From 83a4485aa6cefc9fcdad46ebb1aa9a1af48c8289 Mon Sep 17 00:00:00 2001 From: Aniket Sengupta Date: Mon, 10 Aug 2026 10:28:45 +0200 Subject: [PATCH 1/2] Added to my notebook --- CV_tutorial_Aniket.ipynb | 767 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 767 insertions(+) create mode 100644 CV_tutorial_Aniket.ipynb diff --git a/CV_tutorial_Aniket.ipynb b/CV_tutorial_Aniket.ipynb new file mode 100644 index 0000000..b6c93ae --- /dev/null +++ b/CV_tutorial_Aniket.ipynb @@ -0,0 +1,767 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "674091b5", + "metadata": {}, + "source": [ + "# Gaussian state preparation and operations\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5e1ea2a3", + "metadata": {}, + "outputs": [], + "source": [ + "# import relevant packages\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "from scipy.special import eval_genlaguerre\n", + "import matplotlib.colors as mcolors\n" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "bd428678", + "metadata": {}, + "outputs": [], + "source": [ + "#Single mode Gaussian state preparation and sympletic operations\n", + "\n", + "\n", + "\n", + "#Defining basic guassian operations which we will use later in the code\n", + "\n", + "def sym_phase(theta):\n", + " c, s = np.cos(theta), np.sin(theta)\n", + "\n", + " return np.array([\n", + " [c, -s],\n", + " [s, c]\n", + " ], dtype=float)\n", + "\n", + "\n", + "def sym_squeeze(r):\n", + "\n", + " return np.array([\n", + " [np.exp(r), 0.0],\n", + " [0.0, np.exp(-r)]\n", + " ], dtype=float)\n", + "\n", + "\n", + "def sym_displace(alpha):\n", + "\n", + " if isinstance(alpha, complex):\n", + "\n", + " x = np.sqrt(2) * alpha.real\n", + " p = np.sqrt(2) * alpha.imag\n", + "\n", + " elif isinstance(alpha, (tuple, list, np.ndarray)) and len(alpha) == 2:\n", + "\n", + " x, p = alpha\n", + "\n", + " else:\n", + " raise ValueError(\n", + " \"alpha must be a complex number or a 2-element vector\"\n", + " )\n", + "\n", + " return np.array([x, p], dtype=float)\n", + "\n", + "\n", + "# Defining some functions to extract displacement, phase rotation angles, squeezing directly from the covariance matrix and the mean\n", + "\n", + "def gaussian_parameters_from_cov(V):\n", + " \n", + " # Eigenvalues and eigenvectors\n", + " eigenvalues, eigenvectors = np.linalg.eigh(V)\n", + "\n", + " v_min = eigenvalues[0]\n", + " v_max = eigenvalues[1]\n", + "\n", + " \n", + " r = 0.25 * np.log(v_max / v_min)\n", + "\n", + " # Direction\n", + " v = eigenvectors[:, 0]\n", + "\n", + " theta = np.arctan2(v[1], v[0])\n", + "\n", + " #phase\n", + " phi = 2 * theta\n", + "\n", + " return r, phi\n", + "\n", + "\n", + "def alpha_from_mean(mean):\n", + "\n", + " q, p = mean\n", + "\n", + " return (q + 1j * p) / np.sqrt(2)\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "id": "f7942398", + "metadata": {}, + "outputs": [], + "source": [ + "#Define the class for gaussian state generation and wigner function visualization\n", + "\n", + "\n", + "class GaussianState:\n", + "\n", + " def __init__(self, mean=None, cov=None):\n", + "\n", + " if mean is None:\n", + " mean = np.array([0.0, 0.0])\n", + "\n", + " if cov is None:\n", + " cov = 0.5 * np.eye(2)\n", + "\n", + " self.mean = np.asarray(mean, dtype=float)\n", + " self.cov = np.asarray(cov, dtype=float)\n", + "\n", + "\n", + "\n", + " def gaussian_update(self, S, d):\n", + "\n", + " self.mean = S @ self.mean + d\n", + " self.cov = S @ self.cov @ S.T\n", + "\n", + " return self\n", + "\n", + "\n", + "\n", + " def apply(self, S, d=None):\n", + "\n", + " if d is None:\n", + " d = np.zeros(2)\n", + "\n", + " return self.gaussian_update(S, d)\n", + "\n", + "\n", + "\n", + " def phase(self, theta):\n", + "\n", + " S = sym_phase(theta)\n", + "\n", + " return self.apply(S)\n", + "\n", + "\n", + " def squeeze(self, r):\n", + "\n", + " S = sym_squeeze(r)\n", + "\n", + " return self.apply(S)\n", + "\n", + "\n", + " def displace(self, alpha):\n", + "\n", + " d = sym_displace(alpha)\n", + "\n", + " return self.apply(np.eye(2), d)\n", + "\n", + "\n", + "\n", + " def __repr__(self):\n", + "\n", + " return (\n", + " f\"GaussianState(\\n\"\n", + " f\"mean={self.mean},\\n\"\n", + " f\"cov=\\n{self.cov}\\n\"\n", + " f\")\"\n", + " )\n", + "\n", + " def plot_wigner(self, qlim=(-5, 5), plim=(-5, 5), n=200):\n", + "\n", + " q = np.linspace(*qlim, n)\n", + " p = np.linspace(*plim, n)\n", + "\n", + " Q, P = np.meshgrid(q, p)\n", + "\n", + " R = np.stack((Q, P), axis=-1)\n", + "\n", + " T = R - self.mean\n", + "\n", + " inv_cov = np.linalg.inv(self.cov)\n", + "\n", + " exponent = np.einsum(\n", + " '...i,ij,...j',\n", + " T,\n", + " inv_cov,\n", + " T\n", + " )\n", + "\n", + " W = (\n", + " 1\n", + " / (2 * np.pi * np.sqrt(np.linalg.det(self.cov)))\n", + " * np.exp(-0.5 * exponent)\n", + " )\n", + "\n", + " fig, ax = plt.subplots(figsize=(6, 5))\n", + " # norm= mcolor.TwoSlopeNorm(vmin=W.min(), vcenter=0, vmax=W.max())\n", + " cmap = mcolors.LinearSegmentedColormap.from_list(\n", + " \"white_red\",\n", + " [\"white\", \"red\"]\n", + " )\n", + "\n", + " norm = mcolors.Normalize(\n", + " vmin=0,\n", + " vmax=W.max())\n", + "\n", + " contour = ax.contourf(\n", + " Q,\n", + " P,\n", + " W,\n", + " levels=100,\n", + " cmap=cmap, norm=norm\n", + " )\n", + "\n", + " fig.colorbar(\n", + " contour,\n", + " ax=ax,\n", + " # label=\"Wigner function\"\n", + " )\n", + " ax.grid()\n", + " ax.set_xlabel(\"X\")\n", + " ax.set_ylabel(\"P\")\n", + " ax.set_title(\"Gaussian Wigner Function\")\n", + "\n", + " ax.set_aspect(\"equal\")\n", + "\n", + " fig.tight_layout()\n", + "\n", + " return fig, ax\n", + "\n", + " \n", + "\n", + "\n", + " def fock_distribution(self, n_max=30):\n", + "\n", + " alpha = alpha_from_mean(self.mean)\n", + "\n", + " r, phi = gaussian_parameters_from_cov(self.cov)\n", + "\n", + " tau = -np.exp(1j * phi) * np.tanh(r)\n", + "\n", + " beta = (\n", + " alpha * np.cosh(r)\n", + " + np.conj(alpha)\n", + " * np.exp(1j * phi)\n", + " * np.sinh(r)\n", + " )\n", + "\n", + " c = np.zeros(n_max, dtype=complex)\n", + "\n", + " # Vacuum coefficient derived\n", + " c[0] = (\n", + " 1 / np.sqrt(np.cosh(r))\n", + " * np.exp(\n", + " -0.5 * abs(alpha)**2\n", + " -0.5\n", + " * np.conj(alpha)**2\n", + " * np.exp(1j * phi)\n", + " * np.tanh(r)\n", + " )\n", + " )\n", + "\n", + " # One-photon coefficient from recursion relation\n", + " if n_max > 1:\n", + " c[1] = beta * c[0]\n", + "\n", + " # Higher Fock coefficients\n", + " for n in range(1, n_max - 1):\n", + "\n", + " c[n + 1] = (\n", + " beta * c[n]\n", + " + tau * np.sqrt(n) * c[n - 1]\n", + " ) / np.sqrt(n + 1)\n", + "\n", + " P = np.abs(c)**2\n", + "\n", + " # Normalize because we truncated at n_max\n", + " P /= np.sum(P)\n", + "\n", + " return P\n", + "\n", + " def plot_fock_distribution(self, n_max=30):\n", + "\n", + " P = self.fock_distribution(n_max)\n", + "\n", + " n = np.arange(n_max)\n", + "\n", + " fig, ax = plt.subplots(figsize=(10,8))\n", + "\n", + " ax.bar(n, P)\n", + "\n", + " ax.set_xlabel(r\"Fock state $n$\")\n", + " ax.set_ylabel(r\"$P_n$\")\n", + " \n", + " ax.set_xticks(n)\n", + "\n", + " ax.grid(\n", + " True,\n", + " axis=\"y\",\n", + " linestyle=\"--\",\n", + " alpha=0.3\n", + " )\n", + "\n", + " plt.show()\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "id": "827e787e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GaussianState(\n", + "mean=[2.14819222 2.3206185 ],\n", + "cov=\n", + "[[ 1.26738941 -0.31529057]\n", + " [-0.31529057 0.27569123]]\n", + ")\n" + ] + } + ], + "source": [ + "#Example for Gausssian state inputs and performing Gaussian operations\n", + "\n", + "state = GaussianState() # This initialize a vacuum state\n", + "#Successive operations on Vacuum state\n", + "state.squeeze(0.5)\n", + "state.displace(1+2j)\n", + "state.phase(6)\n", + "print (state)\n" + ] + }, + { + "cell_type": "markdown", + "id": "457048ae", + "metadata": {}, + "source": [ + "# plotting the wigner function for the generated gaussian function" + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "id": "ed413b17", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(
,\n", + " )" + ] + }, + "execution_count": 107, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "state.plot_wigner()" + ] + }, + { + "cell_type": "markdown", + "id": "cca99c04", + "metadata": {}, + "source": [ + "# Plotting the fock state distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "id": "4baf6be0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "state.plot_fock_distribution()" + ] + }, + { + "cell_type": "markdown", + "id": "19693400", + "metadata": {}, + "source": [ + "# Fock state preparation, superposition of fock basis states and wigner function visualization\n" + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "id": "f56a9903", + "metadata": {}, + "outputs": [], + "source": [ + "class FockState:\n", + "\n", + " def __init__(self, state):\n", + "\n", + " self.state = np.asarray(\n", + " state,\n", + " dtype=complex\n", + " )\n", + " norm = np.linalg.norm(self.state)\n", + "\n", + " self.state /= norm\n", + "\n", + " def __repr__(self):\n", + "\n", + " terms = []\n", + "\n", + " for n, c in enumerate(self.state):\n", + "\n", + " if abs(c) > 1e-12:\n", + " terms.append(f\"({c:.3g})|{n}>\")\n", + "\n", + " return \" + \".join(terms)\n", + "\n", + "\n", + "\n", + " def wigner_nm(self, n, m, X, P):\n", + "\n", + " alpha = (X + 1j * P) / np.sqrt(2)\n", + "\n", + " r2 = np.abs(alpha)**2\n", + "\n", + " if n >= m:\n", + "\n", + " W = (\n", + " 2 / np.pi\n", + " * (-1)**m\n", + " * np.sqrt(\n", + " math.factorial(m) / math.factorial(n)\n", + " )\n", + " * np.exp(-2 * r2)\n", + " * (2 * alpha)**(n - m)\n", + " * eval_genlaguerre(\n", + " m,\n", + " n - m,\n", + " 4 * r2\n", + " )\n", + " )\n", + "\n", + " else:\n", + "\n", + " W = np.conj(\n", + " self.wigner_nm(m, n, X, P)\n", + " )\n", + "\n", + " return W\n", + "\n", + "\n", + " def wigner(self, X, P):\n", + "\n", + " W = np.zeros_like(X, dtype=complex)\n", + "\n", + " N = len(self.state)\n", + "\n", + " for n in range(N):\n", + "\n", + " for m in range(N):\n", + "\n", + " c_n = self.state[n]\n", + " c_m = self.state[m]\n", + "\n", + " W_nm = self.wigner_nm(\n", + " n,\n", + " m,\n", + " X,\n", + " P\n", + " )\n", + "\n", + " W += (\n", + " c_n\n", + " * np.conj(c_m)\n", + " * W_nm\n", + " )\n", + "\n", + " return W.real\n", + "\n", + "\n", + " def plot_wigner(self):\n", + "\n", + " q = np.linspace(-5, 5, 200)\n", + " p = np.linspace(-5, 5, 200)\n", + "\n", + " X, P = np.meshgrid(q, p)\n", + "\n", + " W = self.wigner(X, P)\n", + "\n", + " fig, ax = plt.subplots(figsize=(6, 5))\n", + "\n", + " max=np.max(W)\n", + " norm= mcolors.TwoSlopeNorm(vmin=W.min(), vcenter=0, vmax=W.max()) \n", + "\n", + " contour = ax.contourf(\n", + " X,\n", + " P,\n", + " W,\n", + " levels=100,\n", + " cmap=\"RdBu\", norm=norm\n", + " )\n", + "\n", + " fig.colorbar(\n", + " contour,\n", + " ax=ax\n", + " )\n", + " ax.grid(True)\n", + " ax.set_xlabel(\"X\")\n", + " ax.set_ylabel(\"P\")\n", + " ax.set_title(\"Fock state Wigner\")\n", + " ax.set_aspect(\"equal\")\n", + "\n", + " plt.show()\n", + "\n", + " def plot_fock_distribution(self):\n", + "\n", + " P = np.abs(self.state)**2\n", + " \n", + " P /= np.sum(P)\n", + "\n", + " n = np.arange(len(self.state))\n", + "\n", + " fig, ax = plt.subplots(figsize=(6,4))\n", + "\n", + " ax.bar(n, P)\n", + "\n", + " ax.set_xlabel(r\"Fock state $n$\")\n", + " ax.set_ylabel(r\"$P_n$\")\n", + " \n", + " ax.set_xticks(n)\n", + "\n", + " ax.grid(\n", + " True,\n", + " axis=\"y\",\n", + " linestyle=\"--\",\n", + " alpha=0.3\n", + " )\n", + "\n", + " plt.show()\n", + "\n", + "\n", + " \n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "2502a385", + "metadata": {}, + "source": [ + "# Example Superposition of 1- and 2-fock basis state superposition" + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "id": "9be171d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.707+0j)|1> + (0.707+0j)|2>\n" + ] + } + ], + "source": [ + "#Focke state preparation and visualization\n", + "\n", + "state = FockState([0,1,1])\n", + "\n", + "print(state)" + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "id": "41d99c99", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vb6/vTNAbbbQRzZgxw7Fu7ty59jYT++67rxAZDz/8sJ1MyXASJrsXEBAAAABAm/P1r3+dfvzjH9Nzzz1Hu+yyi1h311130bhx42whsHr1avrLX/4i6kOst9569D//8z+Oc/z1r38VIuSmm26q6zBOOBAAAABAkzBx4kSaPHkyHXPMMXTeeeeJglLXX3+9EBE8IoPhIlHf/OY3adq0aUJANAoICAAAAMBALJ6kaDxZ9b2JFAuh9v/9739Pd955p0iO5JEVM2fOFMJCwtUpecjm+uuvbzyekzV5ezJZfdu9gIAAAAAAmohoNEonnXSSWEzwKI0//elPrsfvuOOOnttrBepAAAAAACA0EBAAAAAACA1CGAAAAICBWLKLoongs2C6ESnVkWo74EAAAAAAIDQQEAAAAAAIDQQEAAAAAEKDHAgAAADAQIwn00oiB8INOBAAAAAACA0EBAAAAABCAwEBAAAAgNAgBwIAAABwqwNRixwIKrbl/W1ZB+LKK6+kc845h5YuXdropgAAAAAdR0sKiBtuuIF+/etfi9eVK1c2ujkAAABAx9FyAuK1116jq6++mn7+8583uikAAABAx9JSORCrV6+m4447jq6//noaNmxYo5sDAACgjYknYhRNxKo+T6FY/TmakZYSEJzz8NWvfpUmTZpEjz/+uO/+6XRaLJLly5eL11wuJ5ZmQLajWdrTzOBe4T7hZwq/e/rfA9A4WkZA3HXXXfTMM8/Qq6++GvgYDnVcfvnlZeufeXoG9fT0UDPBbQK4V/iZwu9fM9NMf6fYkQaNJVIsFltifMmmm25K48aNo6222kp8nj9/Pt1///10yimn0CGHHEJHHXVUIAdi/PjxNG/+x9Tb20vNoqL5l3L3PfakeLxl9FxDwL3CfcLPFH73HH/Px61Ly5Ytq/nfcz738OHDaaPT/kTRZPUPm4XMavrwlpPq0tZG0jI91mWXXWaHIJiINcH6xhtvTGPGjDEek0qlxKLDHXWzddbN2KZmBfcK9wk/U/jdG4y/l7FEjGLJ6vMX8siBaCyTJ092fOYciN/85jfCgWBnAgAAAACDR8sN4wQAAABA42lZAfGlL31JDOccOXJko5sCAAAAdBwtG3TnsAUP6wQAAADA4NOyAgIAAACodyEpTqSslkihPQtJtWwIAwAAAACNAwICAAAAAKGBgAAAAABAaJADAQAAAJg6yESUYonqn7MjhfZ8Vm/PbwUAAACAugIBAQAAAIDQIIQBAAAANBmzZs2ip59+moYMGUKHH36475QNPNngo48+Sm+++SaNHj2aDjzwQBo7dmxd2wgHAgAAAHDJgYgnY9UviXBd7ZQpU2j//fenDz74gB5++GFReXnmzJmu+8+ZM4cmTJhAN910E33xxRdipuqNNtqIpk2bVtf/VzgQAAAAQJPw9ttv0xVXXEH33XcfHXbYYfZkkmeccYZwF0x0dXXRQw895HApvvOd79APf/hDOuaYY+rWVjgQAAAAQJNw3333iRDEIYccYq877bTT6K233hLiwsQ666xTFuLg6c67u7vr2lY4EAAAAMAgsHz5csfnVColFpV3332XNt54Y4pGB57vN910U3vbFlts4Xr+W265hebOnSuEBr/+7//+L9UTOBAAAACAqYOMRSlWgyUaK3W148ePp+HDh9vL1VdfXXbNlStXim0qI0aMsLf5USgUqK+vjz777DOx1BM4EAAAAMAgMG/ePOrt7bU/6+4DM3ToUPrkk08c65YuXWpv84JDHWoi5vHHH08LFiwwXqcWwIEAAAAABoHe3l7HYurYN998czH6gp0EyezZs+1tQdl7771pyZIlNH/+fKoXEBAAAABAkzBp0iRatGgR/e1vf7PXcS4D5z7I/AfOpZg6dapIrGRee+01ymQyjvM8+OCDIhTiVz+iGhDCAAAAAEwdZIJrOMSqvzf54OdgkXDppZfSSSedRCeccIIIZzz55JNimKaEBcTll19OW2+9NW255Zb0xhtv0IknnkgTJ06kUaNG0Ysvvkgvv/yySKqsV/iCgQMBAAAANBGXX345PfLII6IYFBeUeuedd2j33Xe3t3P4g3McWDwwLDS4CuVuu+1Ga665pqgZwaMwjj766Lq2Ew4EAAAA0GTssssuYjHBAoJDGHotiFNOOYUGEzgQAAAAAAgNBAQAAAAAQoMQBgAAAGDqIJM8mVYNnrML7fms3p7fCgAAAAB1BQICAAAAAKGBgAAAAABAaJADAQAAAJg6yHiNCknlanCOJgQOBAAAAABCAwEBAAAAgNBAQAAAAAAgNMiBAAAAAAx0JWOUSFafv5ANMZlWKwEHAgAAAAChgYAAAAAAQGggIAAAAAAQGuRAAAAAAAZ6ktEa5UBE2/L+QkAA0OZkC0Xj+kQ0MuhtAQC0DxAQALSJIJDkrO28X9FjX7/z6EBwAABUICAAaFLCdvD1Bk4GAEAFAgKAJqHZBEOl7YZTAdqFrkScksnqu8lYrj272vb8VgC0AK0qGPyAoACgM4CAAGAQaVfREPQ7w50AoH2AgACgznSiaHADYgKA9gECAoAWFw5y1IX+WbzWoA3xOg33hJgAoLWBgACgRUSDLhQGC7fr1lJYyPuGEAdoJrqTMUrWoJBULNeek2lBQADQhMKhUWKh2jZWKyrgSgDQOkBAANAkwqEVREPY71CNoIArAUBzAwEBQIOEQ60Fg2xT0EqUQakmrKB+x0rFBIQEAM0JBAQALSQcGjGio1YVKKsVExASYLBJxKKUjFU/EVaxBudoRiAgABiEjrtS0dDMQ0BNbQsqKqoRExASADQHEBAANJFwqPZ6+QJRoVB6z6/8uRrCPjhVkgQp71ElQgKjNgBoHBAQANS4Mx8M0VCtMKjFdfzERdiS1pUICbgRoB0pFAp0++2304wZM2jIkCF0/PHH06677up5zDvvvEP33HMPzZ07lzbYYAM65ZRTaPz48XVtZ3sGZgCoAu6UKunUuQMMIx7CXIc7cnWplrBtDdImv3bJ7xtkOvJKRFgzh3tAa9KTjNVsCcPkyZPp0ksvpW222Ya6u7tpzz33pGnTprnu/7vf/Y6OOeYYyufzQmi89dZbtPnmm9Pzzz9P9QQOBAAKlQqHoIQRDJW2Ia+MxvAbhRG2o/ZzB9R2ezkUQZyDSh0JhDVAKzNr1iy64447xOvEiRPFumKxSOeffz4dddRRFI2W/2IdfPDBdNppp9nbTj31VNpvv/3oiiuuoAceeKBubYUDAUCVrkOtzh/0SV4+oavLYBHm2kG+TxBXop7ODgDNxoMPPihCD1I8MMceeyx9/PHH9OqrrxqPGTduXJmwWH/99Wnx4sV1bSscCNDx1Fs4VOs0hO08pQPB7ws17EjdnuyDVKQM4kz4uRJhHQm4EaDZWL58ueNzKpUSi8oHH3xA6623XpkYYD788EPaYYcdfK+zcOFCmj59On33u9+legIBATqasOJhsIRDkOsM9lN2mHoQXsM0/cRELYUEkixBNXQlYtRVg7kwItnSOfSkxilTptDUqVMd6/r7+2no0KGOdfIzb/Nj9erVdOSRR9KGG25IF110EdUTCAjQkdTLdahGOPidP2ib1dk4a1GJUsXUafuNtggiJioVEnAjQCsxb9486u3ttT/r7gMzfPhwsZ/KokWLxOuIESM8z9/X10eHHXYYLVu2jJ566imRgFlPICBAx1EP16FewiHIiIWweJ0z6FBLFb0T96oF4eYeVCokwroRSLAEjaS3t9chIExsu+22IvyQyWQomUyKda+//rp43XrrrV2PY3fi8MMPp08++USIh7XWWovqDZIoQUcx2OLBLYnQKwnRK7HQL4GRj8kVLQeiOHCeoEMoTfv7ncOrTUGOCXK/5LmqTbREgiVodo4++mhKp9N066232jUhfvWrX9Fuu+0m6jswnBx53HHH2cM0eX8WD5xoyeJhzJgxg9JWOBCgY6i1ePATDmHO6dc5VtIGSSZXXRgjGfcPWzDy6d5tRk43Z8LkIrg5ErUKa8CNAEHoTkZrlAMRDbwvj6i46aab6KyzzqK77rqLPv30U5HX8Oijj9r78Oe7775biA0erfGjH/1IbN97770diZOjR4+mG264geoFBAToCMKIh2pch1oJh0qEhhQKhXzR/hy13Ihq8BIgqrjwEwgmMVEPIRFGRFQ+zygA9ePkk0+mAw88UDgMPT09wn3o6upyCIM///nPtPPOO4vPXB+Ci07p8LH1BAICtD21FA+1ch3CCAe3ff2chXQ+T9E6dJGpWMy1DVJQuCVW6iLBJDrCColqciNQLwI0K2PGjBEJkSY4OZJDGBIe2hlkeGetgYAAbc1giIfBFA5uooHFgqSgvFfpz1VeA7srHjVeSxcVfoLCFOZwcyWCColauBEAgA4QENlslubPn09jx441DoEBoJXEgynpsBLR4FhvCQV+jRS9RYPcVyelCAY/8cHiQm+LSVCwmAjiOAQVEmHciCBORMv9MQR1h/MfumuQA0FWHYh2o2VGYXAFrpNOOolGjRpF++yzjxgr+x//8R9i3CsA9RIPXln7XqMr/M7htp8Kd766eOCOWi5q564ujv1zBc/FDb/j1GNN1ze1U/8++n3R74lpu9+IDb/RK14gnAFAmwqIl156iQ466CAxfGXOnDn09ttv0+OPP173Slugs8WDG27iwe8cQQSGl3CQ+AkG+V6/Rq0W9Vq6qPATE/L7ye8YREh43T/T/0XY5FS/4wAA5bSMa8dTlapwmc5vfOMb9MgjjzSsTaDzxEPQkEUl4QqTaNAxCQbPUQaRYl1yIdyGcart4TCIei091MFhDvmd1fCGGrrwCmvUK6SBIZ4AtJmAMPHmm2+W1RYHnUsjxEOtch38xIOfcFDPp5avDiIWvESInhPhdj4WB3p+Q1Ax4SUkTPkRbrkRbgmWEBEA1IeWFRA8X/pjjz0mFje4Ohcv+kxouVxOLM2AbEeztKeZ8bpX9RYPhSpCFo7PxXDCIR1COJSOL/IwDOL04nQ2RxSNBRYJXqQz5oRNWxxo24sx5xN+MR9x7N+XV9/nbCHRb61nIZG23scjEZJnZ7Eg30thwJ8dbgTHZhURkXMrq83/FPKuP1O8BqWvm/fv1GC0pSsapS636WNDUNSm2m4XWlJAcNji1FNPpV/+8pciodKNq6++mi6//PKy9c88PaPuBTbCwm0CuFfVoo5LSs37l3F9I8i6vF9JzcGsmU83ugktQTP9neJqjKCxtJyAYMdh0qRJdMUVV9B5553nue8ll1xCF1xwgcOB4JDH7nvs6TuhyWCqaP6l5DbF4y3339Hwe9UOzoOX6xDIcdCPLeSpd8HrtHydbSjjYjz0+80nHgC3J7NkPOY6JDSlOBPy6d6x3bFvrKzaJbsR9nvFUVCdAj2/QX/4c1S/zOXoxWefoZ1328Pz96/TnYhm/DslHWXQOJrjJyEgTzzxhJgwhOdPv/DCC3335zoRploR/AvQLL8EzdymZkXeKzF2P6AzWEqcM29zO48pMY/PY0rWU9fp+/B29RBRYjqmVIuMDfy/c55AxDo4rbyXwiFiHWfnE0Q1oSFPzNcpsHUaMwsGa32fR2jCj6KhU2VRkVYulYrH7M8sDtLFgRwIaUBHigNCIqNsz1oiQmotFhIFpUMvKmKhoHTy6nqJ+v9RNAmCaMzz9894TAfSTH+nmqUdnUzL/A/MnDmTDj30UFG+8+CDD6Y33nhDrI/FYrTFFls0unmgialkyuugD+h+zoNXsqQ+LFNFH4IZZL90rnS+iBXXZ9FQtDpniZdgCCMmuLiOcf/S7MOBcSRfWt9FT7hUEy3VypZ6kqWeYOk1SsOUXInRGUCHBTAv1VKowTmakZYREC+++CJttNFG9M9//tNRA5xDEc8++2xD2wYGn6Chi1qO+/cTB5WKB50g4qE8uVIRI5r6MXX0fmLBbbusyhdYbIQRFNIG0oSEc/jnQFjDJBi8RnCYRITuKUBEANCGAoLzHfxyHkBnECZ04XeeSodr+gmPMOLBTRgEEQ+qcBD75Qt2p9ifzVMhUp2QCLO/7kqUuRRJJcyhtVsVC7ojIZFCQnUjdMHgNtzTS0ToQEQA0GYCAoCw1LPWQ5h9vGbNrJV48EqK1Dt9kwhYXUUuRBAcYiKAKyGFhKwnobsRptoRlYoIE5iECwB/ICBAW1JJ3kNQwoYuVNzyHmolHriTjhbz9nsvB8IkGjLVjM7IhBcVvqNBtLCGju5GVONExEOICFSr7AyS8WjZxHKVkK+FZdqEQECAlqFW8xTU2n3wwst9qAW6eDDhJxxMoiFsaIPFQNl5wggKgyuhhzX83AhdRPglV5om4gqTWAkRATodCAjQEjRqjotmdx9MqJ2/+t5POLgLEO+Kf93JuP+IjIx/eEM6EqYcCd2NCCIi9ORKk4jQ63yEFQUQEaCTgYAAbUUtQxf1DIMMlvtgEg9+wsFPMOgE2j+gmCjbV8NOsjSENCoVEX4gHwIAMxAQoOlpROiiFu2oR/giiPsgo61ifgpZecpjfzchUE1iZY9wFXLeAiGEkBAFqVTREI+WhTQGiLmO0NBFhJQQqhOBUAZQBaucgbYaCsiBAKC56ST3IQxu7oObeDAJh2oqVroSQEiYEi1twWAQEQM1I8rrRbiJCImaWAkRAYA/cCBAR7sP7UAlnXsQ8eB23lzW+3rxhEuVSjeCOBJJc/2IoHkRdtsNIsIN5EMA4A0EBGj7xEkvajCn1KBSsvLzwcpKa5hHWwQTD36iwWvfwILCT0i4hDTUvAjXehHxgbksVBGhm9N+Ja+RDwHAABAQANQJfvJ1y4PoUuL2YpIp6z13Vo12S/zEQ85tis8ABBITSaJkLOqeg5EMLyLcHAV5r8UEaNY6v0JTGNrZOfDPSy0mUUu06URsEBCg7d2HRnfIEu7IvObACCoy7O2xaFl+ALsR6bT5Gtwphy0UpYoHk3AIEs5wExx9Ad2IUkJm3um2GEZqeIkINbFSLzZlfxeXQlPIhwDADAQEADVEdxCqdSHUfUxhDCkivMIY3AFXMqLCSzwEDWkE2c9XSGSC50WEFRFBJ9NCvQcAyoGAAB2Z+1AJpvACdzZh2qC7EGFEhLrdKxdCzJjZR9SVjNGqLAUoAhW87oMuCPIhHI1YLOopKPoC5kbo82q4JldqIkKcwqViJX+O1TAfAoIDdAIQEKCtGYzwhS4i/FyIWosINZShhzBkZytdCBnGCJp46YVJPORczhlPxhz7e4mJvrBuhCYi5NwFuhNhKjalpjqYwhvV5EMA0O5AQICmolnyFdycBbckxyAigpFColoRwZTqHwyICEaUgk6UnqW7LQfCT0SEdSFM4sFNOLhu95mR009EqHkRbuczhTN0EZErmn/ewuRDuAEXovXh35VaTKaV85v+tUWBgAAtS73DF7UQEYybGyFHB0ghoYsIsS1XcJxHWvGqG8EiorRvSUikC+UOhJuIUJHb5L4iATJADoMuDnJZ77BGPBG1j9GdCT3psi+EEyFCN1q1Tl1EiO3K8E5ZIkKOwqik3DVcCNCptKcsAiAgfg8Gbh2I2/Au0/76fiwi1OJG3JlJMaGXzlWfftTzyH14u9xHCgnpRqhOhPrKQkG0IxZVtsUd24KiigcWDn7iQd1PLJm8fQ4WEixYxJLhbaXP0mlgccNOCX+W4qe0bmCRoRwWESyu9AnJ5GfTaBg1H0JH1VphXLJmcdQAqAdwIEDT0Kx/bL0SJd0SK5kgbgRjciR0pyGIG2FjdXYsJIoGQaM7EfxEr4YypIhQXYh4kl2D4AmTQZyL0rkLgUIbrk4EGdwIU2KlUvaakSMzCmTVgSiWHAi9UmXQURlIqAS1ZMWKFXTVVVfRjBkzaMiQIXTiiSfSKaec4nnMF198Qb///e/p3nvvpW222YZuueUWqjcQEKCtCVKYiftQv8EEJlGgXkOiXkvteORxpn3DCgnrhGrjHPukrSf2ZDxGRbmbLRKcDoObiGBMoYwgYY2wQzzdhIQp0VIXEtxG4Ua4iAjGrp9hiQhGHZkRFL+EStB+1GoyrXyIcxSLRTrkkEOEiLjyyitpwYIFdPbZZ9PixYvpggsuMB6zdOlS2m677ei4446j0aNH0/vvv0+DAQQEaEn3odb5D7JjCCok3NpgchqCuhJqWIPFhBQSOm6uhD0vREENgShJll6Ji9wBa9vVfAhxesWF4M6dQw6cw+CVQOmXXCmOdxMSWnvE9TmkoZ1DiqKyWhdKxUpGTsClJlUWIgPXc5t0K2hCJVwIUAseffRRevrpp+m9996jTTfdVKz77LPP6Mc//jGdc845lEyW/yIPGzaMPvzwQ0qlUnTaaacNmoCAngZAgTuHoE+Z3KnIxS1HQs9/MB1j2jdIngQvKWWR50jFSscNbIuJhUUEL9zh6guHLYQTYXXI7ETIUAZ/5s7d/g7K+2qRORBisfIfxHolP8LOjdDyIkw5EYyeEyHzISTc8etVPaX7o5a2rkSwttMsrqAxPPHEE0I4SPHAsCPBLsNLL71kPCbGfx9SKRps4ECAtqeS+SV0ERHGmXBzGiSyLUFCHKqIsFrm2/ZiPkJcP2ooj3aIRI01JAQmRyJTvs12ImRbMwVbRHgVknImWAYpeZ13H7GRDJAXoQzxtPcxHCstab4XRcWB0GfudBuKiWGdoFKWL1/u+Mydvt7xz5s3j9ZZZx3HurFjx9rbdtlll6b5D4CAAB2RPOkWWgiKmyvh1n8GFRQmMSH3NwmPIGGOZCROiywHIlLUwhtanYmubud8GnbIIuMvImQog/fzC1X44QhjcN6FEtrwyotwExHq91Ex5UOI9fk8dcfigUMZnt8FxaXaqw6ESygxDFnrD8j48eMd66dMmUJTp0517pvNlokK+Zm3NRMQEKCjqFZIBBEWJlHhJihMQ0G5bUEERflvb+kPnRxZwEKBO0XhPsjO00VIcMdbVp3SkBehd9p2x2911KZhnGXlrzPmMlGxZLfRqXDkRlQgIkz5EPI+F+0sUzLOl+FGpS4E6GzmzZtHvb299mdT2IGTIOfMmeNYt2jRIntbMwEBATqSsH/wwwiOIKIibMgjyJNvIlnq+AoRKwciFqOo9vQkhUQiGXN8J3tuDV0wKCLCMcRT/356MSiXkIWbeFC3SSHhFtaoVkRI1Ox6vifdsfJQRq1dCIiNzqa3t9chIEzsuOOOdNttt9HKlStp6NChYt1zzz1H0WiUJkyYQM0EkihBQ2nW2g86aqJjkMUtOVNfTMmVeqKl2zVM+4v1loDoSURFRzgsFRdiYngqITrN4V1xO+lyWDJmf5aJliO7EzRqaFIso4cmaUR3goaLdSk7uVImVvLICH7lDp1dCM5ZsL+TJTbcki7z6T7HYq/P9IlloKiUTKzM28mVUrDYyZU+iZUSNamSnRn9508tMOX3s1lpcSkAvDj66KOpu7tbDOFkWEj87Gc/o0MPPZTGjBljj8rYfvvt6fHHH6dGAgcCtCRhZ8FsFodD72j8ciu8nnZN94Cv21+I2Ntj8Wgp/GG5E8l43M6dSMfzdniDjyslWzrDGg60kIbbZFxSRAStB2F/Z0VExFLdQkS4hTVk+0QOhgf60E49J0LC3zkSK5+1sxoXwg24EK2DPhqqmvMEZdSoUTR9+nQ66aSTRGEorgex00470c0332zvk8lk6F//+pcYmSE5+OCD6ZNPPhFhknQ6LQQG8+qrr1K9gIAAwPSLUWVM26tyZTXCopzy83VbnSBfK2a5EjIMoouJVKxoP3XrQiLFxZasYZ+LV2bKRMTooUSL5HqJllDpVidCFQsmeLsUEda3Moc0NJETOpQRLYrvLVEn3GL8REOldSEA8GLvvfemjz76iD744APq6emhcePGObazE/HKK6/QhhtuaK/7xS9+IYTFYAIBATrahajXH3iv8/pVswxH+bmK0YGnnoh1Xls8GMREshBxCAlR5VKrnMfhDOE4sGAIICLs7xrAhTDlRbDzIEXGgJCoTkS4uQ8M35OIVu3Ta1gnxAGoN1zbYbPNNjNuSyQStsMg2XLLLWmwgYAADaMWceMwIqJasRCmk/f6bm7tqEQMmdokRYPIh7A6QG4PuxHi+laIg68nxUQiWhwQElZoQ3cjpJDozuRLosHPibBGTgyM0MgHTqpUEyqdbkQ4ESEnCRPrTNN/R0vOCwVwIdyoxIVAGAO0AxAQoOWptYtQiyF5QUMVtfoejk7Lyo1WEzHVUtqcoiAFBYsJ6UzExWu5kJAMp4Q9vwQnV6oiojs5UGJ6oKZDeS6EEAQeIzF0ZB6ESUTo55Zt4cROiZzXwy2UEbH+P9L5IkVizmm/650LAZoft6ToSs7TjkBAABDyFzxa9LblC5FYTYVFkLapbZLvU5ECxa1Ki7JN8lwsFgZciNJxUkzoQkIex27Esn6ikd1kiwj5VD96aIoWrUwLERFPuCRh+oQ08rny+G0snnQIDlVEiDYbwhKyyJUuU5LdwQed1dKFcAMuBGh1ICBAxxK2Yw6K6RgvURG0LX5tiuRLVeoi+Zz9ORIpCYCYKG5dohhLUCpSapN0HlQxoQsJooTDjeCQBuNIruRho0pn3r+qPJShIoSATyKlFBUsIhxhDU1E+IUyZLtMs3ZGrL+AYuRJ1DnZVq1cCDgVoF2BgAAdh19nXYlo8EM9p5+Y8DteFwz254Jl1yuvwoDIW71mLOnYLxIt/fpHYwnxmojHhGjQhQTDbgQHR2y6EkT9WZETwSKCh0tynQhamXY4DWLGTqU2RInyMIbJfdC3qW5EEBEhQxmOoZxJop4A84lU4kIA0GlAQICG0IjCO15//L1Eg95RB4Wf9L2uFURIhBIOZIkFazRFJL2KInnlGnonbT3ZRwrWazQuxIQuJDjTsORSlIZ9Ou6lJSIYzomQIqIvI3MUBqYRN4UvTDkRujPBYkF1I1QRoZ9XFSt6KEMmVKqCQhgswmXIs5KyThLMhdBBMmX7IfKEaiAaY20qPCEgQNtTiXCoVDSYzuEnJHQxEVTMlAkHXpfLUIQ7Q7E9SxG1XKLc33IeBtpnCYt4UogJXUjw7BrsRvB97GOb3wpp2GgigjtqOTJD5kPkqFSaegBLFAQJY6jDOTURIdYnB1wIdc4MibyunlDpNaxThYe3miZUQjIl6HQgIEDbUmvh4OiwDRStjtl0TjcRYXIi+LOf8+AmHkrbrP14HysHQm4r4eJEiHZmyoUET7Ilyj7zXlElpKHQnxUdMidWSnhkhhrK8EqiFKLAI4whziFHYqh5EbYAMYcy5LwcbsM6pQPBJa6LlvBSXQh9zowwyZQAtDsQEKAtCSse3ISDn2gw7esmJEy4hTHket98DNV5kN9B5jjkshQp5p3fLVfKUbCJp5xOCYsHg5DojnfZboQa0jDBSYucsMgjM5gVlLFDGXEloVKmZoRBFRGq++AYmaE4Hc5hnjGHCxE0F6LSZErUhADtDgQEaCtqIRzCiAYTfLyfiAiaSKm6EdzBO9qrOQ+lAwbaLkZhsGNgiYZipr/8Asq6SLKLIvmUfa1iPEnFRLcQEvFCjqLiPU/CVaT+nMxh8f6eLCY4H0KGMuzaEJm8I/Rgqg2R19obS3YZRYSaD2GqDTEQwsiX5UJYKR3Un81TKmF2iZBMCYAZCAjQNlQrHlyFg9+jsjW6IShe4sFkkbuFNFzDGzmn4yCFQzGbdRcSfFw2S5FEv0NMFHMZKiZ7hCPBXX9XNE75eJftRJj+jHA4gMMZ3EFzZ62HMjhPQcyREXayLavdLCSkiCgXH93ek3ppLoSoqqW024FPMqVrOxHGaBtQSMobCAjQFtRFPAT12Hk/DxGh5j/o4sE0GkVdJ7+XFBEOF4KvqbaRh22qbgSLh3zGIRxU8VBUEhgjqW57mxAPlpgoCYksFVJD7Ff+Bt0uIoLbztOGm5ChDNmxl5wBZc6LAHkQUkhIESGPM6EmVLq6ELxPwJwFPZmykjAGAO0EBAToKPFQU+GgH+PjRKjiQRcOpnkwZOckv6MqIlzbro6uyLKAyA04ECwgrE63qLgUvF51LSLpPiEoVCHBfSxfl1+5WzaJiEwuRkOTA0/x3FnLfAg1lKG7EGYnIZiIEO/LRIe7C6GPyOjuHhAWhUjeHr2hug7pCpIp3cDcGKCdgIAALU1NxYOLcHCOYCjB+QFBkJ29FA+qcPCbPEtuV59yg4QzjO2wxAMLB1tQpFU3QsmFSHWVEjA1IREdMkxsdxMRuWSpaqXMGxjZXXqvhzKkC8HvuUMPqtdymT6KK3kTjBrK8HIhYlYZazkiw1Gd0uBASNFQyvlw/owFCWMA0AlAQICWpd7iwSQc1G1uIkImULqJB1U4VFJQKxGN2TWP+A4UXb4Thy6KVg6EKh6kWChk+qkg8wEUopl+ilpP99FhI2whIa7B23qGi3AJ50dQ9whbROQKpZ44nY/SsGRMdMLdSR6NkTS6EHJERi7r70CweFBfWUjooQwvF0IOI9WrUw5NWoLHciD8akO4hTF0kAfRHsQjtSkkFY+0p+CEgAAth5i/oY7iwUs46Pv5ORFu4kEVDnruXjkD+w64ESUR4fguQriY266KB1U45PtL++f6SyM14l0psS7WlbPFRIxFBB+f7qPosJHigV26EKI7tkRE6TtFaVhqIB9ChgdGdCfEq5cL4RiVoYgCKRpMboQaygjiQsjqlJxMKYWDZZrYbQ0axlBBHgToRCAgQFtRjXgIKhyMWPkPuvvgJh5U0eAXyij5DOKsDhHBE2Lx9aQLIeo3sKDJOGs9qMmSUjywSJCiIWeJCPV9vCtpCwrePz50qAhtSFQREYknrXAGDwEtUHchaudDyFAGd8zDxWuuzIWQQzqDVKV0w8uFkHkPpXk5BnIe1Mm/OJkyWRrBGiiMwSAPAnQ6EBCgbfAd6liBeFAFiFc1SRU1dKGKB/leigeTG+FNxCEiRD6EDGXwaAseoaGHMRwJlKX3UjywWNCdCIlcz/tIMcFuhIoUEex88FdK8QRb8aj4fpwP4QxlxESHbcqFUJMpwyRSBnUh7ARKZegoCwkOY4iWDyFthIZ/jY4gc2MA0O5AQICWIWzWu+d8Fj7iwVhgyqcktVo8Sh1xoYsHVTjo7oNpCKfaQfFDcT7K5ZKL1pNxrDRVNzsg/D2icdc2qqELKR5UJ0IVETHNgZDvdVhARKzRGdyGRHIodcV5SGMplMEOBIcCpAshhURpsq2Be6yGMQaqTHaVFZPySqw0uRDxxFBl37wjmVKGMXRkGCMVj4WaG0MHeRCtD5clr0Vp8libljeHgAAtQWmcfY1CFx7iwW8SLVVE2PkPyvBNPXRhEg8mV0I+1apkyJnt73zSHZhqW07HLctQe6ELBn7Pr/ms07mQn0v5EEnxmujtEetESEMZtSGf/llIxKJxikdTlIpHRCiDa0KwAyFdCDUXop9FgyGMUT7PhXliLcd6FxdCH76phzF6rXoQnOSpy6N0gLkxVJAHAToNCAjQ8s5DqNBFFeIhKDJ0oboLqnhQhYMUDfxUayKdJ/G0q4sJRtZJ4lkzSwmVSVExshi36kQkEmIIppoDoboPqnjI9ZW+e65/4F7Fu+JifVwTFzKkIXMi+BrCiWABE0+KUEYuWpq9k9vMDoTJhViRjFYcxlCFhJcLIRMz3cIYfUqVSjkyI+gsnQwKRYFOBgICNDWVFOtxnbUy4DGVUHQJHciESV08qMJBzrUgPms2C3e8vL301Btz/sbyV4uTmNhKJlTKmTX9kOEKKR5YOOT6Svcq25+jhBAPOYp3x21RIY+RIY2o9fQuh3hGOYmS2xBLUndyqPieJhciGYuKXAjuwNVkSr+aEH5JliYXQk6yxcLBGMawRoyoSJHjRzX1IJA3AdoBCAjQ0uIhVFElF/fBKB6k8PCbWVOrPqm6D17iQRUOUjQYy1pn8uI+8D6peIG68lHhSAyx6hnEC6VQBrsQIhdCaXMkkSLqWznQNst1UBMnVfHAwqFgDXNMZzIOMdFPfcKRYFIjhlEuGafs8tWl63ChKXY6Vi8TYQwZykhEk2UuhHQfOGTA77kTV6Ih1i11TpTlhSwkZSoypcLCwRTGkPBwziHdzqm+uyyhUU09iLDA0WguMBeGNxAQoK1wdR8qEQ/yvY+I8Jp500s8sCiQosHkQsg6BNy/CgdCdScyJEQEn7dkEBRoiBiFkaRidMAJ4Y7d2C4OX1ihCVU88Ktcx+4DX1yuZyFhIppcSpF4KVwS5RlAeSnkqDvZZbsQ3H6xCPehNAJChDFWEcViahhjIA9COg4sDEy1IEyUzeCpzdKplrbmolJy5IW4pVzsSpniW06updaDEOttRyhAezCxFmhjICBAZ7gPQXALdxhEhF5AisMXJveB8RIP8n1Z0p7ymUcDlByIqMOlSBYiQlR0i/VEhXiMIhxKkW0TdRlWeX5ldh9U8SDDGMKV6M9ZeRCWmGCW9JflQ8RWriyVv+ay15x3YbkQPP23fILjERnL+nPiu8jwgBrGSFs5GIzMgxiYI6O/YhfCFiHWaAw5B4d4z26LFqoold2OudaD0Gfn1IGDADoJCAjQELhTcat/UOnshTVxH3wIWgtCH3HhJR6kUCibTtqC1/OTezk50TFzDgSHMvic9ogMBZGjsHqFs30yfKHkPfB7Fg155amc38eUDlWGOCQ8QoOHd0ZXLLVDGbGe4eLeRrN9IheiP1eax2N4V5xWKEmUMozRvyorOvUgeRCVUnIcyvMgJFzgKmGVtQ6aA+ElGjAzJ+gEICBAUzFYUx+XiYeAyZYOYkk7eVJ3Hxj9s5t4YIEgrXTVUpeIzixpCYlclIgLNlmkYtx5la4jcyFIDjNlJyAxsK9MeiwvGlVwiIeMMjKh9EXylMzkS8mUI7somoxSnN2J7hyll64Q52UhIacLl7kQlBoiXCLWPpwfwDkDahhjaV/WMRqj0jwI06Ra6nBQUx6EvZ8cymLd+6QlLMKKCNCexHzK5oc5TzsCAQGaxoUIIx786j6YcC1VXYl48EAvFiXdBy/xIBc37A6NCxxZlrpIroznRSiDXQg+t3AjtHCLdAZMyJwH0W5LPPTlrTks2CGwnY+8mCKiXwthxBJxkZQphYTIgxg6opQLkcuI/xcucZ22Rixwm2UYg0djMKVOPVuWB1Ep9iRbsiCVIQ/ClEip45dIyWBmTtDJQECAtnMe3MIXg4Fpum4ZutDFw5K+rMN5kHUIGLb3ZQcrEw5VhlNCPM2LSo+WCyGFS8wudFVKbKRVzvCF3b5+JXxhvWfxwMJBtKHAS4FKAz6itohgt0IO80wv76NYV0k8sJCQLgTl0hTJ8iyeQykR7xJPcSXx4ByNwXkQnBHKnbmaB8GoiZQ6BUscRMtcBpcpvw0jNEzDOE2JlG4VKasFQzlBqwMBATojZOGW+1CB+2CagVMtHGUsFKUM2dSdBykcuPNibFFBSmEjTQdxGKA/F3W4EKXrl+bICDQEVUMNXbB4kEKCxQMLib480Sju2K3ESxnKyCtlsblCZWHFEooOGUaRVEYIODWMoY7GkN9NzYOg1e5Okkiu1AQFCwkpIvQwhgonZZoSKSVcUCrhUkKD/79MiZP1GsoJQKvQphW6QTtT89EXGoFm5ZSzb1r5DxI1D5JFRLn7UC4eWDjwwp8Xr0xbM1aqS56W9WVFzoA8js+xvD9rn5eFCr8vS0yNp0ohDKs6pY7Mf5CJkywapHgouRElR2JgfZH6VmVEKMM+NjswpwbPtyGmDs9awzmtMIYUitzhyvdqjgEPqRSvYlRGzBYCboLA8R0C5krICpTOdeWJq6oT5FbgSx12W2uCT64G2pW5c+fSpEmTaNSoUTR+/Hi6+OKLKZfL1fyYaoEDAVoe1/wHQ/jCz30IM6W3Xv9BD1+Y3AdGzXeQwqG0PmfsvLzi89yRiQ45VbomC5isNWOnWg+CiSp5EPrcF+Kc+aJDPDD9hYLynDEQzuCkSulClIpRDczu6QhjWPdbhjBk5UY1D0LWg6g1pkRKiWkkhh9CNAQYygnah0YUkspkMnTAAQfQpptuSi+99BItWLCAjjzySMpms/TLX/6yZsfUAvwWgLYiaOlq3zBHCCGhowoJ+aRqvyphClUsqOJBTaqU+/HC+zCrFRdCJmbKuTTkaAy3YaemGTWZspEXtngYeBX7WQKD92f3QbgQWhiDpw23RUQhJ/5P+A+otPfdOl8uKGVc7zFVtwnOg5C1I/SRHCwc3JD3t/S+di6Xy+hcAIzcf//9NHv2bLr55ptpww03pF133ZWmTp1KN954I61YsaJmx9QCCAjQ9lQjBoKi5j/oIkK+5/CFHroofS6JB7mNrXZ1UTuzPsdxPLKjFCKRYRIT6lBOY9vtBMqC7T6waMiwi2It/FlNsJTHyfoRahiDkRN4iXtvOUGsD+xQhpVIKZEjImSlSLG/kvjoVabajyCTc9UShCBANcycOZO22GILWnvtte11++67L/X39wt3oVbHNCyEUSwWKRIZ/GQhvhnXXHMNPfHEE9TV1UXHHnssTZ48edDbAdqPWjkOKuoMm2oM3SkIBsSDe5w+T2oXKEtBd1tDO3ut9SIPIl6krqiS7GlFbOSEVwzXbBDntYpIecGioTsWESKCQxj8zNEdK60XtSGsMtjOMEY/RWUehCFvRS0DrY7EUJFTe9cTHspZq2coVKAEQVi+fLnjcyqVEosKhx/WWmstxzr5eeHChcbzVnJMLQj12/P444/T1ltvTclkkjbZZBOaNm0aDSbHHXcc/fGPf6QzzzyTjjjiCDr77LPpJz/5yaC2AbQJlYy+8KlCqZauNgkHtdKkmvsgkeKBSyyri9zmVmxKznRpEjSmESNBKAmGEjIfYuBzyalwQ07WxchESokMY3jNJaGPkBhMdLenGtSfA9CasPCt1cJwcuPw4cPt5eqrryYT0WjU+Jkf3t2o5JhBcyC++OILkZSx5557iqd+tkVOPPFE2mGHHWjjjTemevPcc8+JOM8LL7xAO+20k1i3atUquvTSS+ncc8+lIUOG1L0NoIXwS6AcRNSMfVOnpK6TgkGF18lRCqW5GuJGAVKz9lo5D6pwGHjPxaVKHTznQfCQTj0PQiJyICxKIzGcYkYvz22qBREUOZzTbSinWgtCnVQLgMFk3rx51Nvb63AgdMaMGUPvvvuuY91nn31mbzNRyTG1IPBv0VNPPUXbbrstPfDAA/S9732P7r77bjrkkEPooYceosGAwxYc35HigTn88MOFiJg1a9agtAEAHXUIp4ocgSFRJ8pSkyfle5HvoIgHUyjDL9lPDZkIAs7boY7AKPseVg5EWFTxoKPWTgCgk+jt7XUsJgGxyy670Jtvvike2tX+N5FI0I477mg8byXHDKoD8fHHH9OXv/xlx7qvfOUrNH/+fBoMeIzr2LFjHevWXXdde5uJdDotFj3+xGNj6z0+NiiyHc3SnmbG7V5F8tr024zSmUaszjtSUDpY5X0kZ37qLUaU/YsRKhYtS5ALPBV5hk6uzZizRz7kczyMkl8LVMjzkqcit61QENeOFAqlokpUEEucCpSIFCgXKVA0UqRodKCjFu/zuYHkwkiRYhHeP0JxipTOIa3RAl8nIr5SOhOhRNxK6MzlKJrPUzSWJNYzeYpSLhKjfDRO+XiCCokkFZJERf4j1kUUiRUonc1TNF6gGFe0zJdKY8ta/rFYhKLRCEUSMcqyPdoVo2KKz5GkQiJB+VhCnDtHUYrw/eIZQvk+ZPqpkMiJ9flc3r4vfE+GJPiPUIF6UxEq9BUpFy1SMVakYpzrYEUoymWnC1HiuyYW3sD/fbFytRONlbbx5F9iSURLSzwilkSciItKxmNFSkWLFIsWKWndc/5/4HbwUrq3bF+XfmYikWIp/aNQpGK+QEX+bpEoFXihIhWsfLB8IUIRK0TD90n8bFmv1o+O/Xmg0eZcsrL9Gkwz/p1qprbUEq7lMG7cOOGs8ygKzm+44oor6Fvf+pYIe8j+mJ3/P//5z2L/IMfUg3iY/6yY9uQQj8cH7T+Rx7Pqao3VFcd5eJsJji9dfvnlZeufeXoG9fT0UDPBbQLBmPHMzJa6VfxTK39yx/E/UWthg6CayBvrm2WlhX8DFlmL5B+z1OzrbqLkpkTrUGnZ1nmqIdbCm8LAgaLF1lIGO6ifLeAULyJy2qvMGtayjby4IwcsYa1wJobVDr5jA383Tlhzcfm95RzOPvcjV1Ln0Ux/p1avXl33a4gcnhqEPiMhztHd3U2PPPIInXHGGSIRkgcMnHDCCXTdddfZ+3BeAz8c560HpSDHNHwUxm233SYSKSWff/656LzVdSeffDKdf/75tW0lkaiutXix85d86dKlVCgUaPTo0cZjLrnkErrgggscDgQnsey+x56OOFQjYQHGv5TcJhZkwP9e7bn7bo57ZSwOpU7tbSXxRQruRaRMLgTPJWHDs25ahZlEYiKHB8STfJddxponjOLXvlyBVmcLIqSwvD9HK7MFWtGfFUmUS7iKYyZPS/tz4nXxKq48mbdnhZSVEUtxenWYY+lpWpR+TsRo5NAUjeiK08ihSVpraBeN7o5Tb1ec1uxJUle0QK/Omkl7fXk7SuZWUmTpQsov/YLyn86n9KIl1Pf5Ulrx8We0asFKSq/I0MqFq2jJijQtzxaor1Cgpdm8+E4c1pAJmTz8kkdj8OuIRIyGx6M0Mhmjrp4kDV17CA1Zq5t61hhGPWNG0dBxa1Ji1GiKrTWeYmuMpfyQ0VTsHk4rKUlL+/O0PJ2nT1b00xerMjTni1W0cHmaPl6ymtKrc7R6eT/192Wpf3WWsiuWUKZvuchfyGfTYjhmPl0KjRQMOS7stDCxVJfId4glUiIfIhZPUCzRTYlhIykej4l8kq7uhHAphvXE6cxNVtKdn4+ieDwh8kt6uxPUk4hSVzJGI4ckRa5GMh4rzeMRc87pweEYWRwrzu6Q5RzI4arys8xv0wsKuZW+HqwS7638d0of0dBObL755vSPf/xD9G96ciTDbkNfX58Y0BD0mHoQ+CeB4yisaPyoV0IlJ2tef/31tGTJEho5cqRY9/zzz4vXCRMmGI8xDZFh+BegWX4JmrlNzYp+r4TFLN8X9Dc8O4TsiGMDYkM5pvSxPOegqDpu0Zj9uSimzGZBERe2fjEaE/Z2jopUZOufCtQVLVI2HSGRIpHPUzIZob50VuRM5CP8gFsQ+7OLtjxdFBUORR5Eweo4YnFHTkKhGKF4MSqW3mRShCPykRilUknRtkgsTt3JFMXiMYpFSwdyZ5koxoQdzv1RhAqU5xBKIUexXJai2QxFMxmKpNPUnc2U6lNkC1TI5kuhmHzRTpLiu5OPRUQoo5iLUZGTEAt83SJFMwmKZuMU40RJDhNwaCaVEnUfuDhUNB6jfKqb4vlSKCGbLoj2FqN58R04tJEt8nwbEUrzko9QOlfKI8lkC0JccaltLgKVt/I/CgbnMxqPlhIoedpuEfAoiHsRK3L4pyg0o7j3+QhFxAymPDy1dL/5+mwLiTCLdW/5/4r/b4v8x5j/j6NRisSi4n7ya1QsMYrGIgNhHqvjL3+1fnYDCohmnVOjmf5ONUs76omXEGCXIewxtSbw/8Dee+8tlkbBCZMjRoygK6+8kn7xi1+I0p08hJNHhQzGKBDQYvDT6CDPxMmdhGmKBB6yKIdZsoPAHTWXcFYny5LJkPx0rI/EkCMwGDkrJx+vFmKqJV1R7szzwnGQoy/4fZInw1L+OCV53oqueGlSra64XV9Cok8hrtfLUIe1+iWO+qHPyqmjjszwmsa7XvcUgHakZcYyDRs2jKZPn0533nmnCEPwiIxly5aJsAoAoQk5U2WYOKb69KiWbdaHLeqdlZ0wyR2ysshtcn/1OD6ntNNN9nelBbJYLIhrxUqhC0e7WbxY3yXe7byP8a6kmNpbTt7FtTPUWhSyNoLXZFQlp2Fwq0fWQ0w0q4sAglNKfs7VYMm35W1vKQ9ojz32oI8++ojefvttEZrYbLPNGt0k0CZwJ1dpZ8sdtqloEMfHZUfJHbwcyik7pkxfwarCWIJdCBYK6pO4FBV8zEDVRlnBMeYoysSx+JJ4KLVF/T6ytDTD9RrEubvjlF7u/M4sDPqsxCwWEXIIp3QfSk5ESVhwDoH4/l1xincn7Hk25KRdagltEbqx/oiq4kGd46NeqCWxg8y9UQnNlrMAwGDQUgJCxr222WabRjcDdIg4CPO0yRa9fOUOJWN15Py+356BcmAyLQ5DkMF515+9B5yHuD2DpUimTHJi34CIkBNW6U++XFLas+1dcaJVGSEeMgUuFMXHR0VBKelESPHgcB+64pZ4iFMsUQphSBHBpbM5hFEQCadJO3wxMC+IsxCWXYVTmV5bdSF4gqygeM2bMRhVLiEmQKfQcgICAC84sbHSGTlVoVFJCWjuODj5UDoS7Ah05Uv5DzIPosvKfbDtcb6cz6Vk3gMjp7/m42X4QowKcCnOxGEX1RuRk13pcD5Dn1pPwxINEhnGkOkYIv+h25n/wKELfo2kugbyH8ToldKfGenSqGW3y+emMKz3KErlBs/gWRqBEfz/UXWDapkLUUOjA4CmAgICtDwcZzfmJxgSKR37csemiY0wbgULFbf5MaQTwR17Kl6gbCZvhzHUzklWovTqsFTnQYoH6T50KfkPfE11xkt12GoxlxUFnexbw8Ml9OuIpElxY6yJswYm02LXoRS6iNJwFgzJmHAf1PCFnf+QtAREPGXfHxYPfD/EhF9iyGtpbg8uyc33wFTCu55U4kRIl8dtOnLQhvDfj1okY+cHN6F7sICAAG1TPrpWBHIf+A9CLCnECI/wk/nIpadNZxjDHoXBr1bIQboOLAh6qDS7psmJkMJCFw+q+8Dnl/kPvES5SibD4iiX9iwrLRyE7nhpSu8sj7yQ4oFzIQpl4kHmPnSN7LKPVcMXnP/ACZSc/yATKPk1m7XcB6VCqJySXE2elFOYy5k4g8zI6TcCw2v0hWlODNXxkeiiwWsysGpBCAS0ChAQoKGohYrqiSM84eNC+MHn0UWGbL/6fWQYI523OqBcwdkRJTXnwXpISXabO7VuF/eBXQ5H/kOFCd8yjKGKCLFeEQ9y6KZ0H7pGdpeFL6LDRpbyH5I9QmTJBEq+H5xAKRYlXBF0UjCTmFDFg2kSLXubkhdhEg1cnMsNmWdStl6vzItEStBhQECAthMSjjyIQa4HIUdBlAyHiKOjkbkQKqOGJu0OVK0HoaIO3+RleCpR5j7I8AUjxRFX12T3wc2BEMmT1iiKXFdcFGuStR+kiJAJk1I8pHpTdu4DuxDsPqRGDKOuEcMoPnQoRXuGOcIX/H/BlTllCENOPS6KVlkjMKTroJP3CCW5uQ6mBEq3GhAmR0IktiroQ29rCQQHaHUgIEDD0AsLhYGfasVEUn55EHVyIVT0MIbaOUgXgqtgci6EpSycJ1D6Ql1EqOKhFLYolVTW3Qd1KRq+i5uIYPGQzmTsMEapKZagUZ6wVfGQ6k1S98gukfvA4sGRPMmjLxIJKqSGOMIXXvkP4or5ghiBUYsaEGoCZTVDOIMkUsoy1qA9ieQzNRnBFUEOBAD1R+YODDqViAj+42I5Hozabh6NoQoJmQshMIiIru6obevrHZd8ClbFw1AWFIr7IBcWVXnpQPAIDGUIZ8Gqt6BXjGQ3gceZSkdCf7bnnAfeJsWDSJzsilNyWI84l+o+RIeOoEjP8NI9iSUpXeTZNEsOBOc/yPCFmv9gSqAMKyK8whdeiZM8v4hEve+oSAmAP3AgQNO5D5WKCNVVcAtjuLoQAUWE6JRdRl6oyGRKiXQhbBQRURqdwfkRMbvYlIoUDowqHoal4tRthzJK7oNjUrBcuqyIlN0+TnrM5ijOyZNCXAx04iwORFKlEuZgx4GFRinvoYtSvd0iaTLZ21PmPvD9YQeikOimXL40wRj/ny7rzznCF8yAiChPoKwljtCFJRTUEuHVDOE0/ayawhNIjgTtBgQEaEqCiAg9jFETTCLCUPZaT6SUYYxEKZZhUcqFYMR3EadxiohEMuYQU25DBNUhhF1a6CJluRB8L0TZ3BCWqxALfbmSOFD+HKglqlk06OKBQxeJ3h7xqrsPavJktpAXORAr0rmy8IVX/gMjZuEMUANCug+c/8DhC32bXwJlkBEY+v13AyIBdBIQEKBpqcSJqNqF0EVEgDkzRD0Il/3KnkQVEcEdkSjrbBASKvIeqOJhCA+htMIWUkgI94HDKlb9h2LWfQgnuwd2SWvLbchSjlLJpMONkMKBBQWLDVU8dFn5D9FhI8TIi+iQYSXnwXIfWDjwFOdZbfSFDF/I+g+m/Ac1gTJMFUpxd13yH0wJlKrbYEqgDDoCw7UtKBkB2hgICNDS+LkQVYmIIFj1IOzDivkyF0INZQg0J0IKCTnxvKzU6JiIyxIOst4DCwcOX3AHVeY+uIRhuLNn4ZDrzwjxwKGHPIcxrDDFwMWUplrCgRMm5YgLKR74NcbiYUivEA888kLcN8V9kMmT+ugLU/hi4JYGFwyq++AGiwU1/0EmUKqCoktzHsKGMWo1ogIORnMRyecCT6Lnd552BAICtLULUc9jVKRIUfMjBjqVchGRSJaKTTlCGha6RS6fdlXxkFCqTpblPgRAJlJKF0LPfZCfWTiIaw/rEeKjTDzI0AXXfTC4D/y6LJ2lFZm8ePUKX/hN581iQc2P0BMn/cIXbvkPOkHFQzUjMDCEE7QDEBCg5UVELVyIWogI3YVw1rYwOBHKb2AyHhdP6m6dlPz+cSXvQYoJ+7tz+CKftcUEj8DQQxilipFJ4rshXQixPhEvuRGWYJDr5DFyuGaZeLBCF8XUUComuqmY6BEjL9hRYfGguw9e4QvxFXwSKKWIcNR2UESCV/hC5j+ozoNaQEqd4TQocAxAJwMBAVoC7owjVdSFCCMiGDchoToMdiKlEsZQR2nIzkVOIqWPzGBYAMjt7Eq4IYWDOt+FXMeCwS98wXCZ6UJmpR3GkOKh9DldCmlYjoS6jd/zaAvpQBjFQ7JHvObjXUIg2CMvLPdBJk8u7WMXIlfahx0IJXyh5j94CQnTkE3dffALXwTNf6gkgRIjMECnAAEB2rbwlKej4CEi5LGMQ4T4DN+UyZRyRAaLGvUJldtvEhF+qB2TLh5U98Fuh4eLwi4CiwTpQvBnWR9CXMOajlsKCOk62OWqNfEgR12ooQsuZyFHXqwU4qFAS4RwUNwHHq6plLPWRUTpvf8IDDf3wTT6QhUSpiqUarVPL4KWsEYCZRvAgryKInM2tThHEwIBAdoGUyjDdVSGQUQwbkKiErgtcuIvZycjhVAwISGPNYkHEbKw3AeTcODcBK4DYU+vnekvcx6kkHBc09pHhi7YveDRFjxRlkM8dA8vVZ3UQherMtaoCysHosx9sEZ6hAlflN0XSyC4uQ+lfTh04RQOMv+hFLIwOxJ+oAIlABAQoAXhJ/l4LfIhDHNlhJnO2zGhlpydU3EhWHyo+RAyXMGd/4Ab4S8k5H6qeLCP5O+iug+GtnOBJ9HeTL8QAqLspIIUEvK9uKblOIjZNblIFAuIIb3WqyUerKRJFg9q6EImTrL7sLy/JB4Wrcw43Ac1fCHciJBDNfVRFyb3QS8e5Ra+YHoM9SH08EWt8h/cHAvkU4BWAw4EaLvEylD5EC4igqlFDXyJFA165+EUEu7HMuqx0n1w4FdF03pS58tFk1x9st8OYaghi9LrgHAQ03OnusVoC5nzIMMWtnhQRl1w6ILDFlx5kus+LF6ZsUde9LkkTzIsIkz5DywW1FoQjrCFh/ugJ0+Wjo36Dt90q/+A/AcAnEBAgJalniJC7KNWmtRDGy6zQYp9DS6Emg+huxF+SOEg91VDF2LkhVv4IpGgiOH8IqzB4sH6zGLC3pYqdciqcLBdBz7OSpjUxUO/JR44dMHCQSZOsngozbppdh9s4eATvpAiwiQe3NwHPXlSFQ6l8EXcISRSAUIYshaH3S7kP7Q14nerFpNp5QZvRuDBBAICdLSIYByjMxjDzHlegsELXUS4uRFyJIZbx6SLh1BtcHlKN61n0SBeLeEgFhYiPEEWT8/tJx7SWfHdOHQhEyfd3IcgtR8c98RFPHgeY0ie9Bp9weijLwAAZiAgQMeJCMbXjWDCTMGrVKN0QxcRsu1B4+Lq93C0V0FMoW2NbogkUsKB4HoQUixI94EFgjrJlsyTUPcTwsFyHQp8Xq7zIF7LxYOa9yBDFzJxcvHKtMiBKMt9UJInZfiiEtzcB7fkSYbdB332TXYg5MynKqbhm0En0Aq6D4QKaEUgIEDHiYhAboQuCrzEhI94UGtDqCIiTMch2+9wH/Q26ROBxVMU8UiwUB0IWzhYokEez24Dn1e4DywkEt2i/bp4UPMeWEhw6KIscdLgPoSetltpswxd+LkPaulqFgpywix2H3r4vyWgCeI2fFP/P1RvOYQBaGcgIEDb4Kz8GExEML5CIqDDEBTZDlVIBNm/DHUYqjpc1QpD2CJCO4xFgo4qGoRY4I5ZCgfLdeD3PFSzjzt+q9aDFA9q3oOs96CHLkzug59YUGtB6OJhYH117gPTlYhRyqV4lAqGb3YWIteoJnNhZKkdgYAAHeNGyA7bz43wFBIBcJuZU0d3I0zbVVyrY6pDT/na+dJxovOPRW0BEeHJrphcacimmPxKE1O6cGCRwt+HQxZ8X9XRFvxZFQ8y74HdBxm6UBMnTe6DDF+4YRplIcWDqWiUFA9+7gPD77v4a/uYIHIiMwlcBQBKQECAjnQjGL/cCJMYcM09CDp7Z0AR4VXLwuRCOGtSWAIizgIiVl7bQimOZR9ntV8XDtJ1yFkhC1nngRMm0/m8UTyooy5WrMoMhC5CuA+uX1cTDyp6dUk58sLkPvglT5owjb4IU74a+Q+g3YCAAG1NJbkRXk/8lQiFaqpZBqqqqYgIMT9H1Loet9WaWryoVZrU22YLCUU4yFyHbGGgPDULCDnagnMeVPEgRcMyreLkQOhioHS1jl8CpSNkoYglU+jCbeSF7j6IstWWA6EnT7rNfeHnPqB8NWgkixcvpq6uLurp6Ql8zOeffy5e11xzzdDX8ylhA0B7iAi3eTS4k3QLI5RCAKUlLEGO9bq22zb1fKKjl4KGRQR3/pyvYHWwheQQRzvUxa4iyXUdxEyaPWLhJEkOV4hcB8t1kCELdaimKh7kiAtOmpR5D+qoC7tolJID4VX7wSEWWCAYxINb3oMaugjjPoRJnpR4uQ86mL67ReEcIw75Vbvk61sH4qWXXqKtt96axo0bRyNGjKCjjz6aVqxY4bp/oVCgu+66i/bcc08aO3YsHXPMMRVdFwICNIRGxJGDCIkgYiLI4oXXdYLsq19DCgkhJoSQsLZZIydMixAbLBqicVs0qMJBH2VhJ0taQzVV8SBHXLB4cOQ9KKELN9zyH3ThYBIPXkjx4Ok+iBwIa0RGiOTJIMWjgv58I58CVAsLhUMOOYR23313Wrp0Kc2dO5fefPNNOvPMM12PWbZsGf31r3+lqVOn0sknn1zxtSEgQMchhUSlYqISqj2nerw8h0m0CBEhXQlFWMhFDMO0FpNocHMdZLKkrPOg5jzo4kHmPaihC9190PEajinyHQziwct9kEjxUIn7gORJ0ApMnz6dFi1aRFdffTUlk0laZ5116Pvf/75wGHi9iZEjR4rte++9d1XXRg4E6Gi8ki0Ztw7fLcmxEoEQZJpyvX3GxEtrVbFY2rckLOJl+8rr5ayCU/xZzqzNOQ78Wb6ycOAZNTlkwZ9ZPPBQTZnzMBC2KOU/qHkP6nTdOkFm3nTkOsiZNwOIB9V9UBF1HxT3QTgQkdK9COs+IHwBmoV//vOftNVWW4nQhYTdiHw+Ty+//DLtt99+dbs2BAQAhk7cz1qu1EkIIhYqP67U8eWKpVd2FvL8vmgJBuUc8nzcx8v1qnDIsAthjbLgz1JEyKm5dfGwaGW6JB7UvIeA7oOfC+EnHvxCF6a6D7V2HxC+AEFYvny543MqlRKLCnf8CxYs8DzPkCFDhIsgkyDXWGMNx3b5WSZI1gsICNDy6PNI1CKRza3DDhKzrkQkBP0OYc4lXrVQjeo0qKJBvpfCQXUd+L2aLOkpHjJWnQdFPFSDl3iQmEIXjB66KHMfYlGSOZapWKQu7gNobbjsezETq8l5mPHjx5PKlClTRB6CCouHnXfembw48sgj6de//rV4H43yMGvn8PJstjRaK+aSAFwrICBAw5CTSlVDmI7XtG/YTmAw21tpG+Q1OI8hRwP7qkJBfpbv3YQDv+eQhRQPss6Dm3gwhS7UmTd1WBDoroRe38FNPHiFLnTHwSQeRN2HaLGu7gNqPwCVefPmUW9vr/1Zdx8YHkkxf/58Cgrv/9prrznWffrpp+J13XXXpXoCAQFallp0xl7nqPQJM2y7KhElHukFVFBchqLmQOhuA6MLB8YUspB5Dn7iIaz7oAsGk3BgwoiHsImTcB/AYNDb2+sQELVgjz32oGuvvVaIE+lwPPzwwyLMscMOOzjCIqNHj6bubu8RTGGAgABgEMIKYYSClzgI0j7u/OX1MtZ79frSbVCFgtxuch3CigdHG12GcLI4CFQHogbiwdV9YKchUhh09wGAWsJDOCdMmEAnnXQS/fKXv6RPPvmELr/8crrwwgvtglIsHlhcTJs2TdSIYBYuXChCH6tXr6Z0Om27HuxoBAUCArQkte7cm1Eo+H1H03X4mLx0EfIFilqJlarbEFQ4MLp4kEM1dfHgaENA90EXEWV1H+okHkzoVSfrmfuA2g+tQzGbFUstzlMvOM/hoYceEkM3TzjhBCEa+D0LCEk8HhfhDLVC5aRJk4RrIZF5F2HCJxAQoOXzIOpJrdpWjVhwa4N+jNyvYI26YNEQLTrdBsYUqiit93YduMKkFA9l308JXdjts/bzEhOmglCqcBCvHuKhEtQ5L+LFIql/2uE+gFZkrbXWoltuucV1+9prr10mDJ577rmqrwsBATqSeoqWwRALpn2ly1DID7gNtvOguA1ewoHxEg92ezxCF56CwZA0KderqOLBfm8YbVFp6EKf40IdfQH3AYBgQECAjqHWoqHaXIVaCQZGugxMX7r0TM0CIWPt4iUcxDGK68C4iQevERduk2VxB6+KCrekSbmv7jqUXsudh0rEg+5+JSNR24Fg90GKh3rUfQCg3YCAAB0Rxqj2/EHFwmAJBl00yPCEWG+957LTkVjEEboovVohDRfXQVwrgHiw2x5gem5dROjbHJ+1kIVcV6l4UFErTjrWGxInK819wNDN9qGYTdemDkQ2Te0IBARoe2o9TLIWyY71Eg3qOdIcyig6HQc34aC6DgPrzeJB4lWqWnb6qrjwy1lwcx2YsOJBxS10wZ+TEaKVAUIXKhh5AUAJCAgAahyWqKdoCCocUnJbNOIQDoyXeBjYVi4e7O9QZXVJFWdFyQHhoG7Tp+b2Eg8SU96DXvOBxUTBuid+oQuMvACgHAgI0JJhDP6DXsuhnI3OZ6jWbVD34e0sIDK5PPFUGCbhIF/1kIWXeDC5D37hC1UguO6jOBN6yEJuVyfH8ioU5ZY0yZgmywobuoD7AMAAEBCgrQkiSoKIh8ESDmHdBnUfdbu9zcd1MIkHiTpc057jIltdvoO6j/Oz2XUorfMXD35Jk3regywYVcg75xDwIsRM4A6QZNnic2FYP5vVnqcdgYAATUOz1oRwEw/NIhzUfThcESkouQ5W/6i7D17iQa31UGm4IkiNBikadOEgj9dDFkxQ8eCWNOlWMCoeCZc4iaqTAEBAgA7Hy31o9GgKN/HgJhzsc1hfqp87/0gstHgIg5ooKQWB23BOdR/1eF04lNaX5zswppwHk3hwS5qUn+WQTUtrVRW68ALuA2hn4ECAlqXWeRBBcSshXe/kSLd99CRJtXvzEg86at5DGPehfLRFNHBehKMolOY66CEL+TmsePDKe3BzHsKELjDnBehUICBAW4cxKj1fmLDFYLgO6n7qdl08iPdZRQgoDoQuHkx5D0Hhjl8dxilFgSmp0pRIqQsHU64D4yYe5PYw4kGdKEsdsmmiFqELuA+tTzHdT0Wfn5Wg52lHICAAqDFhnYdaigcWBeoDs594qAZdRPiNujCJhtIxZtdBDVkwtRYPvF1tfi1DFwB0AhAQoOkI4xoMZhgjqPvgRa1GWbiJB/W133IgvAjrPshOXoY3VFEQ9FhVNKjrvVyHgfVOAVGNeKhn6AJiA3QCEBAADKL7UE3Ow8C+5e6Bl6MQNjHSNByTO3y1DoQuJNyOL1vnIxzcXAe5ny4e5FBNL/EgMYkHPRWkFmWoIR5ApwABAdrehWiW4aFeeQ9hBIa93ZAIqYcwVEyJk2FFBGMSEq7HK4JB398kHNxcB7levg8jHkyTZJmEQpjQBRInAYCAAKBueLkPKm7uQ6PgTlp1NPTCULoo8MMkGtyEg8l1qKd48Mt7MH4fhC46hmIuS8VcvCbnaUfgQICOzoXgzqKCB/OGETZ8ocIds+5CcOct8yC405bhDtlZy3PrTkPQmTXVc8lrqNdWt7u5Dm75Dky14kH/v9fFA0ZdAOAOBARoamoVfmiWMMZgOAZhj3ETEXI/Rj+/V+hCnw1TnldeS99PFQ5BXQexTqswKde5iQeVIM4DchkA8AYCArQNtRyR0agiVfVAFQWqC+ElIiS6IxHmmiphhYPJdTCFLOQ6v9EWfiMudMLmPUBsgE4EAgJQp7sQQcMYYdvBnVjQPIigcEdqCmNIuNNNp0vbu5IxWmUIvXqJCH1opy4EgqIKBnkd9fp+wkG03ydkYSpPHUY8qKMwolUkTUI8tC/FbJqKmRoUksqmqR2BgABtRSu6ENwJmkZZ+MEdrByJ4RfGkJ21mxPB6EIiSM0It311x0KdcjuMcAgTsggrHkxgxAUAwYGAAC0B/2HP1aDjr7ULoV/Ly6XgTk4O5eSOzzSUUz1e3UcVGUFcCOojozjQwxmMLiQkuiAJKha8REOlwkHeG9N6vyJR6jp9veo8mPAbrgn3AXQyEBCgZajVH+swIqJaF6IeYYygLkS3EsJQt5ncCBU3QeGFfg71Ovq53ITDYIsHvqyq4cL+fEE8gE4HAgK0JfUMP9TDhVAdhrAuhC4iIkqn6MxxKHcjJOrIC5MY8MOUK2ESDfUSDpWIBxXkPQDXybRitTlPOwIBAdqWWoUyTOfxExFBXYhaigi36pTlOQ4DfxFNYqJSdMfCTUCEEQ6V5jt4rQ+ij1BpEoA2ExCFQoFeeeUV+vDDD2n8+PH0la98haJ+QUzQdnDHUGwCEeHXRvXcqohQXYhKRQTD+8kOWBUS6YL1PhGjYrTcgWBM6+opIGTbSu0fWG+as8LPdagmWbJa58HtGAA6kZYREM8++yx9+9vfpq6uLtpwww3phRdeoOHDh9NDDz1EY8eObXTzQAcM7fQLVfhtr4WIYNzcCCkkZEfNr33FcMIhSEEqL9HhJhrUNsq2q99Jfle3bdWGLNzEg57HCvEAQBsKiHw+T9OmTaMttthCfO7v76ddd92Vzj//fLr77rsb3TzQxNRysq1GiQjGz40ofY4RKZ2iHtowdf564mUQ3PZTBYPdHvv9wDYv4VCJ6+C1noHzACqhkOmnQrw252lHWkZA7L777o7P7ER87Wtfo7/97W8NaxNo77ky6jW0M4yIYIK6Eeq+pevEiKKlPAm9YxfHVjDaQsV0TlUwqO1S2yy/i98+Xq5DNfkOCFsA0GECwpQP8dhjj9F2223nuk86nRaLZPny5eI1l8uJpRmQ7WiW9jQzpnvFXUWYUIabiPA6T6FQvq9+nqh2vL4Pb88VFZERGZitM2Gtk0IiGdGEgPJZ/sLKa6WsvjKdtz6LDtO6jpULUVo3QMbKl+iuNpRfyJdEirZOFQTic6x0oWK+YHfexfyAcOD18n2B31vCIR7J218jHikdx5pHCgR+L88nhZ5eXVIPUehhiyC/f6ZQR6fRjH+nmqktnUrDBAR37H/+858991lvvfVon332MW679NJLafbs2XTXXXe5Hn/11VfT5ZdfXrb+madnUE9PDzUT3CaAe1UpKcO63gWvN92PVNbl/UpqLLNmPt3gFrQGzfR3avXq1Y1uQlOxatUq+te//kVDhgyhbbfdliKW6Pbik08+oblz59L6669fUS5hwwRENpulf/zjH5777LDDDkYBcc0119C1115L999/P22++eaux19yySV0wQUXOBwIHr2x+x57Um9vLzWLiuZfSm5TPN6yhlBT3KtaOBEUwolwO5fpeH0f1Y1g9GGealhDfNYegU2lr+3r8iP7v18l2mB7SheDj1IyndPhJrggHQavMIF6Hv2cpjwHRroOXuEKfRujD8xyGzUhQk25nBAPO++2R9nPFEZbNPffKeko15NCNk8FQwn3Ss5TT7gvPPnkk2ndddelRYsW0VprrUV///vfRX9n4qWXXhJ94/vvvy8e1N98803ad9996fbbb6ehQ4cGvm7DfhK4kX/4wx9CH3fdddfRD37wA7rvvvto//3399w3lUqJRYd/AZrll6CZ29SsuN0rXhM4J8JDRHidx5QTEdPOJbtD9RymfdTtXTGnkOiOxR1CotvaLnMe5P5iH2udTGUo5iOlp/soz2Zp/pkyldFO+eRCqPkJOqbOVhcKpvwGSZA8B79tQfMdTMfqP1MQD83/d6pZ2tFoPvvsMzrxxBPpsssuo4suuogymYwQA6eeeio9+uijxmPmzZtHV155Je22227i88KFC2nixIn0/e9/n379618HvnZL/Q/wF2NX4S9/+QsdeOCBjW4OaOPESq/hnUylxaYYuZ8+usJUdEp2tGr1SomeQCn2U4QBnz+idJQOwRLAWXDDrXM1uRX6dWohHGotHoIeB0AzMm3aNPH63e9+V7wmk0m68MIL6YgjjqCPP/5YuBI6vE1l7bXXpoMPPphmzZoV6totIyB4qCbfoOOPP54+/fRT273gm3XCCSc0unmgTUUEU8uKlab99OvITtVLSHiJiWIkKhwIfp8p1qdjdAttmISJl2gwtStMuKKWwsHrWADqEXZJubjkYXj11VdFeQMemaiG/xnOiTAJCJ1isUjPP/88bbnllu0pILjiJMd4GDV3gpMhISBAPYd4hi02xXgJhKD7qR2tOuxT4iYmCpGonZQYJIehGtycDD/REFY46NsZiAdQb/L9GcoHSEYMch5Gz0mYMmUKTZ061bGOaxzNnDnT83zrrLMObbXVVuL9kiVLaNSoUY7to0ePtrcF4aqrrqK3336bbrvtNmpLAXHMMceIBYBmExFMUDeiEiHh50q4JV6yeIhqvawp98GPIOEOvS1qm1X8HIUg+7jNZQHnATQ78+bNcyTwm9yHZcuW0U9+8hPP83ANJCkg2IXv6+szjlDhbX7ccsstYrQiu/xbb701taWAAKBZRUQYN8LtPGGFhMQkKApWHQj+rA6VrDb3Qb+OiSCiIUiOg2mfsK6D2zkAaBS9vb2+IwDHjBlDjz/+eOBzbrDBBmW5C/Pnz7e3eXHrrbfS2WefTXfccQdNmjSJwoKZqEDbEyauHSTBzu183LmZOjg+p6nDdOs03fY17c8dtrqYOvtaL27X1hMi9TbL76aHKkyOg8l1CBuyQM4D6AT2339/mjNnDr322mv2Oh6luMYaa9CECRPsukssSnjEhoTzCM8880wxdLNSdx8OBOgIwjoRTC3dCLfzqh2gKbThtb9+DMOdeMGK2fL7qFWjwW06cT9MoqQW4YNqHAev63ld03SOTq8wCVqfvfbai77+9a8LEcBDObk4FBdRvPHGG+2hrp9//jntt99+YsTG0UcfLUYy8jBPnqCS8yek48GJmHJoZxAgIEDHEHYGzyAhDSZMboQ8LxMkR0Ld3+sYlXS+ciFQC0cnjGholHAAIAj5dJpykdqcp55Mnz6drr/+errnnnvEwAL+fOihh9rbWRhwbQgOjzAsMvbee29RzVnNt1hzzTUhIACopYio1o2oVEj4iQm3dskKjvwaG4TO0qvjDutMVCIc/NoQ5jwAtCKpVErUfuDFBIcz1LyKc845RyzVAgcCdBxhRUS1bkSlQkI9r9u5TR1nvYrm1qKTDiscKj1f2PMAAMIDAQE6Er8Ovxo3oloh4XYNv/wH/Tz8Wm8HolpnoFLhEOTcQc8DAKgMCAjQ0dTDjZDnDSIkKhUT6jUGw4Go5UgWL9EQ5FpwHcBgkevPUo4iNTlPOwIBATqeerkRQc/t5Uqo15IEvSa/NjoHolaiIeh1wp4TAFA5EBAAVOlG1FpIeIkJ9Zo6fm2olrAduJ9oYCAcAGhdICAAqFJEVCIkwogJP0GhtyEyiDkQYQVDGGcAjgMAzQ0EBAA1CGmEFRLqdYJcy9Q5BxEVjRYL9cihqPb8AASlkMlRIRqtyXnaEQgIABosJNRrhbmeWyeeb5BIqLZTh3AAoLWAgACgTmGNSoSEvJ6kkuvKByZ+rVYE1NsFqHSyKzgOADQeCAgA6uxGBB2W6XVdlUrbUGuq6cSrmSUT4gGA5gACAoBBFBLViAm9DSZqLS5q2VlXO7U2hAMYbPLpTE1Cgvl0htoRCAgAGiQkaiEmTO2SozD4fbWddjXU6toQDgA0JxAQADSBkKikYFSzUUuxAtEAQPMDAQFAkwmJVhEU9XA3IBwAaB0gIACoIdWOoKi0w66XuBiMEAhEA2hWcv0ZyhWr/93KpTEXBgCgScSEZ0evVKJsZA6EHxAOALQ2cCAAaNEQRysC0QBA+wABAUADO9B2FxQQDAC0LxAQAHRImGOwgGgAoDOAgACgSWjmqpNuQCyAdqbAhaRqkERZyCCJEgDQJB30YAsLCAUAgA4cCABaEK8OvVkqUQIA2ptBnKsPAAAAAO0CHAgAAADAQD6bo3wkUpPztCNwIAAAAAAQGggIAAAAAIQGAgIAAAAAoUEOBAAAAGAg15+lXL76W5PLtmcdCDgQAAAAAAgNBAQAAAAAQoMQBgAAANDivPfeezRz5kwaMmQIHXDAATRixAjfY/75z3/Sm2++SaNHj6a99tqLent7Q10TDgQAAABgINefp1x/rgZLvq7391e/+hVNmDCB/v73v4v3m266Kb3yyiuu+8+fP58mTpxI559/vhAdP/3pT2n8+PH0yCOPhLouHAgAAACgRfnwww/pwgsvpD/84Q904okninVHHXUUnXbaafTSSy8ZjykUCvT73/+ettxyS3vd5MmT6b//+7+FexEUOBAAAABAizJ9+nQRejjuuOPsdWeddRa9/PLL9P777xuPWW+99RzigVlrrbWEsAgDHAgAAABgEFi+fLnjcyqVEks1vPXWWyJkEYvF7HVbbLGFvW2TTTZxPfbee++ljz/+mN5++2166qmn6JZbbgl1bQgIAAAAwECuL0e5GkxjkbPmwuA8A5UpU6bQ1KlTHetWrFhBf/zjHz3Pt/nmm9N+++1n768nTI4cOdIoWHTmzp0rki9fffVV6urqong8nCSAgAAAAAAGgXnz5jlGOpjch2w2S++8847nedRzdHd304IFCxzbpXDo6enxPM9//dd/2e8vuOACmjRpEn300UeUTCYDfBsICAAAAGBQ6O3t9R0qOWrUKPrNb34T+JwcvnjiiSfKEivltqAcdthhdO211wqRs/HGGwc6BkmUAAAAQIty6KGHCgfiySeftNfdfvvttOGGG9LWW28tPq9atUqIkg8++EB85tdiseg4z4wZM4Rjsc466wS+NkIYAAAAgIFcOkfZWsyFkatBIoULXP/h7LPPpmOPPZbOOOMM+uSTT+hPf/oT3X///RSJRMQ+S5YsoXPPPZemTZsm3AUWG8cffzzts88+wvF48cUX6W9/+xv9+te/9g17qMCBAAAAAFqY3/zmN6KuQyaTEUM0OSnyoIMOsrcPHTpUiAw5IuP0008XLsUaa6xBixYtoj333JNmz54takeEAQ4EAAAA0OIccsghYjHBozT0vAoeycFLNcCBAAAAAEBoICAAAAAAEBqEMAAAAAADhUwhdHlnE4Vc9edoRuBAAAAAACA0EBAAAAAACA0EBAAAAABCgxwIAAAAwECWC0nVoAZUNl+/QlKNBA4EAAAAAEIDAQEAAACA0EBAAAAAACA0yIEAAAAADOT68pSLVX9rcvkazMjVhMCBAAAAAEBoICAAAAAAEBoICAAAAACEBjkQAAAAgIFcOke5aLHqe5MrIAcCAAAAAKB1Qxiff/45jR8/nuLxOH388ceNbg4AAADQcbScgCgWi3TKKafQtttuS/l8XnwGAAAAwODScgLimmuuoUwmQ+edd16jmwIAAKCNKWTylK/BUsi0Zw5ESyVRvvTSS/SLX/xCvL711luNbg4AAADQsbSMgFixYgUdd9xxdMMNN9DYsWMDCYh0Oi0WyfLly8VrLpcTSzMg29Es7WlmcK9wn/Azhd89/e8B6EABsWjRIhozZoznPocffjhNnz5dvD/77LNpjz32oCOPPDLwNa6++mq6/PLLy9Y/8/QM6unpoWaC2wRwr/Azhd+/ZqaZ/k6tXr260U3oeCLFBmYh+inIaDQqFmaDDTagefPmUSQSEZ+52YVCgWKxGH33u9+lX/7yl4EcCB69MW/+x9Tb20vNAN8D/qXcfY89xagSgHuFnyn8/jUbzfh3Svw9H7cuLVu2rOZ/z/ncw4cPp3vGbkk90eonw1hdyNM3PnmrLm1tJA39SQjzg/jBBx84Rlw8+eSTdMABB4j1LApMpFIpsZiu2yy/BM3cpmYF9wr3CT9T+N0bjL+XmWye4jUYapBp00JSLdNjsdOgIp0JXi/fAwAAAGBwQM8LAAAAgPZ1IHT23XdfymazsP0BAACABtCyAoKTKZEzAAAAoF705Ys80qD68xTas2IyQhgAAAAACA0EBAAAAAA6J4QBAAAAgBJ///vfacaMGTRkyBA65phjaMstt6QgcHmEqVOniuKOP//5z6m7u5uCAgcCAAAAMNBfKFBfvvqlv1Co6/0999xzxSzViUSC5s6dSxMmTKCHH3440LE/+9nP6Le//a2YJkItvBgEOBAAAABAi/Lqq6/Sb37zG3riiSdon332Eeu6urrE9A/vv/++Xb3ZxPPPP0833ngjXXnllXT66aeHvjYcCAAAAKBF+b//+z9aZ511bPHAfPOb36QPP/yQ3njjDdfjuKz2CSecQDfffDOtscYaFV0bAgIAAAAYBJYvX+5YwoYMTMyePZs23HBDx7qNNtrI3ubGt7/9bTrssMNo//33r/jaCGEAAAAABjIFoph7BCAwGasMhD5v05QpU0QCo8rixYvphz/8oef5vvKVr9DkyZPF+76+Pho2bJhju5ywy23GUnYd3nrrLbrtttuoGiAgAAAAgEFg3rx5jtk4TZM9ciLkl770Jc/zcMhCMnToUJo/f75j+5IlS8Sr28yfLFC23XZb+q//+i/xec6cOeL1e9/7nnAlDjnkkEDfBwICAAAAGAR6e3t9p/NmN+Gcc84JfM6tttqKHnjgAcrn8/akk2+//bZ4dRvKecUVVwjnQpLJZMTrpptuSmuuuWbgayMHAgAAAGhRjjzySJFPcdddd9nreGTFDjvsQJtsson4vHTpUiFKeMQGc+qpp4rPcjn44IPFeh6JMXHixMDXhgMBAAAAGOjPF3jiparvTX+xfnUgNt54Y1EAipMi77vvPlqwYAG999579Oijj9r7rFy5UtR52GuvvWj77bev2bUhIAAAAIAW5rzzzqODDjqI/t//+3/U09NDBxxwAI0cOdLezu+vv/56UWDKxHbbbSe287FhgIAAAAAAWpzNN99cLCa4vLVXXgUPAw2TdyFBDgQAAAAAQgMBAQAAAIDQIIQBAAAAGOjLExUjVhWoKuiv/hRNCRwIAAAAAIQGAgIAAAAAoYGAAAAAAEBokAMBAAAAGEgXuJBU9bcmXcdCUo0EDgQAAAAAQgMBAQAAAIDQQEAAAAAAIDTIgQAAAAAMZApFitSgDkSm2J6FIOBAAAAAACA0EBAAAAAACA0EBAAAAABCgxwIAAAAwEB/vkgF5EC40lEComglsqxYsYKahVwuR6tXr6bly5dTPN5R/x2hwb3CfcLPFH73JPLvuPy7Dgafjuqx5A/cZptu0uimAAAAqNHf9eHDh+NeNoCOEhBjx46lefPm0bBhwygSqUF90hrAzsP48eNFu3p7exvdnKYG9wr3CT9T+N2TsPPA4oH/roPG0FECIhqN0rhx46gZYfEAAYF7hZ8p/P41M832d6rezoOo31CDEEmG2jPMglEYAAAAAAgNBAQAAAAAQtNRIYxmJJVK0ZQpU8QrwL3CzxR+/5qRTv07laFCU52n2YgUMQYGAAAAsOnv76cNN9yQFi5cWLO7svbaa9OcOXOoq6urbe40BAQAAABgEBGZTKZm9yWZTLaVeGAgIAAAAAAQGiRRAgAAACA0EBBNzK233ko777wz3XjjjY1uStNRKBTo3nvvpZNOOom+9rWv0VlnnUXvvvsudTp/+tOf6JBDDqF9992XrrjiCurr62t0k5oOvic33HADHXXUUXTQQQfRD37wA/r8888b3aymLyN/zDHHiL9H8+fPb3RzQJMAAdGkvP766zR16lT697//TR999FGjm9N0nHvuuTRt2jQ68MAD6eKLLxaxygkTJtArr7xCncrPf/5z+s53vkOHHnqoEFQsJviPPnDCPzPvvPMOnXjiieLnaNasWfTlL3+ZFi1ahFvlAossvmfPP/+8yA0AQMCjMEBzsWrVquKWW25ZvP/++4ubb7558aKLLmp0k5qOFStWlK2bMGFC8fTTTy92IqtXry4OHTq0eO2119rrXnjhBS5/V5w5c2ZD29bsPzsrV64sdnV1FW+66aaGtamZeeSRR4qbbLJJ8aGHHhI/T7Nnz250k0CTAAeiCfnP//xP2n333emwww5rdFOalqFDhxrX1TJrupXgJ8OVK1cK90Gy0047iXkCHn/88Ya2rdl/dri2AWfId+rPjheffvopfetb36Lbb7/d+DsHOhsIiCbj7rvvppkzZ9I111zT6Ka0FDNmzBD37YgjjqBOZO7cueJVn1iIP8ttwMz1118vbHnOhwADcImgyZMn0+mnny5yHwDQQSXKOnPZZZfRY4895rnPAw88QGuuuSZ9+OGHdM4559DDDz9MPT091Em8/PLLIm7vxX/8x3/QGWecUbb+/fffp2984xtie6cKiGw2K175SVqlu7vb3gbKeeSRR+iiiy6iX/3qV7TxxhvjFin89Kc/FbNdXnrppbgvwAgERJ05+eST6etf/3qgGeXuu+8+YaOeffbZ9jZ+emT7kJ+ueWlXNtlkE7ruuus89zHNpMqia5999hHL7373O+pURo0aJV6XLFlCa6yxhr2eEwN32GGHBraseXnyySdp0qRJ9OMf/5jOPPPMRjen6fjjH/8oxOdXv/pV8ZnFBMOJuccffzx973vfa3ALQaNBIakmYsGCBWV283HHHUd77LGHEBUTJ05sWNuaES4Lu9deewl79c4776RYLEadCo/W4dK7Dz74oG3Fs5gYM2YM3XzzzULIggGeeuopMdyVn64vueQS3BoD//rXvxzDgF977TXhAPLopx133FH8vIHOBg5EE7HOOuuIRYVLn3IcG+LBCQutvffeW4iHO+64o6PFA7PBBhsIF+YnP/mJeOXEwKuuuoqGDRvWsWEdN55++mmIhwBst912ZbUgmO233x7iAQggIEBLcv755wsRwbkju+22m+OP3k033USdajkffvjhYtIeFg4cDuNiWzJEBkpw8bF8Pk/333+/WFS377zzzsNtAiAgCGG0gI3I8e3x48c3uilNBVedZItep7e3l7bcckvqZGbPni2s5y222IISiUSjm9OUCbumIZvs/q2//voNaVMrwDkQb775pijY1mnTegMzEBAAAAAACA3qQAAAAAAgNBAQAAAAAAgNBAQAAAAAQgMBAQAAAIDQQEAAAAAAIDQQEAAAAAAIDQQEAAAAAEIDAQFAG/DQQw/RrFmzytZz4R+uRlkoFBrSLgBA+wIBAUAbsHDhQtp3333F1OaSxYsX0/777y+qmUaj+FUHANQWVKIEoE047LDDxPTdzzzzjBAMPO0yzxfy7LPPUjyOaW8AALUFAgKANnIhtt56a7roootojTXWoHPOOYdeeeUV2myzzRrdNABAG4LHEgDaBJ6F88Ybb6TJkydTMpmka665BuIBAFA34EAA0EbwNNUbbrihmI3zk08+wWycAIC6gcwqANqIq666ivr7+0XOwxVXXNHo5gAA2hg4EAC0CS+88AJ99atfpenTp1MkEqFJkyaJoZ077rhjo5sGAGhDICAAaANWr15NEyZMoL333pt++9vfinXf+ta36Pnnn6eXX36ZUqlUo5sIAGgzEMIAoA04//zzxSsnTkquu+46WrFiBV122WUNbBkAoF2BgACgxfnoo49o+fLldOedd1JPT4+9vre3l26//Xb6+OOP6YsvvmhoGwEA7QdCGAAAAAAIDRwIAAAAAIQGAgIAAAAAoYGAAAAAAEBoICAAAAAAEBoICAAAAACEBgICAAAAAKGBgAAAAABAaCAgAAAAABAaCAgAAAAAhAYCAgAAAAChgYAAAAAAQGggIAAAAABAYfn/ppjH6aGApOIAAAAASUVORK5CYII=", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "state.plot_fock_distribution()" + ] + }, + { + "cell_type": "markdown", + "id": "54d04150", + "metadata": {}, + "source": [ + "# Example Superposition of 0-, 1- and 2-fock basis state superposition" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "id": "2ebd6b7c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.577+0j)|0> + (0.577+0j)|1> + (0.577+0j)|2>\n" + ] + } + ], + "source": [ + "#Focke state preparation and visualization\n", + "\n", + "state = FockState([1,1,1])\n", + "\n", + "print(state)" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "052aa361", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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/OOl7dUtXvVrrCdE3eF35M2fO+NT1dmZmZovzakC47777TCp79913WwwgSh+nIaTp3/KmyU+npnQddfK3M5oKVPee/0Zja/67N/9111cNO7i6Ni6nA+utW/fI2qam7aUtbaYtdX/rw34Kr7bn3vc22hjHiPB9PUX5aU/+aoHqgdpMpx6Yqqcpxo8fL3l5eZ6adgFu375dpk2b5qnl5+f7jBFxBxClPSCatLxpGvPurlYnTpwwl//qoFcAANA5WL1EV6900cChYzbGjRtnPv9Dzy/Nnz/f85iVK1fKnj175NChQ+YzQR544AE5efKkvPHGG3Lw4EHP44YOHWrOf+pjdLCrXnUzYsQIMzh1+fLlMmbMGHn00UctbSkAAOhUIWTSpEmya9cuefXVV83nhYwaNUo2bNggycnJPuHCPdhTL8XVLh+t6UBSb4sWLTIfWKaDq3bs2GECzerVq80gm+eee86EEh0/AgAAOgfrH9s+YcIEMwWycOFCz+966mX37t03XaZ+7oj2fgAAgM6LL7ADAABWEEIAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAABWEEIAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAABWEEIAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAARG4IKSoqkn379kl5eXlQj6+vr5ejR4/KiRMnpK6uLmTLBQAAERJCqqurZfbs2ZKVlSWPP/649OnTR9auXdviPC+++KJ84xvfMPPdd999MmDAAPnjH//Y7uUCAIAICiFLliyRvXv3SkFBgenZePPNN+WZZ56Rjz76KGAPSFVVlRw5csRMJ0+elHnz5sncuXPl3LlzbV4uAACIsBCybt06EyIyMjLM7ZkzZ8rIkSNN3Z/o6GhZtmyZdO/e3VN76qmn5Nq1a7J///42LxcAAHz9YsSS4uJiOX/+vGRnZ/vUc3Jy5MCBA0Ev5+OPPzY/Bw8e3K7l1tTUmMnNPY6koaHBTMrlcpnJcRwzud2s7p5fRYkjXy3N/O4tcN0lIk6zxNhS3SWOuddNl+iEsB78ukfeNnnvbxUVFdWsbQSqt7WNac17fdhP4dn2dD83PaYEakutrbfUxm6sDceIcD3uNXi1J3/vWy3VA7WxTh9CLl++bH6mp6f71PW2+76buXjxoixYsEAefvhhM/6jPctdsWKFOY3T1IULF8wYE5WQkCCpqakmoOhpIbekpCTp2rWrlJaWyvXr1z31lJQUSUxMNH/XPYD2tjRHTl11SWWdSFY3R6K8WkV+mUtqGxzzGG9HS0Vio0SGpDbWGxyRo1dckhQjMqBrY72mXiS/3CXd4kT6JjXWK2pdUlgh0rOLSM+ExnppjUuKr4lkJIqkxTfWL1S5pKRaJDNZJDm2sV5c6ZLS6yKDUhyJj25cR7apcT+VlJR4nhd90fbu3du0C20fbjExMdKjRw/TjrwHTsfFxZmevoqKCqmsrPTUg2l73u2G/RSeryc9jmiPsHcbU7169TKnqy9dutQhbU9xjAjf416JV3tKS0uT+Ph4897nHSz0PbQ1bc/dbm7G5bQ1vrTTsWPHZPjw4bJz506ZMmWKp66hQmuHDx9ucf6ysjKZOnWqxMbGyrZt28yBuD3L9dcT0q9fP/Pi1TARqp6QIc9vDpv0HNy6R942fbF8hpWekMG573TYNoXjfroVt6lgxYNWekIG5m5mP4Vx28v3OmaFqidEw6z+46Tv1e730E7VE6Jv8LryZ86c8anr7czMzBbn1YCgV8ZoKnv33Xc9AaQ9y9Xkp1NTuiyd/O2MpgLVvee/0dia/+7Nf931VcMOrq6Ny+nAeuvWPbK2qWl7aUubaUvd3/qwn8Kr7bn3vY02xjEifF9PUX7ak79aoHqgNtOpB6bqaYrx48dLXl6ep6ZdgNu3b5dp06Z5avn5+T5jOdwBRGkPiCattiwXAADYZa0nROmVLhoMcnNzZdy4ceazPPT80vz58z2PWblypezZs0cOHToktbW18sADD5hLc9944w05ePCg53FDhw415z+DXS4AAIjgEDJp0iTZtWuXvPrqq+ZzPUaNGiUbNmyQ5ORkn3DhHuypl+Jql4/WdCCpt0WLFslDDz0U9HIBAEAEhxA1YcIEMwWycOFCz+966mX37t0hWS4AALCrU3x3DAAAiDyEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAAC3dghp+s16AAAAHR5Cfvazn0l6err5ltoZM2bI8uXLpbS0NBSLBgAAYSokIeTtt9+W9evXmy+W0y+P0+9oqaioCMWiAQBAmArJd8foN9ZWV1dLdHS0jBkzxkwAAAAdHkJ0PIj2gHTp0kXuueceSUpKCsViAQBAGAvJ6ZipU6fK7Nmz5fXXX5esrCzJyckxp2YAAABC0hNy5MgR+eijj8wg1Pvuu8/0fKiJEyeaya2wsNA8BgAAoN0hJC8vz/R21NXVmduDBw+WXbt2Sb9+/Zo9tn///sEuFgAARKigT8esXr1annjiCTl79qx8+umnMmjQIMnNze3YtQMAAGEr6J6Q06dPy89//nPp06ePmX73u9/JgAEDOnbtAABA2Aq6J0RPw7jHgCgd85Gamirnz5/vqHUDAABhrFVXx/zyl7+Ubdu2eYJHTEyMVFVVddS6AQCAMBZ0CNGrX/QS3OnTp3tOyej4ED1Fs2XLFikpKenYNQUAAJE5JmTDhg3mZ1FRkXzyySeyf/9+81M/rv2ll14y933zm9+Ujz/+2AQUAACAkH5iql6Sq9PMmTM9tTNnzniCSWxsbGsXCQAAIlBIPrb9G9/4hpm+853vhGJxAAAgAoTkY9sBAABaixACAACsIIQAAAArCCEAAMAKQggAALCCEAIAAKwghAAAACsIIQAA4Nb9sLL20o+C1y/FGzZsmKSkpAQ1j35vTUFBgYwaNcp8m683rev93pKSkmT06NEhXW8AAHCLhpDq6mp57LHHzBfg9e/fXwoLC2XVqlWyYMGCgPPs27dPVq5cKR988IFcuHBBdu3aJZMnT/Z5jH6XzcaNG2X48OGe2qBBg8z33AAAgM7BaghZsmSJ7N271/RcZGRkyKZNm2TWrFmSk5MjY8eO9TvPoUOHZO7cuSZoaLAIRIOJBhEAANA5WR0Tsm7dOpk3b54JIEq/FG/kyJGmHsgTTzwhc+bMuekX5Wkvi36hngachoaGkK87AAC4RXtCiouLzTiQ7Oxsn7r2ghw4cKDdy9+6daucPn1azp07J/Hx8fLaa6/JjBkzAj6+pqbGTG7l5eXmpwYYd4hxuVxmchzHTG43q3uHoChx5Kulmd+9Ba67RMRplhhbqrvEMfe66RKdENaDX/fI26amoTcqKqpZ2whUb2sb05r3+rCfwrPt6X5uekwJ1JZaW2+pjd1YG44R4Xrca/BqT/7et1qqB2pjnT6EXL582fxMT0/3qett931tNX36dFm6dKn06tVL6uvrJTc31/SefPbZZzJ48GC/86xYscKcHmpKx51or4pKSEgwg2A1oFRVVfkMeu3atauUlpbK9evXPXUdZJuYmGi2p66uztRuS3Pk1FWXVNaJZHVzJMqrVeSXuaS2wTGP8Xa0VCQ2SmRIamO9wRE5esUlSTEiA7o21mvqRfLLXdItTqRvUmO9otYlhRUiPbuI9ExorJfWuKT4mkhGokhafGP9QpVLSqpFMpNFkmMb68WVLim9LjIoxZH46MZ1ZJsa91NJSYnnedEXbe/evU270PbhFhMTIz169DDtyB14VVxcnHTv3l0qKiqksrLSUw+m7Xm3G/ZTeL6e9DgSHR3t08aU+1h36dKlDml7imNE+B73SrzaU1pamvnHXd/7vIOFvje3pu25283NuJy2xpd2OnbsmBk4unPnTpkyZYqnroNStXb48OEW5//yyy+lX79+fgemNqVPkD6BixcvlmeffTbonhBdvr543VfshKInZMjzm8MmPQe37pG3TV8sn2GlJ2Rw7jsdtk3huJ9uxW0qWPGglZ6Qgbmb2U9h3PbyvY5ZoeoJ0TCr/ziVlZW1eNWrtZ4QfYPXlT9z5oxPXW9nZmaG9G9petMQ0vRvedPkp1NTuo46+dsZTQWqe89/o7E1/92b/7rrq4YdXF0bl9OB9date2RtU9P20pY205a6v/VhP4VX23PvexttjGNE+L6eovy0J3+1QPVAbaZTD0zV0xTjx4+XvLw8T027ALdv3y7Tpk3z1PLz81s1RkTTmHd3tTpx4oS5/FcHvQIAgM7B6iW6y5YtM4FDx2yMGzdO1q5da84vzZ8/3/MY/UyQPXv2mEtzlZ6POn78uDlfpQ4ePGjOcWrviU61tbVmsKtedTNixAgzOHX58uUyZswYefTRR61tKwAA6ESX6E6aNMmM6dBeijVr1pjQsHv3bklOTvY8ZujQoSZAuH3yySeyaNEieeWVV2TChAny+9//3tzWHhT34KodO3bIxYsXZfXq1Wb5zz33nHz44Yd+T7cAAIAI/dh2DRI6BbJw4UKf2w888ICZWqKfO6K9HwAAoPPiC+wAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAABWEEIAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAABWEEIAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAAWEEIAQAAkRtCioqKZN++fVJeXh70PGfPnpXdu3dLWVlZSJcLAAAiIIRUV1fL7NmzJSsrSx5//HHp06ePrF27tsV5NFR897vflTvuuEMmTpwoBw4cCMlyAQBABIWQJUuWyN69e6WgoECOHj0qb775pjzzzDPy0UcfBZzn0KFDMnfu3BYf05blAgCACAoh69atk3nz5klGRoa5PXPmTBk5cqSpB/LEE0/InDlzJDY2NqTLBQAAX68YsaS4uFjOnz8v2dnZPvWcnBy/p1g6erk1NTVmcnOPI2loaDCTcrlcZnIcx0xuN6u751dR4shXSzO/ewtcd4mI0ywxtlR3iWPuddMlOiGsB7/ukbdN3vtbRUVFNWsbgeptbWNa814f9lN4tj3dz02PKYHaUmvrLbWxG2vDMSJcj3sNXu3J3/tWS/VAbazTh5DLly+bn+np6T51ve2+7+tc7ooVK8xpnKYuXLhgxpiohIQESU1NNQGlqqrK85ikpCTp2rWrlJaWyvXr1z31lJQUSUxMNH+3rq7O1G5Lc+TUVZdU1olkdXMkyqtV5Je5pLbBMY/xdrRUJDZKZEhqY73BETl6xSVJMSIDujbWa+pF8std0i1OpG9SY72i1iWFFSI9u4j0TGisl9a4pPiaSEaiSFp8Y/1ClUtKqkUyk0WSYxvrxZUuKb0uMijFkfjoxnVkmxr3U0lJied50Rdt7969TbvQ9uEWExMjPXr0MO3Ie+B0XFycdO/eXSoqKqSystJTD6btebcb9lN4vp70OBIdHe3TxlSvXr2kvr5eLl261CFtT3GMCN/jXolXe0pLS5P4+Hjz3ucdLPQ9tDVtz91ubsbltDW+tNOxY8dk+PDhsnPnTpkyZYqnvmDBAlM7fPhwi/N/+eWX0q9fP9m1a5dMnjy53cv11xOiy9cXr4aJUPWEDHl+c9ik5+DWPfK26YvlM6z0hAzOfafDtikc99OtuE0FKx600hMyMHcz+ymM216+1zErVD0hGmb1Hye9gtX9HtqpekL0DV5X/syZMz51vZ2Zmfm1L1eTn05N6bJ08rczmgpU957/RmNr/rs3/3XXVw07uLo2LqcD661b98japqbtpS1tpi11f+vDfgqvtufe9zbaGMeI8H09RflpT/5qgeqB2kynHpiqpynGjx8veXl5npp2AW7fvl2mTZvmqeXn57dqjEiwywUAAHZZ6wlRy5YtM8EgNzdXxo0bZz7LQ88vzZ8/3/OYlStXyp49e8yluUrPRx0/ftycr1IHDx405zi1l8Pd0xHMcgEAQARfojtp0iQzpqOwsFDWrFkjI0aMMJ+Cmpyc7HnM0KFDZcyYMZ7bn3zyiSxatEheeeUVmTBhgvz+9783t7WnozXLBQAAEdwTojRI6BTIwoULfW4/8MADZmrvcgEAgF2d4rtjAABA5CGEAAAAKwghAADACkIIAACwghACAACsIIQAAAArCCEAAMAKQggAALCCEAIAAKwghAAAACsIIQAAwApCCAAAsIIQAgAArCCEAAAAKwghAADACkIIAACwghACAACsIIQAAAArCCEAAMAKQggAALCCEAIAAKwghAAAACsIIQAAwApCCAAAsIIQAgAArCCEAAAAKwghAADACkIIAACwghACAACsIIQAAAArCCEAAMAKQggAALAiRjqBoqIiOX/+vAwbNkxSUlLaPU9BQYGcPXvWp5aUlCSjR48O6XoDAIBbNIRUV1fLY489Jlu2bJH+/ftLYWGhrFq1ShYsWNCueV566SXZuHGjDB8+3FMbNGiQrF+/vsO3CQAA3AIhZMmSJbJ3717Tc5GRkSGbNm2SWbNmSU5OjowdO7Zd80yePNkEEQAA0DlZHROybt06mTdvngkTaubMmTJy5EhTb+882mOyf/9+E1YaGho6eEsAAMAt0xNSXFxsxnRkZ2f71LVH48CBA+2eZ+vWrXL69Gk5d+6cxMfHy2uvvSYzZswIuD41NTVmcisvLzc/NcC4Q4zL5TKT4zhmcrtZ3TsERYkjXy3N/O4tcN0lIk6zxNhS3SWOuddNl+iEsB78ukfeNjUNvVFRUc3aRqB6W9uY1rzXh/0Unm1P93PTY0qgttTaektt7MbacIwI1+Neg1d78ve+1VI9UBvr9CHk8uXL5md6erpPXW+772vrPNOnT5elS5dKr169pL6+XnJzc2XOnDny2WefyeDBg/0ue8WKFeZUT1MXLlwwvSoqISFBUlNTTUCpqqryGfTatWtXKS0tlevXr3vqOmA2MTHRrFtdXZ2p3ZbmyKmrLqmsE8nq5kiUV6vIL3NJbYNjHuPtaKlIbJTIkNTGeoMjcvSKS5JiRAZ0bazX1Ivkl7ukW5xI36TGekWtSworRHp2EemZ0FgvrXFJ8TWRjESRtPjG+oUql5RUi2QmiyTHNtaLK11Sel1kUIoj8dGN68g2Ne6nkpISz/OiL9revXubdqHtwy0mJkZ69Ohh2pE78Kq4uDjp3r27VFRUSGVlpaceTNvzbjfsp/B8PelxJDo62qeNKfex7tKlSx3S9hTHiPA97pV4tae0tDTzj7u+93kHC32fbU3bc7ebm3E5bY0v7XTs2DEzcHTnzp0yZcoUT10HmGrt8OHDIZlH6ROkT+DixYvl2WefDbonpF+/fubF6776JhQ9IUOe3xw26Tm4dY+8bfpi+QwrPSGDc9/psG0Kx/10K25TwYoHrfSEDMzdzH4K47aX73XMClVPiIZZ/ceprKysxaterfWE6Bu8rvyZM2d86no7MzMzZPMoTW8aQprO502Tn05N6d/Tyd/OaCpQ3Xv+G42t+e/e/NddXzXs4OrauJwOrLdu3SNrm5q2l7a0mbbU/a0P+ym82p5739toYxwjwvf1FOWnPfmrBaoHajOdemCqnqYYP3685OXleWraBbh9+3aZNm2ap5afn+8Z7xHMPJrGvLur1YkTJ8ylvDqAFQAAdA5WL9FdtmyZCQ86ZmPcuHGydu1ac35p/vz5nsesXLlS9uzZI4cOHQpqntraWjNwVa+gGTFihBmcunz5chkzZow8+uij1rYVAAB0okt0J02aJLt27TK9FGvWrDGhYffu3ZKcnOx5zNChQ02ACHYeHVy1Y8cOuXjxoqxevdo89rnnnpMPP/zQ7+kWAAAQoR/bPmHCBDMFsnDhwlbPo58hor0fAACg8+IL7AAAgBWEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAABWEEIAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAABWEEIAAIAVhBAAAGAFIQQAAFhBCAEAAFYQQgAAgBWEEAAAYAUhBAAAWEEIAQAAVhBCAACAFYQQAABgBSEEAABYQQgBAACRG0KKiopk3759Ul5eHtJ52rJcAAAQASGkurpaZs+eLVlZWfL4449Lnz59ZO3ate2epy3LBQAAX68YsWjJkiWyd+9eKSgokIyMDNm0aZPMmjVLcnJyZOzYsW2epy3LBQAAEdQTsm7dOpk3b54JCmrmzJkycuRIU2/PPG1ZLgAAiJCekOLiYjl//rxkZ2f71LW34sCBA22epy3LVTU1NWZyKysrMz+vXLkiDQ0N5neXy2Umx3HM5Hazunv+G3+oUr5amkRJ42NV4LpLRJxmibGlukscc6+bLtEJYT34dY+8bdI24y0qKqpZ2whUb2sbM7Wayg7bpnDcT7fiNulxqdkxpZVtLFC9pTbWUHON/RTGbe+K1zHL7/tWC/VAbayiouLG32lS7zQh5PLly+Znenq6T11vu+9ryzxtWa5asWKFOY3TVP/+/YPcIuCGtNU8E+gY3WhbuMWOWVevXpXU1NTOF0JiY2M9g0i9VVVVSVxcXJvnactyVW5urvzgBz/w3Na0p6FFw4umP7SeXpXUr18/c5VSSkoKTyFChraFjkLbCg3tAdEA0rdv3xYfZy2E6JuTduOcOXPGp663MzMz2zxPW5ar4uPjzeStW7durd4uNKcBhBCCjkDbQkehbbVfSz0g1gemJiYmyvjx4yUvL89Tq6yslO3bt8u0adM8tfz8fM9YjmDmCXa5AADALpdzs1EjHej99983weCHP/yhjBs3znyWx8mTJ+XTTz+V5ORk8xi9ymXPnj1y6NChoOcJ5jH4ero1NQnrYDp6QkDbwq2A41YEXaI7adIk2bVrlxQWFsqaNWtkxIgRsnv3bp+gMHToUBkzZkyr5gnmMeh4enpr8eLFzU5zAbQtdFYctyKoJwQAAESuTvHdMQAAIPIQQgAAgBWEEAAAYAUhBB1ChxodPXrUXJFUW1vLs4yQOnLkiPzlL3/hWUVIXbt2zRyzmn7OFDoOIQQh98UXX8i3vvUtufvuu82XB+qHxH3wwQc802i3N99803wP1F133SX33HMPzyhC4ty5c/LEE0+YT/f83ve+J6NGjTJt7NSpUzzDHYwQgpD7x3/8R/NiPnv2rHkRz507V+bMmeP5QiOgrT7//HPzuT8/+clPeBIRMvpxDhpqL168aD4c8/Tp0xIdHS3/9E//xLPcwbhEFyGlp2Buv/12ee+998zntagLFy5IRkaG/OY3v5FHHnmEZxzt9stf/lKefvrpZt8RBYTKr371K3nyySfNt6vrV4GgY/DMIqTcH7GfnZ3tqfXs2dN8G7H7PgDo7D7++GMZOHAgAaSDWfsCO4Qn/eZh/bbipp9Oq99GrPcBQGe3Y8cO09u2bt0626sS9ugJQUjFxsaaq2Hq6+t96lVVVSacAEBn7wH5h3/4B/nRj34kjz/+uO3VCXuEEISUnnbRy3N1UKqb+7ZeJQMAndW+ffvkvvvuk3/913+VlStX2l6diEAIQUhNmDBBEhISJC8vz1PTLw+8dOmS+WZjAOiMPvnkE3OM+ud//md5+eWXba9OxGBMCEKqa9eu8uMf/1gWLVpkLnFLTU2V559/Xh5++GGfb0MG2uLYsWPmaqv8/HzTw6YBV91xxx2m7QFtvfRbe0BGjx4ts2bN8rQrNXbsWHOaGR2DS3TRITZs2CBvv/22ubzt3nvvlX//939nTAja7YUXXpDt27c3q7/++uvm0nCgLbZs2SIvvvii3/u0V7d79+48sR2EEAIAAKxgTAgAALCCEAIAAKwghAAAACsIIQAAwApCCAAAsIIQAgAArCCEAAAAKwghAL52f/M3fyN79+7lmQciHCEEgA/9BmQNCU2n7373uyH9no7y8vKQLEvDjK5fa73//vty9913h2QdALQN3x0DwId+J4uGhKVLl8oDDzzgqesXE3ZGGmZ0fVurtLRU9u/f3yHrBCA49IQA8GvgwIE+PSEjRozw3HflyhXJzc01PQn6zaM/+9nPTA+KtwMHDsj3vvc9ueuuu8w3k+qXzgWi3zOk38D82Wef+b3/8uXL5ksRp06dKjNnzpRf//rXpn78+HH5/ve/b353r+eKFSvM7WeeecbcvvPOO+Whhx6SV155RWpra819f/3rX+VHP/qRVFVVeeZbs2aN5++99dZb8vd///cyadIkefLJJ+XkyZMttpIPPvjAPBe6PvPnz5eJEyfKv/3bv5mgA6AFDgB4qa2tdfTQsGHDBr/PS319vXPnnXc6OTk5zh//+Efnt7/9rdOnTx/n+9//vucxf/rTn5z4+HhnwYIFzvbt251f//rXzl133eW5X5evj1G/+MUvnJSUFM9tf+6//35n6tSpztatW53Nmzc7//Iv/+L8z//8j3Pt2jXn1VdfNcv7+OOPzVRYWGjmOX78uLm9d+9eZ+PGjc6oUaOcefPmmfuuXr3qvPzyy05CQoJnvqKiInPfkiVLnEGDBjnr16933n//fWfhwoVOamqq535/li9f7nTr1s2ZMmWK84c//MGsY//+/Z0f/OAHtC2gBYQQAH5DyMCBA53s7GzP9L//+7/m/rffftvp0qWLc+7cOc8877zzjhMdHe2cOnXK3B45cqTnDd+turq6WQh58cUXnfT0dOejjz5qcS9oCNA3dn/L0+UE8//U/v37naioKKeqqsrc/r//+z8nKSnJ5zFnz551YmNjzWObhqDnnnsu4LLnzp1rni8NN27PPPOM853vfOem6wVEMsaEAPBLT6V4jwnp37+/+anjL+644w7p3bu357777rvPjCXR0xwpKSly6NAhWblypc/y4uPjfW6/8MILcurUKfnzn/8st912W4t74d5775Vnn31WCgsL5Z577pFhw4Y1W15TZ86cMadYdJ30dI6eimloaDDLyMrK8jvPhx9+aB731FNPmdtf/aNm5omLiwv4t/Rv6POVnJzsqZ0+fdrznAHwjxACoMUxIU1dvXpVkpKSfA8kMTEmFOh9Os5Ceb8h+xMdHS3V1dWecRot+d3vfie/+c1vZPPmzfLjH/9YMjIyzG0NQ/7oOugYDb3/6aeflp49e5pxLBqq3OvnT2VlpdkWHeMSFeU7ZC41NTXg3zpx4oQZ++Lt008/NWNRAARGCAHQKkOGDJFNmzaZXgX3G7UO3NQ348GDB5seEu0N0d4BHdgZyH/913/Jn/70JzPYdMeOHfKtb30r4GNjY2NNT4NOGlrmzJkjCxculHfffdezDtpj4XK5zO86wFXXSXtk3Ff17Nq1y2eZOt+NM0ONhg4dKnV1dea+YC/71b+hg3K//e1ve2plZWWmlydQSAJwA1fHAGiVRx55xLzJrl692tzWN229ckXfcHNyckwPh14Z8pOf/ESOHDnieYz78d5WrVplgoUGkYMHD/r9e9evX5fFixebXhaly9epS5cu5nafPn3Mz6KiIs883bt391xqrPQqlf/8z//0Wa7Od+3aNXOqxu1v//ZvzdU02nty7tw5T33Lli1m8kfDlvYapaWl+fSC6DqOHDkyiGcUiFyEEACtom/eeipEx3xkZmaang8NEL/97W89vRLLli2Tv/u7v5MxY8aY8Rv6mEAfTqZh5YknnjBjPfwFEe0F0Tf0AQMGmLEjffv2lYKCAnnppZfM/bfffrvcf//9Mnr0aMnOzjaX6GqPhvaUaLjR+3VsxvDhw32Wqz0despGx4e4L9HVnpS8vDwTYtx/r1u3bvLzn/884DgSDSH6t71pCNHHu4MSAP9cOjo1wH0AItS+fftk0KBB5s04EO3d0M/F0LEgehrGH+0x0R4KXVZiYqLP8vVNumvXrj5v3DqORE/3+KOnPPSzRnQ8yje/+c1m9+vfuXDhgvTo0cOEI3Xx4kUpLi42IUTn07+hn3fi/cFrOoBU59Og5L1cnffs2bOml6Ol8S0aiHTQar9+/Ty1L7/80pye0jAEIDBCCAAAsILTMQAAwApCCAAAsIIQAgAArCCEAAAAKwghAADACkIIAACwghACAACsIIQAAAArCCEAAMAKQggAALCCEAIAAKwghAAAALHh/wHnan54RzXtPAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "state.plot_fock_distribution()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e73e85b9", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "sciqis (3.13.12.final.0)", + "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": "3.13.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From f4ecfd89379dade48be58c8f17a2157c03d27ea5 Mon Sep 17 00:00:00 2001 From: Aniket Sengupta Date: Mon, 10 Aug 2026 10:40:16 +0200 Subject: [PATCH 2/2] Added to my notebook --- .../cv_submissions/CV_tutorial_Aniket.ipynb | 767 ++++++++++++++++++ 1 file changed, 767 insertions(+) create mode 100644 exercises/cv_submissions/CV_tutorial_Aniket.ipynb diff --git a/exercises/cv_submissions/CV_tutorial_Aniket.ipynb b/exercises/cv_submissions/CV_tutorial_Aniket.ipynb new file mode 100644 index 0000000..b6c93ae --- /dev/null +++ b/exercises/cv_submissions/CV_tutorial_Aniket.ipynb @@ -0,0 +1,767 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "674091b5", + "metadata": {}, + "source": [ + "# Gaussian state preparation and operations\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5e1ea2a3", + "metadata": {}, + "outputs": [], + "source": [ + "# import relevant packages\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "from scipy.special import eval_genlaguerre\n", + "import matplotlib.colors as mcolors\n" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "bd428678", + "metadata": {}, + "outputs": [], + "source": [ + "#Single mode Gaussian state preparation and sympletic operations\n", + "\n", + "\n", + "\n", + "#Defining basic guassian operations which we will use later in the code\n", + "\n", + "def sym_phase(theta):\n", + " c, s = np.cos(theta), np.sin(theta)\n", + "\n", + " return np.array([\n", + " [c, -s],\n", + " [s, c]\n", + " ], dtype=float)\n", + "\n", + "\n", + "def sym_squeeze(r):\n", + "\n", + " return np.array([\n", + " [np.exp(r), 0.0],\n", + " [0.0, np.exp(-r)]\n", + " ], dtype=float)\n", + "\n", + "\n", + "def sym_displace(alpha):\n", + "\n", + " if isinstance(alpha, complex):\n", + "\n", + " x = np.sqrt(2) * alpha.real\n", + " p = np.sqrt(2) * alpha.imag\n", + "\n", + " elif isinstance(alpha, (tuple, list, np.ndarray)) and len(alpha) == 2:\n", + "\n", + " x, p = alpha\n", + "\n", + " else:\n", + " raise ValueError(\n", + " \"alpha must be a complex number or a 2-element vector\"\n", + " )\n", + "\n", + " return np.array([x, p], dtype=float)\n", + "\n", + "\n", + "# Defining some functions to extract displacement, phase rotation angles, squeezing directly from the covariance matrix and the mean\n", + "\n", + "def gaussian_parameters_from_cov(V):\n", + " \n", + " # Eigenvalues and eigenvectors\n", + " eigenvalues, eigenvectors = np.linalg.eigh(V)\n", + "\n", + " v_min = eigenvalues[0]\n", + " v_max = eigenvalues[1]\n", + "\n", + " \n", + " r = 0.25 * np.log(v_max / v_min)\n", + "\n", + " # Direction\n", + " v = eigenvectors[:, 0]\n", + "\n", + " theta = np.arctan2(v[1], v[0])\n", + "\n", + " #phase\n", + " phi = 2 * theta\n", + "\n", + " return r, phi\n", + "\n", + "\n", + "def alpha_from_mean(mean):\n", + "\n", + " q, p = mean\n", + "\n", + " return (q + 1j * p) / np.sqrt(2)\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "id": "f7942398", + "metadata": {}, + "outputs": [], + "source": [ + "#Define the class for gaussian state generation and wigner function visualization\n", + "\n", + "\n", + "class GaussianState:\n", + "\n", + " def __init__(self, mean=None, cov=None):\n", + "\n", + " if mean is None:\n", + " mean = np.array([0.0, 0.0])\n", + "\n", + " if cov is None:\n", + " cov = 0.5 * np.eye(2)\n", + "\n", + " self.mean = np.asarray(mean, dtype=float)\n", + " self.cov = np.asarray(cov, dtype=float)\n", + "\n", + "\n", + "\n", + " def gaussian_update(self, S, d):\n", + "\n", + " self.mean = S @ self.mean + d\n", + " self.cov = S @ self.cov @ S.T\n", + "\n", + " return self\n", + "\n", + "\n", + "\n", + " def apply(self, S, d=None):\n", + "\n", + " if d is None:\n", + " d = np.zeros(2)\n", + "\n", + " return self.gaussian_update(S, d)\n", + "\n", + "\n", + "\n", + " def phase(self, theta):\n", + "\n", + " S = sym_phase(theta)\n", + "\n", + " return self.apply(S)\n", + "\n", + "\n", + " def squeeze(self, r):\n", + "\n", + " S = sym_squeeze(r)\n", + "\n", + " return self.apply(S)\n", + "\n", + "\n", + " def displace(self, alpha):\n", + "\n", + " d = sym_displace(alpha)\n", + "\n", + " return self.apply(np.eye(2), d)\n", + "\n", + "\n", + "\n", + " def __repr__(self):\n", + "\n", + " return (\n", + " f\"GaussianState(\\n\"\n", + " f\"mean={self.mean},\\n\"\n", + " f\"cov=\\n{self.cov}\\n\"\n", + " f\")\"\n", + " )\n", + "\n", + " def plot_wigner(self, qlim=(-5, 5), plim=(-5, 5), n=200):\n", + "\n", + " q = np.linspace(*qlim, n)\n", + " p = np.linspace(*plim, n)\n", + "\n", + " Q, P = np.meshgrid(q, p)\n", + "\n", + " R = np.stack((Q, P), axis=-1)\n", + "\n", + " T = R - self.mean\n", + "\n", + " inv_cov = np.linalg.inv(self.cov)\n", + "\n", + " exponent = np.einsum(\n", + " '...i,ij,...j',\n", + " T,\n", + " inv_cov,\n", + " T\n", + " )\n", + "\n", + " W = (\n", + " 1\n", + " / (2 * np.pi * np.sqrt(np.linalg.det(self.cov)))\n", + " * np.exp(-0.5 * exponent)\n", + " )\n", + "\n", + " fig, ax = plt.subplots(figsize=(6, 5))\n", + " # norm= mcolor.TwoSlopeNorm(vmin=W.min(), vcenter=0, vmax=W.max())\n", + " cmap = mcolors.LinearSegmentedColormap.from_list(\n", + " \"white_red\",\n", + " [\"white\", \"red\"]\n", + " )\n", + "\n", + " norm = mcolors.Normalize(\n", + " vmin=0,\n", + " vmax=W.max())\n", + "\n", + " contour = ax.contourf(\n", + " Q,\n", + " P,\n", + " W,\n", + " levels=100,\n", + " cmap=cmap, norm=norm\n", + " )\n", + "\n", + " fig.colorbar(\n", + " contour,\n", + " ax=ax,\n", + " # label=\"Wigner function\"\n", + " )\n", + " ax.grid()\n", + " ax.set_xlabel(\"X\")\n", + " ax.set_ylabel(\"P\")\n", + " ax.set_title(\"Gaussian Wigner Function\")\n", + "\n", + " ax.set_aspect(\"equal\")\n", + "\n", + " fig.tight_layout()\n", + "\n", + " return fig, ax\n", + "\n", + " \n", + "\n", + "\n", + " def fock_distribution(self, n_max=30):\n", + "\n", + " alpha = alpha_from_mean(self.mean)\n", + "\n", + " r, phi = gaussian_parameters_from_cov(self.cov)\n", + "\n", + " tau = -np.exp(1j * phi) * np.tanh(r)\n", + "\n", + " beta = (\n", + " alpha * np.cosh(r)\n", + " + np.conj(alpha)\n", + " * np.exp(1j * phi)\n", + " * np.sinh(r)\n", + " )\n", + "\n", + " c = np.zeros(n_max, dtype=complex)\n", + "\n", + " # Vacuum coefficient derived\n", + " c[0] = (\n", + " 1 / np.sqrt(np.cosh(r))\n", + " * np.exp(\n", + " -0.5 * abs(alpha)**2\n", + " -0.5\n", + " * np.conj(alpha)**2\n", + " * np.exp(1j * phi)\n", + " * np.tanh(r)\n", + " )\n", + " )\n", + "\n", + " # One-photon coefficient from recursion relation\n", + " if n_max > 1:\n", + " c[1] = beta * c[0]\n", + "\n", + " # Higher Fock coefficients\n", + " for n in range(1, n_max - 1):\n", + "\n", + " c[n + 1] = (\n", + " beta * c[n]\n", + " + tau * np.sqrt(n) * c[n - 1]\n", + " ) / np.sqrt(n + 1)\n", + "\n", + " P = np.abs(c)**2\n", + "\n", + " # Normalize because we truncated at n_max\n", + " P /= np.sum(P)\n", + "\n", + " return P\n", + "\n", + " def plot_fock_distribution(self, n_max=30):\n", + "\n", + " P = self.fock_distribution(n_max)\n", + "\n", + " n = np.arange(n_max)\n", + "\n", + " fig, ax = plt.subplots(figsize=(10,8))\n", + "\n", + " ax.bar(n, P)\n", + "\n", + " ax.set_xlabel(r\"Fock state $n$\")\n", + " ax.set_ylabel(r\"$P_n$\")\n", + " \n", + " ax.set_xticks(n)\n", + "\n", + " ax.grid(\n", + " True,\n", + " axis=\"y\",\n", + " linestyle=\"--\",\n", + " alpha=0.3\n", + " )\n", + "\n", + " plt.show()\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "id": "827e787e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GaussianState(\n", + "mean=[2.14819222 2.3206185 ],\n", + "cov=\n", + "[[ 1.26738941 -0.31529057]\n", + " [-0.31529057 0.27569123]]\n", + ")\n" + ] + } + ], + "source": [ + "#Example for Gausssian state inputs and performing Gaussian operations\n", + "\n", + "state = GaussianState() # This initialize a vacuum state\n", + "#Successive operations on Vacuum state\n", + "state.squeeze(0.5)\n", + "state.displace(1+2j)\n", + "state.phase(6)\n", + "print (state)\n" + ] + }, + { + "cell_type": "markdown", + "id": "457048ae", + "metadata": {}, + "source": [ + "# plotting the wigner function for the generated gaussian function" + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "id": "ed413b17", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(
,\n", + " )" + ] + }, + "execution_count": 107, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "state.plot_wigner()" + ] + }, + { + "cell_type": "markdown", + "id": "cca99c04", + "metadata": {}, + "source": [ + "# Plotting the fock state distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "id": "4baf6be0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "state.plot_fock_distribution()" + ] + }, + { + "cell_type": "markdown", + "id": "19693400", + "metadata": {}, + "source": [ + "# Fock state preparation, superposition of fock basis states and wigner function visualization\n" + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "id": "f56a9903", + "metadata": {}, + "outputs": [], + "source": [ + "class FockState:\n", + "\n", + " def __init__(self, state):\n", + "\n", + " self.state = np.asarray(\n", + " state,\n", + " dtype=complex\n", + " )\n", + " norm = np.linalg.norm(self.state)\n", + "\n", + " self.state /= norm\n", + "\n", + " def __repr__(self):\n", + "\n", + " terms = []\n", + "\n", + " for n, c in enumerate(self.state):\n", + "\n", + " if abs(c) > 1e-12:\n", + " terms.append(f\"({c:.3g})|{n}>\")\n", + "\n", + " return \" + \".join(terms)\n", + "\n", + "\n", + "\n", + " def wigner_nm(self, n, m, X, P):\n", + "\n", + " alpha = (X + 1j * P) / np.sqrt(2)\n", + "\n", + " r2 = np.abs(alpha)**2\n", + "\n", + " if n >= m:\n", + "\n", + " W = (\n", + " 2 / np.pi\n", + " * (-1)**m\n", + " * np.sqrt(\n", + " math.factorial(m) / math.factorial(n)\n", + " )\n", + " * np.exp(-2 * r2)\n", + " * (2 * alpha)**(n - m)\n", + " * eval_genlaguerre(\n", + " m,\n", + " n - m,\n", + " 4 * r2\n", + " )\n", + " )\n", + "\n", + " else:\n", + "\n", + " W = np.conj(\n", + " self.wigner_nm(m, n, X, P)\n", + " )\n", + "\n", + " return W\n", + "\n", + "\n", + " def wigner(self, X, P):\n", + "\n", + " W = np.zeros_like(X, dtype=complex)\n", + "\n", + " N = len(self.state)\n", + "\n", + " for n in range(N):\n", + "\n", + " for m in range(N):\n", + "\n", + " c_n = self.state[n]\n", + " c_m = self.state[m]\n", + "\n", + " W_nm = self.wigner_nm(\n", + " n,\n", + " m,\n", + " X,\n", + " P\n", + " )\n", + "\n", + " W += (\n", + " c_n\n", + " * np.conj(c_m)\n", + " * W_nm\n", + " )\n", + "\n", + " return W.real\n", + "\n", + "\n", + " def plot_wigner(self):\n", + "\n", + " q = np.linspace(-5, 5, 200)\n", + " p = np.linspace(-5, 5, 200)\n", + "\n", + " X, P = np.meshgrid(q, p)\n", + "\n", + " W = self.wigner(X, P)\n", + "\n", + " fig, ax = plt.subplots(figsize=(6, 5))\n", + "\n", + " max=np.max(W)\n", + " norm= mcolors.TwoSlopeNorm(vmin=W.min(), vcenter=0, vmax=W.max()) \n", + "\n", + " contour = ax.contourf(\n", + " X,\n", + " P,\n", + " W,\n", + " levels=100,\n", + " cmap=\"RdBu\", norm=norm\n", + " )\n", + "\n", + " fig.colorbar(\n", + " contour,\n", + " ax=ax\n", + " )\n", + " ax.grid(True)\n", + " ax.set_xlabel(\"X\")\n", + " ax.set_ylabel(\"P\")\n", + " ax.set_title(\"Fock state Wigner\")\n", + " ax.set_aspect(\"equal\")\n", + "\n", + " plt.show()\n", + "\n", + " def plot_fock_distribution(self):\n", + "\n", + " P = np.abs(self.state)**2\n", + " \n", + " P /= np.sum(P)\n", + "\n", + " n = np.arange(len(self.state))\n", + "\n", + " fig, ax = plt.subplots(figsize=(6,4))\n", + "\n", + " ax.bar(n, P)\n", + "\n", + " ax.set_xlabel(r\"Fock state $n$\")\n", + " ax.set_ylabel(r\"$P_n$\")\n", + " \n", + " ax.set_xticks(n)\n", + "\n", + " ax.grid(\n", + " True,\n", + " axis=\"y\",\n", + " linestyle=\"--\",\n", + " alpha=0.3\n", + " )\n", + "\n", + " plt.show()\n", + "\n", + "\n", + " \n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "2502a385", + "metadata": {}, + "source": [ + "# Example Superposition of 1- and 2-fock basis state superposition" + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "id": "9be171d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.707+0j)|1> + (0.707+0j)|2>\n" + ] + } + ], + "source": [ + "#Focke state preparation and visualization\n", + "\n", + "state = FockState([0,1,1])\n", + "\n", + "print(state)" + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "id": "41d99c99", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "state.plot_fock_distribution()" + ] + }, + { + "cell_type": "markdown", + "id": "54d04150", + "metadata": {}, + "source": [ + "# Example Superposition of 0-, 1- and 2-fock basis state superposition" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "id": "2ebd6b7c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.577+0j)|0> + (0.577+0j)|1> + (0.577+0j)|2>\n" + ] + } + ], + "source": [ + "#Focke state preparation and visualization\n", + "\n", + "state = FockState([1,1,1])\n", + "\n", + "print(state)" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "052aa361", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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