     phi: 0.0014042940393152303\n",
      "_d: 417     phi: -0.0013194815738191558\n",
      "_d: 416     phi: 0.001235718861875391\n",
      "_d: 415     phi: -0.001153011956570323\n",
      "_d: 414     phi: 0.0010713665056504588\n",
      "_d: 413     phi: -0.0009907877570266318\n",
      "_d: 412     phi: 0.0009112805729644725\n",
      "_d: 411     phi: -0.0008328494348479421\n",
      "_d: 410     phi: 0.0007554984565314642\n",
      "_d: 409     phi: -0.0006792313883388717\n",
      "_d: 408     phi: 0.0006040516297105761\n",
      "_d: 407     phi: -0.0005299622324582018\n",
      "_d: 406     phi: 0.0004569659127614129\n",
      "_d: 405     phi: -0.0003850650537778386\n",
      "_d: 404     phi: 0.0003142617168811202\n",
      "_d: 403     phi: -0.0002445576437917965\n",
      "_d: 402     phi: 0.00017595426703430957\n",
      "_d: 401     phi: -0.00010845271158176753\n",
      "_d: 400     phi: 4.205380494059119e-05\n",
      "_d: 399     phi: 2.3241922052208643e-05\n",
      "_d: 398     phi: -8.743422550039023e-05\n",
      "_d: 397     phi: 0.0001505231480232837\n",
      "_d: 396     phi: -0.0002125090096422458\n",
      "_d: 395     phi: 0.0002733924077263696\n",
      "_d: 394     phi: -0.00033317420823998937\n",
      "_d: 393     phi: 0.0003918555460959938\n",
      "_d: 392     phi: -0.0004494378167900089\n",
      "_d: 391     phi: 0.0005059226769928859\n",
      "_d: 390     phi: -0.0005613120365930765\n",
      "_d: 389     phi: 0.0006156080595031514\n",
      "_d: 388     phi: -0.0006688131558790232\n",
      "_d: 387     phi: 0.0007209299833806357\n",
      "_d: 386     phi: -0.0007719614394439842\n",
      "_d: 385     phi: 0.0008219106626934378\n",
      "_d: 384     phi: -0.0008707810254951428\n",
      "_d: 383     phi: 0.000918576135457312\n",
      "_d: 382     phi: -0.0009652998280955037\n",
      "_d: 381     phi: 0.0010109561685199982\n",
      "_d: 380     phi: -0.0010555494440872347\n",
      "_d: 379     phi: 0.0010990841662142003\n",
      "_d: 378     phi: -0.0011415650630861415\n",
      "_d: 377     phi: 0.0011829970814857317\n",
      "_d: 376     phi: -0.0012233853795651723\n",
      "_d: 375     phi: 0.001262735328585526\n",
      "_d: 374     phi: -0.001301052505794439\n",
      "_d: 373     phi: 0.0013383426960958855\n",
      "_d: 372     phi: -0.0013746118848539013\n",
      "_d: 371     phi: 0.0014098662595994583\n",
      "_d: 370     phi: -0.0014441122026873096\n",
      "_d: 369     phi: 0.0014773562930009065\n",
      "_d: 368     phi: -0.0015096052985259702\n",
      "_d: 367     phi: 0.001540866177923982\n",
      "_d: 366     phi: -0.0015711460730531092\n",
      "_d: 365     phi: 0.001600452310429104\n",
      "_d: 364     phi: -0.0016287923936373642\n",
      "_d: 363     phi: 0.0016561740046870312\n",
      "_d: 362     phi: -0.001682604996277841\n",
      "_d: 361     phi: 0.0017080933930609151\n",
      "_d: 360     phi: -0.001732647383795955\n",
      "_d: 359     phi: 0.001756275322404892\n",
      "_d: 358     phi: -0.0017789857200642843\n",
      "_d: 357     phi: 0.0018007872461657253\n",
      "_d: 356     phi: -0.0018216887201212804\n",
      "_d: 355     phi: 0.0018416991123435993\n",
      "_d: 354     phi: -0.0018608275358771378\n",
      "_d: 353     phi: 0.001879083247154989\n",
      "_d: 352     phi: -0.0018964756376672039\n",
      "_d: 351     phi: 0.0019130142344151075\n",
      "_d: 350     phi: -0.001928708691548223\n",
      "_d: 349     phi: 0.0019435687906995318\n",
      "_d: 348     phi: -0.001957604432419487\n",
      "_d: 347     phi: 0.0019708256365391103\n",
      "_d: 346     phi: -0.001983242533335577\n",
      "_d: 345     phi: 0.0019948653638466036\n",
      "_d: 344     phi: -0.002005704470994689\n",
      "_d: 343     phi: 0.002015770299719388\n",
      "_d: 342     phi: -0.0020250733880495557\n",
      "_d: 341     phi: 0.002033624367169131\n",
      "_d: 340     phi: -0.0020414339523514274\n",
      "_d: 339     phi: 0.0020485129429721567\n",
      "_d: 338     phi: -0.00205487221346158\n",
      "_d: 337     phi: 0.002060522713088052\n",
      "_d: 336     phi: -0.0020654754570165515\n",
      "_d: 335     phi: 0.0020697415260581583\n",
      "_d: 334     phi: -0.0020733320575286648\n",
      "_d: 333     phi: 0.0020762582450430007\n",
      "_d: 332     phi: -0.002078531329492089\n",
      "_d: 331     phi: 0.002080162598646627\n",
      "_d: 330     phi: -0.0020811633781391216\n",
      "_d: 329     phi: 0.0020815450311762263\n",
      "_d: 328     phi: -0.002081318949474263\n",
      "_d: 327     phi: 0.0020804965529824674\n",
      "_d: 326     phi: -0.0020790892808359323\n",
      "_d: 325     phi: 0.0020771085911174556\n",
      "_d: 324     phi: -0.002074565951825522\n",
      "_d: 323     phi: 0.002071472840866492\n",
      "_d: 322     phi: -0.0020678407367243573\n",
      "_d: 321     phi: 0.0020636811188624285\n",
      "_d: 320     phi: -0.0020590054582459425\n",
      "_d: 319     phi: 0.0020538252178982515\n",
      "_d: 318     phi: -0.002048151843541458\n",
      "_d: 317     phi: 0.002041996764138886\n",
      "_d: 316     phi: -0.0020353713828015862\n",
      "_d: 315     phi: 0.0020282870771872186\n",
      "_d: 314     phi: -0.002020755190719557\n",
      "_d: 313     phi: 0.002012787033062832\n",
      "_d: 312     phi: -0.0020043938714099474\n",
      "_d: 311     phi: 0.0019955869310900806\n",
      "_d: 310     phi: -0.0019863773870139223\n",
      "_d: 309     phi: 0.0019767763644368912\n",
      "_d: 308     phi: -0.0019667949305309327\n",
      "_d: 307     phi: 0.0019564440951554615\n",
      "_d: 306     phi: -0.0019457348027861682\n",
      "_d: 305     phi: 0.0019346779334430692\n",
      "_d: 304     phi: -0.0019232842945444842\n",
      "_d: 303     phi: 0.0019115646221554902\n",
      "_d: 302     phi: -0.0018995295730674586\n",
      "_d: 301     phi: 0.0018871897261083623\n",
      "_d: 300     phi: -0.0018745555743536128\n",
      "_d: 299     phi: 0.0018616375267035382\n",
      "_d: 298     phi: -0.001848445900298421\n",
      "_d: 297     phi: 0.0018349909221500999\n",
      "_d: 296     phi: -0.001821282721794638\n",
      "_d: 295     phi: 0.0018073313332102163\n",
      "_d: 294     phi: -0.0017931466874040226\n",
      "_d: 293     phi: 0.0017787386146950789\n",
      "_d: 292     phi: -0.0017641168375467453\n",
      "_d: 291     phi: 0.0017492909728007155\n",
      "_d: 290     phi: -0.0017342705248694673\n",
      "_d: 289     phi: 0.0017190648882618193\n",
      "_d: 288     phi: -0.001703683340605324\n",
      "_d: 287     phi: 0.0016881350456391937\n",
      "_d: 286     phi: -0.0016724290463832486\n",
      "_d: 285     phi: 0.0016565742682815986\n",
      "_d: 284     phi: -0.0016405795125226585\n",
      "_d: 283     phi: 0.001624453459423325\n",
      "_d: 282     phi: -0.001608204661911573\n",
      "_d: 281     phi: 0.001591841548986492\n",
      "_d: 280     phi: -0.0015753724197749802\n",
      "_d: 279     phi: 0.0015588054464986802\n",
      "_d: 278     phi: -0.0015421486692945264\n",
      "_d: 277     phi: 0.0015254099992280251\n",
      "_d: 276     phi: -0.0015085972130952144\n",
      "_d: 275     phi: 0.00149171795678102\n",
      "_d: 274     phi: -0.0014747797400422936\n",
      "_d: 273     phi: 0.0014577899403532644\n",
      "_d: 272     phi: -0.00144075579759927\n",
      "_d: 271     phi: 0.0014236844181427545\n",
      "_d: 270     phi: -0.0014065827697332914\n",
      "_d: 269     phi: 0.0013894576856531191\n",
      "_d: 268     phi: -0.0013723158598703366\n",
      "_d: 267     phi: 0.001355163851196516\n",
      "_d: 266     phi: -0.0013380080788317965\n",
      "_d: 265     phi: 0.0013208548264756511\n",
      "_d: 264     phi: -0.0013037102380145217\n",
      "_d: 263     phi: 0.0012865803219124965\n",
      "_d: 262     phi: -0.0012694709468682075\n",
      "_d: 261     phi: 0.0012523878464627105\n",
      "_d: 260     phi: -0.0012353366150300602\n",
      "_d: 259     phi: 0.001218322712259663\n",
      "_d: 258     phi: -0.0012013514591717464\n",
      "_d: 257     phi: 0.0011844280430755238\n",
      "_d: 256     phi: -0.0011675575134815679\n",
      "_d: 255     phi: 0.0011507447872078878\n",
      "_d: 254     phi: -0.001133994644438902\n",
      "_d: 253     phi: 0.0011173117340169448\n",
      "_d: 252     phi: -0.0011007005694739478\n",
      "_d: 251     phi: 0.0010841655343995704\n",
      "_d: 250     phi: -0.0010677108787687764\n",
      "_d: 249     phi: 0.0010513407243313586\n",
      "_d: 248     phi: -0.0010350590609995915\n",
      "_d: 247     phi: 0.0010188697522918976\n",
      "_d: 246     phi: -0.0010027765318546015\n",
      "_d: 245     phi: 0.0009867830091276606\n",
      "_d: 244     phi: -0.000970892665731418\n",
      "_d: 243     phi: 0.0009551088613736254\n",
      "_d: 242     phi: -0.0009394348302400606\n",
      "_d: 241     phi: 0.0009238736870058605\n",
      "_d: 240     phi: -0.0009084284232787567\n",
      "_d: 239     phi: 0.0008931019137020168\n",
      "_d: 238     phi: -0.0008778969125019749\n",
      "_d: 237     phi: 0.0008628160595263372\n",
      "_d: 236     phi: -0.0008478618770364104\n",
      "_d: 235     phi: 0.0008330367756978751\n",
      "_d: 234     phi: -0.0008183430513823369\n",
      "_d: 233     phi: 0.0008037828913225586\n",
      "_d: 232     phi: -0.0007893583708988497\n",
      "_d: 231     phi: 0.000775071459902291\n",
      "_d: 230     phi: -0.0007609240192634097\n",
      "_d: 229     phi: 0.0007469178074332037\n",
      "_d: 228     phi: -0.000733054477219125\n",
      "_d: 227     phi: 0.0007193355819475381\n",
      "_d: 226     phi: -0.0007057625727384701\n",
      "_d: 225     phi: 0.0006923368043695338\n",
      "_d: 224     phi: -0.0006790595326214882\n",
      "_d: 223     phi: 0.0006659319202961935\n",
      "_d: 222     phi: -0.0006529550345489877\n",
      "_d: 221     phi: 0.0006401298529290026\n",
      "_d: 220     phi: -0.000627457260555622\n",
      "_d: 219     phi: 0.0006149380565788384\n",
      "_d: 218     phi: -0.0006025729509812578\n",
      "_d: 217     phi: 0.0005903625711084264\n",
      "_d: 216     phi: -0.0005783074588022858\n",
      "_d: 215     phi: 0.0005664080765260877\n",
      "_d: 214     phi: -0.000554664804720017\n",
      "_d: 213     phi: 0.0005430779480434842\n",
      "_d: 212     phi: -0.0005316477324869297\n",
      "_d: 211     phi: 0.0005203743115960593\n",
      "_d: 210     phi: -0.0005092577639935082\n",
      "_d: 209     phi: 0.0004982980991123892\n",
      "_d: 208     phi: -0.00048749525492672237\n",
      "_d: 207     phi: 0.00047684910387999846\n",
      "_d: 206     phi: -0.0004663594500541787\n",
      "_d: 205     phi: 0.0004560260357351031\n",
      "_d: 204     phi: -0.0004458485381718352\n",
      "_d: 203     phi: 0.00043582657619949697\n",
      "_d: 202     phi: -0.0004259597070771051\n",
      "_d: 201     phi: 0.0004162474328989556\n",
      "_d: 200     phi: -0.00040668919773385355\n",
      "_d: 199     phi: 0.0003972843937374332\n",
      "_d: 198     phi: -0.0003880323583610518\n",
      "_d: 197     phi: 0.00037893238044635705\n",
      "_d: 196     phi: -0.00036998369738186384\n",
      "_d: 195     phi: 0.0003611855013192561\n",
      "_d: 194     phi: -0.00035253693610959574\n",
      "_d: 193     phi: 0.00034403710354566293\n",
      "_d: 192     phi: -0.0003356850603501184\n",
      "_d: 191     phi: 0.00032747982429927444\n",
      "_d: 190     phi: -0.00031942037128254226\n",
      "_d: 189     phi: 0.0003115056412223596\n",
      "_d: 188     phi: -0.00030373453527498417\n",
      "_d: 187     phi: 0.0002961059217109127\n",
      "_d: 186     phi: -0.00028861863288510986\n",
      "_d: 185     phi: 0.00028127147127490315\n",
      "_d: 184     phi: -0.0002740632064386219\n",
      "_d: 183     phi: 0.00026699258085828505\n",
      "_d: 182     phi: -0.0002600583068896678\n",
      "_d: 181     phi: 0.0002532590726758664\n",
      "_d: 180     phi: -0.00024659353903509106\n",
      "_d: 179     phi: 0.00024006034522549728\n",
      "_d: 178     phi: -0.00023365810587980618\n",
      "_d: 177     phi: 0.00022738541675308466\n",
      "_d: 176     phi: -0.0002212408515234343\n",
      "_d: 175     phi: 0.0002152229675185715\n",
      "_d: 174     phi: -0.0002093303025899991\n",
      "_d: 173     phi: 0.00020356138070589901\n",
      "_d: 172     phi: -0.00019791470866771006\n",
      "_d: 171     phi: 0.0001923887819018929\n",
      "_d: 170     phi: -0.00018698208096790562\n",
      "_d: 169     phi: 0.0001816930772885154\n",
      "_d: 168     phi: -0.00017652022977800665\n",
      "_d: 167     phi: 0.00017146199031254644\n",
      "_d: 166     phi: -0.0001665168004155009\n",
      "_d: 165     phi: 0.00016168309676688298\n",
      "_d: 164     phi: -0.0001569593077415331\n",
      "_d: 163     phi: 0.00015234385884825262\n",
      "_d: 162     phi: -0.00014783516921770083\n",
      "_d: 161     phi: 0.00014343165715418775\n",
      "_d: 160     phi: -0.000139131736404506\n",
      "_d: 159     phi: 0.00013493382172770558\n",
      "_d: 158     phi: -0.00013083632510804268\n",
      "_d: 157     phi: 0.00012683766126081897\n",
      "_d: 156     phi: -0.0001229362438941907\n",
      "_d: 155     phi: 0.00011913049102084458\n",
      "_d: 154     phi: -0.00011541882126544915\n",
      "_d: 153     phi: 0.00011179965914853639\n",
      "_d: 152     phi: -0.00010827143127515096\n",
      "_d: 151     phi: 0.00010483257162628372\n",
      "_d: 150     phi: -0.00010148151769521157\n",
      "_d: 149     phi: 9.82167156802407e-05\n",
      "_d: 148     phi: -9.503661670796795e-05\n",
      "_d: 147     phi: 9.193968183574538e-05\n",
      "_d: 146     phi: -8.892437826652066e-05\n",
      "_d: 145     phi: 8.598918440654554e-05\n",
      "_d: 144     phi: -8.31325858955301e-05\n",
      "_d: 143     phi: 8.0353080735137e-05\n",
      "_d: 142     phi: -7.76491752339054e-05\n",
      "_d: 141     phi: 7.501938900870609e-05\n",
      "_d: 140     phi: -7.246225105229916e-05\n",
      "_d: 139     phi: 6.997630458733582e-05\n",
      "_d: 138     phi: -6.75601031112239e-05\n",
      "_d: 137     phi: 6.521221520052034e-05\n",
      "_d: 136     phi: -6.293122054264159e-05\n",
      "_d: 135     phi: 6.0715714714226045e-05\n",
      "_d: 134     phi: -5.8564305103703875e-05\n",
      "_d: 133     phi: 5.647561568227295e-05\n",
      "_d: 132     phi: -5.444828297026926e-05\n",
      "_d: 131     phi: 5.2480960669538215e-05\n",
      "_d: 130     phi: -5.057231558855342e-05\n",
      "_d: 129     phi: 4.872103232286141e-05\n",
      "_d: 128     phi: -4.6925809085138495e-05\n",
      "_d: 127     phi: 4.518536236616059e-05\n",
      "_d: 126     phi: -4.349842273221741e-05\n",
      "_d: 125     phi: 4.186373941289424e-05\n",
      "_d: 124     phi: -4.0280076159882004e-05\n",
      "_d: 123     phi: 3.8746215751713036e-05\n",
      "_d: 122     phi: -3.726095571771337e-05\n",
      "_d: 121     phi: 3.582311297378931e-05\n",
      "_d: 120     phi: -3.443151948244782e-05\n",
      "_d: 119     phi: 3.308502679511827e-05\n",
      "_d: 118     phi: -3.1782501683910447e-05\n",
      "_d: 117     phi: 3.052283072793932e-05\n",
      "_d: 116     phi: -2.9304915871072443e-05\n",
      "_d: 115     phi: 2.8127678977642038e-05\n",
      "_d: 114     phi: -2.699005736224524e-05\n",
      "_d: 113     phi: 2.5891008361973528e-05\n",
      "_d: 112     phi: -2.482950479461529e-05\n",
      "_d: 111     phi: 2.380453949530865e-05\n",
      "_d: 110     phi: -2.2815120844030496e-05\n",
      "_d: 109     phi: 2.186027715592763e-05\n",
      "_d: 108     phi: -2.093905224669841e-05\n",
      "_d: 107     phi: 2.00505098342327e-05\n",
      "_d: 106     phi: -1.9193729032043377e-05\n",
      "_d: 105     phi: 1.8367808732555536e-05\n",
      "_d: 104     phi: -1.7571863116667044e-05\n",
      "_d: 103     phi: 1.6805025980498713e-05\n",
      "_d: 102     phi: -1.6066446262228463e-05\n",
      "_d: 101     phi: 1.5355292322601578e-05\n",
      "_d: 100     phi: -1.4670747439206021e-05\n",
      "_d: 99     phi: 1.4012014143814665e-05\n",
      "_d: 98     phi: -1.3378309636836666e-05\n",
      "_d: 97     phi: 1.2768870106145209e-05\n",
      "_d: 96     phi: -1.2182946154914946e-05\n",
      "_d: 95     phi: 1.1619807123154314e-05\n",
      "_d: 94     phi: -1.1078736462828855e-05\n",
      "_d: 93     phi: 1.0559036058093338e-05\n",
      "_d: 92     phi: -1.0060021595044146e-05\n",
      "_d: 91     phi: 9.58102687621065e-06\n",
      "_d: 90     phi: -9.121399168858193e-06\n",
      "_d: 89     phi: 8.680503510590787e-06\n",
      "_d: 88     phi: -8.257718051978905e-06\n",
      "_d: 87     phi: 7.85243835774908e-06\n",
      "_d: 86     phi: -7.4640727253516604e-06\n",
      "_d: 85     phi: 7.092046492116092e-06\n",
      "_d: 84     phi: -6.735797341149111e-06\n",
      "_d: 83     phi: 6.394779596595259e-06\n",
      "_d: 82     phi: -6.068459549314927e-06\n",
      "_d: 81     phi: 5.756319700494699e-06\n",
      "_d: 80     phi: -5.457854116910001e-06\n",
      "_d: 79     phi: 5.172572674562133e-06\n",
      "_d: 78     phi: -4.899996371645927e-06\n",
      "_d: 77     phi: 4.6396616029462706e-06\n",
      "_d: 76     phi: -4.39111546217434e-06\n",
      "_d: 75     phi: 4.153920000913926e-06\n",
      "_d: 74     phi: -3.927647543806197e-06\n",
      "_d: 73     phi: 3.711884928730937e-06\n",
      "_d: 72     phi: -3.50622883014879e-06\n",
      "_d: 71     phi: 3.3102900129757926e-06\n",
      "_d: 70     phi: -3.1236886252488955e-06\n",
      "_d: 69     phi: 2.9460584559474595e-06\n",
      "_d: 68     phi: -2.7770422517551514e-06\n",
      "_d: 67     phi: 2.6162959600776674e-06\n",
      "_d: 66     phi: -2.4634840373830493e-06\n",
      "_d: 65     phi: 2.3182836946557787e-06\n",
      "_d: 64     phi: -2.180380228898072e-06\n",
      "_d: 63     phi: 2.049471247833528e-06\n",
      "_d: 62     phi: -1.925262007281232e-06\n",
      "_d: 61     phi: 1.8074696423656513e-06\n",
      "_d: 60     phi: -1.695818495958286e-06\n",
      "_d: 59     phi: 1.5900443680102692e-06\n",
      "_d: 58     phi: -1.489889847671059e-06\n",
      "_d: 57     phi: 1.3951085418647683e-06\n",
      "_d: 56     phi: -1.3054604269580568e-06\n",
      "_d: 55     phi: 1.22071609439434e-06\n",
      "_d: 54     phi: -1.1406520801084034e-06\n",
      "_d: 53     phi: 1.0650551248557439e-06\n",
      "_d: 52     phi: -9.937175069362673e-07\n",
      "_d: 51     phi: 9.264413134628403e-07\n",
      "_d: 50     phi: -8.630337762191802e-07\n",
      "_d: 49     phi: 8.033115272805191e-07\n",
      "_d: 48     phi: -7.470959593124806e-07\n",
      "_d: 47     phi: 6.942174982519782e-07\n",
      "_d: 46     phi: -6.445109376431976e-07\n",
      "_d: 45     phi: 5.978197245474981e-07\n",
      "_d: 44     phi: -5.539913185649455e-07\n",
      "_d: 43     phi: 5.128814711977543e-07\n",
      "_d: 42     phi: -4.743495833186276e-07\n",
      "_d: 41     phi: 4.382629893651567e-07\n",
      "_d: 40     phi: -4.0449233360558915e-07\n",
      "_d: 39     phi: 3.729158606873987e-07\n",
      "_d: 38     phi: -3.43414784966682e-07\n",
      "_d: 37     phi: 3.158775823496051e-07\n",
      "_d: 36     phi: -2.901953813604596e-07\n",
      "_d: 35     phi: 2.6626626664514685e-07\n",
      "_d: 34     phi: -2.439906541734609e-07\n",
      "_d: 33     phi: 2.2327560450630512e-07\n",
      "_d: 32     phi: -2.0403021714992716e-07\n",
      "_d: 31     phi: 1.8616995018981186e-07\n",
      "_d: 30     phi: -1.696120063655594e-07\n",
      "_d: 29     phi: 1.5427966022438153e-07\n",
      "_d: 28     phi: -1.4009766215148883e-07\n",
      "_d: 27     phi: 1.269965726735201e-07\n",
      "_d: 26     phi: -1.1490815864264026e-07\n",
      "_d: 25     phi: 1.0376973293873245e-07\n",
      "_d: 24     phi: -9.351957339400534e-08\n",
      "_d: 23     phi: 8.410126471922766e-08\n",
      "_d: 22     phi: -7.545910925902256e-08\n",
      "_d: 21     phi: 6.754247951471221e-08\n",
      "_d: 20     phi: -6.030124547348857e-08\n",
      "_d: 19     phi: 5.369013132174657e-08\n",
      "_d: 18     phi: -4.766414012641698e-08\n",
      "_d: 17     phi: 4.218291200531334e-08\n",
      "_d: 16     phi: -3.7206168292673736e-08\n",
      "_d: 15     phi: 3.2698077762541153e-08\n",
      "_d: 14     phi: -2.862269054478244e-08\n",
      "_d: 13     phi: 2.4948311301469504e-08\n",
      "_d: 12     phi: -2.1642955241294434e-08\n",
      "_d: 11     phi: 1.8678716220256254e-08\n",
      "_d: 10     phi: -1.6027226240866234e-08\n",
      "_d: 9     phi: 1.3664026520037937e-08\n",
      "_d: 8     phi: -1.1564039091491138e-08\n",
      "_d: 7     phi: 9.705949039630519e-09\n",
      "_d: 6     phi: -8.067665504570867e-09\n",
      "_d: 5     phi: 6.6307116411175285e-09\n",
      "_d: 4     phi: -5.375697869421365e-09\n",
      "_d: 3     phi: 4.2867244787078545e-09\n",
      "_d: 2     phi: -3.3468404847946574e-09\n",
      "_d: 1     phi: 2.5424507621540607e-09\n",
      "_d: 0     phi: 0.7853981615386494\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7f46bc53d150>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QSP_circuit.h(QSP_circuit.num_qubits-1)\n",
    "\n",
    "# for _d,phi in reversed( list ( enumerate( phi_angles[:6] ) ) ):\n",
    "for _d,phi in reversed( list ( enumerate( phi_angles[:] ) ) ):\n",
    "    print( '_d: {}     phi: {}'.format(_d,phi[0]))\n",
    "\n",
    "    CR_phi_d(_d, phi[0], QSP_circuit, QSP_circuit.num_qubits - n - 1)\n",
    "    if _d>0:\n",
    "        if _d%2:\n",
    "            # Apply U_A\n",
    "            for _i in blockEncoded_i.data:\n",
    "                QSP_circuit.append(_i)\n",
    "            pass\n",
    "        else:\n",
    "            # Apply U_A_i\n",
    "            for _i in blockEncoded.data:\n",
    "                QSP_circuit.append(_i)\n",
    "            pass\n",
    "        \n",
    "QSP_circuit.h(QSP_circuit.num_qubits-1)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "5a19732a-88a6-4251-a691-243778707af0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# QSP_circuit.draw('mpl',style='iqp',scale=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "5c82ed79-6102-495d-9a4c-6584f29b70bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "QSP_result = execute(QSP_circuit,backend,shots=0).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "4d876b06-ee39-4461-acaa-35d8d6fdc122",
   "metadata": {},
   "outputs": [],
   "source": [
    "QSP_matrix = np.array(QSP_result.get_unitary().data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "a0eeedbe-3de1-4cd3-aeb7-31653f2ff9d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1. -0.  0. -0.  0. -0. -0.  0.  0.  0.  0. -0.  0.  0. -0.  0.]\n",
      " [-1.  1. -0.  0. -0.  0. -0. -0.  0.  0. -0.  0. -0.  0.  0. -0.]\n",
      " [ 1. -1.  1. -0.  0. -0.  0. -0.  0. -0.  0. -0.  0. -0.  0.  0.]\n",
      " [-1.  1. -1.  1. -0.  0. -0.  0. -0.  0. -0.  0. -0.  0. -0.  0.]\n",
      " [ 1. -1.  1. -1.  1. -0.  0. -0.  0. -0.  0. -0.  0. -0.  0. -0.]\n",
      " [-1.  1. -1.  1. -1.  1. -0.  0. -0.  0. -0.  0. -0.  0. -0.  0.]\n",
      " [ 1. -1.  1. -1.  1. -1.  1. -0.  0. -0.  0. -0.  0. -0.  0.  0.]\n",
      " [-1.  1. -1.  1. -1.  1. -1.  1. -0.  0. -0.  0. -0.  0.  0.  0.]\n",
      " [ 1. -1.  1. -1.  1. -1.  1. -1.  1. -0.  0. -0.  0. -0. -0.  0.]\n",
      " [-1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -0.  0. -0.  0. -0. -0.]\n",
      " [ 1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -0.  0. -0.  0. -0.]\n",
      " [-1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -0.  0. -0.  0.]\n",
      " [ 1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -0.  0. -0.]\n",
      " [-1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -0.  0.]\n",
      " [ 1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -0.]\n",
      " [-1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1. -1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print((QSP_matrix[0:2**n,0:2**n].real/np.abs(QSP_matrix[0,0].real)).round(6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "772cb851-fd37-48f7-9e1b-a52ffaf02683",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d9baa4c9-15d7-4c78-bae0-6ff6503f0829",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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