aula6_sbf.ipynb

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    "### Computação Quântica com Qiskit\n",
    "\n",
    "##### Jonas Maziero\n",
    "\n",
    "<table>\n",
    "<td> Universidade Federal de Santa Maria <br>\n",
    "Centro de Ciências Naturais e Exatas <br>\n",
    "Departamento de Física <br>\n",
    "https://sites.google.com/site/jonasmaziero <br>\n",
    "jonas.maziero@ufsm.br \n",
    "    </td>\n",
    "    <td><img src='ufsm.jpg' width='250'></td>\n",
    "    <td><img src='inpe_ufsm.jpg' width='550'></td>\n",
    "</table>\n",
    "<table>\n",
    "    <td>Suporte Financeiro:</td>\n",
    "    <td><img src='cnpq.png' width='200'></td>\n",
    "    <td><img src='inct-iq.png' width='330'></td>\n",
    "    <td><img src='capes.png' width='100'></td>\n",
    "    <td><img src='fapergs.png' width='150'></td>\n",
    "    <td><img src='ufsm.jpg' width='75'></td>\n",
    "    </table>"
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    "# Aula 6\n",
    "\n",
    "- Complementaridade quântica;\n",
    "- Interferômetro de Mach-Zehnder (IMZ);\n",
    "- IMZ com informação de caminho;\n",
    "- Apagador quântico;\n",
    "- Apagador quântico com mitigação de erros;\n",
    "- Apagador quântico com emaranhamento parcial."
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   "source": [
    "# Complementaridade quântica"
   ]
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    "### Experimento da dupla fenda de Young\n",
    "<table>\n",
    "    <td><img src='young.jpg' width='150'></td>\n",
    "<td><img src='young_.png' width='250'></td>\n",
    "    <td><img src='feyman.jpg' width='130'> Feynman</td>\n",
    "</table>\n",
    "<table>\n",
    "    <td><img src='fig_2slits_wave.png' width='650'></td>\n",
    "    <td><img src='fig_2slits_particle.png' width='650'></td>\n",
    "    </table>"
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    "## Princípio de complementaridade de Bohr\n",
    "\n",
    "<table>\n",
    "    <td><img src='bohr.jpg' width='700'> Bohr</td>\n",
    "    <td>\"The very nature of quantum theory thus forces us to regard the space-time coordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description\"</td>\n",
    "<td>\"we are presented with a choice of either tracing the path of a particle or observing the interference effect which allows us to escape from the paradoxical necessity of concluding that the behaviour of an electron or a photon should depend on the presence of a slit in the diaphragm which it could be proved not to pass\"</td>\n",
    "</table>\n",
    "\n",
    "N. Bohr, “The Quantum Postulate and the Recent Development of Atomic Theory”, __Nature 121, 3050 (1928)__.\n",
    "$$(W=1,\\ P=0)\\ \\text{or}\\ (W=0,\\ P=1).$$\n",
    "\n",
    "_Para um dado aparato experimental, podemos observar o comportamento ondulatório ou corpuscular, mas não ambos simultaneamente._"
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    "### Comportamentos ondulatório e corpuscular simultâneos\n",
    "\n",
    "<table>\n",
    "    <td><img src='wootters.jpg' width='180'> Wootters</td>\n",
    "    <td><img src='zurek.jpeg' width='160'> Zurek</td>\n",
    "    <td><img src='zurek_.png' width='350'> emaranhamento OHQ-fóton </td>\n",
    "</table>\n",
    "\n",
    "W.K. Wootters and W.H. Zurek, Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr’s principle, __PRD 19, 473 (1979)__.\n",
    "\n",
    "\"The sharpness of the interference pattern can be regarded as a __measure of how wave-like__ the light is. The amount of information we have obtained about the photons' trajectories can be regarded as a __measure of how particle-like__ it is: $V\\propto 1/D.$\""
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    "#### Preditibilidade de caminho\n",
    "D.M. Greenberger and A. Yasin, Simultaneous wave and particle knowledge in a neutron interferometer, __PLA 128, 391 (1988)__.\n",
    "<table>\n",
    "    <tr> <td>Função de onda $\\psi=\\big(ae^{ik_x x}+be^{-ik_x x}\\big)e^{ik_z z}$</td>\n",
    "        <td>Densidade de probabilidade $|\\psi|^2 = a^2+b^2+2ab\\cos(2k_x x +\\phi)$ </td></tr>\n",
    "    <tr><td><img src='greenberger.jpg' width='450'> Daniel Greenberger </td>\n",
    "    <td> Visibilidade interferométrica: $V=\\frac{I_{\\max}-I_{\\min}}{I_{\\max}+I_{\\min}} = \\frac{2ab}{a^2+b^2}$ </td>\n",
    "        <td>Preditibilidade: $P=\\frac{a^2-b^2}{a^2+b^2}$  </td></tr>\n",
    "    <tr><td>Feixes coerentes - igualdade: $P^2+V^2=1$ </td>\n",
    "        <td>Feixes parcialmente coerentes - desigualdade: $P^2+V^2\\le 1$</td></tr>\n",
    "</table>"
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    "## Complementaridade a partir dos postulados da MQ"
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    "$*$ M. L. W. Basso, D. S. S. Chrysosthemos, and J. Maziero, “Quantitative wave–particle duality relations from the density matrix properties,” __Quantum Inf Process, vol. 19, no. 8, p. 254, Jul. 2020__, doi: 10.1007/s11128-020-02753-y.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “Complete complementarity relations for multipartite pure states,” __J. Phys. A: Math. Theor., vol. 53, no. 46, p. 465301, Oct. 2020__, doi: 10.1088/1751-8121/abc361.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “An uncertainty view on complementarity and a complementarity view on uncertainty,” __Quantum Inf Process, vol. 20, no. 6, p. 201, Jun. 2021__, doi: 10.1007/s11128-021-03136-7.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “Complete complementarity relations: Connections with Einstein-Podolsky-Rosen realism and decoherence, and extension to mixed quantum states,” __EPL, vol. 135, no. 6, p. 60002, Nov. 2021__, doi: 10.1209/0295-5075/ac1bc8."
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    "$*$ M. L. W. Basso and J. Maziero, “Entanglement monotones connect distinguishability and predictability,” __Physics Letters A, vol. 425, p. 127875, Feb. 2022__, doi: 10.1016/j.physleta.2021.127875.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “Entanglement monotones from complementarity relations,” __J. Phys. A: Math. Theor., vol. 55, no. 35, p. 355304, Aug. 2022__, doi: 10.1088/1751-8121/ac83fc.\n",
    "\n",
    "$*$ D. S. S. Chrysosthemos, M. L. W. Basso, and J. Maziero, “Quantum coherence versus interferometric visibility in a biased Mach–Zehnder interferometer,” __Quantum Inf Process, vol. 22, no. 1, p. 68, Jan. 2023__, doi: 10.1007/s11128-022-03800-6.\n",
    "\n",
    "$*$ D. S. S. Chrysosthemos, M. L. W. Basso, and J. Maziero, “Quantum simulation of the generalized-entangled quantum eraser and the related complete complementarity relations,” __Phys. Scr., vol. 98, no. 3, p. 035107, Feb. 2023__, doi: 10.1088/1402-4896/acbacb."
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    "$*$ M. L. W. Basso and J. Maziero, “Predictability as a quantum resource,” __Quantum Inf Process, vol. 21, no. 5, p. 187, May 2022__, doi: 10.1007/s11128-022-03503-y.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “Operational connection between predictability and entanglement in entanglement swapping from partially entangled pure states,” __Physics Letters A, vol. 451, p. 128414, Nov. 2022__, doi: 10.1016/j.physleta.2022.128414.\n",
    "\n",
    "$*$ J. Maziero, M. L. W. Basso, and L. C. Céleri, “Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure states,” __Physics Letters A, vol. 457, p. 128576, Jan. 2023__, doi: 10.1016/j.physleta.2022.128576.\n"
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    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “Complete complementarity relations and their Lorentz invariance,” __Proc. R. Soc. A., vol. 477, no. 2253, p. 20210058, Sep. 2021__.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “Complete complementarity relations in curved spacetimes,” __Phys. Rev. A, vol. 103, no. 3, p. 032210, Mar. 2021__.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “Interferometric visibility in curved spacetimes,” __Class. Quantum Grav., vol. 38, no. 13, p. 135007, Jun. 2021__.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “The effect of stationary axisymmetric spacetimes in interferometric visibility,” __Gen Relativ Gravit, vol. 53, no. 7, p. 70, Jul. 2021__.\n",
    "\n",
    "$*$ M. L. W. Basso and J. Maziero, “The Sagnac effect for spin-1/2 particles through local Wigner rotations,” __Quantum Inf Process, vol. 21, no. 2, p. 59, Jan. 2022__."
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    "### Verificação experimental usando IBMQ\n",
    "\n",
    "M.B. Pozzobom; M.L.W. Basso; J. Maziero, Experimental tests of the density matrix's property-based complementarity relations, __Phys. Rev. A 103, 022212 (2021)__.\n",
    "\n",
    "$$C_{l_1}(\\rho_A)+P_{l_1}(\\rho_A)\\le d_A -1;\\ C_{l_1}(\\rho_A)+P_{l_1}(\\rho_A)+W_{l_1}(\\rho_A)=d_A -1 $$\n",
    "\n",
    "<table>\n",
    "    <td><img src='fig_ibmq2.jpg' width='270'></td>\n",
    "    <td><img src='experiment_cr_.png' width='350'></td>\n",
    "    <td><img src='random_circuits.png' width='450'></td>\n",
    "    <td><img src='experiment_cr.png' width='350'></td>\n",
    "    </table>"
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   "source": [
    "# Interferômetro de Mach-Zehnder (IMZ)"
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    "Modo espacial horizontal: $|h\\rangle:=|0\\rangle$, modo espacial vertical: $|v\\rangle:=|1\\rangle.$ <br>\n",
    "Consideraremos um DF com transmitância $50\\ \\%$, i.e., $t=r=0.5$:\n",
    "<table>\n",
    "    <td><img src='fig_imz.png' width='600'></td>\n",
    "<td>\\begin{align}\n",
    "|\\psi_{0}\\rangle & = |0\\rangle, \\\\\n",
    "|\\psi_{1}\\rangle & = (|0\\rangle+i|1\\rangle)/\\sqrt{2}, \\\\\n",
    "|\\psi_{2}\\rangle & = (i|1\\rangle+ii|0\\rangle)/\\sqrt{2} = (-|0\\rangle+i|1\\rangle)/\\sqrt{2}, \\\\\n",
    "|\\psi_{3}\\rangle & = (-|0\\rangle+ie^{i\\phi}|1\\rangle)/\\sqrt{2}, \\\\\n",
    "|\\psi_{4}\\rangle & = (-(|0\\rangle+i|1\\rangle)/\\sqrt{2}+ie^{i\\phi}(i|0\\rangle+|1\\rangle)/\\sqrt{2})/\\sqrt{2} \\\\\n",
    "& = -\\frac{1+e^{i\\phi}}{2}|0\\rangle -i\\frac{1-e^{i\\phi}}{2}|1\\rangle.\n",
    "\\end{align}\n",
    "    </td>\n",
    "    </table>"
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    "Probabilidade do fóton ser detectado em um certo detector:\n",
    "$Pr(D_{0}) = \\left|-(1+e^{i\\phi})/2\\right|^{2} = (1+\\cos\\phi)/2$, \n",
    "$\\ Pr(D_{1}) = 1 - Pr(D_{0}) = (1-\\cos\\phi)/2.$"
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math; import numpy as np; phmax = 4*math.pi; npt = 100; dth = phmax/npt; ph = np.arange(0,phmax+dth,dth)\n",
    "from matplotlib import pyplot as plt; PrD0 = 0.5*(1+np.cos(ph)); plt.plot(ph,PrD0, label=r'$Pr(D_0)$')\n",
    "PrD0 = 0.5*(1-np.cos(ph)); plt.plot(ph,PrD0, label=r'$Pr(D_1)$'); plt.legend(); plt.xlabel(r'$\\phi$'); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cfebef3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simulação dos elementos ópticos envolvidos\n",
    "\n",
    "__Divisor de feixes (DF)__\n",
    "$$U_{df}|0\\rangle = (|0\\rangle + i|1\\rangle)/\\sqrt{2},\\ U_{df}|1\\rangle = (|1\\rangle + i|0\\rangle)/\\sqrt{2}$$\n",
    "Matriz\n",
    "$$U_{df} \\doteq \\begin{bmatrix}\\langle 0|U_{df}|0\\rangle & \\langle 0|U_{df}|1\\rangle \\\\ \\langle 1|U_{df}|0\\rangle & \\langle 1|U_{df}|1\\rangle\\end{bmatrix} = \\frac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & i \\\\ i & 1 \\end{bmatrix} = SHS.$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "36c3733c",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & 0.5 \\sqrt{2} i\\\\0.5 \\sqrt{2} i & 0.5 \\sqrt{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[    sqrt(2)/2, 0.5*sqrt(2)*I],\n",
       "[0.5*sqrt(2)*I,   0.5*sqrt(2)]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix, sqrt\n",
    "S = Matrix([[1,0],[0,1j]]); H = (1/sqrt(2))*Matrix([[1,1],[1,-1]])\n",
    "S*H*S"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d885feb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Espelhos__:\n",
    "$$U_e|0\\rangle = i|1\\rangle,\\ U_e|1\\rangle = i|0\\rangle\\ \\therefore\\ U_e \\doteq \\begin{bmatrix} 0 & i \\\\ i & 0 \\end{bmatrix} = iX = YZ.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d2527268",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1.0 i\\\\1.0 i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[    0, 1.0*I],\n",
       "[1.0*I,     0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = Matrix([[0,-1j],[1j,0]]); Z = Matrix([[1,0],[0,-1]]); Y*Z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d30646f6",
   "metadata": {},
   "source": [
    "__Fase no caminho vertical__\n",
    "$$P(\\phi)|0\\rangle = |0\\rangle,\\ P(\\phi)|1\\rangle = e^{i\\phi}|1\\rangle\\ \\therefore\\ P(\\phi) = \\begin{bmatrix} 1 & 0 \\\\ 0 & e^{i\\phi} \\end{bmatrix}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "542bd2c8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simulação clássica do IMZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "af595438",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 352.675x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "\n",
    "def qc_df(): # divisor de feixes 50:50\n",
    "    qc = QuantumCircuit(1, name='DF')\n",
    "    qc.s(0)\n",
    "    qc.h(0)\n",
    "    qc.s(0)\n",
    "    return qc\n",
    "qcdf = qc_df(); qcdf.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5427414a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAABuCAYAAADVoKRKAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAGoElEQVR4nO3cb2hV9x3H8c/vnCwmMauNYZLVKrbau5irCdSwzjZ7kDSGdVjKno44mIwysWY2umCw6WiVYFaXbQ/KGGRlDN0mjDHGbEuHY9NWdAvrUHBQYTPexNxgdDpRk5J7zh5sE0sSudd7kvPN8f2CPMk5+d0vP/LmnnPyx4VhGApA7Ly4BwDwX8QIGEGMgBHECBhBjIARxAgYQYyAEcQIGEGMgBHECBhBjIARxAgYQYyAEcQIGEGMgBHECBhBjIARxAgYQYyAEcQIGEGMgBHECBhBjIARxAgYQYyAEcQIGEGMgBHECBhBjIARxAgYQYyAEcQIGEGMgBHECBhBjIARxAgYQYyAESVxD5BkYRjqVpCLe4yCVHi+nHORrcce5I8Y59CtIKeqP/w+7jEK8q+WTVrsR/dtwR7kj8tUwAhiBIwgRsAIYgSMIEbACGIEjCBGwAhiBIwgRsAIYgSMIEbACGIEjCBGwIjExTg+Pq7du3dr9erVKisr04oVK7Rr1y7dvn1b7e3tcs5pYGAg7jGBaRL1J1RnzpxRW1ubxsbGtHjxYtXV1WlkZET9/f26cOGCLl68KElqaGiIedLChNkxTX3t63md679xQF5D/RxPNP+mvvO6wtN/ln+wT9669LTjwbm/K9f5bbmnPq+S116NYcLiJSbG8fFxbd68WWNjY+rq6lJPT48qKyslSfv371dPT49KSkrkeZ7WrVsX87QFWrJEftfuWQ+Hw8MKfv5LackSuUcfncfB5o+/c4emXtym3MF+uR+9KVdedudYODmp3MF+6dOV8nd2xDhlcRJzmdrR0aFMJqPOzk719fXdCVGS9u7dq9raWk1NTSmVSqm8vDzGSQvnysvktbbM+OGe/oKC9z+QfF/+K91y1UvjHndOuKoq+R0vSZdGFQz85BPHgrd+Kg2PyP/WDrmqh2OZLwqJiPHcuXM6cuSIli1bpn379k077pzThg0bJC28S9R7CcNQuTf6pYsZeS9+I5GXp3fzvtgk19Ks4HdvK/jrh5Kk4MxZBb/5rdyzzfKanol5wuIkIsbDhw8rCAK1t7eroqJixnMWLVokKVkxBr84ovCDk3Ktz8r/ygtxjzMv/Je2SdVLlfveDxReuaLcwe9L1Uvlb98W92hFS0SMx44dkyQ1NzfPes7w8LCk5MQY/GVQwc8OyaWekL9zR9zjzBtXWSm/82Xp8mVNfXO7lM3K73xZ7q7bkoUqEQ9whoaGJEmrVq2a8fjk5KROnz4tqbgYGxsblc1m8z4/LC2Vfvzmfb/erOuOjip34LvSQw/Jf/UVudLSyNZOPZGS+/jjyNabiz3wGp9U8NyXFL7zrrwvPyev8clI1y9mD2pqajQ4OHhfX5uIGG/evClJmpiYmPH4oUOHdP36dVVXV2v58uX3/TrZbFYjIyP5f0HZIn3qvl9tZuHEhKZe2y/dui2/r1du2WciXf/S6CVpYjK6BedgDyTJS69V7p135epqI1878j3IUyJirKmp0Y0bNzQ4OKjGxsZPHMtkMuru7pYk1dcX94CjpqamoPPD0lJdLuoVp8v1/1D6xz/lbd8mr359xKtLj3z2kcjfGaPeg7lWzB4U+j1yt0TE2NraqvPnz6u3t1ctLS1KpVKSpFOnTmnLli26du2apOLvFwu9/LiZm4r0f4bmfvVrhX/8k1xbq/wXno9s3bt9dP6jSP9naNR7MB+i3oN8JeIBzp49e1RVVaVMJqN0Oq3169drzZo12rhxo9auXaumpiZJC/vhTfDh3xQMvCX3uZT8jgfngc2DJBHvjCtXrtSJEyfU1dWl48ePa2hoSOl0Wt3d3dq6deud+8SFGmN45apyvQekMJR75mmFx08onOVc9/hjco8/Nq/zIRqJiFGS0um0jh49Ou3zV69e1ejoqEpKSlRXVxfDZMULh4el6/+W9L/fNrkHr/2r8olxQUpMjLM5e/asJKm2tvbOD/4XGq+hXt57b8c9hile2yZ5bZviHiNSibhnvJf/x7hQL1Hx4CBGwIgHJsZif8YIzLXE3zOePHky7hGAvCT+nRFYKIgRMIIYASOIETCCGAEjiBEwghgBI4gRMIIYASOIETCCGAEjXBiGs/3ROIoUhqFuBbm4xyhIhefLORfZeuxB/ogRMILLVMAIYgSMIEbACGIEjCBGwAhiBIwgRsAIYgSMIEbACGIEjCBGwAhiBIwgRsAIYgSMIEbACGIEjCBGwAhiBIwgRsAIYgSMIEbACGIEjCBGwAhiBIwgRsCI/wDFc69CBUCkYQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 269.064x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_espelhos():\n",
    "    qc = QuantumCircuit(1, name='E')\n",
    "    qc.z(0)\n",
    "    qc.y(0)\n",
    "    return qc\n",
    "qce = qc_espelhos(); qce.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6d148be9",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 436.286x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_imz(ph): # retorna o circuito quântico para o IMZ (sem as medidas)\n",
    "    qc = QuantumCircuit(1, name='IMZ')\n",
    "    qcdf = qc_df(); qc.append(qcdf, [0])\n",
    "    qce = qc_espelhos(); qc.append(qce, [0])\n",
    "    qc.p(ph, [0])\n",
    "    qcdf = qc_df(); qc.append(qcdf, [0])\n",
    "    return qc\n",
    "qcimz = qc_imz(0); qcimz.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "32183af4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.         0.75463867 0.24780273 0.         0.25830078 0.74279785\n",
      " 1.        ]\n"
     ]
    }
   ],
   "source": [
    "# Simulação clássica\n",
    "from qiskit import Aer, execute\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "nshots = 2**13\n",
    "import numpy as np; import math\n",
    "phmax = 2*math.pi\n",
    "npe = 6\n",
    "dth = phmax/npe\n",
    "ph = np.arange(0,phmax+dth,dth)\n",
    "PD0sim = np.zeros(len(ph))\n",
    "for j in range(0,len(ph)):\n",
    "    qc = QuantumCircuit(1,1)\n",
    "    qcimz = qc_imz(ph[j])\n",
    "    qc.append(qcimz,[0])\n",
    "    qc.measure(0,0)\n",
    "    job = execute(qc, backend=simulator, shots=nshots)\n",
    "    counts = job.result().get_counts()\n",
    "    if '0' in counts:\n",
    "        PD0sim[j] = counts['0']/nshots\n",
    "print(PD0sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1a6d5265",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "npt = 100\n",
    "dtht = phmax/npt\n",
    "pht = np.arange(0,phmax+dtht,dtht)\n",
    "PD0teo = 0.5*(1+np.cos(pht))\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teo, label=r'$Pr(D_0)_{teo}$')\n",
    "plt.plot(ph,PD0sim, 'o', label=r'$Pr(D_0)_{sim}$')\n",
    "plt.legend(); plt.xlabel(r'$\\phi$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7179db4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simulação quântica do IMZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "a24b9cf8",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ibmqfactory.load_account:WARNING:2023-10-10 19:01:18,001: Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    }
   ],
   "source": [
    "import qiskit\n",
    "qiskit.IBMQ.save_account('a221013b3d88dd070a495178c3f732ac683a494e5af4e641383f16d361e9fa7fa22af7f09cad3f88988a3e6e5621c7fe951d8ca6ff0c0371422b211ec0ae9709', \n",
    "                  overwrite = True)\n",
    "qiskit.IBMQ.load_account()\n",
    "#provider = qiskit.IBMQ.get_provider(hub='ibm-q', group='open', project='main')\n",
    "provider = qiskit.IBMQ.get_provider(hub='ibm-q-research-2', group='federal-uni-sant-1', project='main')\n",
    "device = provider.get_backend('ibm_nairobi')\n",
    "nshots = 2**13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "f538753f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cmjwm4rtv5jg008eneq0\n",
      "cmjwm5raa7w0008ped90\n",
      "cmjwm6gaa7w0008ped9g\n",
      "cmjwm7812ghg0088vpq0\n",
      "cmjwm7r8tsq000808kz0\n",
      "cmjwm8s8tsq000808kzg\n",
      "cmjwm9h4acc0008j00zg\n"
     ]
    }
   ],
   "source": [
    "import numpy as np; import math\n",
    "phmax = 2*math.pi\n",
    "npe = 6\n",
    "dth = phmax/npe\n",
    "ph = np.arange(0,phmax+dth,dth)\n",
    "job_ids = []\n",
    "for j in range(0,len(ph)):\n",
    "    qc = QuantumCircuit(1,1)\n",
    "    qcimz = qc_imz(ph[j])\n",
    "    qc.append(qcimz,[0])\n",
    "    qc.measure(0,0)\n",
    "    job = execute(qc, backend=device, shots=nshots)\n",
    "    jobid = job.job_id()\n",
    "    job_ids.append(jobid)\n",
    "    print(jobid)\n",
    "f = open(\"jobs_ids_IMZ.txt\", \"w\")\n",
    "f.write(str(job_ids))\n",
    "f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "024e80fc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.98974609 0.75439453 0.28100586 0.03991699 0.2746582  0.72875977\n",
      " 0.99084473]\n"
     ]
    }
   ],
   "source": [
    "device = provider.get_backend('ibm_nairobi')\n",
    "f = open(\"jobs_ids_IMZ.txt\",\"r\")\n",
    "list_ids_IMZ = f.read().replace(\"'\",\"\").replace(\" \",\"\").replace(\"[\",\"\").replace(\"]\",\"\").split(\",\")\n",
    "f.close()\n",
    "PD0exp = np.zeros(len(ph))\n",
    "for j in range(0,len(ph)):\n",
    "    job = device.retrieve_job(list_ids_IMZ[j])\n",
    "    counts = job.result().get_counts()\n",
    "    if '0' in counts:\n",
    "        PD0exp[j] = counts['0']/nshots\n",
    "print(PD0exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "c06fec9f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "npt = 100; dtht = phmax/npt; pht = np.arange(0,phmax+dtht,dtht)\n",
    "PD0teo = 0.5*(1+np.cos(pht))\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teo, label=r'$Pr(D_0)_{teo}$')\n",
    "plt.plot(ph,PD0sim, 'o', label=r'$Pr(D_0)_{sim}$')\n",
    "plt.plot(ph,PD0exp, '*', label=r'$Pr(D_0)_{exp}$')\n",
    "plt.legend()\n",
    "plt.xlabel(r'$\\phi$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec8a3544",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Visibilidade interferométrica\n",
    "\n",
    "É usada para quantificar, de forma indireta, o comportamento ondulatório do quanton:\n",
    "$$V = \\frac{Pr(|0\\rangle)_\\max - Pr(|0\\rangle)_\\min}{Pr(|0\\rangle)_\\max + Pr(|0\\rangle)_\\min}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "ffb26884",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vsim =  1.0\n",
      "Vexp =  0.9225485551871151\n"
     ]
    }
   ],
   "source": [
    "Vsim = (np.max(PD0sim)-np.min(PD0sim))/(np.max(PD0sim)+np.min(PD0sim)); print('Vsim = ',Vsim)\n",
    "Vexp = (np.max(PD0exp)-np.min(PD0exp))/(np.max(PD0exp)+np.min(PD0exp)); print('Vexp = ',Vexp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf1feed9",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Essa visibilidade interferométrica máxima indica que o quanton está se comportando de forma ondulatória, pois para ter sensibilidade à fase $\\phi$ o quanton tem que estar em um estado de superposição dos estados $|0\\rangle$ e $|1\\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "535288ee",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Problema__: Faça a simulação quântica do IMZ com divisor de feixes viasado, tal como discutido na referência (D. S. S. Chrysosthemos, M. L. W. Basso, and J. Maziero, “Quantum coherence versus interferometric visibility in a biased Mach–Zehnder interferometer,” Quantum Inf Process, vol. 22, no. 1, p. 68, Jan. 2023, doi: 10.1007/s11128-022-03800-6.\n",
    "). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bcd219c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Informação de caminho com divisor de feixes polarizado"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaab762b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<table>\n",
    "    <td><img src='fig_apagador.png' width='600'></td>\n",
    "    <td>Notação:\n",
    "\\begin{cases}\n",
    "\\text{A = polarização do fóton A;} \\\\\n",
    "\\text{A' = modo espacial do fóton A;} \\\\\n",
    "\\text{B = polarização do fóton B;} \\\\\n",
    "\\text{B' = modo espacial do fóton B.}\n",
    "\\end{cases}\n",
    "        Polarização:\n",
    "    $|H\\rangle_{s}=|0\\rangle_{s}\\text{, } |V\\rangle_{s}=|1\\rangle_{s} \\text{ com } s=A,B.$ <br>\n",
    "        Caminho: $|h\\rangle_s = |0\\rangle_{s},\\ |v\\rangle_s =|1\\rangle_{s},\\ s=A',B'$\n",
    "    </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51fe7e9e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 1º sem a PQO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "259a925d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Sequência de estados\n",
    "\\begin{align}\n",
    "BBO:|\\psi_{0}\\rangle & = |\\Psi_+\\rangle_{AB}|00\\rangle_{B'A'} = \\frac{1}{\\sqrt{2}}\\big(|01\\rangle_{AB}+|10\\rangle_{AB}\\big)|0\\rangle_{B'}|0\\rangle_{A'}, \\\\\n",
    "DFP:|\\psi_{1}\\rangle & = U_{dfp}^{BB'}|\\psi_{0}\\rangle \\\\\n",
    "& = \\frac{1}{\\sqrt{2}}\\big(|0\\rangle_{A}U_{dfp}^{BB'}|10\\rangle_{BB'}+|1\\rangle_{A}U_{dfp}^{BB'}|00\\rangle_{BB'}\\big)|0\\rangle_{A'} \\\\\n",
    "& = \\frac{1}{\\sqrt{2}}\\big(|0\\rangle_{A}i|11\\rangle_{BB'}+|1\\rangle_{A}|00\\rangle_{BB'}\\big)|0\\rangle_{A'} \\\\\n",
    "& = \\text{ estado emaranhado nos 3 graus de liberdade }A,B,B'. \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c0c3ed4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\\begin{align}\n",
    "PMO:|\\psi_{2}\\rangle & = U_{pmo}^{BB'}|\\psi_{1}\\rangle \\\\\n",
    "& = \\frac{1}{\\sqrt{2}}\\big(i|0\\rangle_{A}U_{pmo}^{BB'}|11\\rangle_{BB'}+|1\\rangle_{A}U_{pmo}^{BB'}|00\\rangle_{BB'}\\big)|0\\rangle_{A'} \\\\\n",
    "& = \\frac{1}{\\sqrt{2}}\\big(i|0\\rangle_{A}|01\\rangle_{BB'}+|1\\rangle_{A}|00\\rangle_{BB'}\\big)|0\\rangle_{A'} \\\\\n",
    "& = \\frac{1}{\\sqrt{2}}\\big(i|01\\rangle_{AB'}+|10\\rangle_{AB'}\\big)|0\\rangle_{B}|0\\rangle_{A'}, \\\\\n",
    "& = \\text{ emaranhou somente A e B', os descorrelacionando de B.}\n",
    "\\end{align}\n",
    "Vemos assim que, nesse ponto, se medimos a polarização horizontal-vertical de A, obtemos a informação de caminho de B no IMZ."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adaa8f7c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\\begin{align}\n",
    "& espelho:\\ |\\psi_{3}\\rangle = U_{e}^{B'}|\\psi_{2}\\rangle = 2^{-1/2}\\big(iU_{e}^{B'}|01\\rangle_{AB'}+U_{e}^{B'}|10\\rangle_{AB'}\\big)|0\\rangle_{B}|0\\rangle_{A'} \\\\\n",
    "& \\hspace{5cm} = 2^{-1/2}\\big(ii|00\\rangle_{AB'}+i|11\\rangle_{AB'}\\big)|0\\rangle_{B}|0\\rangle_{A'} \\\\\n",
    "& \\hspace{5cm} = 2^{-1/2}\\big(-|00\\rangle_{AB'}+i|11\\rangle_{AB'}\\big)|0\\rangle_{B}|0\\rangle_{A'} \\\\\n",
    "& fase:\\ |\\psi_{4}\\rangle = U_{\\phi}^{B'}|\\psi_{3}\\rangle \\\\\n",
    "& \\hspace{5cm} = 2^{-1/2}\\big(-|00\\rangle_{AB'}+ie^{i\\phi}|11\\rangle_{AB'}\\big)|0\\rangle_{B}|0\\rangle_{A'} \\\\\n",
    "& DF:\\ |\\psi_{5}\\rangle = U_{df}^{B'}|\\psi_{4}\\rangle \\\\\n",
    "& = 2^{-1/2}\\Big(-|0\\rangle_{A}\\big(|0\\rangle_{B'}+i|1\\rangle_{B'}\\big)/\\sqrt{2}+ie^{i\\phi}|1\\rangle_{A}\\big(i|0\\rangle_{B'}+|1\\rangle_{B'}\\big)/\\sqrt{2}\\Big)|0\\rangle_{B}|0\\rangle_{A'} \\\\\n",
    "& = -2^{-1}\\Big(|0\\rangle_{A}\\big(|0\\rangle_{B'}+i|1\\rangle_{B'}\\big) + e^{i\\phi}|1\\rangle_{A}\\big(|0\\rangle_{B'}-i|1\\rangle_{B'}\\big)\\Big)|0\\rangle_{B}|0\\rangle_{A'}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0c5f929",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Probabilidade\n",
    "\\begin{align}\n",
    "Pr(D_0) = Pr(B'=0) & = Pr(A=0,B'=0) + Pr(A=1,B'=0) \\\\\n",
    "& = \\Big|-\\frac{1}{2}\\Big|^2 + \\Big|\\frac{e^{i\\phi}}{2}\\Big|^2 = 1/4 + 1/4 \\\\\n",
    "& = 1/2 = \\text{constante}.\n",
    "\\end{align}\n",
    "\n",
    "Visibilidade interferométrica\n",
    "$$V_{teo} = \\frac{Pr(|0\\rangle)_\\max - Pr(|0\\rangle)_\\min}{Pr(|0\\rangle)_\\max + Pr(|0\\rangle)_\\min} = \\frac{1/2 - 1/2}{1/2 + 1/2} = 0.$$\n",
    "\n",
    "Isso indica um comportamento tipo partícula. Entendemos isso pois a informação sobre o caminho está disponível na polarização do fóton A."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "845e5f72",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simulação dos elementos ópticos\n",
    "\n",
    "#### Divisor de feixes polarizado\n",
    "Reflete a polarização vertical:\n",
    "\\begin{align}\n",
    "U_{dfp}|00\\rangle_{BB'} = |00\\rangle_{BB'},\\ U_{dfp}|01\\rangle_{BB'} = |01\\rangle_{BB'}, \\\\\n",
    "U_{dfp}|10\\rangle_{BB'} = i|11\\rangle_{BB'},\\ U_{dfp}|11\\rangle_{BB'} = i|10\\rangle_{BB'}.\n",
    "\\end{align}\n",
    "Ou seja\n",
    "\\begin{align}\n",
    "U_{dfp} & \\doteq \\begin{bmatrix} 1&0&0&0 \\\\ 0&1&0&0 \\\\ 0&0&0&i \\\\ 0&0&i&0 \\end{bmatrix} = |0\\rangle\\langle 0|_B\\otimes I_{B'} + |1\\rangle\\langle 1|_B\\otimes U_e^{B'} = C_{U_{e}}^{B\\rightarrow B'} \\\\\n",
    "& = C_{Y}^{B\\rightarrow B'}C_{Z}^{B\\rightarrow B'}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72d90f04",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Placa de meia onda\n",
    "Inverte a polarização, se o caminho é $B'=1$:\n",
    "\\begin{align}\n",
    "& U_{pmo}|00\\rangle_{BB'} = |00\\rangle_{BB'},\\ U_{pmo}|10\\rangle_{BB'} = |10\\rangle_{BB'},\\\\\n",
    "& U_{pmo}|01\\rangle_{BB'} = |11\\rangle_{BB'},\\ U_{pmo}|11\\rangle_{BB'} = |01\\rangle_{BB'}.\n",
    "\\end{align}\n",
    "Ou seja\n",
    "\\begin{align}\n",
    "U_{dfp} & \\doteq \\begin{bmatrix} 1&0&0&0 \\\\ 0&0&0&1 \\\\ 0&0&1&0 \\\\ 0&1&0&0 \\end{bmatrix} = I_B\\otimes|0\\rangle\\langle 0|_{B'} + X_B\\otimes|1\\rangle\\langle 1|_{B'} \\\\\n",
    "& = C_X^{B'\\rightarrow B}.\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2914a924",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 0 & 0 & 1\\\\0 & 0 & 1 & 0\\\\0 & 1 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1, 0, 0, 0],\n",
       "[0, 0, 0, 1],\n",
       "[0, 0, 1, 0],\n",
       "[0, 1, 0, 0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix, eye; P0 = Matrix([[1,0],[0,0]]); P1 = Matrix([[0,0],[0,1]]); X = Matrix([[0,1],[1,0]])\n",
    "from sympy.physics.quantum import TensorProduct as tp; tp(eye(2),P0) + tp(X,P1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2909b627",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simulação clássica\n",
    "\n",
    "O BBO prepara o estado $|\\Psi_+\\rangle$ para as polarizações dos fótons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "d171b329",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 287.294x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_bbo():\n",
    "    from qiskit import QuantumCircuit\n",
    "    qc = QuantumCircuit(2, name='BBO')\n",
    "    qc.x(1)\n",
    "    qc.h(0)\n",
    "    qc.cx(0,1)\n",
    "    return qc\n",
    "qcbbo = qc_bbo(); qcbbo.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd0c9a80",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Circuito quântico para o divisor de feixes polarizado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a5a9cca9",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 287.294x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_dfp():\n",
    "    from qiskit import QuantumCircuit\n",
    "    qc = QuantumCircuit(2, name='DFP')\n",
    "    qc.cz(0,1)\n",
    "    qc.cy(0,1)\n",
    "    return qc\n",
    "qcdfp = qc_dfp()\n",
    "qcdfp.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7ab4900",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Circuito quântico para a placa de meia onda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3520a3e6",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 203.683x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_pmo():\n",
    "    from qiskit import QuantumCircuit\n",
    "    qc = QuantumCircuit(2, name='PMO')\n",
    "    qc.cx(1,0)\n",
    "    return qc\n",
    "qcpmo = qc_pmo()\n",
    "qcpmo.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "989b30b1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### Circuito quântico para o IMZ com informação de caminho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "17a3c719",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 621.941x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_imz_ic(ph): # não consideramos o caminho do fóton A\n",
    "    from qiskit import QuantumCircuit\n",
    "    qc = QuantumCircuit(3, name='IMZIC')\n",
    "    qcbbo = qc_bbo(); qc.append(qcbbo, [0,1])\n",
    "    qcdfp = qc_dfp(); qc.append(qcdfp, [1,2])\n",
    "    qcpmo = qc_pmo(); qc.append(qcpmo, [1,2])\n",
    "    qce = qc_espelhos(); qc.append(qce, [2])\n",
    "    qc.p(ph, [2])\n",
    "    qcdf = qc_df(); qc.append(qcdf, [2])\n",
    "    return qc\n",
    "qcimzic = qc_imz_ic(0); qcimzic.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5f3f1505",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1040x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qcimzic.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "8738e777",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1290.83x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qcimzic.decompose().decompose().decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ed9ecd06",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.50402832 0.49023438 0.50488281 0.4954834  0.5078125  0.49279785]\n"
     ]
    }
   ],
   "source": [
    "# Simulação clássica\n",
    "from qiskit import Aer, execute\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "nshots = 2**13\n",
    "import numpy as np; import math\n",
    "phmax = 2*math.pi\n",
    "npe = 5\n",
    "dth = phmax/npe\n",
    "ph = np.arange(0,phmax+dth,dth)\n",
    "PD0sim = np.zeros(len(ph))\n",
    "for j in range(0,len(ph)):\n",
    "    qc = QuantumCircuit(3,2)\n",
    "    qcimzic = qc_imz_ic(ph[j])\n",
    "    qc.append(qcimzic,[0,1,2])\n",
    "    qc.measure([0,2],[0,1])\n",
    "    job = execute(qc, backend=simulator, shots=nshots)\n",
    "    counts = job.result().get_counts()\n",
    "    if '00' in counts:\n",
    "        PD0sim[j] = counts['00']/nshots\n",
    "    if '10' in counts:\n",
    "        PD0sim[j] += counts['10']/nshots\n",
    "print(PD0sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "975d80b1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 454.719x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "79da31dd",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np; import math\n",
    "phmax = 2*math.pi; npt = 100; dpht = phmax/npt\n",
    "pht = np.arange(0,phmax+dtht,dtht)\n",
    "PD0teo = 0.5*np.ones(len(pht))\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teo, label=r'$Pr(D_0)_{teo}$')\n",
    "plt.plot(ph,PD0sim, 'o', label=r'$Pr(D_0)_{sim}$')\n",
    "plt.ylim(0,1); plt.legend()\n",
    "plt.xlabel(r'$\\phi$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c803d6e4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Experimento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "201cfa5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit\n",
    "qiskit.IBMQ.save_account('e20d3045c7c23a3be753606794714e9b47d4331ec46a41b2281e2d601bae27b2b3c1baa0b5cb54f3282a8b5248e552b14c9c556699010660fb94b11d00ff1073', \n",
    "                  overwrite = True)\n",
    "qiskit.IBMQ.load_account()\n",
    "#provider = qiskit.IBMQ.get_provider(hub='ibm-q', group='open', project='main')\n",
    "provider = qiskit.IBMQ.get_provider(hub='ibm-q-research-2', group='federal-uni-sant-1', project='main')\n",
    "device = provider.get_backend('ibm_nairobi')\n",
    "nshots = 2**13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3c530333",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np; import math\n",
    "phmax=2*math.pi\n",
    "npe=5\n",
    "dth=phmax/npe\n",
    "ph=np.arange(0,phmax+dth,dth)\n",
    "job_ids=[]\n",
    "for j in range(0,len(ph)):\n",
    "    qc = QuantumCircuit(3,2)\n",
    "    qcimzic = qc_imz_ic(ph[j])\n",
    "    qc.append(qcimzic,[0,1,2])\n",
    "    qc.measure([0,2],[0,1])\n",
    "    job = execute(qc, backend=device, shots=nshots)\n",
    "    jobid = job.job_id()\n",
    "    job_ids.append(jobid)\n",
    "f = open(\"jobs_ids_IMZIC.txt\", \"w\")\n",
    "f.write(str(job_ids))\n",
    "f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "80fd134f",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['cmm6xxfrcq000080ch30', 'cmm6xy72hnf000830gp0', 'cmm6xyz4acc0008j17y0', 'cmm6y1g4acc0008j17yg', 'cmm6y992hnf000830gq0', 'cmm6ya14acc0008j17z0']\n"
     ]
    }
   ],
   "source": [
    "print(job_ids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "a2c10341",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.51940918 0.52185059 0.5189209  0.52331543 0.51623535 0.51831055]\n"
     ]
    }
   ],
   "source": [
    "f = open(\"jobs_ids_IMZIC.txt\",\"r\")\n",
    "list_ids_IMZIC = f.read().replace(\"'\",\"\").replace(\" \",\"\").replace(\"[\",\"\").replace(\"]\",\"\").split(\",\")\n",
    "f.close()\n",
    "phmax = 2*math.pi\n",
    "npe=5\n",
    "dth = phmax/npe\n",
    "ph = np.arange(0,phmax+dth,dth)\n",
    "PD0exp = np.zeros(len(ph))\n",
    "device = provider.get_backend('ibm_nairobi')\n",
    "for j in range(0,len(ph)):\n",
    "    job = device.retrieve_job(list_ids_IMZIC[j])\n",
    "    counts = job.result().get_counts()\n",
    "    if '00' in counts:\n",
    "        PD0exp[j] = counts['00']/nshots\n",
    "    if '10' in counts:\n",
    "        PD0exp[j] += counts['10']/nshots\n",
    "print(PD0exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c8cf546b",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np; import math\n",
    "phmax = 2*math.pi; npt = 100; dpht = phmax/npt\n",
    "pht = np.arange(0,phmax+dtht,dtht)\n",
    "PD0teo = 0.5*np.ones(len(pht))\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teo, label=r'$Pr(D_0)_{teo}$')\n",
    "plt.plot(ph,PD0sim, 'o', label=r'$Pr(D_0)_{sim}$')\n",
    "plt.plot(ph,PD0exp, '*', label=r'$Pr(D_0)_{exp}$')\n",
    "plt.ylim(0,1); plt.legend(); plt.xlabel(r'$\\phi$'); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5785ed5d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Visibilidade interferométrica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "438ec968",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vsim =  0.01761252446183953\n",
      "Vexp =  0.006810709253170503\n"
     ]
    }
   ],
   "source": [
    "Vsim = (np.max(PD0sim)-np.min(PD0sim))/(np.max(PD0sim)+np.min(PD0sim)); print('Vsim = ',Vsim)\n",
    "Vexp = (np.max(PD0exp)-np.min(PD0exp))/(np.max(PD0exp)+np.min(PD0exp)); print('Vexp = ',Vexp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72edf4fc",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "OBS. Neste caso sem a PQO, mesmo se fizermos pós-seleção nos resultados das medidas de Alice, a visibilidade interferométrica continua sendo nula e o comportamento é portanto tipo partícula."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61a11d0a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Apagador quântico"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72eb1531",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<table>\n",
    "    <td> $2º$ Com a PQO: </td>\n",
    "    <td><img src='fig_apagador.png' width='600'></td>\n",
    "    </table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c66cb8f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Parte do estado que obtivemos ateriormente, depois de aplicar o DF:\n",
    "\\begin{align}\n",
    "& PQO:\\ |\\psi_{6}\\rangle = U_{pqo}^{A}|\\psi_{5}\\rangle  \\\\\n",
    "& = -\\frac{1}{2}\\Big(U_{pqo}^{A}|0\\rangle_{A}\\big(|0\\rangle_{B'}+i|1\\rangle_{B'}\\big) + e^{i\\phi}U_{pqo}^{A}|1\\rangle_{A}\\big(|0\\rangle_{B'}-i|1\\rangle_{B'}\\big)\\Big)|0\\rangle_{B}|0\\rangle_{A'} \\\\\n",
    "& = -\\frac{1}{2\\sqrt{2}}\\Big(\\big(|0\\rangle_{A}+i|1\\rangle_{A}\\big)\\big(|0\\rangle_{B'}+i|1\\rangle_{B'}\\big) \\\\\n",
    "& \\hspace{2cm} + e^{i\\phi}\\big(|0\\rangle_{A}-i|1\\rangle_{A}\\big)\\big(|0\\rangle_{B'}-i|1\\rangle_{B'}\\big)\\Big)|0\\rangle_{B}|0\\rangle_{A'} \\\\\n",
    "& = -\\frac{1}{\\sqrt{2}}\\Big(|\\oplus\\rangle_{A}\\frac{1}{\\sqrt{2}}\\big(|0\\rangle_{B'}+i|1\\rangle_{B'}\\big) + e^{i\\phi}|\\ominus\\rangle_{A}\\frac{1}{\\sqrt{2}}\\big(|0\\rangle_{B'}-i|1\\rangle_{B'}\\big)\\Big)|0\\rangle_{B}|0\\rangle_{A'}.\n",
    "\\end{align}\n",
    "com $$|\\oplus\\rangle_A = (|0\\rangle_A + i|1\\rangle_A)/\\sqrt{2},\\ |\\ominus\\rangle_A = (|0\\rangle_A - i|1\\rangle_A)/\\sqrt{2}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81af17d9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Usa\n",
    "$$|\\psi_{6}\\rangle = -2^{-3/2}\\Big((1+e^{i\\phi})(|00\\rangle_{AB'}-|11\\rangle_{AB'}) + i(1-e^{i\\phi})(|01\\rangle_{AB'}-|10\\rangle_{AB'})\\Big)|0\\rangle_{B}|0\\rangle_{A'}$$\n",
    "__Sem pós-seleção__ nas medidas de Alice:\n",
    "\\begin{align}\n",
    "Pr(B'=0) & = Pr(B'=0,A=0) + Pr(B'=0,A=1) \\\\\n",
    "& = \\Big|\\frac{-(1+e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 + \\Big|\\frac{i(1-e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 \\\\\n",
    "& = \\frac{1}{8}(2+2\\cos\\phi + 2 - 2\\cos\\phi) \\\\\n",
    "& = 1/2.\n",
    "\\end{align}\n",
    "A visibilidade é nula novamente, como esperado pois a PQO não muda o emaranhamento que existe entre $A$ e $B'$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba63ad13",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Com pós-seleção__ nas medidas de Alice  (usa a regra de Bayes):\n",
    "\\begin{align}\n",
    "Pr(B'=0|A=0) & = \\frac{Pr(A=0,B'=0)}{Pr(A=0)} = 2\\Big|\\frac{-(1+e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 \\\\\n",
    "& = \\frac{1+\\cos\\phi}{2}, \\\\\n",
    "Pr(B'=0|A=1) & = \\frac{Pr(A=1,B'=0)}{Pr(A=1)} = 2\\Big|\\frac{i(1-e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 \\\\\n",
    "& = \\frac{1-\\cos\\phi}{2},\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41c8cbff",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "em que usamos\n",
    "\\begin{align}\n",
    "Pr(A=0) & = Pr(A=0,B'=0) + Pr(A=0,B'=1) = \\Big|\\frac{-(1+e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 + \\Big|\\frac{i(1-e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 \\\\\n",
    "& = \\frac{1}{2}, \\\\\n",
    "Pr(A=1) & = Pr(A=1,B'=0) + Pr(A=1,B'=1) = \\Big|\\frac{i(1-e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 + \\Big|\\frac{-(1+e^{i\\phi})}{2\\sqrt{2}}\\Big|^2 \\\\\n",
    "& = \\frac{1}{2}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1baf42fe",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Nos 2 casos teremos visibilidade máxima:\n",
    "\\begin{align}\n",
    "V_0 & = \\frac{Pr(B'=0|A=0)_\\max-Pr(B'=0|A=0)_\\min}{Pr(B'=0|A=0)_\\max+Pr(B'=0|A=0)_\\min} = \\frac{1-0}{1+0} \\\\\n",
    "& = 1, \\\\\n",
    "V_1 & = \\frac{Pr(B'=0|A=1)_\\max-Pr(B'=0|A=1)_\\min}{Pr(B'=0|A=1)_\\max+Pr(B'=0|A=1)_\\min} = \\frac{1-0}{1+0} \\\\\n",
    "& = 1.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dad1bb1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Teoria"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9b57922a",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np; import math; phmax = 2*math.pi; npt = 100; dpht = phmax/npt; pht = np.arange(0,phmax+dpht,dpht)\n",
    "PD0teoA0 = 0.5*(1+np.cos(pht)); PD0teoA1 = 0.5*(1-np.cos(pht))\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teoA0, label=r'$Pr(D_0|A=0)_{teo}$'); plt.plot(pht,PD0teoA1, label=r'$Pr(D_0|A=1)_{teo}$')\n",
    "plt.xlim(0,2*math.pi); plt.xlim(-0.1,phmax+0.1); plt.ylim(-0.01,1.01); plt.legend(); plt.xlabel(r'$\\phi$'); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0ced06b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simulação\n",
    "\n",
    "Simulação da placa de quarto de onda, que muda da base $\\{|0\\rangle,|1\\rangle\\}$ para a base $\\{|\\oplus\\rangle,|\\ominus\\rangle\\}$:\n",
    "$$U_{pqo} = SH.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6e8b5ee1",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 269.064x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_pqo():\n",
    "    from qiskit import QuantumCircuit\n",
    "    qc = QuantumCircuit(1, name='PQO')\n",
    "    qc.h(0)\n",
    "    qc.s(0)\n",
    "    return qc\n",
    "qcpqo = qc_pqo()\n",
    "qcpqo.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "11104f33",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 621.941x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qc_apagadorQ(ph):\n",
    "    from qiskit import QuantumCircuit\n",
    "    qc = QuantumCircuit(3)\n",
    "    qcimzic = qc_imz_ic(ph)\n",
    "    qc.append(qcimzic, [0,1,2])\n",
    "    qcpqo = qc_pqo()\n",
    "    qc.append(qcpqo, [0])\n",
    "    return qc\n",
    "qcaq = qc_apagadorQ(0)\n",
    "qcaq.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "e91b9780",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.         0.74525085 0.24331616 0.         0.25104603 0.75459221\n",
      " 1.        ] [0.         0.25526187 0.74143378 1.         0.74303705 0.24190801\n",
      " 0.        ]\n"
     ]
    }
   ],
   "source": [
    "# Simulação clássica\n",
    "from qiskit import Aer, execute; simulator = Aer.get_backend('qasm_simulator'); nshots = 2**13\n",
    "import numpy as np; import math; phmax = 2*math.pi; npe = 6; dth = phmax/npe; ph = np.arange(0,phmax+dth,dth)\n",
    "PA0sim = np.zeros(len(ph)); PA1sim = np.zeros(len(ph)); PD0A0sim = np.zeros(len(ph)); PD0A1sim = np.zeros(len(ph))\n",
    "for j in range(0,len(ph)):\n",
    "    qc = QuantumCircuit(3,2)\n",
    "    qcaq = qc_apagadorQ(ph[j])\n",
    "    qc.append(qcaq,[0,1,2])\n",
    "    qc.measure([0,2],[0,1])\n",
    "    job = execute(qc, backend=simulator, shots=nshots)\n",
    "    counts = job.result().get_counts()\n",
    "    if '00' in counts:\n",
    "        PA0sim[j] = counts['00']/nshots\n",
    "    if '01' in counts:\n",
    "        PA0sim[j] += counts['01']/nshots\n",
    "    if '10' in counts:\n",
    "        PA1sim[j] = counts['10']/nshots\n",
    "    if '11' in counts:\n",
    "        PA1sim[j] += counts['11']/nshots\n",
    "    if PA0sim[j] != 0 and '00' in counts:\n",
    "        PD0A0sim[j] = (counts['00']/nshots)/PA0sim[j]\n",
    "    if PA1sim[j] != 0 and '10' in counts:\n",
    "        PD0A1sim[j] = (counts['10']/nshots)/PA1sim[j]\n",
    "print(PD0A0sim, PD0A1sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "a866a798",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np; import math\n",
    "phmax = 2*math.pi; npt = 100; dpht = phmax/npt; pht = np.arange(0,phmax+dpht,dpht)\n",
    "PD0teoA0 = 0.5*(1+np.cos(pht)); PD0teoA1 = 0.5*(1-np.cos(pht))\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teoA0, label=r'$Pr(D_0|A=0)_{teo}$')\n",
    "plt.plot(pht,PD0teoA1, label=r'$Pr(D_0|A=1)_{teo}$')\n",
    "plt.plot(ph,PD0A0sim, 'o', label=r'$Pr(D_0|A=0)_{sim}$')\n",
    "plt.plot(ph,PD0A1sim, 's', label=r'$Pr(D_0|A=1)_{sim}$')\n",
    "plt.xlim(-0.1,2*math.pi+0.1); plt.ylim(-0.01,1.02); plt.legend(); plt.xlabel(r'$\\phi$'); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eedc62c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Experimento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "870d0f13",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import qiskit\n",
    "qiskit.IBMQ.save_account('dabd4674f7b3794f740813fec0c5478bfefdebb7d1dca9b7acd41e3f90ed2c8a8b80af26fb3236289fbfc70d0ea334829a836453ac46f96fee68abcb22495ef4', \n",
    "                  overwrite = True)\n",
    "qiskit.IBMQ.load_account()\n",
    "#provider = qiskit.IBMQ.get_provider(hub='ibm-q', group='open', project='main')\n",
    "provider = qiskit.IBMQ.get_provider(hub='ibm-q-research-2', group='federal-uni-sant-1', project='main')\n",
    "device = provider.get_backend('ibm_nairobi')\n",
    "nshots = 2**13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "60aa88a3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cmmx98dz31fg008xwpx0\n",
      "cmmx995gh50g008jgyk0\n",
      "cmmx99xcbtrg0087zb0g\n",
      "cmmx9anz31fg008xwpxg\n",
      "cmmx9b5gh50g008jgykg\n",
      "cmmx9bxz28fg008f8pyg\n",
      "cmmx9cnb9x9g0088qfw0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np; import math\n",
    "phmax=2*math.pi\n",
    "npe=6\n",
    "dth=phmax/npe\n",
    "ph=np.arange(0,phmax+dth,dth)\n",
    "job_ids=[]\n",
    "for j in range(0,len(ph)):\n",
    "    qc = QuantumCircuit(3,2)\n",
    "    qcaq = qc_apagadorQ(ph[j])\n",
    "    qc.append(qcaq,[0,1,2])\n",
    "    qc.measure([0,2],[0,1])\n",
    "    job = execute(qc, backend=device, shots=nshots)\n",
    "    jobid = job.job_id()\n",
    "    job_ids.append(jobid)\n",
    "    print(jobid)\n",
    "f = open(\"jobs_ids_apagador.txt\", \"w\")\n",
    "f.write(str(job_ids))\n",
    "f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "0de44b6b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.90186335 0.7398246  0.33489867 0.16843167 0.42368241 0.76683052\n",
      " 0.90854417] [0.10023795 0.37890521 0.79208876 0.94368197 0.74245209 0.32963279\n",
      " 0.10178042]\n"
     ]
    }
   ],
   "source": [
    "f = open(\"jobs_ids_apagador.txt\",\"r\")\n",
    "list_ids_apagador = f.read().replace(\"'\",\"\").replace(\" \",\"\").replace(\"[\",\"\").replace(\"]\",\"\").split(\",\")\n",
    "f.close()\n",
    "phmax = 2*math.pi; npe=6; dth = phmax/npe; ph = np.arange(0,phmax+dth,dth)\n",
    "PD0A0exp = np.zeros(len(ph)); PD0A1exp = np.zeros(len(ph)); PA0exp = np.zeros(len(ph)); PA1exp = np.zeros(len(ph))\n",
    "device = provider.get_backend('ibm_nairobi')\n",
    "for j in range(0,len(ph)):\n",
    "    job = device.retrieve_job(list_ids_apagador[j])\n",
    "    counts = job.result().get_counts()\n",
    "    if '00' in counts:\n",
    "        PA0exp[j] = counts['00']/nshots\n",
    "    if '01' in counts:\n",
    "        PA0exp[j] += counts['01']/nshots\n",
    "    if '10' in counts:\n",
    "        PA1exp[j] = counts['10']/nshots\n",
    "    if '11' in counts:\n",
    "        PA1exp[j] += counts['11']/nshots\n",
    "    if PA0exp[j] != 0 and '00' in counts:\n",
    "        PD0A0exp[j] = (counts['00']/nshots)/PA0exp[j]\n",
    "    if PA1exp[j] != 0 and '10' in counts:\n",
    "        PD0A1exp[j] = (counts['10']/nshots)/PA1exp[j]\n",
    "print(PD0A0exp,PD0A1exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "a68778cb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZWlri4+NDVFRUif0DBgxAq9WWO+5dSTJkpZraNrdl26z+TPnsOJcSM3niv8f4fFoAvdo6Kx2aEJUX+S1snwm6QvB5GJ78EixslY6q9plr4K//NQzNCfsv/DgfclMgaKEsIiQajBtpuTyzPow/bmfjbGtB8LQ+dG3dgOd71JDcwiI6/3Ov0mFw4c3h2FhULd0qTp79/PzQarUkJiayfv16du3axVtvvYVarSY83LDGwvjx41m7dq3x3JkzZ9KhQwcsLS1NtllWQl5QUIC1tTXm5vdfCnPbtm0cP36cTZs2odFojF8oIiMjadWqlclzgoODmTZtWoVtFy8+ea/U1FQcHR1LHevk5FRqkqqTkxNt2rQhLCysSotS1hVJyGuAu70V38zsx/TgE5yKTWXy+jA2TA2gv69LxScLobTTXxoqqaAH/7Ew5mNQW9R5GFmpKUTs28MDQ0bSzKkOv9CamcGIt8CmORxcDoffhrwMGLFSknJR78UmZ/PUJ6EkpOfRytGaL57rg49rM6XDEtVUnGy3b9/euM/FxYV3332XefPmGY9Rq9UsXbq0xLkJCQm4urqabNPFxQV3d3eT14yOjsbX19f4c1RUFFOmTCE9PZ3WrVuzadMmWrZsWWbMWq2WRYsW0b17dyZOnAhg7L2OjIxk+HDT83RGjx7NiRMnymy3mJ+fn8n9KhPv03q93uR+FxcXbt68afw5KyuLDRs28Morr1R4/domCXkNcbDR8OVzfZj91WkOX77F81+c5Mvn+tKrrZPSoQlRtnPb7ibjvZ+DUe+CmTILhWSnpnBs22Z8evWt24QcDIn3oNfBxhl2z4OwdWBhAw//s27jEKIKEtJzmfRpGAnpefi6NePL5/rQ0sG64hObCGuNORfeVH6ytvV9LL4UERFBYGAga9euRaVS4eDggLe3N2ZmZiWO6d+/f6ke4ry8vFK948XHl9U7npaWxokTJ5g9e7Zx36xZs1iwYAHjxo3j/fffZ8GCBQQHB5cZ84YNG7h06RJbtmwhPT0dMIx5b9asWbmVVpydnXFwqPiOjqmeeycnJ1JTU02+nj8PZQGwsrIqURLxxIkT/Pzzz/UiIZcx5DXIxkLNJ1N6MbC9CzkFRTz7+XHOx6crHZYQpl3aAztmYkjGp8Mj7yuWjNcbAc8bFj0C+PV9+PUDZeMRogy3s/KZvD6MG2m5eLnY8r8ZfSUZ/xOVSoWNhVrxh6me2vLo9XoiIyMJDAykd+/e9OrVC19f3xLJOBh6vHv16lXqfGdnZ9LS0ky2WVZC/uGHH5Kfn8+sWbMASExMJCoqylhiccaMGWzfvr3MmHNzc1myZAkATz31FE5OTsZHVlZWuRM7g4OD0Wg0FT4OHz5c6txOnTqVGiuen59PdHS0yYQ8NTWV5s2bA3D69GkmTpzImTNn6N69O1999RXJyclMnTqVfv360bFjRzZs2GA8Nz4+nscff5yOHTvStWtXfvrppzJf0/2QHvIaZqk25+NnejHls+OcjE1lymfH+XpmP3zd5BaiqEf+OATfTAWd1jCpcdT7igzPyEpNITvVMM4vMSa6xL8Atk7Odd9b3ns65GfBz4th/xKwaAZ9X6jbGIQoR3pOIc98dpw/bmXTytGar57vK2V3G5ErV66QnZ1Nt27dyjwmPz+fy5cv8/rrr5d6zs/Pj4MHD5ps01RCvnXrVlasWMG8efOMQ2Ti4uLw9PQ0fpmwt7dHo9GQnJxsTGjvtWrVKhISEti0aRMeHiUnE69evZq9e/ei0+lKfamA6g1ZGTVqFEuXLi0R144dO8jPz2fUqFEljtXpdFy7ds3YTs+ePRk2bBh//etfGTt2LDqdjhEjRrB8+XICAgLIzMykU6dOTJ48GY1Gw+jRo3nzzTd55JFHuHDhAkOGDCE+Pr7CuCtLEvJaYGOhZsO0ACZ9GkrkjQyeXh/G1ln98HS2UTo0IeBamKHMX1E+dHwUHv+PYRy1AiL27eHYts0l9v38yd3JSf3GT6T/hMl1HRYMeAXyM+GXd2DPa2DZDLpPqvs4hPiTrHwtUz8/TlRCBi7NLPnq+b60cpSe8cakePJleQn5+fPn0Wq1dO/evdRzAwYM4M033yxRq7y4zaKiIkJDQ8nPzycmJoZt27axe/duZs+ezfLly41tlFUZxlRvf0pKCu+88w7PPPMMkyaVfp+MiIhg586dREdHlxgTX6x58+Ymk/zKmDlzJmvXruXxxx9n8eLFJCUlMXfuXCZPnlyqh/zChQtkZ2czcOBA477Tp0/zxhtvAPDjjz9y6tSpEosKqVQqioqK2LdvH61ateKRRx4BoGPHjqSmplJUVFStSbD3koS8lthbafhiel+e/PgYvydlMXl9GNtm95NeDKGsxPOwaQIU5oDPYBi/wbCCpUIeGDISn159DaHFRPPzJ2sZ+sLLuHv5AIYecsU89H9QkAWh/4HvXgJLO+g0Wrl4RJNXoNXxwhcnOXs9DUcbDZue74uXSxOohtTEREREoFarS5U8vFd4eHiJKib3CgoKwsXFhT179hiTy+KEvHhIip2dHa1atWLAgAGEhobSt2/fEm14enoSFxdnnByZmZlJYWEhzs6l35NXrlxJQUEBK1asMBlrly5dAMPETlMJeXU4Ojpy4MABXn75ZcaOHYuNjQ0TJ07k7bffLnVsSEgIbdu2NZaDzMvLIyEhAS8vLwDOnDnDvHnzWLhwYalzz507xwMPPGD8OTIyEj8/vxpLxkHGkNcqZ1sLvnq+L22cbbiWksMLX5wir7B69T2FuG+ZibDpCchPB89AePIrUJee+FOXmjk54+7ta3jcScLdvXyM++p8uMq9VCoYvgJ6TgG9Dr6dATdOKxePaNL0ej3/t+McR6MNdcaDp/XBr4Wd0mGJWrBkyRIKCwtNTswsNm3aNAoKCtBoNKWes7CwYMqUKcal64vb1Ov1xkdGRgZRUVGsX7++VDIO4O7ujp+fHzt37gRg/fr1jBkzxmQs7777LtnZ2WWWNRw8eDB6vb7M86urQ4cO7N27l+zsbG7dusWaNWtKrVAKsGXLFqZPn27s5b969Sru7u7Gnz08PNi7dy/5+fkA3L59m+vXrwPQunVr4zj47Oxs/v73vxur3dQUSchrmbu9FRunBeBgreHs9TTmbQ2/r0UChKiWwlzYMhEy4qC5L0za0jTqjFeXSgWPfFhyRc/0she4EKK2rDsczbZTcZip4KPJPenm6ah0SKIee+211wgLC+PMmTP33ca6detYvnw5HTp04Pvvv+ett96qwQjr1uHDh7l69WqJaipeXl64ubnRsWNH1q1bx9NPP423tzf+/v50796dcePGkZeXBxgmqtrZ2eHv709AQABjx47l6aefrtEYZchKHfB2bca6p3sy5bPj7IpIwNu1GXOHdlA6LNFU6HSwczbcOGVYAGfSN4Z/6xlbJ2f6jZ+o7DAVU8zVhqE9G4ZD0gXY/CRM+9EwrlyIOrDnXALv/HgJgDce82dQh9I1poW4V4sWLdi4cWO1lon39/fn5MmTNRiVcjIyMvjiiy9KlIi0tLQstWrnvVVV7qVWq/nyyy9rMULpIa8z/X1cWDHGMLt5zf7f2XlGetlEHTm0Es7vADONYZhKcx+lIzKpmZMz/SdMVnaYSlms7GHiFrB1hZvnYPsM0MnwM1H7IuLS+Ps3ZwF4tn87pvRrp2g8ouGYMGECw4YNUzqMemH06NE8+uijSodRLknI69ATAZ7MHOQNwOvbIjgVm1LBGUJUU/jXhkohAKNXQbsHFQ2nQXNqC0/9D8wt4VII/CyLBonalZCey/PBJ8kr1BHk58qiR0rXVRZCKXq9vtRS9uL+SUJex+YP78iwzu4UFOl44YtTJKTnVnySEPfjxin4fo5he8DfoEfNjndrkjz7wF//Y9g+9m84+z9l4xGNVl5hETO+OElSZj4d3JuxdmIP1ObykS1EYyV/3XXMzEzFqqe607mlPcnZBcz53xkKi3RKhyUam5wUw8I/RQXg9wg8/C+lI2o8uo6HQfMN27vmws2yV6AT4n4t+eECkTcycLLR8NnUAOysSlfTEEI0HpKQK8DGQs26p3tiZ6XmVGwqb++5qHRIojHR6WDHTEi/Ds7eMGadYgv/NFqDFoDPw4bKK99MgbwMpSMSjci3p+LYfPwaKhWsfqpHg1hULik2g50fnCYpVv4WhLgf8imtkLbNbXl/gmEVrvVHYvgxMkHhiESjceQD+P0nUFvBE1+AlYPSETU+ZmYw9lOwbw0p0YahQVLOVNSAizcz+MfOcwC8+nB7/tJAKqpcDL3JjctpXAq9qXQoQjRIjSohb2jf0If5t2DmXwyTPF/bGkHM7WyFIxIN3h+H4eCd5Y8feR9adFU2nsbMtjlM2GioXnPhOwj7r9IRiQYuK1/Li1+dJq9Qx8D2Lrw8uGZXNaxpGcm5JMVmcOtaJldOJgLw+8lEbl3LJCk2g4xkmSMlRGU1qjrk935Dd2trr3Q4lTJvuB9nrqVx/GoKs786xc6XBmClqbmlWEUTkpEA3z5nWFWyx9MyibMueAbA8OWw53X4aRG06mWY+ClEFen1euZ/G8Eft7Np6WDF6qd6YG6mUjqscn35j2Ol9uVmFvLNihPGn1/67+C6DEmIBqvB95A39G/oGnMz1k7qgUszCy7ezORf351XOiTREBVpYdt0yL4F7l1g1HtKR9R09HkB/MeCTmuYSJsj5UxF1X1xLJbdEQmozVR8NLknzrYWSodUoSHTOqMq40uDykzFkGmd6zgiIRquBt9D3hi+obvbW7FmYg+eXh/G1yevE+TnysiuLZUOSzQkv30I146ChZ1h3LjGWumImg6VCh5bY1gwKPl3+OEVeOJLw34hKuFyYibLQ6IA+L9RnejZpv6tpGuKX98WOLe0LfF5W2zCgt64trFTICohGqYG30PeWL6h9/dxYXaQYQXFhTvOkZiRp3BEosG4cQoOvWXYfuT9ersSZ6NmaQfj1hvGk0f9IPXJRaXla4t4dctZCrQ6HvJzZdqAdkqHdH9Uf/pXCFElDT4h9+vbggkLept8bsKC3vj1bVHHEd2/Vx/uQNdWDqTlFDJvazg6nVRtEBUoyIbtLxiGS/iPhQeeUDqipsujOzz0f4btPa9DSoyi4YiG4YOfLhOVkIGzrQVvj38AVQO7s2Jtp8HG3gK3NnYMmuSHWxs7bOwtsLaTuulCVEWDT8hLaODf0C3UZnz4ZHesNGb8+vttgo9dVTokUd/9tAiSr4B9K3j0AxkmobQBr0Kb/lCQZagFX6RVOiJRjx2LTuaTX/8A4K2xXXGzs1I4oqpr5mTFlOX9Gb+gN13+0orxC3ozZXl/mjk1vNdS3yxatAiVSmV8ODk5MXLkSC5dulSp8wMCAlizZk25bdra2tK1a1cWLlxISkrV5r+oVCoOHTpU5vOTJ09GpVKxbt26KrVbFVeuXGHWrFl0794dtVpNly5dTB63bNkyhg4dWmtx1IRGkZA3pm/ovm7N+McjhmE2K/dc5HJipsIRiXrr8l44ucGw/dd1YN0wxp02ambmMOa/YGkP18MMY/uFMCE9t5D/981Z9HqY2MeTYf4N527un5lrzIw9+yqVCnNNo0gtFBcREUGXLl04duwYx44d44MPPiA0NJSxY8dWeO727duJjY1lxowZ5ba5Y8cOnnzySdavX0/Pnj1JSKiZNVHCw8PZvHkzAOfOnauRNk05f/48u3fvxtfXl86dyx6iPGfOHMLCwjhw4ECtxVJdKr2+4axmkZGRgYODA+np6djblyxrWFSow0xt+Man1+vRafUN9k1Br9czfeMJDl66RaeW9ux8qT+WaimFKO6RdQvW9TNUVek3x1B6T9Qf4V/DjhfATA3P/WQohyjEPV7dcobvzsbTrrkNu18ZiK1lg6+xUK7yPr9rQl5eHjExMXh5eWFl1Th659u1a0dQUBAbN2407lu0aBHLly/n+vXrtG7dutQ5hYWFqNVqBg0aRM+ePVm1alWpNgcPHsyGDRtK7A8PD6d3795MnTqV9evXVyo+lUrFwYMHCQoKKvXciBEjOHPmDB4eHtjZ2fHLL79Uqs2q0ul0mN1ZifrZZ5/l5MmTREZGmjx26tSppKWl8d1339VKLGWp7O9mw8xYTWhM39BVKhVvj38AZ1sLohIy+PDn35UOSdQnej388KohGXfzh8GLlY5I/NkDT4D/GMPY/u0vQGH9Lr8q6tYP4fF8dzYeczMVHz7ZvdEn46Lq0tPTiY2Nxd/fv8R+OztD5ZrcXMN7iqurK8uWLWPhwoV4eHjg4OBATEwMv/76K+PHjzfZZteupReM69atG0FBQezatavasR86dIi9e/eyePFiAgICykyQa0JxMl4ZEyZMICQkhFu3btVaPNXRcLPWRs7Nzoq3xhr+aD75JZqIuDRlAxL1R+S3cGm3oaLHuE9B0zh6gxoVlQoe+QDsWhrG+B9aqXREop5IzsrnX98b1pt46SFfejSQEocNkl5vmPiu9OM+BiJEREQAlBqGceTIERwcHPDy8iI+Pp7bt2/z0UcfER8fz2effcaOHTvYv38/Go2GgIAAk22aSsgBfHx8SExMpKioqMrx3mv+/Pl4e3szc+ZMOnfuTGpqKjdu3CjzeL1ej1arrfBR3QEdAwYMQKvVljvuXUnytbweG+bfgse6efB9eDyvb4vg+zkPYqGW71BNWvZtQwUPgEGvg7t/+ccL5dg4w6Mfwuan4Oha6PxXaNVT6aiEwpb8cIGU7AI6trBjzkO+SofTuBXmwAoPpaOA/4sHC9sqnVKcPPv5+aHVaklMTGT9+vXs2rWLt956C7VaTXh4OADjx49n7dq1xnNnzpxJhw4dsLS0NNlmWQl5QUEB1tbWmJvf/xDZbdu2cfz4cTZt2oRGozF+oYiMjKRVq1YmzwkODmbatGkVtl3W8JjKcnJyok2bNoSFhTFhwoT7bqe2SEJez/1rdGeOXLnNxZuZ/PdwNK883F7pkISS9syHnGTDapwD/qZ0NKIifiOhy3iI3AbfzYEXDoG6/q/AKGrHvguJfB8ej5kK3hn/gHSwiDIVJ9vt29/9zHdxceHdd99l3rx5xmPUajVLly4tcW5CQgKurq4m23RxccHd3d3kNaOjo/H1vfslMSoqiilTppCenk7r1q3ZtGkTLVuWvWihVqtl0aJFdO/enYkTJwLQqVMnwJCQDx8+3OR5o0eP5sSJ0otL/Zmfn1+Fx1TExcWFmzdvGn/Oyspiw4YNvPLKK9Vuu7okIa/nmjez5F+jO/PqlrOsPfA7I7q0oIO7rH7WJF3aY0jsVGbw2FpJ7BqKkW/DHwch6Tz8tspwZ0M0ORl5hSzaaRhLO2OgNw+0dlQ2oKZAY2PonVaaxqbKp0RERBAYGMjatWtRqVQ4ODjg7e1dYsx0REQE/fv3x9HRscS5eXl5pXrHi48vq3c8LS2NEydOMHv2bOO+WbNmsWDBAsaNG8f777/PggULCA4OLjPmDRs2cOnSJbZs2UJ6ejpgGPPerFmzciutODs74+DgUObzxarTc1/MysrKOP4e4MSJE/z888/1IiGXr+cNwGPdPBjSyY3CIj2vb4ugSBYManry0mHXXMN2/5dl6ENDYusCI98xbB9+B5KilI1HKGJlSBQ3M/LwcrHl70M7KB1O06BSGYaKKP2o4voQer2eyMhIAgMD6d27N7169cLX17fUBMbw8HB69SpdwcnZ2Zm0tDSTbZaVkH/44Yfk5+cza9YsABITE4mKijKWWJwxYwbbt28vM+bc3FyWLFkCwFNPPYWTk5PxkZWVVe7EzuDgYDQaTYWPw4cPl9lGZaWmptK8eXMATp8+zcSJEzlz5gzdu3fnq6++Ijk5malTp9KvXz86duxYohpNfHw8jz/+OB07dqRr16789NNP1Y7nXtJD3gCoVCqW/bUrYX8c5uz1ND7/LYbnB3orHZaoSz8thsx4cPaBoIVKRyOqqss4OLcNLu8xDF157idDzXLRJBy9cpvNx68DhgWArDTy/16U7cqVK2RnZ9OtW7cyj8nPz+fy5cu8/nrpO25+fn4cPHjQZJumEvKtW7eyYsUK5s2bZxwiExcXh6enp7F6nb29PRqNhuTkZGNCe69Vq1aRkJDApk2b8PAoOW5/9erV7N27t0SJwnvV1ZAVnU7HtWvXjO307NmTYcOG8de//pWxY8ei0+kYMWIEy5cvJyAggMzMTDp16sTkyZPRaDSMHj2aN998k0ceeYQLFy4wZMgQ4uNr7g6MJOQNRAsHK/7vkU4s3H6O9366xNDO7rRtXrVJIqKB+uMwnL5zm/CxtaCxVjYeUXUqlWEl1Y9+gxsnIXQd9J+jdFSiDuQWFLFgu+F2/dOBbejrXTqZEeJexZMvy0vIz58/j1arpXv37qWeGzBgAG+++SZxcXHGWuXFbRYVFREaGkp+fj4xMTFs27aN3bt3M3v2bJYvv7ueRVkVTVQmevtTUlJ45513eOaZZ5g0aZLJ17Nz506io6NLjIkv1rx5c5NJfmXk5OQQEhICQGxsLBkZGWzbtg2AQYMGlRhLf+HCBbKzsxk4cKBx3+nTp3njjTcA+PHHHzl16lSJxZRUKhVFRUXs27ePVq1a8cgjjwDQsWNHUlNTKSoqqpGhNCAJeYPyVIAnP4THczQ6mcXfnSd4WoDJPw7RiGjzYdffDdsBz0O7AcrGI+6fvQcMW2qoIX9wOfj/FRxKL+whGpe1B37nWkoOHg5WzB/RUelwRAMQERGBWq0ud+XJ8PDwElVM7hUUFISLiwt79uwxJpfFCXnxkBQ7OztatWrFgAEDCA0NpW/fviXa8PT0JC4uDr1ej0qlIjMzk8LCQpydnUtdb+XKlRQUFLBixQqTsRYvZx8ZGWkyIa+OpKSkUhVTin/+c1WWkJAQ2rZtaywHmZeXR0JCAl5eXgCcOXOGefPmsXBh6bvQ586d44EHHjD+HBkZiZ+fX40l4yBjyBsUlUrF8jFdsTA345fLt/gx8mbFJ4mG7bc1kBINzVrAw/9SOhpRXT2mQJt+hnJsPy5QOhpRy64kZfLpr38AsOTxLthZaRSOSDQES5YsobCw0OTEzGLTpk2joKAAjab075SFhQVTpkwxLl1f3KZerzc+MjIyiIqKYv369aWScQB3d3f8/PzYuXMnAOvXr2fMmDEmY3n33XfJzs4us6zh4MGD0ev1ZZ5fHe3atSvxuu59/LlE4pYtW5g+fbqxI/Pq1au4u7sbf/bw8GDv3r3k5+cDcPv2ba5fNww1a926tXEcfHZ2Nn//+9+N1W5qiiTkDYyXiy2zgnwAQz3brHytwhGJWpMSA7++Z9gevhysan65aVHHzMzgkfdBZQ5RP8Dlmp0UJOoPvV7P4p3nKSzSM6STG0M7my41J0RteO211wgLC+PMmTP33ca6detYvnw5HTp04Pvvv+ett96qwQjr1uHDh7l69WqJaipeXl64ubnRsWNH1q1bx9NPP423tzf+/v50796dcePGkZeXBxgmqtrZ2eHv709AQABjx47l6aefrtEYZchKA/RikA87z9zgWkoOa/b/zv+N6qR0SKKm6fWGmuPaPPAaZJgUKBoHd38InA3H/g17XgOvgTIvoBH6PjyeY38kY6Ux41+jZQEvUbdatGjBxo0bq7VMvL+/PydPnqzBqJSTkZHBF198UaJEpKWlZalVO++tqnIvtVrNl19+WYsRSg95g2SlMWfJ44Y3+M+OxHDpZqbCEYkadykEft8LZpo7PaoyV6BRCVoAdh6QehWOrFI6GlHDMvIKWbrLUN7y5cHt8XSueh1qIaprwoQJDBs2TOkw6oXRo0fz6KOPKh1GuSQhb6Ae8nNjhH8LinR6Fu08V+aMaNEAFWQbescBBrwCLrI6a6NjaQcjVhq2j3wIydHKxiNq1Ac/XeZ2Vj7errY8P9BL6XCEqBWmxmmL+ycJeQP2z9GdsbEw58TVVL49fUPpcERN+eVdSL8ODm1gYM1OGhH1SOfHwedhKMqHkNcMw5REgxd5I50vjl0FYOnjXbBUS81xIUTFJCFvwDwcrXn1YUPv6YqQKNJyChSOSFTbrUtwdK1he9Q7YCG3uhstlQpGvQvmlhC9Hy58p3REopp0Oj2Ldkai0xtWWB7g66J0SEKIBkIS8gZu+oNetHdrRkp2Aav2/a50OKI69HpDKTydFjqMBL+RSkckaltzH3jwb4btnxZBYa6i4Yjq+fZ0HGevp9HMUs2iR2SyvRCi8iQhb+A05ndn8H8ZGsuVJJng2WBd3gvRB8DcAkaYXmBBNEID/gb2rQ3DlIrvjogGJytfyzt7LwHw8mBf3OytFI5ICNGQSELeCDzY3oUhndwp0ulZtjtK6XDE/dAWwN7/M2wHzgZnb2XjEXXHwgaGLjFsH/kQMuKVjUfcl/8cvMKtzHzaNrfh2QHtlA5HCNHASELeSPzjkU5ozFUcunSLg5eSlA5HVNXxTwwrctq6yUTOpqjLOPAMNKzgue8NpaMRVXQ9JYf1R2IA+MeoTjKRUwhRZZKQNxJeLrZMG2Aor7Vs1wUKi3QKRyQqLfs2HH7HsP3wYlmRsylSqe6WQYz4Gq6fUDYeUSUrQqIo0OoY4NtcVuQUQtwXScgbkTmDfWlua0H0rWy+PBardDiisg4sg/x0aPEAdJ+sdDRCKa163v3//+MC0MmX6oYg9I9k9kTexEwFix/tjEoW8RJC3AdJyBsReysN84b7AbBq32VSsqUMYr13MxJOBxu2R74NZnKru0l7+J9g0QxunIRzW5WORlSgSKdnyQ8XAJjUtw0dW8jdLSHE/ZGEvJF5orcnnVrak5Gn5cOfLysdjihPcZlDvQ46/xXa9lc6IqE0uxYwcK5he98bhlVbRb31zcnrRCVkYGelZu5QP6XDEUI0YJKQNzLmZir++WhnADaFSRnEeu3SHrj6q2FhmKFvKh2NqC8CXwLHNpAZL2UQ67GsfC3v/2Qoc/jqw+1xtrVQOCIhREMmCXkj1M+nOcM6u6PTw9s/XlI6HGFKkfZuNY1+L4JTW0XDEfWIxgqG3CmD+NsayJKqSfXRp7/8we2sAto1t2FKv3ZKhyMaoUWLFqFSqYwPJycnRo4cyaVLlftcDwgIYM2aNeW2aWtrS9euXVm4cCEpKSlVik+lUnHo0KEyn588eTIqlYp169ZVqd2qunz5MiNGjMDW1hY3NzdeffVVcnNLLrK2bNkyhg4dWqtxVFeVE/LKvHBTsrOzWbBgAT4+PtjY2NC+fXveeOMN8vPz7ytwUb7XR3TE3EzFzxcSOR5TtT8yUQfOfgW3L4G1Mzz4d6WjEfWN/xjw6AmF2XDoLaWjEX+SlJnHp7/+ARjeay3U0rfV2BTpijhx8wQhf4Rw4uYJinRFdR5DREQEXbp04dixYxw7dowPPviA0NBQxo4dW+G527dvJzY2lhkzZpTb5o4dO3jyySdZv349PXv2JCEhoUZiDw8PZ/PmzQCcO3euRto0JS0tjcGDB5OZmcm3337Le++9x6ZNm0q97jlz5hAWFsaBAwdqLZbqUlfl4OIX3rZtW7799luSkpKYO3cuycnJfPXVV+WeO3v2bHbu3Mny5cvp0qULx48fZ/HixaSkpJT6Bieqz9etGU8GePK/sGus3BPF9tn9ZfZ/fVGQDQfvlLgb9DpYOSgbj6h/VCoYthQ2PgKnNhoWi3Jpr3RU4o7V+34np6CI7p6OjOzSQulwRA3bF7uPt46/RWJOonGfu407C/osYEjbIXUWR0REBEFBQQQGBgIQGBhIdHQ0y5cvJy4ujtatW5c6p7CwELVazapVq5g0aRLW1tal2hw8eLCxTYBhw4YxevRoevfuzeLFi1m/fn21Y58/fz6urq54eHgQGRlZ7fbK8vHHH5OamsrZs2dxcXEBQK1WM3nyZP7xj3/QqVMnABwdHRkzZgyrV69m8ODBtRZPdVTpa33xC//uu+8YMWIEU6ZMYc2aNWzatImoqLJXiNRqtWzdupW///3vvPzyyzz00EPMnz+f559/nq+//rraL0KY9rch7bGxMOfMtTR+jLypdDii2LH/QNZNcGoHvZ9TOhpRX7V7EDqMAH0R7F+idDTijuhbWWw5cR2AhSM7SkdHI7Mvdh9zD80tkYwDJOUkMffQXPbF7quTONLT04mNjcXf37/Efjs7OwDjyARXV1eWLVvGwoUL8fDwwMHBgZiYGH799VfGjx9vss2uXbuWul63bt0ICgpi165d1Y790KFD7N27l8WLFxMQEFCrCXlISAhDhgwxJuMA48aNw9LSkpCQkBLHTpgwgZCQEG7dulVr8VRHlRLyqrzwe+n1erRaLQ4OJXsCHR0d0ev1VQxZVJabnRXPDzQswf7O3kuyWFB9kHULfltt2B68GNQyEUyUY8gboDKDqB/g+nGloxHAOz9epEinZ0gnN/p6N1c6HFGDinRFvHX8LfSUzkuK9719/O06Gb4SEREBQOfOnUvsP3LkCA4ODnh5eREfH8/t27f56KOPiI+P57PPPmPHjh3s378fjUZDQECAyTZNJeQAPj4+JCYmUlRUvdc3f/58vL29mTlzJp07dyY1NZUbN26UeXxxjljRw1S+GBUVZewFL2ZpaYmPj0+pjuIBAwag1WrLHfeupCol5FV54ffSaDRMmzaNtWvXEhYWRlZWFgcPHuTTTz9lzpw5ZZ6Xn59PRkZGiYeomhf+4o1LMwtibmez5fg1pcNp1LJSUzi6dRNZqeWM2f/lHSjIhJbdwb/icYCiiXPrBN0nGbZ/WmwolSkUc/JqCnvPJ2KmgvkjOiodjqhhp5NOl+oZv5cePTdzbnI66XStx1KcPPv5+aHVarlx4wZLlixh165dLFy4ELVaTXh4OADjx48nODiYkSNHMnz4cE6ePEmHDh2wtLQ02WZZCXlBQQHW1taYm9//ehjbtm3j+PHjLF26FI1GY/xCUV4veXBwMBqNpsLH4cOHS52bmpqKo6Njqf1OTk6lJqk6OTnRpk0bwsLC7vv11aYqjSGvygv/s3Xr1jFr1qwS45Zefvll/vnPf5Z5zsqVK1myRG7VVkczSzWvPtyexd+dZ9W+3xnTszXNLKv0v11UUnZqCse2bcanV1+aOTmXPiA5Gk5uMGwPWwpmMhFMVELQ/8G5b+F6KFwKgY6PKB1Rk6TX61m55yJgWO+hvbudwhGJmnYrp3JDGSp7XHUUJ9vt29+dO+Li4sK7777LvHnzjMeo1WqWLl1a4tyEhARcXV1Ntuni4oK7u7vJa0ZHR+Pr62v8OSoqiilTppCenk7r1q3ZtGkTLVu2LDNmrVbLokWL6N69OxMnTgQwduJGRkYyfPhwk+eNHj2aEydOlNluMT8/07X+TQ0b0+v1Jve7uLhw82bFQ3j/+OMPFi1axP/+978Kj60pVc7MqvLC77VgwQJ27drFJ598gp+fH6dOneJf//oXTk5OZSbdCxcuZO7cucafMzIy8PT0rGrITd5Tfdqw4berxNzO5pPD0cwdJgtYKGL/m6DTgu9Q8PqL0tGIhsKhlWFS55EP4Od/QfvhYC5fquva3vOJnIpNxUpjxt+HdlA6HFELXG1KJ7HVOa46IiIiCAwMZO3atahUKhwcHPD29sbsno6ciIgI+vfvX6qjNC8vr1TvePHxZfWOp6WlceLECWbPnm3cN2vWLBYsWMC4ceN4//33WbBgAcHBwWXGvGHDBi5dusSWLVtIT08HDGPemzVrVm6lFWdn51JDmk0x1XPv5OREamqqydfz5xEdAFZWVpWqDOjt7V2nyThUcchKeS/cycmpzPMiIyN57733+Pjjj5kxYwZ/+ctf+Pvf/87SpUtZsWIFSUmm6+xaWlpib29f4iGqTmNuxuvDDUn4+iMx3M6SUpM1JSs1hcQ/rhgeMdEAJMZEG/cZh6/En4ELOwEVDJW7PqKKHvyboURm8u8QXrcfEgKKdHreu7MI0HMPeuFub6VwRKI29HTribuNOypMdzCqUNHCpgU93XrWahx6vZ7IyEgCAwPp3bs3vXr1wtfXt0QyDoYe7169epU639nZmbS0NJNtlpWQf/jhh+Tn5zNr1iwAEhMTiYqKMpZYnDFjBtu3by8z5tzcXGPn6lNPPYWTk5PxkZWVVWtDVjp16lRqyHR+fj7R0dEmE/LU1FSaN7879yMkJITAwEB69OiBv78/p08bhiO99NJLbNiwwbg9Z84chg4dSqtWrXjvvfcIDg5m0KBBtG7dmv3795f52qqiSt0s5b3w6dOnl3nehQsXAOjevXuJ/d27d0er1RIbG4ubm1tVQhFVNKJLC7q1diA8Lp3/HIzmn6M7V3ySqFDEvj0c27a5xL6fP7m7umK/8RPpP2EyHFhm2PHAk+Becta8EBWycoCB/w9++gccetvwe6Qu3QMmasfOMze4kpSFg7WGmYN8lA5H1BJzM3MW9FnA3ENzUaEqMbmzOEmf32c+5mb3P8a6Mq5cuUJ2djbdunUr85j8/HwuX77M66+/Xuo5Pz8/Dh48aLJNUwn51q1bWbFiBfPmzTMOkYmLi8PT09M4+sHe3h6NRkNycnKJhLbYqlWrSEhIYNOmTXh4eJR4bvXq1ezduxedTlfqSwVUb8jKqFGjWLp0aYm4duzYQX5+PqNGjSpxrE6n49q1a8Z2ioqKmDlzJufOncPR0ZHc3Fzj6z179izPP/+8cbtLly78+OOPXLx4kd69e/Pvf/+bw4cP89lnnxEcHMzDDz9cYfwVqVJCXpUXfq+2bQ2rEJ46dYo2bdoY9588eRKAdu3aVTVuUUUqlYr/N8yPKRuO81VYLM8P9MLD0briE0W5HhgyEp9efQFDz/jPn6xl6Asv4+5l+NC2dXKG2KNwZR+YqSFogZLhioYs4Dk49m/IiIOTn0PgLKUjahIKtDo+3HcZgFmDfLC30igckahNQ9oO4YOgD0zWIZ/fZ36d1CEvnnxZXkJ+/vx5tFptqY5OMFQTefPNN0vUKi9us6ioiNDQUPLz84mJiWHbtm3s3r2b2bNns3z5cmMbZVXAMzU8OSUlhXfeeYdnnnmGSZMmmXw9O3fuJDo6usSY+GLNmzc3meRXxsyZM1m7di2PP/44ixcvNq6PM3ny5FI95BcuXCA7O5uBAwca99nY2PDKK6/wxBNPMGLECNRqNTqdjosXL+Lv749Op+P8+fP88MMPmJubo1Kp8PHx4bnn7pYsrsxwm8qoUkJe2Rf+3HPPERwcjFarBaB379706dOHWbNmkZiYiJ+fHydOnODNN9/kySefNDn5QNS8ge1d6OPlzPGYFNYe+J2VYx9QOqQGr5mTc6kJnO5ePrh735kYo9fDjjsTbno8A85edRyhaDQ01oaFpHb9HX59D3o+Axa2SkfV6H198jpxqbm42lkytX9bpcMRdWBI2yE85PkQp5NOcyvnFq42rvR061nrPePFIiIiUKvVpUoe3is8PLxEFZN7BQUF4eLiwp49e4wrVhYn5MVDUuzs7GjVqhUDBgwgNDSUvn37lmjD09OTuLg44xzBzMxMCgsLcXYuXbBg5cqVFBQUsGLFCpOxdunSBTAMXzaVkFeHo6MjBw4c4OWXX2bs2LHY2NgwceJE3n777VLHhoSE0LZtW2M5SHNzcyIiIti7dy+ffPIJ//nPfwgJCeH333+nbdu2WFhYcOnSJTw9PY2v+8yZMzz44IPGNsPDw8v94lQl+iq6dOmSftiwYXobGxu9i4uL/uWXX9bn5OSUOGbq1Kn6PzedmJiof+GFF/Tt2rXTW1lZ6du3b69fsGCBPjMzs9LXTk9P1wP69PT0qoYt7jgek6xvO3+X3nvhbn3MrSylw2lUbkb/rn/viUf0N6N/v7vz95/1+n/Z6/Vvuur16TeUC040DtoCvX7VA4bfqV/eVzqaRi+3QKsPWPazvu38XfqNv8UoHU6DVtuf37m5ufoLFy7oc3Nza6X9hmbu3Ln6hx56qFptDBw4UL99+3a9Xq/Xf/DBB/pnnnmmxPOA/uDBg9W6Rl3q0aOHfsmSJcafL168qNfpdHq9Xq//6aef9IMGDdLr9Xr9li1b9NOnTzduT5061XjO3Llz9R9//LHx5wcffFB/6tSpcq9b2d/NKk/V79ChA3v37i33mI0bN7Jx48YS+9zc3Pj444+rejlRwwLaORPk58qhS7dYte8yq57qoXRIjYatkzP9xk80DFMBQ+/4/ju9431mgL1H2ScLURnmGkMZxB0vwG+roPd0sHZUOqpG64tjV0nKzKeVozVP9ZEKX6LheO211/Dx8eHMmTP06HF/n/Pr1q1j6tSpzJ8/n1atWrFp06YajrLuHD58mKtXr/LKK68Y97333nscPnyYZs2a4ezsbMxR7/1vdubMmRITZ0+fPm0s6ajX64mKijLeAagulV7fcFaayMjIwMHBgfT0dKm4Ug2RN9J5dO0RVCr48dW/4NdC6unWigvfwzfPgEUzeDUcbF0qPkeIiuiKYF1/uHUR/vIaDF6kdESNQlJsBke/vUL/cb64tbUnM6+Qv7xzkNScQt4Z/wBP9JaEvDpq+/M7Ly+PmJgYvLy8sLKSKjhgmKzp4ODAsGHDaqV9lUrFwYMHCQoKqpX2a9IPP/yASqXi0UcfrfNrV/Z3U1YmaYK6tHJgVNcW6PXwwc+XlA6ncdIVwcE7E2QCX5RkXNQcM3N46B+G7dB1kH1b2XgaiYuhN7lxOY1LoYZFQzYcuUpqTiHerraM7dFK4eiEqLoJEybUWjLe0IwePVqRZLwqJCFvouYO7YCZyrDYRfj1NKXDaXzObTP0YFo5Qv85SkcjGptOo6FldyjIgiMfKh1Ng5WRnEtSbAa3rmVy5aShosbvJxOJvpTCzgN/YK9TMXdoB9Tm8lEpxJ/p9foG0TveUMi7TBPl62bHX+/0+rz/82WFo2lkirRwaKVhe8CrhhrSQtQklQoeXmzYPv4pZCQoG08D9eU/jrF15Um+WXGC3MxCAHIzC/nxw7OMT9EwM8OKUV3KXipcCCFqiiTkTdjfHu6AuZmKXy7f4vS10iuwivsU8TWkxoCNC/SdqXQ0orHyeRja9IOifMMET1FlQ6Z1BjPT06iK0NNiWCvMzEyv2iiEEDVJEvImrE1zG8b1NPSSr973u8LRNBJFWvjlXcP2gFelTrSoPSrV3YWmTn4uveT34XqLSL71f9/kczu6vod9z2t1HJEQoqmShLyJm/NQe8zNVBy+fItTsdJLXm339o4HPFfx8UJUh9cg6SW/T0W6It46/pZxeXQ9uhL/Arxz4h2KdEWKxCeEaFokIW/i7vaS61i2/wdC/gjhxM0T8iF0P6R3XNQ16SW/b6eTTpOYk0iuJpMcTQa3bK9z2PtrbtleJ0eTQa4mk5s5NzmddFrpUIUQTUCVFwYSjU+PjnHsTnubK+bpzP/VsM/dxp0FfRYwpO0QZYOr5wrj49Gm3rmzcGkPRMeBtSvYDoDz51E7OaHxkAWBRO0ojI9Hm+MKFj3h5jnY8gYMuLvwhfz+le1Wzi0Asi3T+arnG+hURaCCKLejmOnN0ZkVlThOCCFqkyTkTdy+2H2sPLUQM03JiU1JOUnMPTSXD4I+kKS8DIXx8USPGIm+oOCeva6Gf757GgCVhQU+P+6RpEjUuD///uWpW3At/Bxt1jyJldaQTMrvX9lcbVyN28XJNwAqDMm5ieOEEKK2yJCVJuzPYyhdszwZff4lXLM8jfvePv62DF8pgzY19U/JeGn6goK7PehC1KA///7la8y50sKZfI25cZ/8/pWtp1tP3G3cUWG6iooKFS1sWtDTrWcdRyaEaIokIW/CisdQFutwK4BWGR3ocCsAAD16GUMphGiUzM3MWdBngcnnipP0+X3mY25mbvIYIYSoSZKQN2G3cm7RLN8Jl6zWuGS1xue2oSfI53ZP475m+U4yhlKIeipPbU66tQXp1hZkWFsCkGFtadyXp5ZksjxD2g7hzX7voNeWXLzL3cZdhusJIeqUjCFvwlxtXHn69BvGn4uHqVhrmzH+3Gt3j3vMrq5DE0JUwrXm9lxp4Vxi3zlPN+O2780UOtZ1UA3M7zHtyPp9Pr5tkvj7iBa42bjR062n9IwLIeqU9JA3YT3denLC/zvjBKbi27TF/+pURZz0/17GUApRT7VJzmDA5esMuHydrteTAOh6Pcm4r01yhsIR1m/puYV8cTQWMOO1QY/wiPcjBLQIkGS8CSuMjyf3/PkyH4Xx8XUWy6JFi1CpVMaHk5MTI0eO5NKlS5U6PyAggDVr1pTbpq2tLV27dmXhwoWkpKRUKT6VSsWhQ4fKfH7y5MmoVCrWrVtXpXar4sqVK8yaNYvu3bujVqvp0qWLyeOWLVvG0KFDay2OmiA95E2YuZk5Tz82mhVmHzDu3LxSz2/v8gH/ePT/yYdTWfSml9wWoq5YaYuMFVWK2efm45Bb/mRjYfDF0atk5mvp4N6MoZ3clQ5HKMx05ayS6rJyUUREBF26dOHTTz8FICoqirlz5zJ27FjOnz9f7rnbt28nNjaWGTNmlNtmRkYGx48fZ/Xq1WzevJljx47RsmXLasceHh7O5s2bATh37ly12yvL+fPn2b17N3379kWn06HT6UweN2fOHN555x0OHDjA4MGDay2e6pAe8iZuSNshzO09Fyi9Ul1+0ijaWPVVLLZ67+qvSkcghLhP2flaPvstBoCXHvLFzMx0tRXRdNS3ylkRERH06tWLwMBAAgMDmTZtGi+99BIXLlwgLi7O5DmFhYXo9XpWrVrFpEmTsLa2LtVmQECAsc1hw4axaNEi9u3bx40bN1i8eHGNxD5//nxcXV3p3r07kZGRNdKmKaNHj+b69ets27aNnj3Lvpvv6OjImDFjWL16da3FUl2SkAuCOjyItb2GZh5qmg8rpJmHmkKNioxcbz46eEXp8OonvR511FeozMrvJVdZWKB2cqqjoERTonZyQmVhYfzZsrAI35spWBbe7TFXmetR28iNUFM2hcWSllOIl4stjz4gddpF/ZKenk5sbCz+/v4l9tvZGeZ05ebmAuDq6sqyZctYuHAhHh4eODg4EBMTw6+//sr48eNNttm1a9dS1+vWrRtBQUHs2rWr2rEfOnSIvXv3snjxYgICAmo1ITczq3waO2HCBEJCQrh1q34WqpB3akEzJyumLh+Amdowpkw/Rs+5a2msWneUH8Lj+fuQDrRzkWXgS7iyD012JD5/bYZ27FawdjB5mKyUKGqLxsMDnx/3lOitM07g1Oth67Ooc/5Ac/0H8PJTJMb6Kq+wiE9+MfSOzw7ywVx6x0U9ExERAUDnzp1L7D9y5AgODg54eXkRHx/P7du3+eijjxg2bBifffYZZmZm7N+/H41GQ0BAgMk2TSXkAD4+Puzbt4+ioiLMze9/qOr8+fPx9vZm5syZfPTRR6SmpnLjxg1atWpl8ni9Xk9RUcXrnZibm6NS3f/f6oABA9BqtRw6dIgJEybcdzu1RRJyAYC55u63TJVKxQNtnXjIz5WDl26x7lA0b49/QMHo6hm9Hn55FwDNoGfR9O6vcECiqdJ4eJT9hU/3OmyfAaH/gcDZYCFfqot9c/I6t7PyaeVozZgeppMEIZRUnDz7+fmh1WpJTExk/fr17Nq1i7feegu1Wk14eDgA48ePZ+3atcZzZ86cSYcOHbC0tDTZZlkJeUFBAdbW1tVKxrdt28bx48fZtGkTGo3G+IUiMjKyzIQ8ODiYadOmVdj2wYMHCQoKuu/YnJycaNOmDWFhYZKQi4ZlzuD2HLx0i29Px/HKkPa0crSu+KSm4OoRuB4G5pbQ/2WloxHCNP+xcHAFpMbAqY3Q7yWlI6oXCrQ6/nsoGoBZg7zRmMvITVH/FCfb7du3N+5zcXHh3XffZd68ecZj1Go1S5cuLXFuQkICrq6uJtt0cXHB3d30BObo6Gh8fX2NP0dFRTFlyhTS09Np3bo1mzZtKnfCp1arZdGiRXTv3p2JEycC0KlTJ8CQkA8fPtzkeaNHj+bEiRNltlvMz6/6d/pcXFy4efNmhcf98ccfLFq0iP/973/VvmZlSUIuytSrrRP9fZpzNDqZjw9H8+bjpssJNTl3esfpOQXsWigbixBlMVfDwLnw/cvw2xro/RxorJSOSnE7zsQRn56Hq50lE3p7Kh2OECZFREQQGBjI2rVrUalUODg44O3tXWLMdEREBP3798fR0bHEuXl5eaV6x4uPL6t3PC0tjRMnTjB79mzjvlmzZrFgwQLGjRvH+++/z4IFCwgODi4z5g0bNnDp0iW2bNlCeno6YBjz3qxZs3IrrTg7O+PgYHrY572q03NfzMrKyjj+vjze3t51moyDTOoUFZgz2PBtecuJ6yRl5CkcTT1w/QTEHAYzNQx4VelohCjfA0+BfWvIuglnv1I6GsVpi3Ssu9M7PvMv3lhppKSrqH/0ej2RkZEEBgbSu3dvevXqha+vb6kJjOHh4fTq1avU+c7OzqSlpZlss6yE/MMPPyQ/P59Zs2YBkJiYSFRUFGPHjgVgxowZbN++vcyYc3NzWbJkCQBPPfUUTk5OxkdWVla5EzuDg4PRaDQVPg4fPlxmG5WVmppK8+bNjT+HhIQQGBhIjx498Pf35/Tp0wC89NJLbNiwwbg9Z84chg4dSqtWrXjvvfcIDg5m0KBBtG7dmv3791c7LpAeclGBft7N6dnGkdPX0vjstxgWjuykdEjKOvKB4d9uT4Gj9K6Jek5tYfjiuOc1+G019HzW0HPeRIVE3uRqcg5ONhom9W2jdDiinimuXFRRHfLarpx15coVsrOz6datW5nH5Ofnc/nyZV5//fVSz/n5+XHw4EGTbZpKyLdu3cqKFSuYN2+ecYhMXFwcnp6exkmU9vb2aDQakpOTSyS0xVatWkVCQgKbNm3C40/zWlavXs3evXvR6XQmq6LU1ZAVnU7HtWvXjO0UFRUxc+ZMzp07h6OjI7m5ucbXe/bsWZ5//nnjdpcuXfjxxx+5ePEivXv35t///jeHDx/ms88+Izg4mIcffrhasYEk5KICKpWKF4N8ef6Lk2wKvcaLQb44WGuUDksZSVFwKQRQwYC/KR2NEJXT42k4/DakXYPzO+CB+jeZqS7o9Xpj7/iz/b2wsZCPP1GSqcpFf1YXlbOKJ1+Wl5CfP38erVZL9+7dSz03YMAA3nzzTeLi4mjdunWJNouKiggNDSU/P5+YmBi2bdvG7t27mT17NsuXLze2oS9j4TtTVU5SUlJ45513eOaZZ5g0aZLJ17Nz506io6NLjIkv1rx5c5NJfmXk5OQQEhICQGxsLBkZGWzbtg2AQYMGlRhLf+HCBbKzsxk4cKBxn42NDa+88gpPPPEEI0aMQK1Wo9PpuHjxIv7+/uh0Os6fP88PP/xgrPLi4+PDc889Z2yjMsNtKkPekUSFBnd0o4N7My4nZvFVaCwvPeRb8UmN0W93FhToNBpcSr+pCFEvWdhA4Cw4sAyOfAhdx0M1Soc1VIcv3yIqIQMbC3Om9m+rdDiiniq3clEdiYiIQK1Wlyp5eK/w8PASVUzuFRQUhIuLC3v27DGu1FmckBcPSbGzs6NVq1YMGDCA0NBQ+vYtuQigp6cncXFx6PV6VCoVmZmZFBYW4uzsXOp6K1eupKCggBUrVpiMtXg5+8jISJMJeXUkJSWVqphS/POfq7KEhITQtm1bYzlIc3NzIiIi2Lt3L5988gn/+c9/CAkJ4ffff6dt27ZYWFhw6dIlPD09ja/7zJkzPPjgg8Y2w8PDy/3iVBUyhlxUyMxMxewgHwA+/y2GvMKK64U2OmnX4NxWw/aDf1M0FCGqLOB5sGgGSefh95+VjkYRxb3jk/q0wdHGooKjhVDOkiVLKCwsNDkxs9i0adMoKChAoyl9x9rCwoIpU6YYl64vblOv1xsfGRkZREVFsX79+lLJOIC7uzt+fn7s3LkTgPXr1zNmzBiTsbz77rtkZ2eXWdZw8ODB6PX6Ms+vjnbt2pV4Xfc+/lwiccuWLUyfPt3Yy3/p0iUsLCx47LHHePnll8nJyQEMQ1R69Ohh3L53nP7p06dLrAh65syZclcIrQpJyEWlPPqAB60crbmdVcDWU6aX7G3Ujn0EOi14DYJWpSfRCFGvWTtB7zt1fo98qGwsCjgVm0pYTAoacxXPDfRSOhwhat1rr71GWFgYZ86cue821q1bx/Lly+nQoQPff/89b731Vg1GWLcOHz7M1atXeeWVV4z73nvvPfz8/OjZsydvv/02H3/8MWBIsosT8jNnzpSZkOv1eqKioox3AKpLhqyIStGYm/HCX7z51/fn+eSXaCYGeKJuKvV7s5Ph1J1STw/+XdlYhLhfgS9B2Mdw7ShcC4U2gUpHVGf+e9jQOz6mRytaOsh6CqLxa9GiBRs3bqzWMvH+/v6cPHmyBqNSTkZGBl988UWJEpGffvqpyWPv/eLx5y8h906WValU3L59u8ZibCIZlagJT/T2xNnWguspuew+l6B0OHUn7L+gzYWW3cE7SOlohLg/9i0N1YGgSfWSX07M5OcLiahU8MJffJQOR4g6M2HCBIYNG6Z0GPXC6NGjefTRR5UOo1ySkItKs7YwZ1r/doBhPGZZs7AblfxMOP6JYfvBvzfJyXCiEen/KqCCyz9C4nmlo6kTxb3jwzu3wNetmcLRCNF4mBqnLe6fJOSiSqb0a4ethTkXb2Zy6NL93wprME4FQ14aNPc1VFcRoiFz8YXOjxm2i6sGNWJxqTl8fzYegFlB0jsuhKi/JCEXVeJwz4IaxVULGi1tPhz7t2F7wKtgJqv6iUageB7EuW2QGqtsLLVs/a8xaHV6+vs0p7uno9LhCCFEmSQhF1X23IPeaMxVHL+awqnYshdQaPDObYXMBLBrCQ88qXQ0QtQMjx7g/RDoiwzVgxqp1OwCvj5xHcBYtlUIIeorSchFlbVwsGJMD0O90U9+aaS95DodHF1r2A6cDeqy68EK0eAMeNXw75kvISdF2VhqyZehseQWFuHvYc+Dvi5KhyOEEOWShFzclxf+4g3ATxcS+eNWlsLR1ILff4JbF8HCDno9q3Q0QtQs7yBo0RUKc+DEeqWjqXF5hUUEH70KGN6rTC33LYQQ9Ykk5OK++LrZ8XBHN/R6+PTXGKXDqXlH1xj+7f0sWDkoGooQNU6lulNxBUNt8sJcZeOpYdtOxZGcXUArR2se6dpS6XCEEKJCkpCL+1bcS/7t6ThuZeYrHE0NijsFsb+BmRr6zlY6GiFqh/9fwcETcm5D+OYKD28oinR61v/6BwDPPejVdBYwE0I0aPJOJe5bHy9nunk6UqDV8cWxq0qHU3OO3ikH1/UJcGilbCxC1BZzDfR7ybB99N+gK1I2nhry84WbXE3OwcFaw5MBnkqHI4QQlSIJubhvKpWKmXd6yb8MjSWnQKtwRDUgORqifjBs939Z2ViEqG09ngErR0iJhkshSkdTbXq9no9/MfSOPxPYFltLtcIRCSFE5UhCLqpluH8L2ja3IS2nkG/ulBhr0I59BHod+A4F985KRyNE7bJsBgHPGbZ/Ww0NfPXdk7GpnLmWhoXajKl3VhUWQoiGQBJyUS3mZiqeH2joJV9/JAZtkU7hiKoh+zac3WTYHvCKsrEIUVf6zARzC4g7AddClY6mWj4+bOgdH9ezFa52UqpUNGyLFi1CpVIZH05OTowcOZJLly5V6vyAgADWrFlTbpu2trZ07dqVhQsXkpJStRKoKpWKQ4cOlfn85MmTUalUrFu3rkrtVtXly5cZMWIEtra2uLm58eqrr5KbW3Ki+rJlyxg6dGitxlFdkpCLapvQqzXOthbEpeayJ/Km0uHcv+OfgjbPsHBKu4FKRyNE3bBzh24TDdtH15R/bD12JSmLfVGJqFQYOwmEaMgiIiLo0qULx44d49ixY3zwwQeEhoYyduzYCs/dvn07sbGxzJgxo9w2d+zYwZNPPsn69evp2bMnCQkJNRJ7eHg4mzcbJoufO3euRto0JS0tjcGDB5OZmcm3337Le++9x6ZNm0q97jlz5hAWFsaBAwdqLZbqkoRcVJuVxpwp/doC8Mkvf6BviLe9C3Lg+CeG7f6vGMrCCdFU9H8ZUBnGkd+6rHQ096W4ssrQTu74uDZTOBrRGCTFZrDzg9MkxWYocv2IiAh69epFYGAggYGBTJs2jZdeeokLFy4QFxdn8pzCwkL0ej2rVq1i0qRJWFtbl2ozICDA2OawYcNYtGgR+/bt48aNGyxevLhGYp8/fz6urq50796dyMjIGmnTlI8//pjU1FS+++47RowYwZQpU1izZg2bNm0iKirKeJyjoyNjxoxh9erVtRZLdUlCLmrElH7tsNKYce5GOmExDXDlv/DNkJsCjm2h02NKRyNE3XJpD36jDNuhHykby324lZnP9jM3gLvlWIWorouhN7lxOY1LoXV/5zc9PZ3Y2Fj8/f1L7LezswMwDslwdXVl2bJlLFy4EA8PDxwcHIiJieHXX39l/PjxJtvs2rVrqet169aNoKAgdu3aVe3YDx06xN69e1m8eDEBAQG1mpCHhIQwZMgQXFzursY7btw4LC0tCQkpOVF9woQJhISEcOvWrVqLpzokIRc1wtnWgnE9WwN3e6oaDJ0OQv9j2A58EcylMoNogvrPMfwbvsUwn6IB+TI0lgKtjh5tHOndzlnpcEQDlpGcS1JsBreuZXLlZCIAv59M5Na1TJJiM8hIrptFtCIiIgDo3LlkcYEjR47g4OCAl5cX8fHx3L59m48++oj4+Hg+++wzduzYwf79+9FoNAQEBJhs01RCDuDj40NiYiJFRdUrgTp//ny8vb2ZOXMmnTt3JjU1lRs3bpR5vF6vR6vVVvgwdfc9KiqKTp06ldhnaWmJj49PiR5ygAEDBqDVassd964kyTxEjZn+oBebwq6xLyqJ6FtZDee28eUfIfkKWDpAj8lKRyOEMtr0M8yfiD8DJ9ZD0AKlI6qUvMIivgqNBeD5B6V3XFTPl/84VmpfbmYh36w4Yfz5pf8OrvU4ipNnPz8/tFotiYmJrF+/nl27dvHWW2+hVqsJDw8HYPz48axdu9Z47syZM+nQoQOWlpYm2ywrIS8oKMDa2hpzc/P7jnvbtm0cP36cTZs2odFojF8oIiMjadXK9LoewcHBTJs2rcK2Dx48SFBQUIl9qampODo6ljrWycmp1CRVJycn2rRpQ1hYGBMmTKjcC6pDkpCLGuPj2owhndzYF5XEZ0diWDHG9B99vXPs34Z/ez8LlnaKhiKEYlQq6DcHvn3OMMF5wKugsa74PIV9ezqOlOwCWjtZM9zfXelwRAM3ZFpn9gdHodeV7o1Vmal4eGonE2fVvOJku3379sZ9Li4uvPvuu8ybN894jFqtZunSpSXOTUhIwNXV1WSbLi4uuLub/juJjo7G19fX+HNUVBRTpkwhPT2d1q1bs2nTJlq2bFlmzFqtlkWLFtG9e3cmTjRMFC/uvY6MjGT48OEmzxs9ejQnTpww+dy9/Pz8TO5XmZjzpdfrTe53cXHh5s36WXxCEnJRo54f6M2+qCS+PRXHvGF+ONtaKB1S+W6chtjfwExtKP8mRFPW+a+w7w1Ivw4R30CvqUpHVC6dTs9nv8YAMH2AF2pzGYUpqsevbwucW9qW6BEvNmFBb1zb1E2nTUREBIGBgaxduxaVSoWDgwPe3t6YmZmVOKZ///6leojz8vJK9Y4XH19W73haWhonTpxg9uzZxn2zZs1iwYIFjBs3jvfff58FCxYQHBxcZswbNmzg0qVLbNmyhfT0dMAw5r1Zs2blVlpxdnbGwcGhzOeLmeq5d3JyIjU11eTr+fNQFgArK6tSJRHrC3n3EjWqr5czXVs5kK/VGW8j12vH7kxg6zIOHEzfThOiyTBXQ99Zhu1jHxnmV9RjBy4m8cftbOys1DwR4Kl0OKKxUf3p3zqi1+uJjIwkMDCQ3r1706tXL3x9fUsk42Do8e7Vq1ep852dnUlLSzPZZlkJ+Ycffkh+fj6zZhn+/hMTE4mKijKWWJwxYwbbt28vM+bc3FyWLFkCwFNPPYWTk5PxkZWVVe7EzuDgYDQaTYWPw4cPlzq3U6dOpcaK5+fnEx0dbTIhT01NpXnz5safk5OTmTp1Kv369aNjx45s2LDB+Ny9Q4GOHDlC165dSUxM5JVXXuGxxx6jX79+eHl5lfgSUx3SQy5qlEql4vmBXry65SxfHLvKC3/xxkpz/+PRalXadTi/w7Dd7yVlYxGivug5BQ69BbcvwZV90GGY0hGVaf0RwwTySX3a0MxSPs5EzbC202Bjb0EzJ0s6DfAg6rd4slLzsbbT1Mn1r1y5QnZ2Nt26dSvzmPz8fC5fvszrr79e6jk/Pz8OHjxosk1TCfnWrVtZsWIF8+bNMw6RiYuLw9PT0zjsw97eHo1GQ3JycomEttiqVatISEhg06ZNeHh4lHhu9erV7N27F51OV+pLBVRvyMqoUaNYunRpibh27NhBfn4+o0aNKnGsTqfj2rVrxnZ0Oh0TJ05k+fLlBAQEkJmZSadOnZg8eTKWlpasWLGChx9+mMDAQF544QV27dqFu7s7p0+fxt3dnV9++YXCwkI6duxIZGQkXbp0qfA1lEfewUSNG9W1JW/tuUhCeh7fnb3BkwFtlA7JtLD/gr7IsAhQy7Lf+IRoUqzsDUNVjv0bjq2ttwl55I10Qv9IQW2m4tkB7ZQORzQizZysmLK8P2Zqw2qW/gM90Gn1mGvqZlBB8eTL8hLy8+fPo9Vq6d69e6nnBgwYwJtvvklcXBytW7cu0WZRURGhoaHk5+cTExPDtm3b2L17N7Nnz2b58uXGNspaT8TUuOyUlBTeeecdnnnmGSZNmmTy9ezcuZPo6OgSY+KLNW/e3GSSXxkzZ85k7dq1PP744yxevJikpCTmzp3L5MmTS/WQX7hwgezsbAYONCz89+OPP3Lq1KkSiwipVCpjlZkOHTowfPhwRo4cyb59+/D29kan03Hu3Dm++eYbY8+9j48PycnJ9xX/vWTIiqhxGnMzpt35gFz/a0z9XCgoLwNOf2HY7v+ysrEIUd/0nQUqc4j5BRIilI7GpE/vlFd95IGWtHSo/5NPRcNirjEzJp8qlarOknEwJLBqtbpUycN7hYeHl6hicq+goCBcXFzYs2dPiTbBMC68X79+jB49mrfffpsWLVoQGhrKf/7zH9Tqu320np6exMXFGT+/MzMzKSwsxNm5dFnRlStXUlBQwIoVK0zGWtxzXBv1yB0dHTlw4AC2traMHTuWuXPnMnHiRD799NNSx4aEhNC2bVtjOcgzZ84wb948zp49a3xcv34dGxsbAK5fv87Ro0exsLAwVoi5fPky9vb2xrsAeXl5REVFlTkUqCokIRe14qk7t5B/T8ri8OV6WIT/zJeQnwEuHcB3qNLRCFG/OHqC/18N28fq30JB8Wm57IowLPE9Y6CUOhSNy5IlSygsLDQ5MbPYtGnTKCgoQKMpPYzGwsKCKVOmGJeuL25Tr9cbHxkZGURFRbF+/Xr69u1bqg13d3f8/PzYuXMnAOvXr2fMmDEmY3n33XfJzs4us6zh4MGD0ev1ZZ5fXR06dGDv3r1kZ2dz69Yt1qxZU2qFUoAtW7Ywffp04xctDw8P9u7dS35+PgC3b9/m+vXrgGFs+ejRo1mzZg3Tp09n2bJlAJw+fZqUlBTj4kJvvPEG48ePN/lFpaokIRe1wt5Kw5N3Jlmtv1MFod4o0kLofw3b/V4CE2PahGjy+t1ZKChyG2TEKxvLnwQfvUqRTk+gtzNdWlVcnUGIpua1114jLCyMM2fO3Hcb69atY/ny5XTo0IHvv/+et956qwYjrFuHDx/m6tWrvPLKK8Z9Tz/9NN7e3vj7+9O9e3fGjRtHXl4e2dnZjB49mgULFjBkyBDmzZvH119/TUxMDKdPn+bFF19k3LhxdO7cmczMTN5///0aiVHGkIta82z/dnz+WwxHrtzm4s0MOrawVzokg4s/QPo1sGkODzypdDRC1E+tekKb/nDtqKEu+ZB/KR0RANn5Wv53/BogCwEJUZYWLVqwcePGai0T7+/vz8mTJ2swKuVkZGTwxRdflCgRqdFoSlRVudfRo0eN246Ojsba5adPn2bFihW8++67NR6jdA2KWuPpbMOILi0A2HCkHvWSh64z/Nv7uQax8IkQiun3ouHfU59DQY6ysdyx7VQcmXlavFxsGdzRTelwhKi3JkyYwLBh9XNSdl0bPXo0jz76aLXbiYyMLHeybXVIQi5q1XMPegGw82w8t7PyFY4GiDsF18PA3AICnlc6GiHqN79R4NQOclMhYovS0aDT6fn8N8OX+2kD2mFmVscFooUQRnq9vtRS9o1dUlKSyfHpNaHKCfnly5cZMWIEtra2uLm58eqrr1Z61aOUlBRefPFFWrZsiZWVFR06dODjjz+uctCi4ejZxoluno4U1JeFgkKLFwIaD3ayzLYQ5TIzv7tQUOg6xRcK2n8xiavJOdhbqRnXs7WisQghRE2qUkKelpbG4MGDyczM5Ntvv+W9995j06ZNJWo4liUrK4tBgwZx8uRJVq9ezY8//shrr71mrPcoGieVSmXsJf8qNJa8QgX/f6fHwfmdhu3iW/FCiPL1eBos7eH2ZYjer2gon91ZCGhi3zbYykJAQohGpErvaB9//DGpqamcPXsWFxcXQwNqNZMnT+Yf//iHyWVKi61YsYLc3FyOHz9u7O5varc6mqqRXVrQ0sGKhPQ8vg+P54neCi1xffyTuwsBtah+zVAhmgRLO8Pqncf+bSiB2F6ZMqHn4w0LAZmbqZjar50iMQghRG2pUg95SEgIQ4YMMSbjAOPGjcPS0pKQkJByz92wYQPPPfdcrY29EfWXxtyMqf3bAYbJnYosFJSfBac2Grb7vVT31xeiIevzAqjM4I+DkHhBkRA+uzMxfFTXlng4yueIEKJxqVJCHhUVVaoX3NLSEh8fH6Kioso8LyYmhsTERJycnHj00UextLSkefPmvPTSS+WOP8/PzycjI6PEQzRMEwPaYK0x5+LNTI5GV3+J2SoL3wx56eDsA+2H1/31hWjInNpCp9GG7dD/1PnlkzLy+CHcUAu9eAicEEI0JlVKyFNTU0vUcCzm5ORESkpKmecV12987bXXcHNzIyQkhDfeeIPg4OASRdr/bOXKlTg4OBgfnp4KDXUQ1eZgo2FCb8MkrM/qugSiTne31GHgbFkISIj7EXjnzlLEN5BVt6vvfhkaS2GRnl5tneju6Vin1xZCiLpQ5cykeMnRe+n1epP7i+nuzMzv1KkTGzZs4OGHH+bll1/mzTffZMOGDcaE/c8WLlxIenq68VG8pKlomKYN8EKlggMXk4i+lVV3F/59L6REg5UDdJtYd9cVojHx7AOtekFRPpw0vZhGbcgrLGJTmGEhIOkdF0I0VlVKyJ2cnEhNTS21Py0tDScnpzLPc3Z2BmDw4MEl9g8ePBidTlfmcBdLS0vs7e1LPETD5eViy8N3FvIoriVcJ4pvsfd6Fiyb1d11hWhMVCoIvFOd6MR60NbNugI7z9wgJbuAVo7WDOsspUqFEI1TlRLyTp06lUqe8/PziY6OLrfCio+PDxYWFqX2F0/uM5MhBE3G9AGGHq5vT90gPaew9i94MxJifgGVOQRUXJ5TCFGOzo+DnQdkJ0Hk9lq/nF6vZ8OdL+/P9m+H2lw+K4QQjVOV3t1GjRrF/v37SU6+Oylvx44d5OfnM2rUqDLPs7CwYOjQoezfX7KG7f79+1Gr1XTu3LmKYYuGqp9Pczq2sCO3sIgtJ67V/gXD7owd7/wYOMocBCGqxVwDfe58sQ39D9RyxaTfriRzOTELGwtzngiQv18hRONVpYR85syZODo68vjjj7N3716+/PJLXn75ZSZPnlyih/y5555DrS5Z4vyf//wn4eHhTJkyhZ9++olVq1bxr3/9izlz5uDq6lozr0bUeyqVimkD2gHwxbFYtEW1uPJf9m2I2GrY7ju79q4jRFPS61lQW8PNCLh2rFYvVTy0bUKv1jhYa2r1WkIIoaQqJeSOjo4cOHAAW1tbxo4dy9y5c5k4cSKffvppieOKiopKrcDZp08fdu/ezYULFxg9ejTvvPMOL7/8Mu+88071X4VoUB7v3gpnWwtupOXy04XE2rvQyc8NE9A8ehompAkhqs/GGbo9adiuxRKIMbez2X8xCcC4joEQTcmiRYtQqVTGh5OTEyNHjuTSpUuVOj8gIIA1a9aU26atrS1du3Zl4cKF5VbLM0WlUnHo0KEyn588eTIqlYp169ZVqd2quHLlCrNmzaJ79+6o1Wq6dOli8rhly5YxdKgyi5pVVpUH5HXo0IG9e/eSnZ3NrVu3WLNmTanFfjZu3Ghy8ZehQ4dy8uRJ8vPziY+P56233kKjkV6PpsZKY87kvm2AWpzcqS0wTDwDw0S0cqoACSGqqPiO08XdkBpbK5cIPnoVgMEd3fB2lcnYoumJiIigS5cuHDt2jGPHjvHBBx8QGhrK2LFjKzx3+/btxMbGMmNGyblTf25zx44dPPnkk6xfv56ePXuSkJBQI7GHh4ezefNmAM6dO1cjbZpy/vx5du/eja+vb7nDn+fMmUNYWBgHDhyotViqS2bICEU8HdgWtZmKE1dTiYhLq/kLXNgJWTehWQvDRDQhRM1x6wjeD4FeB8c/qfHm03ML+eakocxt8URwIepaVmoKR7duIiu1aj3HNSUiIoJevXoRGBhIYGAg06ZN46WXXuLChQvExcWZPKewsBC9Xs+qVauYNGlSqQ7TiIgIAgICjG0OGzaMRYsWsW/fPm7cuMHixYtrJPb58+fj6upK9+7diYyMrJE2TRk9ejTXr19n27Zt9OzZs8zjHB0dGTNmDKtXr661WKpLEnKhCHd7Kx59oCUAn/92tWYb1+vv3krv8zyoS1f4EUJUU3EJxNNfQn7Nriuw9eR1cgqK6ODejAG+zWu0bSEqKzs1hWPbNpOtQEKenp5ObGws/v7+Jfbb2dkBGFc5d3V1ZdmyZSxcuBAPDw8cHByIiYnh119/Zfz48Sbb7Nq1a6nrdevWjaCgIHbt2lXt2A8dOsTevXtZvHgxAQEBtZqQV6VK34QJEwgJCeHWrbpd2KyyJCEXipl2p+drV0Q8SRl5Ndfw9eMQfwbMLaHXtJprVwhxl+8QaO4L+ekQvrnGmi3S6dl4Z7iKYTExGW4mmp6IiAiAUsMwjhw5goODA15eXsTHx3P79m0++ugj4uPj+eyzz9ixYwf79+9Ho9EQEBBgsk1TCTkYSlQnJiaWmgNYVfPnz8fb25uZM2fSuXNnUlNTuXHjRpnH6/V6tFpthQ9TQ6GrYsCAAWi12nLHvStJEnKhmG6ejvRq60RhkZ6vQmtwHGpx7/gDT4CtS821K4S4y8wM+s4ybIeuA13NVEz6+UIicam5ONloGNOjVY20KURlZaWmkPjHFcMjJhqAxJho4766Gr5SnDz7+fmh1Wq5ceMGS5YsYdeuXSxcuBC1Wk14eDgA48ePJzg4mJEjRzJ8+HBOnjxJhw4dsLS0NNlmWQl5QUEB1tbWmJub33fc27Zt4/jx4yxduhSNRmP8QlFeL3lwcDAajabCx+HDh+87LjAsbtmmTRvCwsKq1U5tUVd8iBC1Z/oAL07FprIp7BovPuSLleb+3wgASLsOUT8YtgOl1KEQtarbRNi/FFKi4co+6DCs2k0WT/Se2KdN9d8PhKiiiH17OLat5B2fnz9Za9zuN34i/SdMrvU4ipPt9u3bG/e5uLjw7rvvMm/ePOMxarWapUuXljg3ISHBZDnp8PBwXFxccHc3veJtdHQ0vr6+xp+joqKYMmUK6enptG7dmk2bNtGyZcsyY9ZqtSxatIju3bszceJEAGNJ7MjISIYPH27yvNGjR3PixIky2y3m5+dX4TEVcXFx4ebNm9VupzZIQi4UNdzfHQ8HK+LT8/g+PJ4neldz8Y8Tn4K+CLz+Au7+FR8vhLh/ls2g5zNw7N+GO1PVTMjPx6cTFpOC2kzFM/3a1lCQQlTeA0NG4tOrL2DoGf/5k7UMfeFl3L18ALB1cq6TOCIiIggMDGTt2rWoVCocHBzw9vYuMWY6IiKC/v374+joWOLcvLy8Ur3jxceX1TuelpbGiRMnmD37bkfWrFmzWLBgAePGjeP9999nwYIFBAcHlxnzhg0buHTpElu2bCE9PR0wjHlv1qxZuZVWnJ2dcXBwKPP5YtXpuS9mZWVlHH9f38iQFaEotbkZz/RrB8DG365Wb4xYQTacuvNmIQsBCVE3+rwAKjP44yAkXaxWU8UTvEd2bUlLB+vyDxaiFjRzcsbd29fwuJOEu3v5GPc1q4OEXK/XExkZSWBgIL1796ZXr174+vqWmsAYHh5Or169Sp3v7OxMWlqayTbLSsg//PBD8vPzmTXLMAwtMTGRqKgoY4nFGTNmsH379jJjzs3NZcmSJQA89dRTODk5GR9ZWVn1YsgKQGpqKs2b350onpyczNSpU+nXrx8dO3Zkw4YNxufGjx/P2rWGuyNHjhyha9euJCYm8sorr/DYY4/Rr18/vLy8SnyJqQ7pIReKm9jHk9X7L3MhIYPjMSn09b7PqgoR30BeGji1gw6mb40JIWqYU1vwGwUXd8Hxj+HRD++rmdtZ+Xx/Nh7AuJqvEE3RlStXyM7Oplu3bmUek5+fz+XLl3n99ddLPefn58fBgwdNtmkqId+6dSsrVqxg3rx5xiEycXFxeHp6GidV29vbo9FoSE5OLpHQFlu1ahUJCQls2rQJDw+PEs+tXr2avXv3otPpTFZFqashKzqdjmvXrhnb0el0TJw4keXLlxMQEEBmZiadOnVi8uTJWFpasmLFCh5++GECAwN54YUX2LVrF+7u7pw+fRp3d3d++eUXCgsL6dixI5GRkWUuSlRZkpALxTnaWDCmR2s2H7/G579dvb+EXK+HsI8N231mgpmMPRWizgTONiTk4Vvg4X+CtVOVm9gcdo2CIh3dPB3p2abq5wtR02ydnOk3fmKdDVMpVjz5sryE/Pz582i1Wrp3717quQEDBvDmm28SFxdH69atS7RZVFREaGgo+fn5xMTEsG3bNnbv3s3s2bNZvny5sY2y7labqnqUkpLCO++8wzPPPMOkSZNMvp6dO3cSHR1dYkx8sebNm5tM8isjJyeHkJAQAGJjY8nIyGDbtm0ADBo0qMRY+gsXLpCdnc3AgQMB+PHHHzl16lSJxZNUKpWxykyHDh0YPnw4I0eOZN++fXh7e6PT6Th37hzffPONsefex8eH5OTk+4r/XpKQi3ph2oB2bD5+jZ8u3OR6Sg6ezjZVa+CPQ3ArCiyaQY/an3AjhLhH2wHg3gUSI+H0FzDg1SqdXqDV8eWdSkvT+rerhQCFqLpmTs51MoHzzyIiIlCr1eWuPBkeHl6iism9goKCcHFxYc+ePcZkszghLx6SYmdnR6tWrRgwYAChoaH07du3RBuenp7ExcWh1+tRqVRkZmZSWFiIs3PpLycrV66koKCAFStWmIy1uOc4MjLSZEJeHUlJSUyYMKHEvuKfDx48SFBQkHF/SEgIbdu2NZaDPHPmDPPmzWPhwoUm275+/TpHjx7FwsKCVq0MFZ8uX76Mvb298S5AXl4eUVFRZQ4FqgoZQy7qhQ7udgzwbY5Oz/2VQAz7r+Hf7pPAquLJIUKIGqRS3S2BePxTKNJW6fQ9kQkkZebjZmfJqK5lV3EQoilYsmQJhYWFJidmFps2bRoFBQVoNJpSz1lYWDBlyhTj0vXFber1euMjIyODqKgo1q9fXyoZB3B3d8fPz4+dO3cCsH79esaMGWMylnfffZfs7Gxj0vpngwcPRq/Xl3l+dbRr167E67r3cW8yDrBlyxamT59u7OX38PBg79695OfnA3D79m2uXzesEJycnMzo0aNZs2YN06dPZ9myZQCcPn2alJQU4+JCb7zxBuPHjzf5RaWqJCEX9ca0/oaFgjYfv0ZOQRU+0JOj4fJew3afmbUQmRCiQl0ngE1zSL8Ol0KqdGrxZM6nA9tioZaPJSGq67XXXiMsLIwzZ87cdxvr1q1j+fLldOjQge+//5633nqrBiOsW4cPH+bq1au88sorxn1PP/003t7e+Pv70717d8aNG0deXh7Z2dmMHj2aBQsWMGTIEObNm8fXX39NTEwMp0+f5sUXX2TcuHF07tyZzMxM3n///RqJUYasiHpjcEc32ja3ITY5h+2nb/B0YCXLnh3/FNCD71Bw8a3wcCFELdBYQa9n4df3DXesOj9WqdPOXEvl7PU0LMzNmNinTe3GKEQT0aJFCzZu3FitZeL9/f05efJkDUalnIyMDL744osSJSI1Gk2Jqir3Onr0qHHb0dHRWLv89OnTrFixgnfffbfGY5SuCFFvmJmpmFpcAvFoJUsg5mXAma8M24Gzai84IUTFAp4HMzXE/gYJEZU6pbh3fHQ3D1ztyr5FL4SomgkTJjBsWPUX62oMRo8ezaOPPlrtdiIjI8udbFsdkpCLemVC79bYWphzJSmLI1duV3zC2f9BQSa4dACfh2s/QCFE2ew9oPPjhu3ieR3luJmeR8i5BEBKHQrR0Jgap93YJSUlYW1dO2skSEIu6hU7Kw0T7qzWWdxzViadzlD3GKDvTMPEMiGEsooX5Tq3FbLKv13+VWgsWp2ePu2c6dJKJmMLIZouSchFvTO1fztUKjhwMYmY29llH3jlZ0j5Aywd4IGn6i5AIUTZWvcGj55QVACnPi/zsLzCIv53/BoAz0rvuBCiiZOEXNQ7Xi62POTnBsAXx66WfWDxLfGez4Bls9oPTAhRMZXKsFAQwInPoKjQ5GE/hMeTkl2Ah4MVwzq712GAQghR/0hCLuqlZ+8sDrL1ZByZeSY+0G9dgugDoDKDPjNKPy+EUE7nv0Izd8i6CRe+K/W0Xq9n49GrADzTrx1qc/koEkI0bfIuKOqlge1d8HVrRla+lm9PxZU+IOzO2HG/UeDUrk5jE0JUQG0BvZ8zbJuY3Hniairn4zOw0pgxsY9nHQcnGrNKVecSog5V9ndSEnJRL6lUKqbe6SUPPhaLTnfPL3RuGoTfWYGsrywEJES91HsamGkg7gTEnSrx1MajMQCM6dEKRxsLJaITjUzxipU5OTkKRyJEScW/k6ZWVb2XLAwk6q2xPVrxzo8XibmdzeHLt3ioo2FcOWe+hMIccOsM7QYqG6QQwrRmbtBlHERsMfSSt/4UgBtpuew9nwhg/NItRHWZm5vj6OhIUlISADY2NsYl0oVQgl6vJycnh6SkJBwdHTE3Ny/3eEnIRb1la6nmyd6erD8Sw+dHrxoScl0RHP/EcEDfWVLqUIj6LHCWISE/vwOGLQW7FnwVGkuRTk8/7+Z0bGGvdISiEWnRogWAMSkXoj5wdHQ0/m6WRxJyUa9N6deOz36L4ZfLt7iSlIVvymFIuwbWTtB1gtLhCSHK49EDPPvC9TA4+Tl5D77OZil1KGqJSqWiZcuWuLm5UVhourqPEHVJo9FU2DNeTBJyUa+1aW7DkE7u/HwhkS+OXeXNtOJSh1PBwkbZ4IQQFes7805CvoHvrSaQllNIaydrhnSSUoeidpibm1c6CRKivpBJnaLem3ZnnGn4qaMQ8wuozCHgeWWDEkJUTqfHwM4DspOI/fUrAKb2a4e5mQw3E0KIYpKQi3qvn09zOrg340ldiGFHp0fBUUqlCdEgmGsgwFACcXjWTqw1ZjzRW/5+hRDiXpKQi3pPpVLxQm9nxpj/BkBRgJQ6FKJB6fUshSoND5jF8De/VBxsyi//JYQQTY0k5KJBeFz3M9aqAs7r2nIgx0fpcIQQVXA934ad2v4ATGKPwtEIIUT9Iwm5qP+KtGhOfQbA50Uj2HjsqrLxCCGq5MvQWD7XDgfALno3pN9QOCIhhKhfJCEX9d+l3ZARR5G1M7t0/fjtSjKXEzOVjkoIUQk5BVq2HL/GBX07Ul0DQF8EJzcoHZYQQtQrkpCL+i/sYwDMe08nqHMbAD7/7aqCAQkhKmv76Rtk5Glp29wGh6A5hp2nPofCPGUDE0KIekQSclG/JURA7G9gpoaA55h2ZzGRHWfiSMspUDY2IUS59Ho9G49eBQylDs06PgoOnpCTDJHblA1OCCHqEUnIRf12p3eczo+DvQd9vJzp1NKevEIdX5+4rmxsQohy/XYlmStJWdhamDO+d2swV99dQyDsv6DXKxugEELUE5KQi/or+zac22rY7jsLMJRALF4o6ItjsWiLdAoFJ4SoyOe/xQAwvldr7K3ulDrsOQXU1nDzHFw7pmB0QghRf0hCLuqvUxuhKB88ekLrAOPux7p74GxrwY20XPZFJSoXnxCiTFdvZ3PgUhIAU+98iQbAxhkeeMKwHfbfug9MCCHqIUnIRf1UVAgnDKUO6TsLVHeX2bbSmDOxj2GlP5ncKUT99MWxWPR6CPJzxdu1Wckn+95Z3CtqF6TJ0DMhhJCEXNRPUd9DZjw0cwf/MaWefiawHeZmKsJiUjgfn65AgEKIsmTla9l60pBoTxvgVfoAd3/w+ouhBOKJ9XUcnRBC1D+SkIv6qXgyZ+/poLYo9XQLBytGdmkBwEbpJReiXvn2VByZ+Vq8XW0Z6Oti+qA780I4HQwFOXUXnBBC1EOSkIv658ZpuB4GZhroNa3Mw4pLIH4XHk9yVn4dBSeEKI9Od7fU4bP922FmpjJ9YIcR4NgWclPh3Dd1F6AQQtRDkpCL+qd4oleXcWDnXuZhPds48UBrBwq0OjYfv1ZHwQkhynP48i1ibmdjZ6lmXM/WZR9oZg59XjBsh0oJRCFE0yYJuahfMm9C5HbDdvHErzKoVCqevVO94cvQWAqlBKIQivv8Tu/4EwGe2Fqqyz+4x9OgsYVbURDzS+0HJ4QQ9ZQk5KJ+ObkBdIXg2Rda9azw8EceaIlLM0sSM/LZE3mzDgIUQpTlSlIWv1y+hUplWJmzQtaO0H2iYVtKIAohmjBJyEX9oc03JORwd8JXBSzV5jwd2Aa4uwiJEEIZG48a/gaHdHKnTXObyp1U/Ld+aQ+k/FFLkQkhRP0mCbmoPyK3Q/YtsPOATqMrfdrkvm3RmKs4cy2Ns9fTai8+IUSZ0nMK+fbUDeDuhOtKcWkPvkMAPRz/tFZiE0KI+k4SclE/6PUQts6w3ed5MNdU+lRXO0tGP+ABwEbpJRdCEd+cvE5uYRF+7nb0825etZOLe8nPfAX5mTUfnBBC1HOSkIv64VooJISD2gp6Plvl04sXH9l9LoGkjLwaDk4IUZ4inZ7gY1cBQ++4SlVGqcOy+DwMzX0hPwPObq75AIUQop6ThFzUD8W9410ngG0Ve9eArq0d6N3WicIiPV+FxtZwcEKI8vx8IZG41FycbDT8tUerqjdgZna3lzzsv6CTiklCiKZFEnKhvLTrELXLsF3JyZymFPeSbwq7Rr62qCYiE0JUQvFkzol92mClMb+/RrpNBEt7SImG6P01GJ0QQtR/kpAL5Z1YD/oiaDcQWnS572aG+bvT0sGK5OwCfghPqMEAhRBliUrIIPSPFMzNVDwd2Pb+G7JsBj2eMWyHrquZ4IQQooGQhFwoqyAHTm00bFejdxxAY27GM/0MCcHnv8Wgl5X/hKh1xeVGR3RpgYejdfUa6zMDUBl6yG9dqn5wQgjRQEhCLpQVsQXy0sCxLfiNrHZzEwPaYKUx43x8BsdjUqofnxANRFJsBjs/OE1SbEadXfN2Vj47z8YDMP3OkLFqcfaCjo8YtmWhICFEEyIJuVCOXg+hdz50+84Es/sce3oPJ1sLxvRoDcAGKYEompCLoTe5cTmNS6F1t2Lt/8KuUaDV0a21Az3bONZMo8V3ys5uhhz5Ui2EaBokIRfKiT4Aty+BRTPo8XSNNTv9zqIkP19I5HpKTo21K0R9k5GcS1JsBreuZXLlZCIAv59M5Na1TJJiM8hIzq21axdodXx5p6LR9Ae9ql7qsCztHgT3rqDNhdNf1EybQghRz6mVDkA0YcUTt3o8DVYONdZse3c7BrZ34dffbxN89CqLHu1cY20LUZ98+Y9jpfblZhbyzYoTxp9f+u/gWrn27nPx3MrMx93ekpFdWtZcwyoVBM6G716E459Av5eqtFCYEEI0RNJDLpRx+3e48jOggj4v1HjzxeNZvz55nax8bY23L0R9MGRaZ1RmpnumVWYqhkyrnS+jer2ez3+7CsAzgW2xUNfwR0mXcWDjAhk3IOqHmm1bCCHqIUnIhTKKJ2x1GAHNfWq8+UEdXPF2sSUzT8u3p+JqvH0h6gO/vi2YsKC3yecmLOiNX98WtXLdU7GpRMSlY6k2Y2KfNjV/AY0VBDxn2JbJnUKIJkASclH3clPh7P8M24Gza+USZmYqpt0ZS77x6FV0OimBKBo51Z/+rUXFveNjerSieTPL2rlI7+fATAPXwyDuVO1cQwgh6okqJ+SXL19mxIgR2Nra4ubmxquvvkpubtUmDu3YsQOVSkWXLve/CIxowE5/CYU54NYZvP5Sa5cZ27M1dlZqYm5nc+hyUq1dRwglWdtpsLG3wK2NHYMm+eHWxg4bewus7Wpn3HVcag57Ig0Lbz1750tvrbBzNwxdAQiThYKEEI1blSZ1pqWlMXjwYNq2bcu3335LUlISc+fOJTk5ma+++qpSbeTm5jJ37lzc3d3vK2DRwBVpDRO1wNA7XlOVGUywtVQzsU8bPvnlDzYcucrgjvI7JxqfZk5WTFneHzO1CpVKhf9AD3RaPeaa2rkB+uWxWHR6GODbnI4t7GvlGkaBswxrFZzfAUOXgn0NTh4VQoh6pErv2B9//DGpqal89913jBgxgilTprBmzRo2bdpEVFRUpdpYuXIlbdq0YcSIEfcVsGjgLu2G9Otg7QxdJ9T65ab0a4uZCo5cuc2lm5m1fj0hlGCuMTOWHVSpVLWWjOcUaNl8/BoA0/rXwEJAFfHoAW36gU4LJz6t/esJIYRCqvSuHRISwpAhQ3BxcTHuGzduHJaWloSEhFR4fnR0NO+//z5r1qypeqSicTj2H8O/vaeDpprLbFdCaycbhvsbJrZ9LgsFCVEt356KIyNPS7vmNgzu6FY3Fy2eZ3LycyisvbrqQgihpCol5FFRUXTq1KnEPktLS3x8fCrVQ/7qq68yZcoUunXrVqnr5efnk5GRUeIhGrAbp+B6qGGiVp8ZdXbZ5x409ORtP3OD5Kz8OruuEI2JTqdnw53JnNMGeGFWRrnFGtfxUXBsA7kpEL6lbq4phBB1rEoJeWpqKo6OjqX2Ozk5kZJS/hLHP/zwA0ePHmXp0qWVvt7KlStxcHAwPjw9PasSrqhvinvHu4wDu9opx2ZKr7ZOPNDagQKtjk1h1+rsukI0JgcvJRFzOxs7KzXje7WuuwubmUOfmYbt0HWgl4pJQojGp8oDDU0tj6zX68tdNjkvL4+//e1vLFmypMRwl4osXLiQ9PR04+P69etVDVfUF+k34MJOw3a/F+v00iqVythL/sWxWPK1RXV6fSEag8+OGIZ8TezTBlvLOl7kueczYNEMbl+CK/vr9tpCCFEHqpSQOzk5kZqaWmp/WloaTk5OZZ63atUqzMzMmDhxImlpaaSlpVFQUIBOpzNum2JpaYm9vX2Jh2igjn9imJjV9kFoWbkhSzVpVNeWtLC34nZWPj+EJ9T59YVoyC7EZ3A0OhlzMxVT+7er+wCsHKDHM4bt0I/q/vpCCFHLqpSQd+rUqdRY8fz8fKKjo0uNLb/XxYsXuXLlCq6urjg5OeHk5MTmzZuJiorCycmJDRs23F/0omEoyIZTGw3bddw7XkxjbsaU/m0BQ0+fXm57C1FpG+5MiB7RpQWtHGt/MrZJfWcCKog+AEmVq+olhBANRZUS8lGjRrF//36Sk5ON+3bs2EF+fj6jRo0q87wFCxZw8ODBEo/hw4fTrl07Dh48yGOPPXb/r0DUmKzUFI5u3URWavnzAars7P8gLw2cvKCDcuUuJ/Vpg7XGnKiEDI79kVzxCUIIkjLz+P5sPHB3grQinL2g4yOG7dD/KBeHEELUgiol5DNnzsTR0ZHHH3+cvXv38uWXX/Lyyy8zefLkEj3kzz33HGr13TGGHTt2JCgoqMSjRYsW2NraEhQUhIeHR829InHfslNTOLZtM9k1mZDrdIaJWGAoX2ZmXnNtV5GjjQXjerUCYMMRKYEoRGV8FXqNgiIdPdo40rNN2UMT60S/lwz/hn8N2beVjUUIIWpQlRJyR0dHDhw4gK2tLWPHjmXu3LlMnDiRTz8tuWBDUVERRUUycU4Av/8EKdFg6QDdJysdDdMGGHr49l80VIwQQpQtr7CITaGxgMK948Xa9IOW3aEoH07KUEchRONR5SorHTp0YO/evWRnZ3Pr1i3WrFmDtXXJMYUbN26scIzuxo0biYyMrOrlRQ3LSk0h8Y8rhkdMNACJMdHGfdUevlI8AavXFLBsVs1oq8/HtRmDO7qh18tCQUJU5LuzN0jOLqCVozUj/OuuVGmZVKq7veTHPwWtrCsghGgc6rh2lahvIvbt4di2zSX2/fzJWuN2v/ET6T/hPnu2b0ZCzC+guqeOcD3w3INeHLiYxNaTcfy/oX442GiUDkmIekev17PhyFUApvZvi9q8yv03taPzX+Hnf0JmAkR+C90nKR2REEJUmyTkTdwDQ0bi06svYOgZ//mTtQx94WXcvXwAsHVyvv/Gj93pHe/8GDjWn0Wd+vs0p2MLOy7ezOR/x68xO8hH6ZCEqHd+/f02lxIzsbUw58mANkqHc5fawrDS7/43De8x3SYaes6FEKIBqyddHkIpzZyccff2NTzuJOHuXj7Gfc3uNyHPSIBzWw3b/V6uoWhrhkql4vmB3gBsPBpDgVancERC1D+f/voHAE8EeOJgXc/uIvWaBhobSIyEPw4pHY0QQlSbJOSidhz/BHSFhklYrXspHU0pj3XzwM3OksSMfHZFxCsdjhD1ysWbGfz6+23MVDB9QD2YzPlnNs7Q42nD9jFZKEgI0fBJQi6MbJ2c6Td+YvWGqYBhIaDiCgjFE7DqGQu1mXHFwU9/lYWChLjX+l/vLgTk6WyjcDRlCJwNqODKz5B0UelohBCiWiQhF0bNnJzpP2Hy/Q9TKXbvQkB+ZS8YpbTJfe9ZKChaFgoSAiApI4/vzt4AMA7tqpecve8uFHTs38rGIoQQ1SQJuahZuqK7t5D7vaToQkAVcbSxYELv1sDd8bJCNHVfHIulsEhPr7ZOyi8EVJH+d+anRHwNWUnKxiKEENUgCbmoWZdCIDUGrBwbRDmy6QO8UKng4KVbXEnKVDocIRSVU6DlqzDDQkAzBtbDseN/5tkXWvWGogI4sV7paIQQ4r5JQi5q1tE7t457TwcLW2VjqYR2LrYM7eQO3B03K0RT9e2pONJyCmnjbMPQzvVgIaCKqFTQf45h+8R6KMxVNh4hhLhPkpCLmhN3Eq6HgpkG+rygdDSVNuMvhnGy28/c4FamrPwnmqYinZ7Pjhi+lE4f0A5zswZS27vjaHBsAznJEL654uOFEKIekoRc1JziiVVdJ4B9S2VjqYLebZ3o5ulIgVbHV6GxSocjhCL2RyVyNTkHeys1E3rXn4W8KmSuhsAXDdvH/gM6WVdACNHwSEIuakZqLFz4zrBdT0sdluX/t3ff0VFVexvHvzPpCSkDJKGH0EOTJgiCFCNNEQGx4VWx4fWKKDa89ooVvdeO+iIqIliwIggICgICBpASWoDQE0gP6TPz/nEgXKQGQvZM8nzWmsXOyTnkYYA5v9mzi81mKx0v+8nSZPKLnIYTiVS8w0O2RlwQQ0iAl23i3P56CAiHtM2webbpNCIiZaaCXMrH0rfB7YJGvaFWa9Npyqx/q1rUcwSRfrCILxN2ndHvkZqczTcTEkhNzi7ndCLnVsKODJZtT8fPx8aNXRuajlN2AaHQ6Sar/ft/jUYRETkTKsjl7OWlQ8LHVvvCu81mOUO+PnZu6W71kn+wcCtOV9k3CtqwdB+7N2Wycem+8o4nck5N/NVa9nNwu7rUCg80nOYMdfmnNX9lx2JrPksZ5Waks/iLKeRmpJ+DcCIiJ6eCXM7e8g+hOA9qtbF6yL3UVZ3qEx7kR3JaHj+vO72iOjstn9TkbPbvyGHLihQANq9IYf+OHFKTs8lO06oP4tm2HTjI7PXWv/fbL/LgjYBOJaw2tL3Kav/+nzJffjAjnSVfTuWgCnIRMcDLBgqKxykugGXvWe1ud1vLkHmpkABfbugawxu/bOG937bSv3UtbKf483zyyJJjjuXnFDP9+eWlX//r3T7lnlWkvHywcCtuN/RpEUWz6FDTcc5Ot9Gwagokfg9pSVCjselEIiKnRT3kcnZWT4WD+yGsHrQaYjrNWbuha0P8fe2s2pnJ8u0Zpzw/fmRLbCdYHs5mtxE/smV5RxQpNwdyC/nyT2vOhFf3jh8WFQdN+wLuIzsGn0RuRjopW7dYj21JAKRsSyo9puErIlJR1EMuZ87lOrLUYdc7wcfPbJ5yEBkawLAO9Zi6bAcTf0uic2z1k57fvEstqtcOOapH/LDh4zoR2cDLexylUvt4STKFJS7OqxdOl1P8W/ca3e6GzT9bPeW9/w0hNU946l9zf2LJl0evXT5n4hul7a5XXku34SPOWVQRkcNUkMuZ2zgT0rZAYDh0uMF0mnJzW49YPl++g7mJqWxOyaHp6X6MbwPc//OriAfLKyrh4yXbAbj9osanHJ7lNRp2hzodYE8CLJtoFeUn0DZ+AI07dgGsnvE5E9/gkttHEx1rDXUJcVSSNyki4vE0ZEXO3OJDy4t1usVadqySaBRZjUviogF4f+HWU54fFOpHcJg/UQ1C6Xldc6IahBIc5k9QqPd/YiCV1xcrdpGZV0yD6sH0b13LdJzyY7MdWe1p2ftQlHfCU6s5qhPdqIn1OFSER8c2Lj1WTQW5iFQQ9ZDLmdnxB+z8A3z8ocso02nK3aiejfl5fQrfrNzD/X2bExV24qXgqjkCueG5bth9bdhsNlr1qIOrxI2Pn97vimcqcbr4YJH1ZvO2HrH4nGAehNeKuxwcDSFjuzV0pfNtphOJiJyUKgY5M4d7x9teDaGVqHftkI4xDjrFOChyupi0ePspz/fxs5d+5G+z2VSMi0ebtW4fO9PzqR7iz5Ud65uOU/7sPtD1Lqu95E1wlpzykhBHdbpeea2GqYiIEaoapOz2b4QNP1jtbqPNZjmHDq868emSZLILig2nESkfbrebd3+1VhT5xwUxBPn7GE50jrQbAUHVrV7yxG9PeXo1R3W6DR+hYSoiYoQKcim7w1tTt7gMIpubzXIOxcdF0ySqGjmFJXz2xw7TcUTKxaItB1i7O5sgPx9u7NbQdJxzxz8YutxhtRe9Bm7NtBYRz6WCXMomaxf8Nc1qX3iP0Sjnmt1u446e1kSvDxdto6DYaTiRyNl7Z4HVO35N5/pUD/E3nOYc63wb+IXAvjWQNM90GhGRE1JBLmWz5G1wFUPDHlD/fNNpzrnLz6tDnfBA9ucU8nXCbtNxRM7Kqp2ZLE5Kw9du49YelWAjoFMJrg4db7Lai143mURE5KRUkMvpy0uHPz+y2t3vMZmkwvj72ksLl/d+S8Lp0sfe4r3ePdQ7PrhdXepGBBlOU0G6/gvsfrB9Iew8dgMvERFPoIJcTt+yiVB8EGq1gcYXm05TYa7pXJ+IYD+S0/L4ae1e03FEzsiW1Fxmr98HwB09q0Dv+GHhda3VoMAaSy4i4oFUkMvpKToIf7xrtbvfa22+UUUE+/ty06HJb+8sSMKtyWHihSb+loTbDZe0jD793WcriwvHADbY+COkbjCdRkTkGCrI5fQkfAz5GeCIhZZXmE5T4W7s2pBgfx/W7clm4eYDpuOIlMnerHxmrLTmQPyzV2PDaQyIbAZxl1nt3/9jNouIyHGoIJdTKymCxW9a7QvHWJtuVDGOEH+u7dwAOLJKhYi3+HDhNoqdbi5oVJ0ODRym45hx4b3Wr2umQ+ZOs1lERP5GBbmc2povIHsXVIuG8641ncaYW3vE4udjY8nWNFbuyDAdR+S0ZBws4rNl1jr6/+zVxHAag+p1hNiLwFVi7d4pIuJBVJDLybmc8PvrVvuCO8Ev0Ggck2qHB3FFu7oAvDVfveTiHSYv2U5ekZOWtcO4qGlN03HM6n6ol/zPyZC732wWEZH/oYJcTi7xOziwCQLDodPNptMYd0evxthsMDcxhcS92abjiJxUTkExk37fDsCdvRtjq0KTsY+rUW+o0x5K8mHp26bTiIiUUkEuJ+Z2w2+vWu0u/4TAMLN5PEDjyGpc2qY2AG/N32I4jcjJfbp0B1n5xTSODGFA69qm45hns8FFD1jtZe9bE9VFRDyACnI5sU2zIWUN+FeDLqNMp/EY/+ptjcP9cc1ekvbnGk4jcnz5RU4+XLQVgDt7NcHHXsV7xw9rNgCiWkJRjlWUi4h4ABXkcnxuN/z2stU+/xZrC2oBIK52GPFx0bjdWnFFPNfny3dwILeI+tWDuLxdHdNxPIfdDj3us9pL34bCHLN5RERQQS4nsnUB7F4BvoHQ9S7TaTzOXX2sXvIZK3ezMz3PcBqRoxWWOHnvV6t3/J89m+Dno5f6o7QaAtUbW0NWVvyf6TQiIirI5QQWHho73vEmqBZlNIonalc/gh5Na+J0uXnvN/WSi2f5OmE3+7ILqBUWyLCOdU3H8Tx2nyO95IvfhOJ8s3lEpMpTQV7FFe/ZQ/66dUc/5n5OfsJS8jODKG50temIHuuuQ2PJpy/fRUp2geE0IpYSp4u3F1gTjm+/qBEBvlVvI6/T0vYqCG8AB1Mh4RPTaUSkivM1HUDMKd6zh6T+A3AXFR3nu5EA2H4ZSeNZP+FXR2NQ/65Loxp0blidZdvTmfjbVh67rKXpSFJFOV1OElIT2J+3n8RdsDPdSY2QwNLdZeU4fPyg+xj48T5rr4WON4Gvv+lUIlJFqYe8CivJyDhBMX6Eu6iIkgwtDXYih8eST/kjmbTcQsNppCqamzyXfl/14+bZN/PQwof4aNtDhDR5kd4dUwjyV+/4SbW7HqrVguzdsHqq6TQiUoWpIBc5Cz2a1uS8euEUFLt4f+E203GkipmbPJexC8aSkpdy1HG7bxaz97/E3OS5hpJ5Cb9A6Dbaai98FZzFZvOISJWlglzkLNhsNu6+uCng4uOV85ie+B3L9y3H6XKajiaVnNPl5IVlL+DGfew3bWADXlz2ov4tnkqnkRASCZnJ8Nc002lEpIrSGHKRs+QK+ouI5i/htGfyzDLrWHRwNOM6jyM+Jt5sOKm0ElITjukZ/19u3OzL20dCagLn1zq/ApN5j+I9e6whefWugyVvw1cvgm8bsFu3Rl+HQ/NnRKRCqCAXOQtzk+dy36/34bYf3UuZmpfK2AVjmdBrgopyOSf25+0v1/OqmmMntUcCJfDlNaXn2Pz9NaldRCqEhqyInKGTDRk4fExDBuRciQyOLNfzqhpNahcRT6KCXOQMlWXIgEh56xDVgejgaGzYjvt9GzZqBdeiQ1SHCk4mIiJlpYK8CvN1OLD5n3zdXZu/P74ORwUl8i4aMiAm+dh9GNd5HG7cuP/2Ic3hIv2hzg/hY9fShyIink5jyKswvzp1aDz5VUomXQM2Gwz/GBxHbySiSU0npiEDYlrv+hcTkXMr6YFfYPPLKj0eHRzNQ50f0vwFEREvoYK8ivPb8CF+1YuhzVXQfYDpOF7l8JCB1LzU4y89BxoyIOfUzDV72bmrCaGBj/DfkRHkOzOIDI6kQ1QH9YyLiHgRFeRV2Z5VsHEm2Oxw0QOm03idw0MGxi4Yiw3bUUX54SEEd7Ydq8JIzgmny81/520G4NbuTegd09RwIhEROVMaQ16V/fKs9WvrKyGymdksXio+Jp4JvSYQFRx11HFft4OC3dezbnOMoWRS2X23ejebU3MJC/Tlpgsbmo5TeWn3ThGpAOohr6p2LIUtc8DmA73GmU7j1eJj4uldvzcJqQnsz9tPZHAkOZn1uPmjBD5emsytPRpRKzzQdEypRIqdLl6bY/WOj+rZmPAgP8OJvM/hSe0nW/rQZnfju2setG1XccFEpEpSQV4Vud0w7xmr3f56qNHYbJ5KwMfuc9RuiO5oN+c3dLB8ewZv/LKZ54a0MZhOKpsvVuxiR3oeNav5M1K942fEr04dGs/66cTrjK+bge/yCfitfw/i/wn+wRUbUESqFA1ZqYq2zofkReDjDz0fNJ2mUrLZbDzQrwUA05bvZEdanuFEUlkUFDtLx47/q3cTgv3Vr3Km/OrUIahVq+M/hj6IX926kJsCyyaajioilZwK8qrG7YZ5T1vt82+F8Hpm81RinWOrc1GzSEpcbl6fu8l0HKkkPl2azL7sAuqEB3JdlwanvkDOjK8/9HrYav/+OhRknfR0EZGzoYK8qtnwI+xZCX4h0H2s6TSV3v19rcmyM1btZnNKjuE04u1yC0t4Z0ESAHdf3JQAX63gc061vRpqNoP8DFjytuk0IlKJlbkg37RpE/379yckJISoqCjGjBlDfn7+Sa/Jzs7mySefpEuXLkRERBAZGUn//v1JSNCW4hXK5YT5z1ntC+6Aatqw5lxrWy+C/q1q4XbDhDnqJZezM2nRNtIOFhFbM4RhHfXp1jln94Hej1jtJW/CwTSzeUSk0ipTQZ6ZmUmfPn3Iycnhq6++4pVXXmHKlCncdtttJ71ux44dvPfee8THxzNt2jQmTZqE0+mkW7duKsor0tqvIXU9BIRDt9Gm01QZY/s2w2aDn9buY+1ufewtZyYrr5iJC7cCcE98U/x89AFnhYi7HGq1haJc+P0102lEpJIq02yg9957j4yMDFatWkXNmjWt38DXlxEjRvDII48QFxd33OtiY2NJSkoiOPjILPX4+HgaNWrEG2+8waRJk87ijyCnxVkMC5632hfeDUEOs3mqkGbRoVzRri4zVu7m5dkbmXxzZ9ORxAu991sSOQUltKgVyqC2dUzHqTrsdujzGHw2HJa9Dxf8C8Jqm04lIpVMmbpYZs6cSXx8fGkxDjBs2DACAgKYOXPmCa8LCQk5qhgHCAwMJC4ujj179pQxspyRhI8hfSsE14Qud5hOU+XcE98UX7uNXzftZ0mSPvaWsknJLuD/ft8GwNhLmmG32wwnqmKaXgL1L4CSAvj1BdNpRKQSKlNBnpiYeEwveEBAAI0bNyYxMbFMP/jgwYOsXLnyhL3qUo4Kc2HBoZtIz4cgoJrZPFVQTI2Q0hUxXvgpEbfbbTiReJPX5myioNhFxxgHl7SMNh2n6rHZ4JKnrHbCx7B/o9k8IlLplKkgz8jIICIi4pjjDoeD9PT0Mv3gRx99lLy8PO66664TnlNYWEh2dvZRDzkDS96Eg6lQvRF0vMl0mirr7oubEuLvw+pdWfy4Zq/pOOIlNqfkMH3FTgD+PbAFNpt6x41ocAG0uAzcLpj7lOk0IlLJlHlW0PFuBm63u0w3ic8++4zXX3+dCRMm0KRJkxOeN378eMLDw0sf9evXL2tcyUmB3/9rtS9+3FpbV4yoWS2AUT2tXVFfmrWRohKX4UTiDV6ctQGXG/q1iqZjTHXTcaq2i58Amw9s/BGSF5tOIyKVSJkKcofDQcZxthnOzMzE4Ti9SYJz5sxh5MiRPPDAA9x5550nPffhhx8mKyur9LFz586yxBWwxjsWH4S6HaHlFabTVHm39oglMjSAHel5TPkj2XQc8XB/bE1jbmIqPnYbD/ZvYTqORDaDDjdY7TmPWxutiYiUgzIV5HFxcceMFS8sLCQpKem0xoIvW7aMoUOHMnz4cF588cVTnh8QEEBYWNhRDymDA5vhz8lW+5JnrHGQYlSwvy/3xlubBb3xyxayC4oNJxJP5Xa7ef6nDQBcc359Gkdq7odH6DUO/IJh13JI/M50GhGpJMpUkA8cOJB58+aRlnZklYgZM2ZQWFjIwIEDT3ptYmIiAwcO5MILL2TSpEkaB1kR5j4Jbic0GwANLzSdRg65qlM9GkeGkH6wiPd+TTIdRzzUzDX7WL0zk2B/H8bENzUdRw4LrXVkH4e5T1lLyoqInKUyFeSjRo0iIiKCwYMHM3v2bD755BNGjx7NiBEjjuohv+WWW/D1PbLEeWpqKv369cPPz48HHniAP//8k6VLl7J06VJWrlxZfn8aOWLHH7DhB7DZIf5J02nkf/j62Hno0PCDDxdtY19WgeFE4mmKSly8PNvqHb+tRyOiQgMNJ5KjdBsNIZGQngR/fmQ6jYhUAmUqyCMiIvjll18ICQlh6NChjB07lmuvvZb333//qPOcTidOp7P06/Xr17Nz50727dtHfHw8Xbt2LX0MGTKkfP4kcoTbDXMes9rtr4cojT31NJe0jOb8hg4Kil1MmKMl1ORoU5ftYHtaHjWrBXDbRY1Mx5G/Cwi1lpAFa0nZAq0AJiJnx+b2ogWRs7OzCQ8PJysrS+PJT2bt1/DlSGuc4+gE7SrnoRJ2ZDD07cXYbPD9Xd1pXTfcdCTxAFl5xfR8ZT6ZecU8c0Vr/nFBjOlIcjzOYniri9VL3v1efRJ5Crp/i5xcmZc9FA9XnG/N/ge48B4V4x6sQwMHg86rg9sNT/+wvspvFpSanM03ExJITa7avY2vz9tEZl4xzaKrce35WurVY/n4Qd9nrfaStyB9m9k8IuLVVJBXNovfhKydEFbvyMQj8VjjBrQg0M/Osm3p/LR2n+k4Rm1Yuo/dmzLZuLTqPg9bUnP5ZIm1HOZjl7XE10cv0R6t+QBo1AucRUeGCYqInAG92lcm2Xtg0QSrfclT4B9sNo+cUt2IIG6/yNos6PmZiRQUO09xReWSnZZPanI2+3fksGVFCgCbV6Swf0cOqcnZZKflG05YsZ79cT0lLjfxcVH0aBppOo6cis0G/cZbk+cTv4dtC00nEhEv5XvqU8RrzH0KivOg/gXQepjpNHKa7ujZiOnLd7IrI58PF23jX71PvHttZfPJI0uOOZafU8z055eXfv2vd/tUZCRj5m9MZcHG/fj52Hjk0pam48jpim4JnW6G5R/ArIdh1K9g9zGdSkS8jHrIK4tdK+Cvz612//HaBMiLBPv7Mm6AtRLOW/O3kJJddZZBjB/ZEpv9+P9WbXYb8SOrRmFa7HTx7A/rAbipW0Nia4YYTiRl0uvfEBgOKWsg4WPTaUTEC6kgrwzcbpg1zmq3GwF1O5jNI2U2uF0d2jeIIK/IyUuzqs4yiM271GL4uE7H/d7wcZ1o3qVWBScy45MlySTtP0iNEH9GX6xNgLxOSA3o9bDV/uVZKMgym0dEvI4K8spgzRfWNs5+IXDx46bTyBmw2Ww8MagVAF8l7GL1zkyzgUyw/e3XKiL9YBGvz90EwH19mxMW6Gc4kZyR82+Fms0g7wD8+pLpNCLiZVSQe7uC7CPLHPYYa23rLF6pXf0IhravC8Dj363D5aoayyAGhfoRHOZPVINQel7XnKgGoQSH+RMUWjUK05dnbyS7oIS42mFcrWUOvZePH/R73mr/8S6kbjCbR0S8iiZ1ersFL0DOXnDEQte7TKeRszRuQAt+Xp/C6p2ZTFuxk2s7NzAd6Zyr5gjkhue6Yfe1YbPZaNWjDq4SNz5+lb+/IGFHBp8v3wHAU5e3wucE4+nFSzS9BJoNgE0/wcz74cbvNZ9HRE5L5b/jVWb71lg9MQADXwG/QLN55KxFhQUy9pJmALzw0wbScgsNJ6oYPn52bIcKF5vNViWK8RKni8e+WYvbDcM61KNzbHXTkaQ8DHgBfINg+0JrOKGIyGmo/He9ysrlgh/vA7cTWg6GpvGmE0k5uaFrDHG1w8jKL+bFWfrYu7L6dGky6/ZkExboy8MDW5iOI+XF0RAuut9qz34E8jNNphERL6GC3Fut/gx2/mFN5Ow33nQaKUe+PnaevaI1ANNX7GLF9nTDiaS8peYU8OrP1kTOB/u3oGa1AMOJpFx1Gw01msLBVJj/vOk0IuIFVJB7o7x0+PnQNs29H4bwumbzSLnrGOPgmkMT/B79Zi0lTpfhRFKenv8xkZzCEs6rF14l5glUOb4BcOkrVnv5+7BnldE4IuL5VJB7o3lPQX46RLWELneYTiPnyEP9W+AI9mPDvhw+WrzddBwpJ4uTDvDNqj3YbPDsFW00kbOyatQLWl8Jbhf8ONYaZigicgIqyL3NrhXw52SrfekEa6ktqZQcIf481N8aW/zanE3sy6o6O3hWVkUl1kROgOu7xNCmXrjhRHJO9XsO/ENh95+Q8JHpNCLiwVSQe5OSIvjubsBt7cgZ09V0IjnHrupUn/YNIjhY5OTxb9fidleNtckrq7cXbCFp/0FqVvPn/r7NTceRcy20FvR51GrPeRKy9xqNIyKeSwW5N1k0AVLXQXBNuOQZ02mkAtjtNsYPbYOfj42f16fw4xrd0L3Vxn05vDV/CwCPD2pFeLA+3aoSOt8GdTpAYdahlbH0plpEjqWC3FukrIffDk0SGvgShNQwm0cqTItaYdzZqwkAT3y7joyDRYYTSVk5XW4e/HI1xU438XHRDGpb23QkqSh2Hxj8Ftj9YOOPsG6G6UQi4oFUkHsDlxO+uwtcxdB8ILQaajqRVLB/9W5C8+hQ0g4W8fQP603HkTL6v0XbWL0ri9BAX54b0rp0EySpIqJbQo/7rPbMB+Bgmtk8IuJxVJB7g6VvW5OCAsKtiZy6mVc5/r52XryyLXYbzFi5m/kbUk1HktO0/cBBXvl5IwCPDIwjOkw76lZJPe6zVsbKOwCzxplOIyIeRgW5p0tLgl+etdp9n4EwfdRdVbWrH8Et3WMB+PeMNeQUFBtOJKficrl56Ku/KCxxcWGTGlx9aG15qYJ8/eHyN8FmhzXTYdNs04lExIOoIPdkLpe1qkpJAcT2hA43mE4kho29pDkxNYLZm1XACz9tMB1HTmHq8h38sS2dID8fxg9pq6EqVV29jnDBnVb7+3ugINtoHBHxHCrIPdmKDyF5EfgFw6D/aKiKEOTvwwtD2wIw5Y8d/L7lgOFEciI70/MYP9N603R/v+Y0qBFsOJF4hN6PgCMWcvbA7H+bTiMiHkIFuafavxF+PrR+7cVPQPVYs3nEY3RtXIPrL7C2W79v+moy87TqiqdxutyMnb6K3MISOsY4uKlbQ9ORxFP4B8PgNwEbrPwEEn8wnahc5Gaks/iLKeRmpJuOIuKVKlVBXmleEEqK4OvbrKEqjftA59tNJxIP8++BcTSqGcK+7AIemaENgzzNe78lsXx7BiH+Prx2VTt87Pp0S/5Hw+7QbbTV/v5uyEkxm6ccHMxIZ8mXUzno7fdfEUMqVUFeaV4QFoyHvashyAGD3wZ7pfprknIQ7O/L69e0w9du48c1e5mxcrfpSHLI2t1ZTPh5EwBPXt5KQ1Xk+Po8CtFtIC8Nvv2XNgwSqeJU6Xma5MWw6DWrPei/WlVFTqhtvQjuiW8KWBsG7UzPM5xI8oucjPl8JSUuNwNa1+LKjvVMRxJP5RsAw94HnwDYMgeWf2A6UZnlZqSTsnWL9diWBEDKtqTSY17/abVIBfI1HeBs5Wakl/aI/+8LwmEhjupUc1Q3kq3MCrLg61GAG9pdDy0vN51IPNw/ezVhwcb9rEjO4L7pq5l6+wUaHmHQ+J8SSdp/kKjQAJ4f0karqsjJRcXBJU/DrIesOUOxPSGymelUp+2vuT+x5MupRx2bM/GN0nbXK6+l2/ARFR1LxCvZ3F40+DQ7O5vw8HCysrIICwsDYPEXU455QfhfXvWCMOMOWD0VHA3hjkUQEGo6kXiBnel5DPjPQnILS3iwf3Pu7NXEdKQqaf7GVEZOWg7Axzd35qJmkYYTiVdwuWDKMEj6BWqfB7fMtdYs9wJ/7xCbM/ENLrl9NNGxjYGjO8SOd/8WkSO8voe8bfwAGnfsApz4BcErrJ5mFeM2OwyZqGJcTlv96sE8eXkr7v9iNRN+3kSX2Op0jPGSf/eVREp2AQ98sRqAkRc2VDEup89ut+YKvdPVmjs07yno95zpVKel2nE+gY6ObUx0I3UKiJSV148hr+aoTnSjJtbjUBF++AUhulET7xiukrIefrjHavd8CBp0MRpHvM+wDnUZdF4dSlxu7vpsJWm5haYjVRnFThd3fZbAgdwiWtQK5aH+LUxHEm8TVhsGv2W1l7wJ678zm0dEKpzXF+RerzAHpt8AxXnWEocXPWA6kXghm83G+KFtaBQZwt6sAu6Ztgqny2tGo3m1l2dvZPn2DEIDfHnn+o4E+vmYjiTeqMWlR5ZC/PZfkJZ08vM9TIijOl2vvNZ7PpUW8TCVqiD3uhcEtxu+Gw1pmyGsLgx9H+y6mcuZqRbgy7vXdyTIz4eFmw/wxi+bTUeq9Gat3cfE37YC8PLwtsTWDDGcSLzaxU9Ag65QmH2ooybfdKLTVs1RnW7DR3jHp9IiHqhSFeRe94Kw7H1YNwPsvjD8IwipaTqReLlm0aE8P7Q1AP+Zt5nfNu03nKjySk47WDpu/NbusfRvrSVK5Sz5+MGVkyAkElLWwsz7TScSkQpSqQpyr7JzOcz+t9Xu+xzU72w2j1QaQ9rXY0SXBrjdMObzlezJ9J5eNm9RUOzkn58mkFNYQqcYBw8N0LhxKSdhteHK/7Mm+K/8FBI+MZ1IRCqACnITclLgi5vAVQwtr4Auo0wnkkrmscta0qZuOBl5xfxzSgIFxU7TkSoNt9vNv2esYf3ebGqE+PPmdR3w89FLqZSj2Iug9yNWe+b9sPtPs3lE5JzTXaSiFefD59dC9i6o0RQufwO0eYiUs0A/H94e0YGIYD9W78zk/i9W49Ikz3Lxzq9JfJ2wGx+7jf9e255a4YGmI0ll1H0sNOsPJQUw9VrI2mU6kYicQyrIK5LLZW3+s/tPCHLAddMgUBskyLlRv3ow717fET8fGz/8tZfX52mS59n6ac1eXpq1EYAnB7Xkwiaa9yHniN1uTfSPagm5KTD1GijMNZ1KRM4RFeQVacHzsP4bsPvB1VOgRmPTiaSSu6BRDZ4b0gaA/87bzDcrdxtO5L3+2pXJvdNXAXBTt4b8o2tDo3mkCggMszpuQiJh3xr4+jZwafiZSGWkgryirP4cfnvZag/6DzS80GweqTKu6lSfO3pab/4e/PIvVmxPN5zI++zNyufWySsoKHbRq3kkj14aZzqSVBURDeCaqeATABtnwpzHTScSkXNABXlFSF5irTcO0P1eaD/CbB6pch7s15y+LaMpcrq4/ZM/2ZGWZzqS1zhYWMItH60gNaeQ5tGhvHFte3w1iVMqUv3zYcg7VnvJm/DnR0bjiEj5013lXNu31hr75yyCuEHQR70bUvHsdhuvX9OO1nXDSD9YxA3/9wep2QWmY3m8gmInoz75k/V7s6lZzZ8Pb+pEaKCf6VhSFbUeBr0OLZX7w1hI/N5sHhEpVyrIz6UDW+CTK6AgE+qdD0PesybqiBgQ7O/LBzecTz1HENvT8vjHh8vIOFhkOpbHKna6GD11JYu2HCDY34f3b+hEPUew6VhSlfV8ENqNALcTvrwZtswznUhEyomqw3Mlcwd8PBgO7odabWDEl+CvbbXFrFrhgUy5tQtRoQFsTMnhxknLyCkoNh3L4zhdbu7/YjVz1qcQ4Gvngxs70b6Bw3QsqepsNhj0X2g52PrU9fMRkLzYdCoRKQcqyM+FnH0w+XJrrfGazeAf30BQhOlUIgDE1Ahhyq1dqB7iz1+7srjloxXkF2nlhsPcbjePfrOGb1ftwddu453rO9CtsZY3FA/h4wtDP4CmfaEkH6ZcBbsTTKcSkbOkgry85aXDx1dAxjaIiIEbvoUQ3czFszSNDuXjmzsTGuDLsu3pjPr0TwpLVJS73W6e+zGRqct2YrfBf65pT58W0aZjiRzN1x+u+hhiukNRDnw6FFLWm04lImdBBXl5yt4LH10K+xMhtLZVjIfVMZ1K5Lha1w1n0sjzCfLz4bdN+7l18gryikpMxzLG5XLz1Pfr+WDRNgBeGNaWS9vWNpxK5AT8guC6z6FuR8jPgMmXwZ6VplOJyBlSQV5e0pLg//pC6nqoVssqxqvHmk4lclKdGlbngxs7EeTnw8LNBxjxwR9k5lW9iZ7FThdjp6/io8XbAXhmcCuu6lTfbCiRUwkIteYn1W4HeWnw0WWw7TfTqUTkDKggLw97/4L/629N5HTEwi2zIbK56VQip+XCJjWZclsXwoP8WLkjk6veW8K+rKqzJGJ+kZPbP17BN4fGjL9+dTvtwineI7g63Pg9NOwBRbnw6TAtiSjihVSQn63kxdYwlYOpEN0GbvkZHA1NpxIpkw4NHHxxR1eiwwLYlJLLsHcWs+3AQdOxzrms/GL+8eEfzN+4n0A/O+/f0Ikr2tc1HUukbALDrJ7yFpdZq69MvwESPjGdSkTKQAX52Vj7NXwyBAqzoUE3GPkjVIsynUrkjDSLDuXLO7oRWzOE3Zn5DH93MSu2p5uOdc7sSMvj6veWsCI5g7BAXz69pQu9W+j/r3gpv0AYPhna/wPcLvjuLljwIrhcppOJyGlQQX4mnCUw+xH4ciSUFECz/vCPryEw3HQykbNSv3ow00d1pVWdMA7kFnHNxKV89Ps23G636Wjlav7GVAa9uYgN+3KIDA1g2qiudGpY3XQskbPj4wuXvwEXjrG+XvA8fH4d5GcajSUip2Zze9GdNjs7m/DwcLKysggLCzMTIne/VYhvX2h9feE90Ocx64VQpJI4WFjCQ1/9xQ9/7QVgSPu6PD+kDUH+PoaTnR2Xy81b87cwYe4m3G44r34E717fgdrhQaajiZSvlZ/CD2PBWQjVG8HVUyC6pbE4HnH/FvFgKsjLYudya2xezh7wrwZXvAMtL6/4HCIVwO128+GibYz/aQNOl5u42mG8d31HGtTwzu3js/KLuW/6KuYmpgJwXZcGPDGoJQG+3v0mQ+SE9qyEaf+ArJ3gFwyD34TWw4xEMX7/FvFwKshPR0kRLJoAv70CrmJr982rP9VKKlIlLElKY/TUBA7kFhEa4Msjl8Zx9fn1sdlspqOdtoWb9/Pw12vYlZGPv6+dZwe35qrztayhVAEH0+Crm2HrAuvrdiOg77PW6iwVSAW5yMmpID+VXX9ak2NSD+2CFnc5DH7LmtUuUkXszcrnX1MSSNiRCUDXRjV4YVgbYmqEmA12Cpl5RTz7YyJf/rkLgHqOIN4e0YG29SLMBhOpSC4n/PIMLHodcENIFFz6CrQcXGERVJCLnJwK8hMpOgjzn4elb1sz1oNrwsCXoNVQ8KKeQZHy4nS5mfT7Nl75eSMFxS4C/ezcd0lzRl7YEF8fz5sf/tOavTz27ToO5BZis8GNXRvyQL/mhARovodUUTv+sDqYDmyyvo4bBANfgdBa5/xHqyAXOTkV5H/nLIZVn8FvL1vj7gDaXg39xkNIjXPzM0W8yI60PMZ9/ReLk9IAaFErlHsvaUbfltEeMYxl5Y4MJszZxMLNBwBoHBnCS1e2pWOMVlERobgAFr4Ci14DVwkEhEO3u6DLHef0k18V5CInV+ZurU2bNtG/f39CQkKIiopizJgx5Ofnn9a1kydPpkWLFgQGBtK6dWu++OKLMgc+Z5wl1qz0NzrC93dbxXhYPbjuCxg6UcW4yCENagQz5dYuvDisDWGBvmzYl8OoT/5k0JuLmLs+xdgSiX/tymTkpGUMeXsxCzcfwNdu4+4+TZg5poeKcZHD/AKhz6Nw+wKo3Q4Ks2D+c/CfttY8qcIc0wlFqqQy9ZBnZmbSunVrYmJieOyxx0hNTWXs2LH079+fTz/99KTXfvnllwwfPpxx48bRt29fvvnmG9544w1mzZpF3759T+vnH+8ddvGePZRkZJzwGl+HA786dU78m+ZnWBv8LHkT0rdax0KioPu90Gkk+Gk5NJETycwr4v2FW/no9+0cLHIC0LZeOLd0j6Vvy1qnvUyi0+UkITWB/Xn7iQyOpENUB3zsp762xOni96Q0Pl68nXkbrNVTfOw2hravy+g+Tb12RRiRCuFywroZ8OuLR4axBFWHC/4J510LESef+FyW+696yEVOrkwF+YsvvsjTTz9NcnIyNWvWBOCzzz5jxIgRrF+/nri4uBNeGxcXR5s2bZg+fXrpsX79+pGVlcXSpUtP6+f//T908Z49JPUfgLuo6ITX2Pz9aTzrp6OL8pIi2Pwz/PU5bJptbTUM1jjx7vdAp1vAXzdykdOVfrCIib9tZfLi7eQXW4V5tQBfBrSuxZAOdbkgtgZ2+/GHs8xNnssLy14gJS+l9Fh0cDTjOo8jPib+uNes35PN1wm7+Hb1HvbnFAJgt8EV7etyd5+mNKzp2ZNNRTyKywlrv7IK87QtR4437GEN2Ww5+JjhLGW9/6ogFzm5MhXkPXv2JCIigm+//bb0WGFhIeHh4Tz33HPcd999x71u27ZtNGrUiK+//pohQ4aUHp88eTIjR44kNTW1tMA/mb//h85ft47tw6485XUNp00hyFEEu5Zbj22/WT3jh0W3hnbXQYcbIaDaKX8/ETm+A7mFfLx4O1+v3M2ujCND2WqHB9K1UQ3aN4igfQMHzWuF4udjZ27yXMYuGIubo1+GbFjF+4ReE+hT/2K2pR1k5Y5MVu7IYNm2dDan5pae6wj247K2dRh5YUMaRer/r8gZc5bAuq8h4eMjm98B+AZaxXn9zlCvE9TtSH7SrtO7/371JUGtWqkgFzmFMi03kJiYyM0333zUsYCAABo3bkxiYuJJrwOO6UFv2bIlbrebDRs20L1797JEKZtJAyCi4Ohj1WpB2+HQ9hqo1frc/WyRKqRmtQDG9m3OPfHNWJGcwYyVu/jhr73szSrg65W7+XrlbgAC/ew0r1WNXdWePqYYB0qPPfDL0zh3lJCd7zzq+/4+duJbRjGkfT16NovE39fzVnkR8To+vtD2KuuRuRPWTIfV0+DARtgyx3oAYANXI6NRRSqbMhXkGRkZREREHHPc4XCQnp5+0uuAY651OBwAJ7y2sLCQwsLC0q+zs7PLEvcIl9MaF3743X29ztDgAjiNMaoiUnZ2u43OsdXpHFudJwa1YunWNKuHe2cmq3ZkkF1Qwtq0lQRXO/H4U4ASewZ5tk0E+Dalbb1w2jdw0K5+BBc2rkl4sF8F/WlEqqCI+tDjPug+FlLWQvKSI58yZ2yDzB1ApOmUIpVGmRfkPd6yZm63+7SWO/v7OYdHy5zo2vHjx/PUU0+VNeKxrpsGXfpo/XARAwL9fOjVPIpezaMAcLncbD1wkOmJWUzdfurrHxxYh5vb98PPA9c6F6n0bDao1cZ6dLndOnbwAPz2Pfz8ktlsIpVIme5wDoejtLf7f2VmZpb2dp/oOuCYazMzM4/6/t89/PDDZGVllT527txZlrhHhNZSMS7iIex2G02iqnFJ86andX6HejEqxkU8SUhNaNDZdAqRSqVMd7m4uLhjxooXFhaSlJR0yhVWgGOuXb9+PTabjRYtWhz3uoCAAMLCwo56iEjl0CGqA9HB0aUTOP/Oho1awbXoENWhgpOJiIhUrDIV5AMHDmTevHmkpaWVHpsxYwaFhYUMHDjwhNfFxsbSokULpk2bdtTxqVOn0rlz59NaYUVEKhcfuw/jOo8DOKYoP/z1Q50fOq31yEVERLxZmQryUaNGERERweDBg5k9ezaffPIJo0ePZsSIEUf1kN9yyy34+h49PP3pp59m+vTpPPLIIyxYsIB7772Xn3/+maeffvqMw/s6HNj8/U96js3fH9+TDKcREXPiY+KZ0GsCUcFRRx2PDo5mQq8JJ1yHXETM0v1XpHyVaR1ygE2bNjF69GgWLVpEcHAw1157LS+++CJBQUd2tLzpppuYPHnyMVtoT548meeff57t27fTpEkTnnzySYYPH37aP/uc7NQpIsad6U6dImKOduoUKT9lLshNysrKIiIigp07d+o/tIiIiJfIzs6mfv36ZGZmEh4ebjqOiMcp87KHJuXk5ABQv359w0lERESkrHJyclSQixyHV/WQu1wu9uzZQ2ho6HHXLj/8Dlw96KdHz1fZ6TkrGz1fZafnrGz0fJWdiefM7XaTk5NDnTp1sNu1jKnI33lVD7ndbqdevXqnPE9LJJaNnq+y03NWNnq+yk7PWdno+Sq7in7O1DMucmJ6myoiIiIiYpAKchERERERgypVQR4QEMATTzxBQECA6SheQc9X2ek5Kxs9X2Wn56xs9HyVnZ4zEc/jVZM6RUREREQqm0rVQy4iIiIi4m1UkIuIiIiIGKSCXERERETEoEpRkG/atIn+/fsTEhJCVFQUY8aMIT8/33Qsj7VlyxbuuOMO2rVrh6+vL61btzYdyaN98cUXXHHFFdSvX5+QkBDatm3LO++8g8vlMh3NY82ePZuePXsSGRlJQEAAjRo1YuzYsWRlZZmO5hVyc3OpV68eNpuNFStWmI7jkT766CNsNtsxj3HjxpmO5tE+/PBDzjvvPAIDA4mKiuLyyy83HUlE8LKNgY4nMzOTPn36EBMTw1dffUVqaipjx44lLS2NTz/91HQ8j7Ru3Tp+/PFHunTpgsvlUmF5Cq+++ioxMTG8/PLLREdHM3/+fO6++262bt3Kyy+/bDqeR0pPT6dbt27cc889OBwO1q5dy5NPPsnatWv5+eefTcfzeM888wwlJSWmY3iFWbNmHbXhTN26dQ2m8WxPPvkkr732Go888ghdunQhPT2dWbNmmY4lIgBuL/fCCy+4g4OD3fv37y89NmXKFDfgXr9+vcFknsvpdJa2b7zxRnerVq0MpvF8qampxxy799573YGBge6CggIDibzTxIkT3YB79+7dpqN4tMTERHdISIj73XffdQPu5cuXm47kkSZNmuQGjnrtlxNbv36928fHxz179mzTUUTkOLx+yMrMmTOJj4+nZs2apceGDRtGQEAAM2fONJjMc9ntXv/XXqEiIyOPOda+fXsKCgpIT083kMg71ahRA4Di4mLDSTzb3XffzR133EHz5s1NR5FK5KOPPqJRo0b07dvXdBQROQ6vr8wSExOJi4s76lhAQACNGzcmMTHRUCqp7BYuXEj16tWJiooyHcWjOZ1OCgoKSEhI4Omnn2bQoEHExMSYjuWxvvzyS1avXs3jjz9uOorXaNWqFT4+PjRq1Ijx48fjdDpNR/JIS5cupU2bNjzzzDNERUXh7+9Pz549WbVqleloIkIlGEOekZFBRETEMccdDod6L+WcWLFiBZMmTeKJJ57Ax8fHdByPFhMTw+7duwHo378/U6dONZzIc+Xl5TF27FjGjx9PWFiY6Tger3bt2jz11FN06dIFm83Gd999x6OPPsru3bt58803TcfzOPv27SMhIYF169bx7rvv4u/vz1NPPcUll1zC5s2bj3sfFZGK4/UFOYDNZjvmmNvtPu5xkbOxb98+hg0bRufOnXnooYdMx/F4M2fOJDc3l3Xr1vHMM88waNAg5syZozcyx/Hss88SHR3NTTfdZDqKV+jXrx/9+vUr/bpv374EBQWVTlqsXbu2wXSex+VykZuby1dffUWrVq0A6NixI7GxsUycOJEHH3zQcEKRqs3rh6w4HA4yMjKOOZ6ZmYnD4TCQSCqrrKwsBgwYQHBwMN999x1+fn6mI3m8tm3b0q1bN2677TZmzJjB/PnzmTFjhulYHic5OZlXX32Vp556iuzsbDIzM8nNzQWsJRAPt+XkrrrqKpxOp4ZhHEf16tWJjo4uLcbB+pShRYsWrFu3zmAyEYFKUJDHxcUdM1a8sLCQpKSkY8aWi5ypgoICLr/8clJSUpg1a1bpBEU5fe3atcPHx4ctW7aYjuJxtm3bRlFREZdeeikOhwOHw8GgQYMA6N27N/Hx8YYTege32206gsc60f3Q7XZror+IB/D6/4UDBw5k3rx5pKWllR6bMWMGhYWFDBw40GAyqSxKSkq46qqrWL16NbNmzdKkxDO0ZMkSnE4njRo1Mh3F47Rr14758+cf9XjttdcAePfdd3n77bcNJ/QO06ZNw8fHh/bt25uO4nEuu+wyUlJSWLt2bemx3bt3s2HDBs477zyDyUQEwOb28i6FzMxMWrduTcOGDXnsscdKNwbq16+fNgY6gby8vNIlId966y2SkpKYMGECQOnuinLEqFGjmDhxIi+99BI9evQ46nstW7bUBLzjGDp0KJ06daJt27YEBQWxevVqXnrpJaKjo1m+fDn+/v6mI3q8BQsW0Lt3b5YvX06nTp1Mx/E4/fr14+KLLy7dafi7775j4sSJjBkzpvTNjBzhdDrp3LkzOTk5PPvss/j7+/P000+TmprKxo0bCQkJMR1RpErz+oIcYNOmTYwePZpFixYRHBzMtddey4svvkhQUJDpaB5p+/btxMbGHvd78+fPp1evXhUbyMM1bNiQ5OTk435Pz9fxvfDCC0ybNo2kpCRcLhcNGzZk6NCh3H///XoDc5pUkJ/cmDFj+Omnn9i1axcul4tmzZpx6623Mnr0aE3oP4HU1FTuvfdefvzxR4qLi+nZsyevvfaa1rwX8QCVoiAXEREREfFWXj+GXERERETEm6kgFxERERExSAW5iIiIiIhBKshFRERERAxSQS4iIiIiYpAKchERERERg1SQi4iIiIgYpIJcRERERMQgFeQiIiIiIgapIBcRERERMUgFuYh4jK+++gofHx9yc3NNRxEREakwKshFxGOsWLGCFi1aUK1aNdNRREREKowKchHxGH/++SedOnUyHUNERKRCqSAXEaPy8vK47777qFWrFnPmzGHKlCmcd955/PHHH6ajiYiIVAgV5CJijMvlYtCgQXz//feMGzcOgPHjx+N0OrniiivIz883nFBEROTcU0EuIsa8+uqrLFu2jLlz59K4cWMAbr/9dp577jn27dunXnIREakSVJCLiDHvv/8+N910Ew0aNGDVqlU0bNiQ8PBwYmNjAWs4i4iISGWnglxEjNi0aRObN28mPj4egNWrV9OuXTsA9u7dC1BamIuIiFRmKshFxIitW7cCULt2bQBWrVrFeeedB8CsWbNo3LgxcXFxxvKJiIhUFBXkImLE4bXGd+zYQW5uLlu3bqVdu3bs3r2bDz/8kFGjRhlOKCIiUjF8TQcQkarp/PPPp06dOjz++OMkJyfjdrvZtm0b48aNo0OHDowdO9Z0RBERkQphc7vdbtMhRKRqWrFiBbfddhtr1qzB6XQSFRXFddddx3PPPUdwcLDpeCIiIhVCBbmIGHfzzTezfft2fvnlF9NRREREKpzGkIuIcQkJCbRv3950DBERESNUkIuIUYWFhaxbt04FuYiIVFkasiIiIiIiYpB6yEVEREREDFJBLiIiIiJikApyERERERGDVJCLiIiIiBikglxERERExCAV5CIiIiIiBqkgFxERERExSAW5iIiIiIhBKshFRERERAxSQS4iIiIiYtD/A6nNUfKgKfQ6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np; import math\n",
    "phmax = 2*math.pi; npt = 100; dpht = phmax/npt\n",
    "pht = np.arange(0,phmax+dpht,dpht)\n",
    "PD0teoA0 = 0.5*(1+np.cos(pht)); PD0teoA1 = 0.5*(1-np.cos(pht))\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teoA0, label=r'$Pr(D_0|A=0)_{teo}$'); plt.plot(pht,PD0teoA1, label=r'$Pr(D_0|A=1)_{teo}$')\n",
    "plt.plot(ph,PD0A0sim, 'o', label=r'$Pr(D_0|A=0)_{sim}$'); plt.plot(ph,PD0A1sim, 's', label=r'$Pr(D_0|A=1)_{sim}$')\n",
    "plt.plot(ph,PD0A0exp, '*', label=r'$Pr(D_0|A=0)_{exp}$'); plt.plot(ph,PD0A1exp, '+', label=r'$Pr(D_0|A=1)_{exp}$')\n",
    "plt.xlim(-0.1,2*math.pi+0.1); plt.ylim(-0.02,1.02); plt.legend(bbox_to_anchor=(1.4, 1.0),loc='upper right')\n",
    "plt.xlabel(r'$\\phi$'); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "2053af44",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VsimA0 =  1.0\n",
      "VsimA1 =  1.0\n",
      "VexpA0 =  0.6872136538969289\n",
      "VexpA1 =  0.8079585388655659\n"
     ]
    }
   ],
   "source": [
    "VsimA0 = (np.max(PD0A0sim)-np.min(PD0A0sim))/(np.max(PD0A0sim)+np.min(PD0A0sim))\n",
    "print('VsimA0 = ',VsimA0)\n",
    "VsimA1 = (np.max(PD0A1sim)-np.min(PD0A1sim))/(np.max(PD0A1sim)+np.min(PD0A1sim))\n",
    "print('VsimA1 = ',VsimA1)\n",
    "VexpA0 = (np.max(PD0A0exp)-np.min(PD0A0exp))/(np.max(PD0A0exp)+np.min(PD0A0exp))\n",
    "print('VexpA0 = ',VexpA0)\n",
    "VexpA1 = (np.max(PD0A1exp)-np.min(PD0A1exp))/(np.max(PD0A1exp)+np.min(PD0A1exp))\n",
    "print('VexpA1 = ',VexpA1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f50e8e35",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Exercício__: Faça a simulação quântica do apagador quântico emaranhado introduzido na referência (D. S. S. Chrysosthemos, M. L. W. Basso, and J. Maziero, “Quantum simulation of the generalized-entangled quantum eraser and the related complete complementarity relations,” Phys. Scr., vol. 98, no. 3, p. 035107, Feb. 2023, doi: 10.1088/1402-4896/acbacb.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e83ab6ae",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Apagador quântico com mitigação de erros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "851f28f6",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ibmqfactory.load_account:WARNING:2023-10-15 15:26:32,748: Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    }
   ],
   "source": [
    "import qiskit\n",
    "qiskit.IBMQ.save_account('e20d3045c7c23a3be753606794714e9b47d4331ec46a41b2281e2d601bae27b2b3c1baa0b5cb54f3282a8b5248e552b14c9c556699010660fb94b11d00ff1073', \n",
    "                  overwrite = True)\n",
    "qiskit.IBMQ.load_account()\n",
    "#provider = qiskit.IBMQ.get_provider(hub='ibm-q', group='open', project='main')\n",
    "provider = qiskit.IBMQ.get_provider(hub='ibm-q-research-2', group='federal-uni-sant-1', project='main')\n",
    "device = provider.get_backend('ibm_nairobi')\n",
    "nshots = 2**13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "8d942040",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit import QuantumRegister, execute\n",
    "from qiskit.ignis.mitigation.measurement import complete_meas_cal\n",
    "qr = QuantumRegister(3)\n",
    "qubit_list = [0, 2]\n",
    "meas_calibs, state_labels = complete_meas_cal(qubit_list = qubit_list, qr = qr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "f79cded2",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuário\\AppData\\Local\\Temp\\ipykernel_25336\\3547184236.py:2: DeprecationWarning: The qiskit.ignis package is deprecated and has been supersceded by the qiskit-experiments project. Refer to the migration guide: https://github.com/Qiskit/qiskit-ignis#migration-guide on how to migrate to the new project.\n",
      "  from qiskit.ignis.mitigation.measurement import complete_meas_cal\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cmp2xzqyj8fg0080m0e0\n"
     ]
    }
   ],
   "source": [
    "job = execute(meas_calibs, backend=device, shots=nshots)\n",
    "print(job.job_id())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "5531cb14",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.ignis.mitigation.measurement import CompleteMeasFitter\n",
    "job = device.retrieve_job('cmp2xzqyj8fg0080m0e0')\n",
    "cal_results = job.result()\n",
    "meas_fitter = CompleteMeasFitter(cal_results, state_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "3d1cf7e2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.93327349 0.72177812 0.21121983 0.00241503 0.33105879 0.76105233\n",
      " 0.94035836] [0.03352468 0.38239959 0.89636664 1.08370551 0.83076149 0.31798791\n",
      " 0.03535019]\n"
     ]
    }
   ],
   "source": [
    "f = open(\"jobs_ids_apagador.txt\",\"r\")\n",
    "list_ids_apagador = f.read().replace(\"'\",\"\").replace(\" \",\"\").replace(\"[\",\"\").replace(\"]\",\"\").split(\",\")\n",
    "f.close()\n",
    "phmax = 2*math.pi; npe=6; dth = phmax/npe; ph = np.arange(0,phmax+dth,dth)\n",
    "PD0A0exp_mit = np.zeros(len(ph)); PD0A1exp_mit = np.zeros(len(ph)); PA0exp_mit = np.zeros(len(ph)); PA1exp_mit = np.zeros(len(ph))\n",
    "device = provider.get_backend('ibm_nairobi')\n",
    "for j in range(0,len(ph)):\n",
    "    job = device.retrieve_job(list_ids_apagador[j])\n",
    "    mitigated_results = meas_fitter.filter.apply(job.result())\n",
    "    mitigated_counts = mitigated_results.get_counts()\n",
    "    if '00' in counts:\n",
    "        PA0exp_mit[j] = mitigated_counts['00']/nshots\n",
    "    if '01' in counts:\n",
    "        PA0exp_mit[j] += mitigated_counts['01']/nshots\n",
    "    if '10' in counts:\n",
    "        PA1exp_mit[j] = mitigated_counts['10']/nshots\n",
    "    if '11' in counts:\n",
    "        PA1exp_mit[j] += mitigated_counts['11']/nshots\n",
    "    if PA0exp_mit[j] != 0 and '00' in mitigated_counts:\n",
    "        PD0A0exp_mit[j] = (mitigated_counts['00']/nshots)/PA0exp[j]\n",
    "    if PA1exp[j] != 0 and '10' in mitigated_counts:\n",
    "        PD0A1exp_mit[j] = (mitigated_counts['10']/nshots)/PA1exp[j]\n",
    "print(PD0A0exp_mit, PD0A1exp_mit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "db038983",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib; matplotlib.rcParams.update({'font.size':11}); plt.figure(figsize = (7,5), dpi = 100)\n",
    "import numpy as np; import math; phmax = 2*math.pi; npt = 100; dpht = phmax/npt; pht = np.arange(0,phmax+dpht,dpht)\n",
    "PD0teoA0 = 0.5*(1+np.cos(pht)); PD0teoA1 = 0.5*(1-np.cos(pht)); from matplotlib import pyplot as plt\n",
    "plt.plot(pht,PD0teoA0, label=r'$Pr(D_0|A=0)_{teo}$'); plt.plot(pht,PD0teoA1, label=r'$Pr(D_0|A=1)_{teo}$')\n",
    "plt.plot(ph,PD0A0sim, 'o', label=r'$Pr(D_0|A=0)_{sim}$'); plt.plot(ph,PD0A1sim, 's', label=r'$Pr(D_0|A=1)_{sim}$')\n",
    "plt.plot(ph,PD0A0exp, '*', label=r'$Pr(D_0|A=0)_{exp}$'); plt.plot(ph,PD0A1exp, 'v', label=r'$Pr(D_0|A=1)_{exp}$')\n",
    "plt.plot(ph,PD0A0exp_mit, '^', label=r'$Pr(D_0|A=0)_{expmit}$'); plt.plot(ph,PD0A1exp_mit, '+', label=r'$Pr(D_0|A=1)_{expmit}$')\n",
    "plt.xlim(-0.1,2*math.pi+0.1); plt.ylim(-0.03,1.03); plt.legend(bbox_to_anchor=(1.4, 1.0),loc='upper right')\n",
    "plt.xlabel(r'$\\phi$'); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "a87a0e88",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VsimA0 =  1.0\n",
      "VsimA1 =  1.0\n",
      "VexpA0 =  0.6872136538969289\n",
      "VexpA1 =  0.8702297080449518\n",
      "VexpA0_mit =  0.994876750773789\n",
      "VexpA1_mit =  0.960384205779108\n"
     ]
    }
   ],
   "source": [
    "VsimA0 = (np.max(PD0A0sim)-np.min(PD0A0sim))/(np.max(PD0A0sim)+np.min(PD0A0sim)); print('VsimA0 = ',VsimA0)\n",
    "VsimA1 = (np.max(PD0A1sim)-np.min(PD0A1sim))/(np.max(PD0A1sim)+np.min(PD0A1sim)); print('VsimA1 = ',VsimA1)\n",
    "VexpA0 = (np.max(PD0A0exp)-np.min(PD0A0exp))/(np.max(PD0A0exp)+np.min(PD0A0exp)); print('VexpA0 = ',VexpA0)\n",
    "VexpA1 = (np.max(PD0A1exp)-np.min(PD0A1exp))/(np.max(PD0A1exp)+np.min(PD0A1exp)); print('VexpA1 = ',VexpA1)\n",
    "VexpA0_mit = (np.max(PD0A0exp_mit)-np.min(PD0A0exp_mit))/(np.max(PD0A0exp_mit)+np.min(PD0A0exp_mit))\n",
    "print('VexpA0_mit = ',VexpA0_mit)\n",
    "VexpA1_mit = (np.max(PD0A1exp_mit)-np.min(PD0A1exp_mit))/(np.max(PD0A1exp_mit)+np.min(PD0A1exp_mit))\n",
    "print('VexpA1_mit = ',VexpA1_mit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ec912d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Problema__: Aplique mitigação de erros para o sistema considerado em um dos problemas anteriores, e compare os resultados obtidos com e sem mitigação de erros."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b510884",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Apagamento parcial de informação de caminho"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "419bb745",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Emaranhamento controlável\n",
    "\n",
    "Vamos considerar o mesmo sistema considerado anteriormente. No entanto, não usaremos o estado maximamente emaranhado preparado pelo BBO mas sim um estado inicial com emaranhamento controlável entre as polarizações dos fótons:\n",
    "$$|\\Psi(\\alpha)\\rangle_{AB} = \\cos\\alpha|01\\rangle_{AB} - \\sin\\alpha|10\\rangle_{AB},$$\n",
    "com \n",
    "$$\\alpha\\in[0,\\pi/4].$$\n",
    "Teremos assim os extremos \n",
    "$$|\\Psi(\\alpha=0)\\rangle_{AB} = |01\\rangle_{AB},$$\n",
    "que é um estado separável (não emaranhado), e \n",
    "$$|\\Psi(\\alpha=\\pi/4)\\rangle_{AB} = |\\Psi_-\\rangle_{AB},$$\n",
    "que é um estado maximamente emaranhado."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10b24f32",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Apagador quântico com emaranhamento parcial\n",
    "Vamos refazer as contas (desconsideramos $A'$)\n",
    "\\begin{align}\n",
    "& \\text{BBO+: } |\\Psi(\\alpha)\\rangle_{AB}|0\\rangle_{B'} = \\big(\\cos\\alpha|01\\rangle_{AB} - \\sin\\alpha|10\\rangle_{AB}\\big)|0\\rangle_{B'}, \\\\\n",
    "& \\text{DFP: } i\\cos\\alpha|011\\rangle_{ABB'} - \\sin\\alpha|100\\rangle_{ABB'}, \\\\\n",
    "& \\text{PMO: } i\\cos\\alpha|001\\rangle_{ABB'} - \\sin\\alpha|100\\rangle_{ABB'} = \\big(i\\cos\\alpha|01\\rangle_{AB'} - \\sin\\alpha|10\\rangle_{AB'}\\big)|0\\rangle_{B}, \\\\\n",
    "& \\text{Esp: } \\big(i^2\\cos\\alpha|00\\rangle_{AB'} - i\\sin\\alpha|11\\rangle_{AB'}\\big)|0\\rangle_{B} = -\\big(\\cos\\alpha|00\\rangle_{AB'} + i\\sin\\alpha|11\\rangle_{AB'}\\big)|0\\rangle_{B}, \\\\\n",
    "& \\text{fase: } -\\big(\\cos\\alpha|00\\rangle_{AB'} + ie^{i\\phi}\\sin\\alpha|11\\rangle_{AB'}\\big)|0\\rangle_{B}, \\\\\n",
    "& \\text{DF: } -2^{-1/2}\\big(\\cos\\alpha|0\\rangle_A(|0\\rangle_{B'} + i|1\\rangle_{B'}) + ie^{i\\phi}\\sin\\alpha|1\\rangle_A(|1\\rangle_{B'} +i|0\\rangle_{B'}\\big)|0\\rangle_{B}, \\\\\n",
    "& \\text{PQO:} \\frac{-1}{2}\\big(\\cos\\alpha(|0\\rangle_A+i|1\\rangle_A)(|0\\rangle_{B'} + i|1\\rangle_{B'}) + ie^{i\\phi}\\sin\\alpha(|0\\rangle_A-i|1\\rangle_A)(|1\\rangle_{B'} +i|0\\rangle_{B'}\\big)|0\\rangle_{B}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "deb45ef1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Estado final:__\n",
    "$$-2^{-1}\\big((\\cos\\alpha-e^{i\\phi}\\sin\\alpha)(|00\\rangle_{AB'}-|11\\rangle_{AB'}) + i(\\cos\\alpha+e^{i\\phi}\\sin\\alpha)(|01\\rangle_{AB'} +|10\\rangle_{AB'})\\big)$$\n",
    "__Sem pós-seleção:__\n",
    "\\begin{align}\n",
    "Pr(B'=0) & = Pr(A=0,B'=0) + Pr(A=1,B'=0) \\\\\n",
    "& = 2^{-2}\\Big(|\\cos\\alpha-e^{i\\phi}\\sin\\alpha|^2 + |i(\\cos\\alpha+e^{i\\phi}\\sin\\alpha)|^2\\Big) \\\\\n",
    "& = 2^{-2}\\big(\\cos^2\\alpha + \\sin^2\\alpha - 2\\sin\\alpha\\cos\\alpha\\cos\\phi \\\\\n",
    "& \\hspace{2cm} + \\cos^2\\alpha + \\sin^2\\alpha + 2\\sin\\alpha\\cos\\alpha\\cos\\phi\\big) \\\\\n",
    "& = 2^{-2}\\big(1 - \\sin(2\\alpha)\\cos\\phi + 1 + \\sin(2\\alpha)\\cos\\phi\\big) \\\\\n",
    "& = 1/2.\n",
    "\\end{align}\n",
    "Visibilidade nula: $V=0$. Se entende pois o DFP cria correlação $BB'$ indenpendentemente de $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d216c65a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Com pós-seleção:__ <br>\n",
    "Usamos \n",
    "\\begin{align}\n",
    "Pr(A=0) & = Pr(A=0,B'=0) + Pr(A=0,B'=1) \\\\\n",
    "& = 2^{-2}\\Big(|-(\\cos\\alpha-e^{i\\phi}\\sin\\alpha)|^2 + |-i (\\cos\\alpha+e^{i\\phi}\\sin\\alpha)|^2\\Big) \\\\\n",
    "& = 2^{-1}\n",
    "\\end{align}\n",
    "para escrever (usa a regra de Bayes)\n",
    "\\begin{align}\n",
    "Pr(B'=0|A=0) & = Pr(B'=0,A=0)/Pr(A=0) \\\\\n",
    "& = 2^{-2}|\\cos\\alpha-e^{i\\phi}\\sin\\alpha|^2\\big/2^{-1} \\\\\n",
    "& = 2^{-1}\\big( \\cos^2\\alpha + \\sin^2\\alpha - 2\\sin\\alpha\\cos\\alpha\\cos\\phi \\big) \\\\\n",
    "& = 2^{-1}\\big(1 - \\sin(2\\alpha)\\cos\\phi\\big).\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6212325",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Usando\n",
    "\\begin{align}\n",
    "& \\partial_\\phi Pr(B'=0|A=0) = 2^{-1}\\sin(2\\alpha)\\sin\\phi = 0\\ \\therefore\\ \\phi = 0,\\pi, \\\\\n",
    "& \\partial_{\\phi\\phi} Pr(B'=0|A=0) = 2^{-1}\\sin(2\\alpha)\\cos\\phi\\ \\therefore\\ >(\\phi=0)_\\min,<0(\\phi=\\pi)_\\max, \\\\\n",
    "\\end{align}\n",
    "obtemos a visibilidade interferométrica\n",
    "\\begin{align}\n",
    "V & = \\frac{Pr(B'=0|A=0)_\\max - Pr(B'=0|A=0)_\\min}{Pr(B'=0|A=0)_\\max + Pr(B'=0|A=0)_\\min} \\\\\n",
    "& = \\frac{2^{-1}(1+\\sin(2\\alpha)) - 2^{-1}(1-\\sin(2\\alpha))}{2^{-1}(1+\\sin(2\\alpha)) + 2^{-1}(1-\\sin(2\\alpha))} \\\\\n",
    "& = \\sin(2\\alpha).\n",
    "\\end{align}\n",
    "A visibilidade aumenta com $\\alpha$, e é portanto proporcional ao emaranhamento inicial entre $A$ e $B$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "685a0d98",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math; import numpy as np\n",
    "al_max = math.pi/4; npt = 100; dalt = al_max/npt\n",
    "alt = np.arange(0,al_max+dalt,dalt)\n",
    "Vteo = np.sin(2*alt)\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(alt,Vteo, label=r'$V_{teo}(A=0)$')\n",
    "plt.xlim(-0.01,al_max+0.01); plt.ylim(-0.01,1.01)\n",
    "plt.xlabel(r'$\\alpha$'); plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3edc10bc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 370.906x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "\n",
    "def qc_Psi(al): # prepara o estado parcialmente emaranhado\n",
    "    qc = QuantumCircuit(2, name = r'$|\\Psi\\rangle$')\n",
    "    qc.u(2*al,0,0, 0)\n",
    "    qc.cx(0,1)\n",
    "    qc.z(0)\n",
    "    qc.x(1)\n",
    "    return qc\n",
    "qcpsi = qc_Psi(0.1); qcpsi.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "f067ce46",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02289782, 0.70566562, 1.        ])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulação clássica\n",
    "from qiskit import Aer, execute; simulator = Aer.get_backend('qasm_simulator'); nshots = 2**13\n",
    "import math; import numpy as np\n",
    "almax = math.pi/4; npa=2; dal = almax/npa; al = np.arange(0,almax+dal,dal)\n",
    "phmax = 2*math.pi; npe=4; dph = phmax/npe; ph = np.arange(0,phmax+dph,dph); VA0sim = np.zeros(len(al))\n",
    "for j in range(0,len(al)):\n",
    "    PD0A0sim = np.zeros(len(ph)); PA0sim = np.zeros(len(ph))\n",
    "    for k in range(0,len(ph)):\n",
    "        qc = QuantumCircuit(3,2)\n",
    "        qcpsi = qc_Psi(al[j]); qc.append(qcpsi, [0,1])\n",
    "        qcdfp = qc_dfp(); qc.append(qcdfp, [1,2]); qcpmo = qc_pmo(); qc.append(qcpmo, [1,2])\n",
    "        qce = qc_espelhos(); qc.append(qce, [2]); qc.p(ph[k], [2])\n",
    "        qcdf = qc_df(); qc.append(qcdf, [2]); qcpqo = qc_pqo(); qc.append(qcpqo, [0])\n",
    "        qc.measure([0,2],[0,1])\n",
    "        job = execute(qc, backend=simulator, shots=nshots); counts = job.result().get_counts()\n",
    "        if '00' in counts:\n",
    "            PA0sim[k] = counts['00']/nshots\n",
    "        if '01' in counts:\n",
    "            PA0sim[k] += counts['01']/nshots\n",
    "        if PA0sim[k] != 0:\n",
    "            if '00' in counts:\n",
    "                PD0A0sim[k] = (counts['00']/nshots)/PA0sim[k]\n",
    "    VA0sim[j] = (np.max(PD0A0sim)-np.min(PD0A0sim))/(np.max(PD0A0sim)+np.min(PD0A0sim))\n",
    "VA0sim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "82df5874",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.50048924, 1.        , 0.50891331, 0.        ])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PD0A0sim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "31714ee1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 789.163x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "d3b290df",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math; import numpy as np\n",
    "al_max = math.pi/4; npt = 100; dalt = al_max/npt; alt = np.arange(0,al_max+dalt,dalt)\n",
    "Vteo = np.sin(2*alt)\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(alt,Vteo, label=r'$V_{teo}(A=0)$')\n",
    "plt.plot(al,VA0sim, 'o', label=r'$V_{sim}(A=0)$')\n",
    "plt.xlim(-0.01,al_max+0.01); plt.ylim(-0.01,1.02); plt.xlabel(r'$\\alpha$'); plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "a36712a6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cmqg3rq47e1g0083h6w0\n",
      "cmqg3sqd1ztg00833gg0\n",
      "cmqg3tfd1ztg00833ggg\n",
      "cmqg3v7cxjt0008mfgmg\n",
      "cmqg3vzd1ztg00833gh0\n",
      "cmqg3wfd1ztg00833ghg\n",
      "cmqg3x7qpryg008dsyag\n",
      "cmqg3xz47e1g0083h6wg\n",
      "cmqg3yqrcp70008sezgg\n",
      "cmqg3zfcxjt0008mfgn0\n",
      "cmqg4003vp900080nm8g\n",
      "cmqg40r47e1g0083h6x0\n",
      "cmqg41gd1ztg00833gk0\n",
      "cmqg430qpryg008dsyc0\n",
      "cmqg43rqpryg008dsydg\n"
     ]
    }
   ],
   "source": [
    "# Experimento (simulação quântica)\n",
    "from qiskit import execute; import math; import numpy as np\n",
    "almax = math.pi/4; npa = 2; dal = almax/npa; al = np.arange(0,almax+dal,dal)\n",
    "phmax = 2*math.pi; npe=4; dph = phmax/npe; ph = np.arange(0,phmax+dph,dph)\n",
    "job_ids=[]\n",
    "for j in range(0,len(al)):\n",
    "    for k in range(0,len(ph)):\n",
    "        qc = QuantumCircuit(3,2); qcpsi = qc_Psi(al[j]); qc.append(qcpsi, [0,1])\n",
    "        qcdfp = qc_dfp(); qc.append(qcdfp, [1,2]); qcpmo = qc_pmo(); qc.append(qcpmo, [1,2])\n",
    "        qce = qc_espelhos(); qc.append(qce, [2]); qc.p(ph[k], [2])\n",
    "        qcdf = qc_df(); qc.append(qcdf, [2]); qcpqo = qc_pqo(); qc.append(qcpqo, [0]); qc.measure([0,2],[0,1])\n",
    "        job = execute(qc, backend=device, shots=nshots); jobid = job.job_id(); job_ids.append(jobid); print(jobid)\n",
    "f = open(\"jobs_ids_apagador_parcial.txt\", \"w\"); f.write(str(job_ids)); f.close()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "1c85cd85",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0609929 , 0.49312914, 0.66276514])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = open(\"jobs_ids_apagador_parcial.txt\",\"r\")\n",
    "list_ids_apagador_parcial = f.read().replace(\"'\",\"\").replace(\" \",\"\").replace(\"[\",\"\").replace(\"]\",\"\").split(\",\")\n",
    "f.close()\n",
    "import math; import numpy as np\n",
    "almax = math.pi/4; npa=2; dal = almax/npa; al = np.arange(0,almax+dal,dal)\n",
    "phmax = 2*math.pi; npe=4; dph = phmax/npe; ph = np.arange(0,phmax+dph,dph); VA0exp = np.zeros(len(al))\n",
    "for j in range(0,len(al)):\n",
    "    PD0A0exp = np.zeros(len(ph)); PA0exp = np.zeros(len(ph))\n",
    "    for k in range(0,len(ph)):\n",
    "        job = device.retrieve_job(list_ids_apagador_parcial[(npe+1)*j+k])\n",
    "        counts = job.result().get_counts()\n",
    "        if '00' in counts:\n",
    "            PA0exp[k] = counts['00']/nshots\n",
    "        if '01' in counts:\n",
    "            PA0exp[k] += counts['01']/nshots\n",
    "        if PA0exp[k] != 0:\n",
    "            if '00' in counts:\n",
    "                PD0A0exp[k] = (counts['00']/nshots)/PA0exp[k]\n",
    "    VA0exp[j] = (np.max(PD0A0exp)-np.min(PD0A0exp))/(np.max(PD0A0exp)+np.min(PD0A0exp))\n",
    "VA0exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "e9343d3f",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math; import numpy as np\n",
    "al_max = math.pi/4; npt = 100; dalt = al_max/npt; alt = np.arange(0,al_max+dalt,dalt); Vteo = np.sin(2*alt)\n",
    "from matplotlib import pyplot as plt\n",
    "plt.plot(alt,Vteo, label=r'$V_{teo}(A=0)$')\n",
    "plt.plot(al,VA0sim, 'o', label=r'$V_{sim}(A=0)$')\n",
    "plt.plot(al,VA0exp, '^', label=r'$V_{exp}(A=0)$')\n",
    "plt.xlim(-0.01,al_max+0.01); plt.ylim(-0.01,1.02); plt.xlabel(r'$\\alpha$'); plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0af89258",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  },
  "rise": {
   "theme": "sky"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}