mipt_spectrum_rmt.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33f5b0c2-bb1e-401f-b54a-45ff79549bd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "This notebook demonstrates how to compute spectrum of random matrices \n",
    "\\Lambda_P=PU^{\\dag}PUP and \\Lambda_P=PU^{\\dag}(1-P)UP.\n",
    "Here P is a projector (with a specified rank) and U is random unitary.\n",
    "U can be either drawn from the Haar-random or the Cayley ensemble.\n",
    "\n",
    "Packages information:\n",
    "---------------------\n",
    "numpy version = 1.26.4\n",
    "scipy version = 1.13.1\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "41665f0f-5a29-4741-af20-32a5f3c24234",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.stats import unitary_group\n",
    "from scipy.linalg import logm\n",
    "from numpy.linalg import matrix_power\n",
    "from numpy.linalg import inv\n",
    "from numpy.linalg import eig\n",
    "from tqdm import tqdm\n",
    "import random\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3904e7ad-3445-443c-90f2-33538b316a52",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Rand_mx_simulation:\n",
    "    \"\"\"\n",
    "    Attributes\n",
    "    ----------\n",
    "    n : int\n",
    "        Dimensionality of the Hilbert space. Normally n=2**k.\n",
    "    b : float\n",
    "        Projection dimension. rank[P]=b*n. Requirement that b*n is integer.\n",
    "    sigma : float\n",
    "        Parameter characterizing the GUE ensemble variance. sigma = sqrt(gamma/2^n)\n",
    "    sigma_err : float\n",
    "        Parameter characterizing the error GUE ensemble variance(if present).\n",
    "    runs : int\n",
    "        Number of random-matrix realizations over which the averaging is performed.\n",
    "    P0_flag : bool\n",
    "        If true, then \\Lambda_P=PU^{\\dag}PUP.\n",
    "        If not, then \\Lambda_P=PU^{\\dag}(1-P)UP\n",
    "    CUE_flag : bool\n",
    "        If true, random-Haar unitaries are used. \n",
    "        If not, unitaries are drawn from the Cayley ensemble.\n",
    "    initial_state : str\n",
    "        Initial state. Possible options: \"pure\"(|000...00>) or \n",
    "        \"mixed\"(fully mixed state)\n",
    "    \"\"\"\n",
    "    def __init__(self,\n",
    "                 n=2048,\n",
    "                 b=1/4,\n",
    "                 sigma=1/np.sqrt(2048),\n",
    "                 sigma_err=0.0/np.sqrt(2048),\n",
    "                 runs=1,\n",
    "                 P0_flag=True,\n",
    "                 CUE_flag=False,\n",
    "                 initial_state='pure'\n",
    "                ):\n",
    "        self.n = n\n",
    "        self.b = b\n",
    "        self.sigma = sigma\n",
    "        self.sigma_err = sigma_err\n",
    "        self.runs = runs\n",
    "        self.P0_flag = P0_flag\n",
    "        self.CUE_flag = CUE_flag\n",
    "        self.initial_state = initial_state\n",
    "        \n",
    "        if np.log2(self.n).is_integer() == False:\n",
    "            raise ValueError(\"n is not 2^k\")\n",
    "        if (self.b*self.n).is_integer() == False:\n",
    "            raise ValueError(\"b*n is not integer\")\n",
    "\n",
    "        #setting up the projector\n",
    "        self.P = np.zeros((self.n, self.n))\n",
    "        for i in range(int(self.b*self.n)):\n",
    "            self.P[i,i] = 1\n",
    "\n",
    "        #setting up the initial state\n",
    "        if self.initial_state=='mixed':\n",
    "            self.rho_0 = np.identity(self.n)/self.n \n",
    "        if self.initial_state=='pure':\n",
    "            self.rho_0 = np.zeros((self.n, self.n))\n",
    "            self.rho_0[0,0] = 1\n",
    "\n",
    "    \n",
    "    def generate_U(self,\n",
    "        sigmaH : float,\n",
    "        CUE_flag0 : bool\n",
    "    ):\n",
    "        \"\"\"\n",
    "        Generates random matrix U, either from Haar-random or Cayley ensemble.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        sigmaH : float\n",
    "            Variance of the GUE ensemble used to generate Cayley ensemble.\n",
    "        CUE_flag0 : bool\n",
    "            If true, random-Haar unitaries are used. \n",
    "            If not, unitaries are drawn from the Cayley ensemble.\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        U : numpy.ndarray\n",
    "            Random matrix U.\n",
    "        \"\"\"\n",
    "        if CUE_flag0==True:\n",
    "            np.random.RandomState()\n",
    "            U = unitary_group.rvs(dim=self.n,random_state=np.random.RandomState())\n",
    "        else:\n",
    "            np.random.RandomState()\n",
    "            x = (np.random.normal(loc=0.0,scale=sigmaH,size=(self.n,self.n))\n",
    "                 + np.random.normal(loc=0.0,scale=sigmaH,size=(self.n,self.n))*1j )\n",
    "            H = (x+x.conj().T)/2\n",
    "            U = np.dot( (1j*np.identity(self.n)+H), inv((1j*np.identity(self.n)-H)) )\n",
    "        return U\n",
    "\n",
    "    \n",
    "    def generate_Lambda_P(self, \n",
    "        U : np.ndarray, \n",
    "        U_err : np.ndarray, \n",
    "        l : int = 1\n",
    "    ):\n",
    "        \"\"\"\n",
    "        Generates random matrix Lambda_P=(PU^{\\dag})^lP(UP)^l or Lambda_P=PU^{\\dag}(1-P)UP.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        U : np.ndarray\n",
    "            Random unitary.\n",
    "        U_err : np.ndarray\n",
    "            Unitary representing an error in the generation of U.\n",
    "        l : int\n",
    "            Lambda_P=(PU^{\\dag})^lP(UP)^l. Standart case is l=1.\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        Lambda_P : numpy.ndarray\n",
    "            Random matrix Lambda_P.\n",
    "        \"\"\"\n",
    "        \n",
    "        if self.P0_flag==True:     #Lambda_P=(PU^{\\dag})^lP(UP)^l\n",
    "            PUdag = np.dot( self.P, np.dot( U.conj().T, U_err ) )\n",
    "            UP = np.dot( U, self.P )\n",
    "            Lambda_P = np.dot( \n",
    "                np.dot( matrix_power(PUdag, l), self.P), \n",
    "                matrix_power(UP, l) \n",
    "            )\n",
    "        else:    #Lambda_P=PU^{\\dag}(1-P)UP\n",
    "            Lambda_P = np.dot( \n",
    "                np.dot( \n",
    "                    np.dot( \n",
    "                        np.dot( self.P, np.dot( U.conj().T, U_err ) ), \n",
    "                        np.identity(self.n)-self.P \n",
    "                    ), \n",
    "                    U \n",
    "                ), \n",
    "                self.P \n",
    "            )\n",
    "        return Lambda_P\n",
    "    \n",
    "    def get_eignevals_W(self,\n",
    "        l : int = 1\n",
    "    ):\n",
    "        \"\"\"\n",
    "        Generates random matrix Lambda_P=(PU^{\\dag})^lP(UP)^l or Lambda_P=PU^{\\dag}(1-P)UP\n",
    "        and computes its eigenvalues.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        U : np.ndarray\n",
    "            Random unitary.\n",
    "        \"\"\"\n",
    "        self.eigenvals = []\n",
    "        for i in range(self.runs):\n",
    "            U = self.generate_U(\n",
    "                sigmaH=self.sigma,\n",
    "                CUE_flag0=self.CUE_flag\n",
    "            )\n",
    "            U_err = self.generate_U(\n",
    "                sigmaH=self.sigma_err,\n",
    "                CUE_flag0=False\n",
    "            )\n",
    "            Lambda_P = self.generate_Lambda_P(\n",
    "                U, \n",
    "                U_err, \n",
    "                l\n",
    "            )            \n",
    "            self.eigenvals.append( np.linalg.eigh(Lambda_P)[0] )\n",
    "            \n",
    "        #flatten to combine eigenvalues from different runs\n",
    "        self.eigenvals=np.ndarray.flatten(np.array(self.eigenvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "024b5d7f-fe6c-4c47-b3a5-8532a93086e5",
   "metadata": {},
   "source": [
    "## Results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6552e996-af42-48e7-b070-e95d090ab4ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 45.5 s, sys: 1.55 s, total: 47.1 s\n",
      "Wall time: 10.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "L=10\n",
    "runs=10\n",
    "b=1/4\n",
    "\n",
    "Lambda_P = Rand_mx_simulation(\n",
    "                n=2**L,\n",
    "                b=b,\n",
    "                sigma=np.sqrt(2.0)/np.sqrt(2**L),\n",
    "                runs=runs,\n",
    "                P0_flag=True,\n",
    "                CUE_flag=False,\n",
    "                initial_state='pure'\n",
    "            )\n",
    "Lambda_P.get_eignevals_W()\n",
    "\n",
    "eigenvals_0D = Lambda_P.eigenvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b8a00ed4-7507-40e0-9885-d2a6eadf5bab",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "modes_one = round(len([i for i in eigenvals_0D if 0.99<i<1.01])/10/2**L,2)\n",
    "plt.hist(eigenvals_0D,\n",
    "         bins=np.linspace(0,1,200),\n",
    "         weights=np.ones_like(eigenvals_0D)/10,\n",
    "         label='RMT CUE result for $N=2^L$, 10 realizations\\n# of modes with $0.99<\\lambda<1.01$ is %s*$2^L$' % modes_one\n",
    "        )\n",
    "plt.ylim(0,6)\n",
    "plt.title('Eigenvalue distribution, L=%s qubits, b=%s' % (L,b))\n",
    "plt.legend()\n",
    "plt.xlabel(r'$\\lambda$')\n",
    "plt.ylabel(r'$P(\\lambda)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d4c20c86-6693-44a1-8029-b668bb4e72a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 46.8 s, sys: 1.69 s, total: 48.5 s\n",
      "Wall time: 10.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "L=10\n",
    "runs=10\n",
    "b=1/2\n",
    "\n",
    "Lambda_P = Rand_mx_simulation(\n",
    "                n=2**L,\n",
    "                b=b,\n",
    "                sigma=np.sqrt(2.0)/np.sqrt(2**L),\n",
    "                runs=runs,\n",
    "                P0_flag=True,\n",
    "                CUE_flag=False,\n",
    "                initial_state='pure'\n",
    "            )\n",
    "Lambda_P.get_eignevals_W()\n",
    "\n",
    "eigenvals_0D = Lambda_P.eigenvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7beb5131-b3f4-4538-bdfb-42ac8d5ad7e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "modes_one = round(len([i for i in eigenvals_0D if 0.99<i<1.01])/10/2**L,2)\n",
    "plt.hist(eigenvals_0D, \n",
    "         bins=np.linspace(0,1,200), \n",
    "         weights=np.ones_like(eigenvals_0D)/10, \n",
    "         label='RMT CUE result for $N=2^L$, 10 realizations\\n# of modes with $0.99<\\lambda<1.01$ is %s*$2^L$' % modes_one \n",
    "        )\n",
    "plt.ylim(0,6)\n",
    "plt.title('Eigenvalue distribution, L=%s qubits, b=%s' % (L,b))\n",
    "plt.legend()\n",
    "plt.xlabel(r'$\\lambda$')\n",
    "plt.ylabel(r'$P(\\lambda)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c670b45b-f083-4e98-9871-9b512f39b4f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 51.2 s, sys: 2.07 s, total: 53.2 s\n",
      "Wall time: 12.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "L=10\n",
    "runs=10\n",
    "b=3/4\n",
    "\n",
    "Lambda_P = Rand_mx_simulation(\n",
    "                n=2**L,\n",
    "                b=b,\n",
    "                sigma=np.sqrt(2.0)/np.sqrt(2**L),\n",
    "                runs=runs,\n",
    "                P0_flag=True,\n",
    "                CUE_flag=False,\n",
    "                initial_state='pure'\n",
    "            )\n",
    "Lambda_P.get_eignevals_W()\n",
    "\n",
    "eigenvals_0D = Lambda_P.eigenvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "17b96124-c5d4-4956-a712-6b93c1d94444",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZDEZGRmoXoT158gQ//PBDufUrf4T++OMPBAYGqqbv2rVLrVzz5s3RtGlT/P7771i8eLHO29GjRw/89NNP2LVrl9opjM2bN+tUj6GhITp37owWLVpg06ZNSEhIwKBBgyq9VyEpKQm///672mmhzZs3w9LSEu3btweg3nZFk7XibQc87/XQNraePXsiKioKt2/fVuuK//7772FmZiaJIZ5VfUqoX79+mDNnDjZs2IAZM2aopq9fvx6mpqZl3jvH3NwcnTp1wo4dO/DZZ5+pkpLMzEz85z//USvr4OAAExMT/PHHH2rTf/nll1Lr37RpE3x8fFTvf/rpJ+Tn55d5fxVt9083NzdMmDABhw4dwvHjx8ssW5bStr179+6q34mKnhJ68803MW7cOJw+fRqdO3cG8Dxp27hxIzp37lzi9FFp4uLi8Mcff2D69OlqPTjl+f777wHUrdsB6IoJSy1w4cKFEteXAM9PORQfUaI0ZcoUfPfdd+jbty/mz58PBwcHbN68Gf/9738B/C/Lt7CwwMqVKxEaGoqHDx9i4MCBsLe3x7179/D777/j3r17iIyMrFDco0aNwqeffoohQ4bA1NS0xMiaoKAgLFu2DEOGDMGYMWPw4MEDLF26VPUjWRZHR0f06tULERERqFevHtzd3XHo0CHs2LGjRNmvv/4affv2RWBgIEaOHImGDRvi4cOHuHTpEhISEvDzzz+Xup4RI0bg3//+N0aMGIFFixahadOm2Lt3r9p1QKX56quvcPjwYQQFBcHNzQ1Pnz5VjaTq1asXgOcHRnd3d/zyyy/o2bMnbG1tUb9+fVVSoStnZ2e8/vrrmDdvHpycnLBx40ZER0fj008/hZmZGQCgY8eOaN68OaZOnYr8/HzUq1cPUVFR+O2330rU5+XlhR07diAyMhI+Pj4wMDAo9fTk3LlzsXv3bvTo0QMff/wxbG1tsWnTJuzZswdLliyBtbW1ztsTExODHj16YO7cuVrdVffatWvYtm1biemenp7w9PSEh4dHhdr2r7/+Uh0kr127BgCq9Xh4eKjapFWrVhg9ejTmzp0LQ0NDdOzYEQcOHMA333yDhQsXlnvaYcGCBejTpw969+6Nf/3rXygoKMCnn34Kc3Nz1akL4HmyP2zYMHz33Xd46aWX4O3tjTNnzpSZSO/YsQNGRkbo3bu3apSQt7c33n777VKXKW3/rFevHnr06IEhQ4agRYsWsLS0xNmzZ7Fv3z61nkxdPz9DQ0P07t0bYWFhKCwsxKeffoqMjAzVzeuUMel6ihx4/nv05Zdf4q233sInn3wCe3t7rF69GpcvXy4xFLtnz56IjY3V+Lu7du1aAMDo0aM1rmfz5s3YsWMHgoKC4O7ujsePH+Pnn3/G1q1bMXLkyBLXmFER+r7qlyqurFFCAMSaNWtUZYuPEhJCiAsXLohevXoJExMTYWtrK0aPHi02bNggAIjff/9drWxsbKwICgoStra2wtjYWDRs2FAEBQWJn3/+WVVGOdrg3r17GuMsPupECCG6dOkiAIihQ4dq3MbvvvtONG/eXCgUCtG4cWMREREh1q5dW6K+4qMXhBAiLS1NDBw4UNja2gpra2sxbNgwERcXp3H0xO+//y7efvttYW9vL4yNjYWjo6N49dVXxVdffaUxrqJu3rwpBgwYICwsLISlpaUYMGCAamRBWaOETp48Kd58803h7u4uFAqFsLOzE35+fmLXrl1q9R88eFC0a9dOKBQKAUD1OZbW3prWJcTzfSAoKEhs27ZNtGrVSsjlcuHh4SGWLVtWYvk///xTBAQECCsrK9GgQQMxceJEsWfPnhKjhB4+fCgGDhwobGxshEwmU1snNIweOX/+vAgODhbW1tZCLpcLb2/vEp+FcpRH0X1LCM0jX/7zn/8IAFp9TmV9VzSNctFFWd/F4t+7vLw8MXfuXOHm5ibkcrlo1qyZ+OKLL7Re165du0SbNm2EXC4Xbm5u4pNPPtH4eaenp4t3331XODg4CHNzcxEcHCxSUlJKHSUUHx8vgoODVfvx4MGDxd9//61Wp6bvmab98+nTp2Ls2LGiTZs2wsrKSpiamormzZuLuXPnqkajCaH956f87D/99FMRHh4uXFxchFwuF+3atRP79+/Xuu3Kc+fOHTFixAhha2srTExMxMsvvyyio6NLlPPz89M4EiwnJ0dYW1uLV155pdR1nDx5UvTs2VM4OjoKY2NjYWZmJjp27ChWr15d5ohEEkImRDl34KI6ZcyYMdiyZQsePHgAuVyu73CIyjR9+nRs2bIFV65cKfG8lrpk3rx5CA8PL/eGilLDz490wVNCddj8+fPh7OyMxo0bIysrC7t378a3336LOXPmMFmhGuHIkSP46KOPeLCrofj5kS6YsNRhxsbG+Oyzz3Dz5k3k5+ejadOmWLZsmU5Daon0SduLK0ma+PmRLnhKiIiIiCRPMgO+b926hWHDhsHOzg5mZmZo27ZtmY9oJyIiorpDEqeEHj16hK5du6JHjx749ddfYW9vj2vXrsHGxkbfoREREZEESOKU0MyZM3H8+HEcO3ZM36EQERGRBEkiYfH09ERgYCBu3ryJ2NhYNGzYEOPGjcN7772nsXxubq7aLacLCwvx8OFD2NnZVfgZH0RERFS9hBDIzMyEs7Nz+Y8l0NcNYIpSKBRCoVCIWbNmiYSEBPHVV18JExMTsWHDBo3llTc64osvvvjiiy++av7rxo0b5eYKkuhhkcvl6NChA06cOKGaNmnSJJw9exYnT54sUb54D0t6ejrc3Nxw48YNWFlZVXp8redqvs36hfBAjdOJiIhqg6LHv6o45mVkZMDV1RWPHz8u9/Eckrjo1snJSe0BfADQsmVLbN++XWN5hUKh8XkyVlZWVZKwGCjMNE6vinURERFJRdHjX1Ue87S5nEMSw5q7du2Ky5cvq037888/4e7urqeIiIiISEokkbB88MEHOHXqFBYvXoyrV69i8+bN+OabbzB+/Hh9h0ZEREQSIImEpWPHjoiKisKWLVvQunVrLFiwAMuXL8fQoUP1HRoRERFJgCSuYQGA1157Da+99pq+w6izCgoK8OzZM32HQURU4xgbG8PQ0FDfYdR6kklYSD+EELhz5w4eP36s71CIiGosGxsbODo68l5gVYgJSx2nTFbs7e1hZmbGLxsRkQ6EEMjJycHdu3cBPB/1SlWDCUsdVlBQoEpW7Ozs9B0OEVGNZGpqCgC4e/cu7O3teXqoikjiolvSD+U1K2Zmmu8zQ0RE2lH+jvJawKrDhIV4GoiI6AXxd7TqMWEhIiIiyWPCQkRERJLHhIWIqIp9/vnnmDt3rr7DIKrRmLAQEVWxCxcuoFWrVvoOg6hGY8JCRBXm7++PKVOm6LycEAJjxoyBra0tZDIZEhMTKz02Kblw4QJat26t7zCqTdH9oqL7SEXXR7UXExaqsUaOHAmZTAaZTAYjIyO4ubnh/fffx6NHj0qUGTt2bInlx40bB5lMhpEjRwKAqq7SXspymty5cwcTJ05E48aNoVAo4OrqiuDgYBw6dEhVprQf1Z07d6qNMCi6XUVfffr00b2Rqpm2B459+/Zh/fr12L17N9LS0qrkYP7KK69AJpNhy5YtatNXr14Ne3v7SltPREQEOnbsCEtLS9jb2+ONN95Qe/q8EALXrl1Ds2bNKlT/0aNHERwcDGdnZ8hkMuzcuVNjudWrV6NRo0YwMTGBj48Pjh07VqH1VbYdO3ZgwYIFlVafpn2sstdB0sSEhWq0Pn36IC0tDSkpKfj222/xn//8B+PGjVMr4+rqiq1bt+LJkyeqaU+fPsWWLVvg5uammpaWlqZ6LV++HFZWVmrTVqxYoTGGlJQU+Pj44PDhw1iyZAnOnz+Pffv2oUePHhV+4rhyu4q+ih94y5KXl1eh9VaXa9euwcnJCV26dIGjoyOMjHS/h2VZ2yiEQGJiIpycnLB9+3a1eQkJCWjfvr3O6ytNbGwsxo8fj1OnTiE6Ohr5+fkICAhAdnY2AOD69etwcXGp0DYCQHZ2Nry9vbFq1apSy/z444+YMmUKZs+ejXPnzqF79+7o27cvUlNTtV5PVe0ztra2sLS0rJK6q3MdpH9MWKhGUygUcHR0hIuLCwICAhASEoIDBw6olWnfvj3c3NywY8cO1bQdO3bA1dUV7dq1U01zdHRUvaytrSGTyUpM00TZU3PmzBkMHDgQzZo1Q6tWrRAWFoZTp0690HYVfdWrV6/U8v7+/pgwYQLCwsJQv3599O7dG8DzA/eSJUvQuHFjmJqawtvbG9u2bVMtt23bNnh5ecHU1BR2dnbo1auX6kALAB4eHli+fLnautq2bYt58+aViGHkyJGIjY3FihUrVL1CKSkpGstNnDgRqampkMlk8PDwAADk5uZi0qRJsLe3h4mJCbp164azZ8+Wu42aXLlyBZmZmZgzZw5+/fVX5OTkqObFx8fDx8en1GV1tW/fPowcORKtWrWCt7c31q1bh9TUVMTHxwN48etX+vbti4ULF6J///6lllm2bBlGjx6Nd999Fy1btsTy5cvh6uqKyMjIUpfR1J7l7S/K7e3WrRtsbGxgZ2eH1157DdeuXStzPcoekZSUFI29h/7+/lrVX9o+VrzXpbx9SRnXpEmTMH36dNja2sLR0bHEfl3e94OqFxMWqjWuX7+Offv2wdjYuMS8d955B+vWrVO9/+677zBq1KgXXufDhw+xb98+jB8/Hubm5iXm29jYvPA6tLVhwwYYGRnh+PHj+PrrrwEAc+bMwbp16xAZGYmkpCR88MEHGDZsGGJjY5GWlobBgwdj1KhRuHTpEmJiYtC/f38IISq0/hUrVsDX1xfvvfeeqlfI1dVVY7n58+fDxcUFaWlpqgPJ9OnTsX37dmzYsAEJCQlo0qQJAgMD8fDhwzK3UZP4+HiYmJjg3XffhZWVFX799VcAzw9kSUlJGntYFi9eDAsLizJf2pxmSU9PB/D8v36g6q9fycvLQ3x8PAICAtSmBwQE4MSJE2UuW7w9y9pflLKzsxEWFoazZ8/i0KFDMDAwwJtvvonCwsJyY3V1dVXrNTx37hzs7OzwyiuvaFW/tvuYNvuScvvNzc1x+vRpLFmyBPPnz0d0dDQAVPr3g14cnyVENdru3bthYWGBgoICPH36FMDz/zaLGz58OGbNmqX6D+/48ePYunUrYmJiXmj9V69ehRACLVq0eKF6ilNuV1EzZszARx99VOoyTZo0wZIlS1Tvs7OzsWzZMhw+fBi+vr4AgMaNG+O3337D119/jalTpyI/Px/9+/eHu7s7AMDLy6vCMVtbW0Mul8PMzAyOjo5llrO0tIShoaGqXHZ2NiIjI7F+/Xr07dsXALBmzRpER0dj7dq1mDZtmsZtLE1CQgLatGkDuVyON998E9u2bcOAAQPwxx9/4NmzZxp7WMaOHYu33367zHobNmxY5nwhBMLCwtCtWzdVkpKUlIQDBw5gzZo1AICXX34ZW7duLXcbtHX//n0UFBTAwcFBbbqDgwPu3LlT5rJF27O8/cXPzw8AMGDAALU61q5dC3t7e1y8eLHcxKzoZ/706VO88cYb8PX1VevZKK/+8vYxbfclAGjTpo1quHnTpk2xatUqHDp0CL1790ZaWlqlfj/oxTFhoRqtR48eiIyMRE5ODr799lv8+eefmDhxYoly9evXR1BQEDZs2AAhBIKCglC/fv0XXr/yv63Kvi23cruKUv7HXpoOHTqovb948SKePn1a4tRJXl4e2rVrB29vb/Ts2RNeXl4IDAxEQEAABg4cWOapp6py7do1PHv2DF27dlVNMzY2RqdOnXDp0iXVtOLbWJr4+HhVL0r//v3Rv39/5ObmIj4+Hra2tqrTUEXZ2tqW28blmTBhAv744w/89ttvqmmbN29+oTq1VXwfFEKUu18Wbc/y9hela9eu4aOPPsKpU6dw//59Vc9KamqqTj1Jo0ePRmZmJqKjo2Fg8L/O/hetX9t9CXiesBTl5OSkeuqylL4f9BwTFqrRzM3N0aRJEwDAF198gR49eiA8PFzjiIFRo0ZhwoQJAIAvv/yyUtbftGlTyGQyXLp0CW+88UaZZa2srFSnC4p6/PgxrKys1KYV3S5tFT8lpfyh37NnT4meAYVCAUNDQ0RHR+PEiRM4cOAAVq5cidmzZ+P06dNo1KgRAMDAwKBEF3hVPNyttMSv+EFX02k3Tc6dO4chQ4YAeH6tglwux/79+5GQkKB28C1q8eLFWLx4cZn1/vrrr+jevbvGeRMnTsSuXbtw9OhRuLi4aBVnZahfvz4MDQ1L9KbcvXu3RK9LcUXbs7z9RSk4OBiurq5Ys2YNnJ2dUVhYiNatW+t00e7ChQuxb98+nDlzpsTFsi9av7b7EoASp49lMpmqHbT5flD14jUsVKvMnTsXS5cuxe3bt0vM69OnD/Ly8pCXl4fAwMBKWZ+trS0CAwPx5ZdfarwY7/Hjx6q/W7Rogbi4uBJlzp49i+bNm1dKPEV5enpCoVAgNTUVTZo0UXspz/vLZDJ07doV4eHhOHfuHORyOaKiolR1NGjQAGlpaar3GRkZSE5OLnWdcrkcBQUFOsfapEkTyOVytZ6JZ8+eIS4uDi1bttSpruvXr+Px48eqHhYjIyMEBwdj+/btZV5wO3bsWCQmJpb50tTDI4TAhAkTsGPHDhw+fLjaD2ZyuRw+Pj6qay+UoqOj0aVLF63r0WZ/efDgAS5duoQ5c+agZ8+eaNmypdptBLSxfft2zJ8/Hz/99BNeeukltXna1F/ePlaZ+1J53w+qXuxhoVrF398frVq1wuLFi0sMAzU0NFR1CRsaGlbaOlevXo0uXbqgU6dOmD9/Ptq0aYP8/HxER0cjMjJStc5x48Zh1apVGD9+PMaMGQNTU1PVefUffvhBrc7c3NwS/zEbGRnpdBrL0tISU6dOxQcffIDCwkJ069YNGRkZOHHiBCwsLNCiRQscOnQIAQEBsLe3x+nTp3Hv3j21H/VXX30V69evR3BwMOrVq4ePPvqozLbz8PDA6dOnkZKSAgsLC9ja2qp195fG3Nwc77//PqZNmwZbW1u4ublhyZIlyMnJwejRo7XeZuD56SC5XK52+mDAgAEYPnw4cnJyMH36dI3LVfSU0Pjx47F582b88ssvsLS0VH1u1tbWMDU11bm+4rKysnD16lXV++TkZCQmJqraCQDCwsIwfPhwdOjQAb6+vvjmm2+Qmpqq8f5DpSlvfwkNDUW9evVgZ2eHb775Bk5OTkhNTcXMmTO1XseFCxcwYsQIzJgxA61atVK1lVwuh62trVb1a9rHiqqsfen06dPlfj+oejFhoVonLCwM77zzDmbMmFFiXvFTL5WhUaNGSEhIwKJFi/Cvf/0LaWlpaNCgAXx8fNSuQ/Hw8MCxY8cwe/ZsBAQE4OnTp2jWrBnWr1+Pt956S63Offv2wcnJSW1a8+bN8d///len2BYsWAB7e3tERETg+vXrsLGxQfv27fHhhx/CysoKR48exfLly5GRkQF3d3d8/vnnqgsVAWDWrFm4fv06XnvtNVhbW2PBggVl9rBMnToVoaGh8PT0xJMnT5CcnKzxehFNPvnkExQWFmL48OHIzMxEhw4dsH//fp2vGUhISFBdnKnUu3dvFBQUIC8vr1LvwQJA9RkXHZoLAOvWrSvzZoMAsH79erzzzjtljjyJi4tDjx49VO/DwsIAAKGhoVi/fj0AICQkBA8ePMD8+fNVN+Lbu3ev6mJRbZW1vwDPTxFu3boVkyZNQuvWrdG8eXN88cUXJba9rG3JycnBwoULsXDhQtV0Pz8/xMTEaFW/pn2suMrYl7T5flD1kolaMEYrIyMD1tbWSE9Pr5IDksfMPRqnp3wSVOnrqk5Pnz5FcnKy6u6YRFS95s2bh5iYmBcerUb6V1t/T4se/6rimKfL8Zs9LEREerJ///5S76BMROqYsBAR6cnJkyf1HQJRjcGEhTQq7TRYVanpp9eIiKhqcVgzERERSR4TFiIiIpI8JixEREQkeUxYiIiISPKYsBAREZHkMWEhIiIiyWPCQkRERJLHhIWIiKiYzz//HHPnztV3GFQEbxxHGvFGbkRUl124cIEPOpQY9rAQlUIIgTFjxsDW1hYymQyJiYl6jcff3x9TpkzRawxFaROP1GKuLnPmzIFCocCQIUP0HUq1qI2f84ULF9C6dWt9h0FFMGGhWuHevXswNjZGTk4O8vPzYW5ujtTU1Beqc9++fVi/fj12796NtLQ0/ngVs2PHDixYsED1vjIPWqtXr1Y99dbHxwfHjh0rd5nMzExMmTIF7u7uMDU1RZcuXXD27Fmt51em6dOnY9myZdiyZQuuXr1aJes4evQogoOD4ezsDJlMhp07d2q1XHltW5F6i+8LuqrI5z1v3jzIZDK1l6OjY4ly/v7+JaZFRESgY8eOsLS0hL29Pd544w1cvnxZNV8IgWvXrqFZs2YV3iaqfExYqFY4efIk2rZtCzMzM8THx8PW1hZubm4vVOe1a9fg5OSELl26wNHREUZGPINalK2tLSwtLSu93h9//BFTpkzB7Nmzce7cOXTv3h19+/YtNwF99913ER0djR9++AHnz59HQEAAevXqhVu3bmk1X1ePHj1CVlaWxnlWVlYYNWoUDAwMcP78+QrVX946srOz4e3tjVWrVmldnzZtW5F6X2RfqOjnDQCtWrVCWlqa6qVs6+PHj+PgwYNqZQ8ePIjjx48DAGJjYzF+/HicOnUK0dHRyM/PR0BAALKzswEA169fh4uLC7/zUiNqgfT0dAFApKenV0n97jN2a3zVdE+ePBEXL14UT5480XcoL2zGjBli8uTJQgghli5dKkJCQspd5unTp2LixImiQYMGQqFQiK5du4ozZ84IIYQIDQ0VAFQvd3d3jXX4+fmJCRMmiMmTJwsbGxthb28vvv76a5GVlSVGjhwpLCwsROPGjcXevXu1XrcQQmRlZYnhw4cLc3Nz4ejoKJYuXSr8/PxU2yiEEIWFheLTTz8VjRo1EiYmJqJNmzbi559/VlvPzz//LFq3bi1MTEyEra2t6Nmzp8jKyiqxHbt27RLW1taioKBACCHEuXPnBAAxdepUVZkxY8aIQYMGqW27Mp7i7QVAJCcnCz8/PzFx4kQxbdo0Ua9ePeHg4CDmzp1b5ufSqVMnMXbsWLVpLVq0EDNnzix1mZycHGFoaCh271b/Xnp7e4vZs2eXO19bz549E7t37xZvvfWWUCgUIjExsdSyGRkZwsLCQsyfP1/r+nVdhxIAERUVVW45XdtW23qL75va7ncViUlp7ty5wtvbW+O81NRUMXDgQPH++++L9u3bi/fff1+EhISImzdvaix/9+5dAUDExsYKIYTYuXOn2r6ujdr0e1pUVR/zdDl+s4eFaqzU1FTY2NjAxsYGy5Ytw9dffw0bGxt8+OGH2LlzJ2xsbDBu3LhSl58+fTq2b9+ODRs2ICEhAU2aNEFgYCAePnyIFStWYP78+XBxcUFaWlqZpw42bNiA+vXr48yZM5g4cSLef/99vPXWW+jSpQsSEhIQGBiI4cOHIycnR6t1A8C0adNw5MgRREVF4cCBA4iJiUF8fLzaeufMmYN169YhMjISSUlJ+OCDDzBs2DDExsYCANLS0jB48GCMGjUKly5dQkxMDPr37w8hRIlteOWVV5CZmYlz584BeP4faP369VV1AUBMTAz8/Pw0tsGKFSvg6+uL9957T/Xfrqurq6p9zM3Ncfr0aSxZsgTz589HdHS0xnry8vIQHx+PgIAAtekBAQE4ceJEqZ9Bfn4+CgoKYGJiojbd1NQUv/32W7nzy3P+/HlMnToVLi4uGDFiBOzs7HDkyBF4e3uXusycOXOQlZWFCxculFt/Rdehi4q2ra502e9eNKYrV67A2dkZjRo1wqBBg3D9+nUAgKurK37++WdYW1sjISEBNjY22Lp1Kxo2bKixnvT0dADPe4oAXr8iWVWSMlUz9rBUTE3/j+DZs2ciOTlZ/P7778LY2FgkJiaKq1evCgsLCxEbGyuSk5PFvXv3NC6blZUljI2NxaZNm1TT8vLyhLOzs1iyZIkQQoh///vfpfasKPn5+Ylu3bqp3ufn5wtzc3MxfPhw1bS0tDQBQJw8eVKrdWdmZgq5XC62bt2qmv/gwQNhamqq+i82KytLmJiYiBMnTqjFM3r0aDF48GAhhBDx8fECgEhJSSlzG5Tat28vli5dKoQQ4o033hCLFi0ScrlcZGRkqLbh0qVLatte9L/q4u81tY8QQnTs2FHMmDFDYwy3bt0SAMTx48fVpi9atEg0a9aszPh9fX2Fn5+fuHXrlsjPzxc//PCDkMlkquXKm1/c/fv3xYoVK0S7du2EXC4X/fr1E9u3bxe5ubllxiGEEHFxcUIul4ugoCDh6elZarkXWUdR0KInpCJtq029Qqh/9rrsdy/yee/du1ds27ZN/PHHHyI6Olr4+fkJBwcHcf/+fXHz5k0REhIixo4dK9q3by/Gjh1bag9LYWGhCA4OVttPBw8eLOzs7IS7u7twd3fXqse2pv+elkZKPSw8QUc1lpGRETw8PPDTTz+hY8eO8Pb2xvHjx+Hg4IBXXnmlzGWvXbuGZ8+eoWvXrqppxsbG6NSpEy5duqRTHG3atFH9bWhoCDs7O3h5eammOTg4AADu3r2r1bqvXbuGvLw8+Pr6qubb2tqiefPmqvcXL17E06dP0bt3b7VY8vLy0K5dOwCAt7c3evbsCS8vLwQGBiIgIAADBw5EvXr1NG6Hv78/YmJiEBYWhmPHjmHhwoXYvn07fvvtNzx+/BgODg5o0aKFTm1TvH0AwMnJSdUWpZHJZGrvhRAlphX3ww8/YNSoUWjYsCEMDQ3Rvn17DBkyBAkJCVrNL27lypUIDw9H9+7dcfXqVVWPUXkKCwvxz3/+ExMmTEDnzp0xdOhQ5OXlQS6XV9o6XkRF2lYXuu53FY2p6JBjLy8v+Pr64qWXXsKGDRvQuXNnvPvuu+jVqxf8/f0RGRmJgwcPIiUlpUQvy4QJE/DHH3+o9bRt3rxZl02masKEhWqsVq1a4a+//sKzZ89QWFgICwsL5OfnIz8/HxYWFnB3d0dSUpLGZcX/d09Xxo+3sbGx2nuZTKY2TVlfYWGhVusWGrrOi1PWtWfPnhI/wAqFAsDz5Ck6OhonTpzAgQMHsHLlSsyePRunT59Go0aNStTp7++PtWvX4vfff4eBgQE8PT3h5+eH2NhYPHr0qNTTQeXR1D7K+IurX78+DA0NcefOHbXpd+/eVSV+pXnppZcQGxuL7OxsZGRkwMnJCSEhIaptLW9+cWPGjIGxsTE2bNgAT09PDBgwAMOHD0ePHj1gYFD62fSVK1fi3r17mD9/PlJTU5Gfn4/Lly+rJbEvuo6KeJG21YUu+11lxmRubg4vLy9cuXIFYWFhJeb36tWrxLSJEydi165dOHr0KFxcXHRaH1U/XsNCNdbevXuRmJgIR0dHbNy4EYmJiWjdujWWL1+OxMRE7N27t9RlmzRpArlcrvZf1bNnzxAXF4eWLVtWadzlrbtJkyYwNjbGqVOnVPMfPXqEP//8U/Xe09MTCoUCqampaNKkidqr6H/pMpkMXbt2RXh4OM6dOwe5XI6oqCiNcSmvY1m+fDn8/Pwgk8ng5+eHmJiYMq9fUZLL5SgoKKhos6jq8PHxKXGNS3R0NLp06aJVHebm5nBycsKjR4+wf/9+9OvXT6f5Ss7Ozpg9ezb+/PNP7N+/HwqFAgMGDIC7uztmzpypMRm+desWPvroI6xevRrm5uZo2rQpFApFqdexVGQdFVUZbastbfe7yowpNzcXly5dgpOTk9r0mJiYEmWFEJgwYQJ27NiBw4cPl5q0krSwh+UFeMzco/qbd4atfu7u7rhz5w7+/vtv9OvXDwYGBrh48SL69+8PZ2fnMpc1NzfH+++/j2nTpqmGQC9ZsgQ5OTkYPXp0lcZd3rotLCwwevRoTJs2DXZ2dnBwcMDs2bPV/uO2tLTE1KlT8cEHH6CwsBDdunVDRkYGTpw4AQsLC4SGhuL06dM4dOgQAgICYG9vj9OnT+PevXulJmTW1tZo27YtNm7ciBUrVgB4nsS89dZbePbsmcb7WRTl4eGB06dPIyUlBRYWFqoLGHUVFhaG4cOHo0OHDvD19cU333yD1NRUjB07VlVm1apViIqKwqFDh1TT9u/fDyEEmjdvjqtXr2LatGlo3rw53nnnHa3ml6VLly7o0qULVqxYgZ07d2LDhg1YunQpzp07p9ZzMmnSJPTt2xdBQc9/D4yMjNCyZUutLrzVdh1KWVlZavd4SU5ORmJiomqf0tRG2rRtefWWR9f9rqKf99SpUxEcHAw3NzfcvXsXCxcuREZGBkJDQ8uNcfz48di8eTN++eUXWFpaqnp4rK2tYWpqWu7ypB9MWKhGi4mJQceOHWFiYoJjx46hYcOG5SYrSp988gkKCwsxfPhwZGZmokOHDti/f3+Z59orS3nr/uyzz5CVlYXXX38dlpaW+Ne//qUayaC0YMEC2NvbIyIiAtevX4eNjQ3at2+PDz/8EMDze4EcPXoUy5cvR0ZGBtzd3fH555+XebvxHj16ICEhQZWc1KtXD56enrh9+3a5PU9Tp05FaGgoPD098eTJEyQnJ1eobUJCQvDgwQPMnz9fdcO+vXv3wt3dXVXm/v37uHbtmtpy6enpmDVrFm7evAlbW1sMGDAAixYtUp2SKm++NkxMTDBo0CAMGjQIt2/fhoWFhWre7t27cfjw4RLXQHl5eWk9Uqi8dRQVFxeHHj16qN4rT4OEhoZi/fr1GttIm7Ytr97y6LrfVfTzvnnzJgYPHoz79++jQYMGePnll3Hq1Cm15UoTGRkJoORN5datW4eRI0eWuzzph0xoc8Jc4jIyMmBtbY309HRYWVlVev1Fe1JKUxN7WJ4+fYrk5GTVHSaJiKhiauvvaVWfSdDl+M1rWIiIiEjymLAQERGR5DFhISIiIsljwkJERESSx4SFiIiIJE8SCcu8efMgk8nUXo6OjvoOi4iIiCRCMvdhadWqFQ4ePKh6b2hoqMdo6pbSbpNORETa4e9o1ZNMwmJkZMRelWoml8thYGCA27dvo0GDBpDL5ZX6EDQiotpOCIG8vDzcu3cPBgYGGh9ySZVDMgnLlStX4OzsDIVCgc6dO2Px4sVo3LixvsOq1QwMDNCoUSOkpaXh9u3b+g6HiKjGMjMzg5ubW6U/tJL+RxIJS+fOnfH999+jWbNm+Pvvv7Fw4UJ06dIFSUlJsLOzK1E+NzcXubm5qvcZGRnVGW6tIpfL4ebmhvz8/Bd+cB0RUV1kaGgIIyMj9lBXMUkkLEWfMeHl5QVfX1+89NJL2LBhg8bHhEdERCA8PLw6Q6zVZDIZjI2NdXqmChERUXWSZN+Vubk5vLy8cOXKFY3zZ82ahfT0dNXrxo0b1RwhERERVSdJ9LAUl5ubi0uXLqF79+4a5ysUCigUimqOioiIiPRFEj0sU6dORWxsLJKTk3H69GkMHDgQGRkZCA0N1XdoREREJAGS6GG5efMmBg8ejPv376NBgwZ4+eWXcerUKbi7u+s7NCIiIpIASSQsW7du1XcIREREJGGSOCVEREREVBYmLERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5TFgqicfMPfCYuUffYRAREdVKTFiIiIhI8piwEBERkeQxYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JCREREkmek7wBqq6IPQkz5JEiPkRAREdV87GEhIiIiyWPCQkRERJLHhIWIiIgkjwkLERERSR4TFiIiIpI8JixEREQkeUxYiIiISPKYsBAREZHkMWEhIiIiyWPCQkRERJLHhIWIiIgkjwkLERERSR4TFiIiIpI8JixEREQkeUxYiIiISPKYsBAREZHkMWEhIiIiyWPCQkRERJLHhIWIiIgkT3IJS0REBGQyGaZMmaLvUIiIiEgiJJWwnD17Ft988w3atGmj71CIiIhIQiSTsGRlZWHo0KFYs2YN6tWrp+9wiIiISEIkk7CMHz8eQUFB6NWrV7llc3NzkZGRofYiIiKi2stI3wEAwNatW5GQkICzZ89qVT4iIgLh4eFVHFXFeMzcU+q0lE+CqjscIiKiWkHvPSw3btzA5MmTsXHjRpiYmGi1zKxZs5Cenq563bhxo4qjJCIiIn3Sew9LfHw87t69Cx8fH9W0goICHD16FKtWrUJubi4MDQ3VllEoFFAoFNUdKhEREemJ3hOWnj174vz582rT3nnnHbRo0QIzZswokawQERFR3aP3hMXS0hKtW7dWm2Zubg47O7sS04mIiKhu0vs1LERERETl0XsPiyYxMTH6DoGIiIgkhD0sREREJHlMWIiIiEjymLAQERGR5DFhISIiIsljwkJERESSx4SFiIiIJI8JCxEREUkeExYiIiKSPCYsREREJHlMWIiIiEjymLAQERGR5DFhISIiIsljwqIHHjP3wGPmHn2HQUREVGMwYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5TFiIiIhI8oz0HUBd4jFzj75DICIiqpHYw0JERESSx4SFiIiIJI8JCxEREUkeExYiIiKSPCYsREREJHkvNEro2bNnuHPnDnJyctCgQQPY2tpWVlxEREREKjr3sGRlZeHrr7+Gv78/rK2t4eHhAU9PTzRo0ADu7u547733cPbs2aqIlYiIiOoonRKWf//73/Dw8MCaNWvw6quvYseOHUhMTMTly5dx8uRJzJ07F/n5+ejduzf69OmDK1euVFXcREREVIfodEroxIkTOHLkCLy8vDTO79SpE0aNGoWvvvoKa9euRWxsLJo2bVopgRIREVHdpVPC8vPPP2tVTqFQYNy4cRUKiIiIiKg4jhIiIiIiyWPCQkRERJJXKQ8/zM/Px+XLl3HhwgXVKyoqqjKqrnOUD0hM+SRIz5EQERFJh84Jy/Xr13H+/Hm15OTPP/9Efn4+5HI5WrZsWepFuUREREQVoVPCMmzYMGzZsgUymQxmZmbIzs5GUFAQPv74Y3h5eaFp06YwNDTUOYjIyEhERkYiJSUFANCqVSt8/PHH6Nu3r851ERERUe2j0zUs27Ztw8qVK5GVlYXbt29jwoQJOHDgAM6ePQt3d/cKJSsA4OLigk8++QRxcXGIi4vDq6++in79+iEpKalC9REREVHtolPCMm3aNIwYMQImJiawsLDAihUrcPz4cRw5cgSenp7Yt29fhYIIDg7GP/7xDzRr1gzNmjXDokWLYGFhgVOnTlWoPiIiIqpddEpYFixYAAsLC7VpPj4+OHPmDKZMmYKQkBAMGTIE9+7dq3BABQUF2Lp1K7Kzs+Hr66uxTG5uLjIyMtReREREVHtVyrBmmUyGyZMn4+LFi8jNzUWLFi10ruP8+fOwsLCAQqHA2LFjERUVBU9PT41lIyIiYG1trXq5urq+6CYQERGRhOmUsKSmppY5v2HDhti+fTu+//57AMCtW7e0rrt58+ZITEzEqVOn8P777yM0NBQXL17UWHbWrFlIT09XvW7cuKH9RhAREVGNo1PC0rFjR7z33ns4c+ZMqWXS09Nx69YttG7dGjt27NC6brlcjiZNmqBDhw6IiIiAt7c3VqxYobGsQqGAlZWV2ouIiIhqL52GNV+6dAmLFy9Gnz59YGxsjA4dOsDZ2RkmJiZ49OgRLl68iKSkJHTo0AGfffbZCw1LFkIgNze3wssTERFR7aFTwmJra4ulS5di4cKF+PXXX3H06FGkpKTgyZMnqF+/PoYOHYrAwEC0bt1apyA+/PBD9O3bF66ursjMzMTWrVsRExNT4VFHREREVLtU6Nb8f//9N4yMjDB48GB06tTphYP4+++/MXz4cKSlpcHa2hpt2rTBvn370Lt37xeum4iIiGo+nROWLVu2IDQ0FPn5+ZDJZGjXrh1+/fVXNGjQoMJBrF27tsLL1hbKZwgRERFRSToPaw4PD8eIESNw9epVHD58GAYGBpg5c2ZVxEZEREQEoIIPP9y/fz/c3d3RuHFj/PDDD2jfvj17SYiIiKjK6NzDkp+fD1NTU9X75s2bo7CwEHfu3KnUwIiIiIiUKnSn2w0bNuDEiRPIysoCABgZGSEnJ6dSAyMiIiJS0vmUULdu3bBw4UJkZmbCwMAAjRo1wtOnT7F27Vr06tULPj4+vJEbERERVSqdE5ajR48CAK5cuYL4+HgkJCQgPj4ekZGRiIiIgIGBAZo2bYpLly5VerC1DUcGERERaadC92EBgKZNm6Jp06YYNGiQalpycjLi4uJw7ty5SgmOiIiICHiBhEWTRo0aoVGjRnjrrbcqs1oiIiKq4yp00S0RERFRdWLCQkRERJLHhIWIiIgkr1KvYaHKU9YIopRPgqoxEiIiIv1jDwsRERFJHhMWIiIikjwmLERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JSy3jM3MOHKhIRUa3DhIWIiIgkjwkLERERSR4TFiIiIpI8JixEREQkeUxYiIiISPL48MMajKOBiIiormAPCxEREUkeExYiIiKSPCYsREREJHlMWIiIiEjymLAQERGR5HGUUA3E0UFERFTXsIeFiIiIJI8JCxEREUkeExYiIiKSPCYsREREJHlMWIiIiEjyOEqoDlGOLkr5JKhK66/KdRARUd3EHhYiIiKSPCYsREREJHlMWIiIiEjymLAQERGR5DFhISIiIsnjKKFaqqznDVX1aCEiIqLKxh4WIiIikjwmLERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JCFeYxc0+Zo5GIiIgqCxMWIiIikjxJJCwRERHo2LEjLC0tYW9vjzfeeAOXL1/Wd1hEREQkEZJIWGJjYzF+/HicOnUK0dHRyM/PR0BAALKzs/UdGhEREUmAJO50u2/fPrX369atg729PeLj4/HKK6/oKSoiIiKSCkn0sBSXnp4OALC1tdVzJERERCQFkuhhKUoIgbCwMHTr1g2tW7fWWCY3Nxe5ubmq9xkZGdUVHhEREemB5BKWCRMm4I8//sBvv/1WapmIiAiEh4dXY1S1ky5DkivzQYm6PHyRD2okIiJAYqeEJk6ciF27duHIkSNwcXEptdysWbOQnp6uet24caMaoyQiIqLqJokeFiEEJk6ciKioKMTExKBRo0ZlllcoFFAoFNUUHREREembJBKW8ePHY/Pmzfjll19gaWmJO3fuAACsra1hamqq5+iIiIhI3yRxSigyMhLp6enw9/eHk5OT6vXjjz/qOzQiIiKSAEn0sAgh9B0CERERSZgkEhaSvqIjijhih4iIqpskTgkRERERlYUJCxEREUkeExYiIiKSPCYsREREJHlMWIiIiEjyOEqIqoU2zy160ZFIVfncIW3q5nOPiIiqDntYiIiISPKYsBAREZHkMWEhIiIiyWPCQkRERJLHhIWIiIgkj6OEqEpUx4iZFx25U3xeZcdcWaOeNC3PEUlEVNewh4WIiIgkjwkLERERSR4TFiIiIpI8JixEREQkeUxYiIiISPI4Soh0ps1zgaqzntqCI3+IiErHHhYiIiKSPCYsREREJHlMWIiIiEjymLAQERGR5DFhISIiIsnjKCF6YWWN9qnoSKDiy73oiKKKjsCR2kgmbdq6OkcZ6Xtkk77XT0TVhz0sREREJHlMWIiIiEjymLAQERGR5DFhISIiIsljwkJERESSx1FCVOPpMqJI07zKGoGkS9mio1qqeiRS0fqV6y0eh6YyL7q+surh6B4i0hV7WIiIiEjymLAQERGR5DFhISIiIsljwkJERESSx4SFiIiIJI8JCxEREUkehzUTVYCuQ5Gr8yGKZQ0Z1iYObYY8V/b26DIUuirWq1RWm+kyBLysMpU1pLsyh6IT1QTsYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjyOEiIqRteHJ0p1HS+qIg91rKz6KkNteMAiRwIR/Q97WIiIiEjymLAQERGR5DFhISIiIsljwkJERESSx4SFiIiIJI+jhIioSlV0RJQ+nlekb1UZY03YfqKysIeFiIiIJE8SCcvRo0cRHBwMZ2dnyGQy7Ny5U98hERERkYRIImHJzs6Gt7c3Vq1ape9QiIiISIIkcQ1L37590bdvX32HQURERBIliYRFV7m5ucjNzVW9z8jI0GM0REREVNVqZMISERGB8PBwfYdBpFFVPDOnqp7DI5XnFim9aDyali8+rSqfe6TN+qsSRwJRbSaJa1h0NWvWLKSnp6teN27c0HdIREREVIVqZA+LQqGAQqHQdxhERERUTWpkDwsRERHVLZLoYcnKysLVq1dV75OTk5GYmAhbW1u4ubnpMTIiIiKSAkkkLHFxcejRo4fqfVhYGAAgNDQU69ev11NUREREJBWSSFj8/f0hhNB3GES1ir5HK+ljdExV1qPvEVW6jACq6GghjjIiKeM1LERERCR5TFiIiIhI8piwEBERkeQxYSEiIiLJY8JCREREkieJUUJEVDH6HrlS11XVqJrKGq1U0ecmFZ9WdPs4koj0hT0sREREJHlMWIiIiEjymLAQERGR5DFhISIiIsljwkJERESSx4SFiIiIJI/DmomI9Ky2DU/n0GeqCuxhISIiIsljwkJERESSx4SFiIiIJI8JCxEREUkeExYiIiKSPI4SIiJ6QRUZ5VOZI4P0McqII4GourGHhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5TFiIiIhI8jhKiIioDqns0T1FRyhxxBBVJfawEBERkeQxYSEiIiLJY8JCREREkseEhYiIiCSPCQsRERFJHkcJERHVQfp4/hDRi2APCxEREUkeExYiIiKSPCYsREREJHlMWIiIiEjymLAQERGR5HGUEBERlYkjikgK2MNCREREkseEhYiIiCSPCQsRERFJHhMWIiIikjwmLERERCR5HCVERESVgqOJqCqxh4WIiIgkjwkLERERSR4TFiIiIpI8JixEREQkeUxYiIiISPKYsBAREZHkMWEhIqIq4TFzD4c6U6WRTMKyevVqNGrUCCYmJvDx8cGxY8f0HRIRERFJhCQSlh9//BFTpkzB7Nmzce7cOXTv3h19+/ZFamqqvkMjIiIiCZBEwrJs2TKMHj0a7777Llq2bInly5fD1dUVkZGR+g6NiIiIJEDvCUteXh7i4+MREBCgNj0gIAAnTpzQU1REREQkJXp/ltD9+/dRUFAABwcHtekODg64c+eOxmVyc3ORm5urep+eng4AyMjIqJIYC3NzqqReIqK6oKp+m6nqFT3+VcXnqKxTCFFuWb0nLEoymUztvRCixDSliIgIhIeHl5ju6upaJbEREVHFWS/XdwRUGaryc8zMzIS1tXWZZfSesNSvXx+GhoYlelPu3r1botdFadasWQgLC1O9LywsxMOHD2FnZ1dqklNRGRkZcHV1xY0bN2BlZVWpddP/sJ2rB9u5erCdqwfbufpUVVsLIZCZmQlnZ+dyy+o9YZHL5fDx8UF0dDTefPNN1fTo6Gj069dP4zIKhQIKhUJtmo2NTVWGCSsrK34hqgHbuXqwnasH27l6sJ2rT1W0dXk9K0p6T1gAICwsDMOHD0eHDh3g6+uLb775BqmpqRg7dqy+QyMiIiIJkETCEhISggcPHmD+/PlIS0tD69atsXfvXri7u+s7NCIiIpIASSQsADBu3DiMGzdO32GUoFAoMHfu3BKnoKhysZ2rB9u5erCdqwfbufpIoa1lQpuxRERERER6pPcbxxERERGVhwkLERERSR4TFiIiIpI8JixEREQkeUxYAKxevRqNGjWCiYkJfHx8cOzYsTLLx8bGwsfHByYmJmjcuDG++uqraoq0ZtOlnXfs2IHevXujQYMGsLKygq+vL/bv31+N0dZcuu7PSsePH4eRkRHatm1btQHWErq2c25uLmbPng13d3coFAq89NJL+O6776op2ppL13betGkTvL29YWZmBicnJ7zzzjt48OBBNUVbMx09ehTBwcFwdnaGTCbDzp07y11GL8dBUcdt3bpVGBsbizVr1oiLFy+KyZMnC3Nzc/HXX39pLH/9+nVhZmYmJk+eLC5evCjWrFkjjI2NxbZt26o58ppF13aePHmy+PTTT8WZM2fEn3/+KWbNmiWMjY1FQkJCNUdes+jazkqPHz8WjRs3FgEBAcLb27t6gq3BKtLOr7/+uujcubOIjo4WycnJ4vTp0+L48ePVGHXNo2s7Hzt2TBgYGIgVK1aI69evi2PHjolWrVqJN954o5ojr1n27t0rZs+eLbZv3y4AiKioqDLL6+s4WOcTlk6dOomxY8eqTWvRooWYOXOmxvLTp08XLVq0UJv2z3/+U7z88stVFmNtoGs7a+Lp6SnCw8MrO7RapaLtHBISIubMmSPmzp3LhEULurbzr7/+KqytrcWDBw+qI7xaQ9d2/uyzz0Tjxo3Vpn3xxRfCxcWlymKsbbRJWPR1HKzTp4Ty8vIQHx+PgIAAtekBAQE4ceKExmVOnjxZonxgYCDi4uLw7NmzKou1JqtIOxdXWFiIzMxM2NraVkWItUJF23ndunW4du0a5s6dW9Uh1goVaeddu3ahQ4cOWLJkCRo2bIhmzZph6tSpePLkSXWEXCNVpJ27dOmCmzdvYu/evRBC4O+//8a2bdsQFBRUHSHXGfo6DkrmTrf6cP/+fRQUFJR4KrSDg0OJp0cr3blzR2P5/Px83L9/H05OTlUWb01VkXYu7vPPP0d2djbefvvtqgixVqhIO1+5cgUzZ87EsWPHYGRUp38OtFaRdr5+/Tp+++03mJiYICoqCvfv38e4cePw8OFDXsdSioq0c5cuXbBp0yaEhITg6dOnyM/Px+uvv46VK1dWR8h1hr6Og3W6h0VJJpOpvRdClJhWXnlN00mdru2stGXLFsybNw8//vgj7O3tqyq8WkPbdi4oKMCQIUMQHh6OZs2aVVd4tYYu+3NhYSFkMhk2bdqETp064R//+AeWLVuG9evXs5elHLq088WLFzFp0iR8/PHHiI+Px759+5CcnMwH6VYBfRwH6/S/VPXr14ehoWGJbP3u3bslskclR0dHjeWNjIxgZ2dXZbHWZBVpZ6Uff/wRo0ePxs8//4xevXpVZZg1nq7tnJmZibi4OJw7dw4TJkwA8PzAKoSAkZERDhw4gFdffbVaYq9JKrI/Ozk5oWHDhrC2tlZNa9myJYQQuHnzJpo2bVqlMddEFWnniIgIdO3aFdOmTQMAtGnTBubm5ujevTsWLlzIHvBKoq/jYJ3uYZHL5fDx8UF0dLTa9OjoaHTp0kXjMr6+viXKHzhwAB06dICxsXGVxVqTVaSdgec9KyNHjsTmzZt5DloLurazlZUVzp8/j8TERNVr7NixaN68ORITE9G5c+fqCr1Gqcj+3LVrV9y+fRtZWVmqaX/++ScMDAzg4uJSpfHWVBVp55ycHBgYqB/WDA0NAfyvB4BenN6Og1V6SW8NoBw2t3btWnHx4kUxZcoUYW5uLlJSUoQQQsycOVMMHz5cVV45nOuDDz4QFy9eFGvXruWwZi3o2s6bN28WRkZG4ssvvxRpaWmq1+PHj/W1CTWCru1cHEcJaUfXds7MzBQuLi5i4MCBIikpScTGxoqmTZuKd999V1+bUCPo2s7r1q0TRkZGYvXq1eLatWvit99+Ex06dBCdOnXS1ybUCJmZmeLcuXPi3LlzAoBYtmyZOHfunGr4uFSOg3U+YRFCiC+//FK4u7sLuVwu2rdvL2JjY1XzQkNDhZ+fn1r5mJgY0a5dOyGXy4WHh4eIjIys5ohrJl3a2c/PTwAo8QoNDa3+wGsYXffnopiwaE/Xdr506ZLo1auXMDU1FS4uLiIsLEzk5ORUc9Q1j67t/MUXXwhPT09hamoqnJycxNChQ8XNmzerOeqa5ciRI2X+3krlOCgTgv1kREREJG11+hoWIiIiqhmYsBAREZHkMWEhIiIiyWPCQkRERJLHhIWIiIgkjwkLERERSR4TFiIiIpI8JixEREQkeUxYiEiy5syZA4VCgSFDhug7FCLSM97plogkKyMjAz/88AMmTJiAK1euoEmTJvoOiYj0hD0sRCRZVlZWGDVqFAwMDHD+/Hl9h0NEesSEhYgkLT8/H2ZmZrhw4YK+QyEiPWLCQkSSNmfOHGRlZTFhIarjeA0LEUlWfHw8unTpgt69eyM5ORlJSUn6DomI9IQJCxFJUmFhITp16gQ/Pz907twZQ4cORXZ2NuRyub5DIyI94CkhIpKklStX4t69e5g/fz68vLyQn5+Py5cv6zssItITJixEJDm3bt3CRx99hNWrV8Pc3BxNmzaFQqHgdSxEdRgTFiKSnEmTJqFv374ICgoCABgZGaFly5ZMWIjqMCN9B0BEVNTu3btx+PBhXLp0SW26l5cXExaiOowX3RIREZHk8ZQQERERSR4TFiIiIpI8JixEREQkeUxYiIiISPKYsBAREZHkMWEhIiIiyWPCQkRERJLHhIWIiIgkjwkLERERSR4TFiIiIpI8JixEREQkeUxYiIiISPL+D5Lysy7f4+KBAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "modes_one = round(len([i for i in eigenvals_0D if 0.99<i<1.01])/10/2**L,2)\n",
    "plt.hist(eigenvals_0D, \n",
    "         bins=np.linspace(0,1,200), \n",
    "         weights=np.ones_like(eigenvals_0D)/10, \n",
    "         label='RMT CUE result for $N=2^L$, 10 realizations\\n# of modes with $0.99<\\lambda<1.01$ is %s*$2^L$' % modes_one \n",
    "        )\n",
    "plt.ylim(0,6)\n",
    "plt.title('Eigenvalue distribution, L=%s qubits, b=%s' % (L,b))\n",
    "plt.legend()\n",
    "plt.xlabel(r'$\\lambda$')\n",
    "plt.ylabel(r'$P(\\lambda)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be7a5386-9c8d-44fa-9e05-2d7bcd42227b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}