{ "cells": [ { "cell_type": "markdown", "id": "3ea00c2e", "metadata": {}, "source": [ "# Trotter-Suzuki decomposition of $U(t)$\n", "\n", "In this notebook we introduce the Trotter-Suzuki decomposition to approximate the time-evolution operator $U(t) = \\exp(-i H t)$ for a Hamiltonian $H$. We study the error and cost of the approximation.\n", "We take the nearest-neighbor 1D Heisenberg Hamiltonian to illustrate the method. We consider first and second order Trotter-Suzuki formulas.\n", "\n", "## Introduction\n", "\n", "We start by introducing the general idea of Trotterization. We would like to compute the exponentiation of an operator $H$. For small systems, it can be performed exactly by $\\texttt{quimb}$ or $\\texttt{scipy}$ linear algebra methods. In the $\\texttt{qpe-toolbox}$, the method `get_U_exact` of the `Hamiltonian` class returns the quantum gate implementing the exact time evolution using $\\texttt{quimb}$'s `expm` matrix exponentiation routine. For larger systems however, computing the exact exponential is too expensive and we need to use approximations such as Trotterization.\n", "\n", "Let us decompose the operator as $H = A + B$. In practice, we decompose the Hamiltonian into a sum of operators whose exponentiation can be easily implemented, e.g. Pauli strings. When $A$ and $B$ commute, as for scalar numbers, the exponential of the sum is the product of exponentials:\n", "\n", "$$ e^{A+B} = e^A e^B, $$\n", "but in general $A$ and $B$ do not commute, hence the previous expression does not hold.\n", "Trotterization provides an approximation of the exponential of a sum based on the [Baker-Campbell-Hausdorff formula](https://en.wikipedia.org/wiki/Baker%E2%80%93Campbell%E2%80%93Hausdorff_formula).\n", "\n", "The Trotter product formula gives the following expression:\n", "\n", "$$ e^{A+B} = \\lim_{r \\to \\infty} \\left( e^{\\frac{A}{r}} e^{\\frac{B}{r}} \\right)^r. $$" ] }, { "cell_type": "code", "execution_count": 1, "id": "de8825f3", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:06:17.249281Z", "iopub.status.busy": "2026-04-03T04:06:17.249107Z", "iopub.status.idle": "2026-04-03T04:06:19.085604Z", "shell.execute_reply": "2026-04-03T04:06:19.084795Z" } }, "outputs": [], "source": [ "import time\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import quimb as qu\n", "import quimb.tensor as qtn\n", "from tqdm import notebook as tqdm\n", "\n", "from qpe_toolbox.hamiltonian import heisenberg_hamiltonian" ] }, { "cell_type": "code", "execution_count": 2, "id": "dbd8afd7", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:06:19.087409Z", "iopub.status.busy": "2026-04-03T04:06:19.087051Z", "iopub.status.idle": "2026-04-03T04:06:19.089915Z", "shell.execute_reply": "2026-04-03T04:06:19.089334Z" } }, "outputs": [], "source": [ "plt.rcParams.update({\"font.size\": 12})" ] }, { "cell_type": "markdown", "id": "4a6c87c5", "metadata": { "lines_to_next_cell": 2 }, "source": [ "Now consider a general Hamiltonian, written as a sum of generally non-commuting terms:\n", "\n", "$$ H = \\sum_{\\ell=1}^L H_\\ell. $$\n", "In this example, we take a 1D Heisenberg Hamiltonian with $n=4$ spins and open boundary conditions.\n", "We want to compute the time-evolution operator $U(t) = \\exp(-iHt)$. Let us split the time interval into $r$ timesteps of size $t/r$." ] }, { "cell_type": "code", "execution_count": 3, "id": "427938b7", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:06:19.091474Z", "iopub.status.busy": "2026-04-03T04:06:19.091331Z", "iopub.status.idle": "2026-04-03T04:06:19.093928Z", "shell.execute_reply": "2026-04-03T04:06:19.093180Z" } }, "outputs": [], "source": [ "n_qubits = 4\n", "h_spin = heisenberg_hamiltonian(n_qubits)\n", "qubit_reg = list(range(n_qubits))" ] }, { "cell_type": "markdown", "id": "c2699255", "metadata": {}, "source": [ "### First-order Trotter-Suzuki formula\n", "The Trotter-Suzuki decompositions give approximations of $U$ with increasing precision. The first-order Trotter-Suzuki decomposition is given by:\n", "\n", "$$ e^{-i H \\frac{t}{r}} = e^{-i H_1 \\frac{t}{r}} \\dots e^{-i H_L \\frac{t}{r}} + \\mathcal{O} \\left(\\left(\\frac{t}{r}\\right)^2 \\right). $$\n", "Along the full time evolution $t$ errors accumulate:\n", "\n", "$$ e^{-i H t} = \\left( e^{-i H_1 \\frac{t}{r}} \\dots e^{-iH_L \\frac{t}{r}} \\right)^r + \\mathcal{O} \\left(\\frac{t^2}{r}\\right), $$\n", "so that the error is linear in the timestep $\\delta t \\equiv t/r$.\n", "\n", "### Second-order Trotter-Suzuki formula\n", "Higher order decompositions can be obtained recursively. Here we go up to the second order Trotter-Suzuki decomposition:\n", "\n", "$$ e^{-i H \\frac{t}{r}} = e^{-i H_1 \\frac{t}{2r}} \\dots e^{-i H_{L-1} \\frac{t}{2r}} e^{-i H_L \\frac{t}{r}} e^{-i H_{L-1} \\frac{t}{2r}} \\dots e^{-i H_1 \\frac{t}{2r}} + \\mathcal{O} \\left(\\left(\\frac{t}{r}\\right)^3 \\right), $$\n", "which gives:\n", "\n", "$$ e^{-i H t} = \\left( e^{-i H_1 \\frac{t}{2r}} \\dots e^{-i H_{L-1} \\frac{t}{2r}} e^{-i H_L \\frac{t}{r}} e^{-i H_{L-1} \\frac{t}{2r}} \\dots e^{-i H_1 \\frac{t}{2r}} \\right)^r + \\mathcal{O} \\left(\\frac{t^3}{r^2} \\right). $$\n", "\n", "The error is now quadratic in $\\delta t$.\n", "\n", "In $\\texttt{qpe-toolbox}$, first- and second-order Trotterization are implemented by the `get_trotter_step` method of the `Hamiltonian` class.\n", "\n", "Below, we visualize the circuits for one timestep:" ] }, { "cell_type": "code", "execution_count": 4, "id": "e7b2d8f7", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:06:19.095347Z", "iopub.status.busy": "2026-04-03T04:06:19.095165Z", "iopub.status.idle": "2026-04-03T04:06:19.700841Z", "shell.execute_reply": "2026-04-03T04:06:19.700142Z" } }, "outputs": [ { "data": { "image/png": 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6gIuamxrXZlm/BrujyJfHZ3h7RgUsFOUgt27NEm3dmiXHrluzZNG6NUumDf8MRVGU/Us8JKYBn8h3Exgq1VcIKPRQAETiIaGyTyeHJV49+zzyfj4XU0zh/mA4Et2rc1oBfw64OabAQ8DlbEkIOyhS5KHQo3OhgO/szT4GcoIUy0vvWNuGEO0Isb30jrWvlDa0fb60oc03VvtRFGVE8sH+mx+NAesXjOlo9tx/gfOBUiCGPdVj61ArLlu+IgiEgG83NzW+PW4j3AN7/KHs9Hpd2NzU2OP8+93A77DbTXUDn25uatxnhZBa64QOlGqCiJQcA0gED0lJ9aIK+di+2q+iHCjWrVmiC0GFEHxF14VHCKRpSvf6p5c8Zkm+umDx6raJHqOiKMoYWeZz4c11MqoJcGu40hZnA/8cr4EpQ7MQHpAjCkJsCcw7G/h2OBJNYHd96V/6Bv174JKsqa6SAPGQmK8JTvHruIfavhCQ7yZ/u8kX4yFxfTAmM3tzbKUNbS6EuFtzuc90+/MLNJe9W8s0Co1k30/MdPJzpQ1tS1rKSrr2Zj+KooxYD8BoJ3UMWL97TEez57Y2NzX+E2DZ8hX3YncDuX3Z8hWLmpsad7SDXrZ8hY7dPeRp4JcTMtJRGMu7CC8ApzY3NaaXLV9xIfBD4JIx3P4OrXUiIAT/dOucmOej0O0k0aUylPYkCT5zg7hNSiomyVwiRZl0nGBFi9ejBQsKXHm6bp/FSylJpa0LuzqN09atWVK6YPHqhyZ4qIqiKHtNwOG6YNi71rqGF4tZ4zEmZXfhSNSHnV597KyZoVPfs+XPogAz53MyFt1uM/Fn4CHszi/9SwA7zbv/34ODH1Y4Eu0F+k7zH/2+IzMvFYwgoKWlLc4C9m6utxA/1D3es9yBwryB1f003YUnrzCQ0fQFRrL3j8AH92o/iqKM1DZgQzLDPJ9n5NNCkhkk8DKwfZ+NbA81NzVay5aviAL3AsuAPw34cTmwEDijuakx95vsJLDXAYtly1eUYGdWXDwgnWQqDH9isKeE4A8BDyfn+3fdh88DXjdFHb1cmTFYD/xiX41BUfZzX/R6tKVFRa5dTpaEEPi8Oq6ponjb9sxf1q1ZcviCxauTEzhORVGUvWYhtlhSZmDoO+g71pNkgPbxGdX+Lx4SOvB+AVcIKJLwooRfBmPy+ZE8PxyJCuygwrHAMcBc7MDCO2/nH3+v3Gx9KGNxjDtLnoUlIW2SnmZurK+prspa3d7Zj49dAxr9QY08r9Wbp4vstTL6CSF864vPvOzuSHQ+kMDO4EgM832qP5MDoLShzY8QV7kDBXnZWhG4fAGPmep7b2lD2+EtZSWvDzcuRVH2zqIKKVvrxI2pDLWmNbLCm6YFKTvX6ueT+Cb534H1wNdxAhbLlq+YBnwXuLm5qfG/Ezi2EdvbgMU84FZg2dyjFrwTuvTy90pp/R57HtB5I9lAPCTygI8AR2CfJLQEY/KtbOu31okjNMHZeb6hAyJOm5nCbd18s7VO/GpRhbSGWi/LWIqAQ4COYEwOOd9HUfZ369YsEULw1YICV37WkyWXhs+reRNJKwTcPr4jVBRFGVprnVggBFcLOErCO1Ly+0UV8ols64cj0QLg3cWHfXrqkrduNQMu053tLrpz8WsB/9o3oz+wxEPiBAH3uTUKfC6KNcCQnJswuGxVSKyWEArGZGLw88KRqI4dmDjWWaZiF317Bfvk+sWa6qpOex8rr+xK8bciuyjqLiwJHSm6JHw5GJM5W/E5AYP+AMJu53fx0MrjTBfnAp5c2zElaeB/wDuAHygCZjnfB2DIoIflTFVJAH1TZixc0DV7oUvkqN8phED3+vONRO8y7Cr/iqLse7cB13f14S/Oy10/R0ro6sPC/ruetOfJzU2NctnyFb8E6pYtX3FBc1PjA8BKoBh4dtnyFZcP8bT/NTc1/m8chzmsvQ1Y3AM0Njc1vhyORE8/4shjzgOqt7zz5mGJZN9Xw5HoVQOjygPFQ0II+J6AL3h13C6NPEuSThr8cFVIxCWUBWNyqLl7lwW85Of6T6Rr4NLxZAxOBx4Z7iDiIfEeAdUC3q0LDEviWhUSL0v4VjAm/zayl2J3pQ1thwAnO/98pqWs5J093ZaijKG5uib8/dNAsvH79YJU2rqMSfxGrCjKwaG1TuQJwZ26xmkBL4W6hmZJZF+KS5+5QWyUkosWVci3w5GoG3gX0AG8GzgOMDp8cx6XiP8kDM4JuPEO3r6U0J0RSUtovz/7T4bKKhtGPCTmCIgXeZjuHnCJ7gbNp1Pca3Be0uCueEhcGIxJGY5E87AzKI7FnvLhBbqAF4H7gFdqqqt2qwsRjMlH4iFxSUeKJreGx6tTJASkTXpSJhkJXw3G5Fh8RjUmDL4TcOHJdn5pSjAt2XdMx+obr77pod1uhjlZHG52Bi/8Q31v6p58oek5M30AhKa7gBlD7SNXNomiKHtmUYXsaK0TH0sb3NvRi1UYQBsq08K07GBF2kAClyyqkB3jPdZRuhW7NfPXgAeAEkAAN2RZP4odmJ00hNzDDBan6OZVwK+AD889asGr2C/AMcBRG1998ZtHHHlsFfCSs2yoqa7aEWlfFRK/cWtcWuhhlzmDUkLCIN1n8KKE9wyOzj9zg6gv9PM5X84YOHT20t2V8n06tuUbfwYOBbYM9QYfD4llmuDmAjdFbs3O0JASDAndabosSc3SmPzeaF6b0oa2OQhRD+Is3e22QAgzkxYgH0XK8paykldHsz1FGUvr1iw53u0SD02b5snZESSTsWjvyDx0zKLVS8drbIqiKIO11gldCFYHvJyc5929cGYyjdmVYOMriRNPXd25bDnwAWAt8DrwBPBMTXVVMh4S+QIe8ugcE3CR59J2ft73Zuhud01/I37YZ2+0NPfvB56vTFaittyHnZ3QLSvrx7Xg26qQ+HWem6v9rqGnUUgJ7Sk6Xig66xsvTDvXBA5zfvQmdpDiReCdbDe1BnM6t1ws4CLAJWE10DRUBseeWhUSt3l1Pj5UJxkpoSNNl2kRXhqTN+/Nfkob2t6nuT1/9hZMmZJrvUxvVzpv09r7Zr79zF+xX7cpwGygEPjRaIIW8ZCYDlyj2TUxdAmPSvh5MCZf2YtDUZRJ4aabbgoAxwPPX3PNNX17u73WOnEhcCcQ8Lrt1qX914fJDNKZBtKHHax4YG/3d7Aaze9tbzMsHsfuWf7b115ZdxXwbHNT45OhSy9bKqV8C3gGO4CxCJDhSPQN4KV3v/0n9+GCTwwOVoAdMAi48ZiS+UmTz4Uj0d8AhzvLnLOKTjj6BO9zJkOn3e2QsXTtqe4LPwh8HDuK9JdwJPpfYFNNdVUSIB4Shwm4qdhL0cCbzUKAW8AUL4XtKb4SD4kHgzG5eiQvSGlD21yE+K87UDBD9/hEf8q9lBIznbow09f1eGlD2xktZSUbRrI9RdkH3jBM6ZJSkm1KCEAmI00pUZ1CFEWZaBe6dY7P9+2eGQHg86CnDWZbffrt2Hft+4ANwM0DL4iDMdkTD4nTUyaXp02+Acx0frRBwvcfPvRTD1ua+5PAJ8OR6O2TNWghassXIogiOA8hDKR0ibry55B8R1bW/2Nf7z8eEm4Bn/Dp2c/DhIA8N8UzE+u/8ALnfh94ElhfU13VO5p9tdYJN1BafCYXAJqUrAKaF1XIMc+CkfCZlMlMQ3JGnotCt2a3vUubyF6DLin5xd4GKxxxy8hkpGUitKFfQiklRjqZLOh645fYgYoPYGfsdmJnDgfDkehrwMb+c9qsOwuJqwT8zO/C69HxCSBj8e4+gytXhcStEr4SjE3a+feKMu4WVcj7W+vEHOCTqQzXpjLMH/Djl4GfA7ctqpCdEzPCg8/eZlgsbG5q7Fm2fMUfsKPly4EMkAa+2NzU+BhAOBItBI52lvlnvfnb5XPMN0r8ruxVWE0LtmTcHX876pv96SrdwOtH+58y31t09y3TC+20wGzP3dbFlqbN37ggI32XY6cfPs3OCtHbgLfO2fiLD8+QW5fnubMX4UqZ0J3m/qUxedFIXpfSO9Y+4skrPE33+IacnGimUzLd2/l0y+UL3z2S7SnKvvDi00vuLCx0fdTvG3peiJSSrdvSHabJ6QsWr1433uNTFEXp978bxKqiPM7y5LjFYlqwuUvf3PjOt4/BPgfJ1FRX5ax8Hg/ZZxEDL9bCkehM4ArswMftNdVVe323biyJ2vLzESKG31OEWxc70kJNC/pSXUj5Y1lRf32254cj0SOAuTXVVaPqABWORF1AAVBweNfTRy7e2tIyzSeLcj3HtKA9xXNLY/LE0eyrX2uduEAI7vC48PjcFAGkDLpTGQwp+eKiCtm4J9sdSjwkjgIOl4ju56ae/6mjux45y2f0zAZM4F8SfhyMybVjtb/SO9Z+QdNdP/AUTCkcfONASkmmt6vXzKRub7l84edhR92Pq4GTgKew558XYMdU3gFec5aNNdVVPQOO6yO64PfFXoq0IbJGutJ0Zyzqlsbkd8bq2BRlvI11hsVArXVCYGeyFWBfi26fxAU29yuj+b3tccBiT4UjUf3il6Mbpnrl3GGm0LMlKXrih13zvi7v7PVAZ/+dkmduEH/L8/K+vCHutkgJHb10ZwyiJ1XIn4YjUQ+wAHgO+z/cof3L+1+p/skMT2pKrnFICVuT9Nw9f+U8dgZjMoAxOJWxtKFtvtD0J71F04pz3blOdmztkJb53paykhFV0VaUsbZuzZJjheDRqVPcU92Dyq9LKenqNnqTSeueY09evXyChqgoigLAMzeItw8pZGau2lUAmzvplpKivT2ZDEeiM7CDFt1MoqCFqC2fjuBF8v1ThixhLyV0JzqxZKmsrF81+MfhSHQx9pSAl2qqq/7oPKZhd8sowJ5qUJBlCfRvx5/p8J33+o3XHuIz/bnGa1jwtln41gNzv/wTYPOgZWtNdZWR7bmtdSKoCe6akk+Ra1ASgmlBew9dpsVnFlXIWK4xDCceEmcLqBOCuS6BZYFI4fGkNf8NfqPz28HYyAu3j0ZpQ5tAiGohtM+5/HkFuturIcDKpMkkejukZf4bKT/RUlay4zVy6rNcjD23fAN20GLugGWqs+pW4DUhzdcufvl7dxd7OWJwwdJ+UsK2JJ0SDg/G5LhOK1KUsbIvAxbKvjOpAxYAq0Ji/RQfRw8XsNiaoFPCrGBs19S/1jqRLwSrPC6OyfOS73bZb7ppA3qSdJoWf5aSzwx30rIqJN6e5hvBSVBST9171Dd/JIU2cHsSO3DRv6Tfnr34PX2zT7jUHSjIWWEjk+gxjERvRUtZyS9z71lR9p11a5acIgT3eD2a3+/XC4UAw5Bmb5/RbVn8XUquWLB49W5F0BRFUcbTMzeI16cXMEfL0WZOStjSSfdJFbJwLPY5IGjRA9xWU13VFw8JNxDE7ia2FfhPMCbH7T1S1Jb/H173t/F7sreNzxjQl/rnV96ZdQF2kcf+gMMFwKnARmAddje3AufrwLMgCztQM9TS1f996YaVrcVeFmS7EAboyZB4R5tRHz/88/dhF4+cgd1Vo38/29k1iPEO0H75zJVSCNZPyWe+O8ukE9OCbd1slpJDF1XInJk02cRD4lJNUF/osWuY7di2hJ40PRmLByQs21dBC4DShraFCPFV4BxAB/EU0voh8GhLWcmoTtCdbOYjcAIYh/asXXTqlr+umOY183I9rydNX8LkumBM/nZPj0NRJpIKWOyfxrOGxZ56MG1yVLZiTWBH5oHtg4MVAIsqZE9rnTg9lWFZ2iCCZA4Agqek5HrgwRHeYXnNkMx05whYWBKENLuk0G7Brv7sxm57tdv3psuzEHL0qdpB6K5MYqpT7RnslljtI5iHOAX4tIBrsD/0t0r4BdAQjMmeXM/NpbVOFDrba19UsefbUfYvCxavfnLdmiWHb+twX5re4vm/wvy+rS7dfFJKblyweLWqsaIoymTxt2SaTwd82c8ZMgYIwTNjtcOa6qrN4Uj0NuAKpHXFvz/hmeaC69waui7wmJJMxsJcFRJ1Eq4flxoAgjI8ruzBCgCXjibFWRby29rO8xEdOB27dehm7Omxm7Cn8g4OSPSNpBBmPLTyez0Z6ouGqEUGdkAhaZAqZPP3aqqrOvofD0eiPuyAz4wBy3vYmcFhPNpZGlgy5e5D3Hr2YegaeFx4Uxnej92xrj9b5HjsaRE5swXiIXGIgF9NGWKqhC6g0EN+V5rz0xaXAQ05X4y90FJWshY7MLbXaqqrurCLza4F+MfywGUeYV463PNcGgFhctxYjGEgZ8qVHzCGazurKIqSy4QELCT8tM8g5NOz16HoM+iV8ONs21hUIdPAH5xlT8fxk4TBLW4PWe/IJAzSAn5TU121cbjtlTa09WpGejl2gaTs+00n+6ZtXXc0douZOdjTTGLhSPSfOdrAvkfAvT4XeX4dvybAlMxIGPwkZfKdeEicE4zJF4Yb40CtdeIcTfA9TbBQ2O1c3c/cIB6Vkm/n6muvHDgWLF6dCUeiTwJ/A75fU121faLHpCiK0i8ciRYe4V32wlnFf8n4vKY++OISnJkQSTotyffHct811VWbv/71b/7+jE233+PVjJIit/3Z28+yu4l9LWNxbDwkrtjboIVzE8PPzqkZhQOWAvcMMSMzXEqoEEhBplM3H5xiurayMxihAWdhF0E/BPh7TXXVtr0YbqNh8cGuNBfnu8nvn6EiJWQs6E7T6bSn7xj4JOfGzOvOMvDY83ACGLO9Gy71uOWQBVYH8rgoeqNvzsfCkWg39uv1XuzX6i/hSHQ9kBqwpGuqq3ZkSgj4nN+16+9zIKdoaEEmxTcZg4BFaUObD/t329VSVrJHGSGj5bESHVJn2H1ZIDflHXdiOBK9FHgLuyPJptEWSO0XD4kiAV90Fr8EsSokNkr7nDemCnwqijJaExKwCMbkulUh8evONJ8v9FAw8ANDSugxSHWKwm2Pz1l+V3DfDuWutMn3EgYBv2v31yJtQsJgu7SrwY7Eass0eizTmGK3z96dZRqYltlV0LlxJbAY+24AwJnAyeFI9FXgFeBV7DmeMh4Shwr4W7GXaQPTL10CCjzkeU3yutI8GA+JBcGY7BrJQJ+pE9fqGt8tDFDk1ne2c00bXNjVx+mtdeKavZ0bquwfDOS5LsTJDNN5R1EUZbw4F++LgAs3pk40uoz/1Lq6t3yhOI/CgTUNTAu6+ugyLZqw+8uPqQ+88oPjdcGCYi/+wbECzb4TX9CRotSQnAv8M8fx6NjTLwYHIwZ/P/DkQWJPSekCunQpNmUsaypZOkvYz5BIKdO/m7Z1taysH3xh2BKORB8GTnG2vceCMSnjIXFZ2uKz7Sn+TxPkaQJpWugS/ifhq8GYfHyk23Mujl8BXmmtWzlfSK6GobvC9JMS2WcWFjvHUwIciZ05stRZdhGORNM4AYyL9MBnivW+nNt3aSBgVjwkCkd6bjVYaUNbKUJUIcTRQghTSilK71jbiJTVLWUlb+zJNkchnjaRUtrneNkkDLq2Fc79M/b/vdOxAyuEI9EO7ADGjmUEmcCzBDzqczE74MLbf36fsVjYm+FmwyIUD4l9Os1GUZQDz4TUsAA7VUzAtcC33Boul0bAkqRTJqYltLvunxt+MqMHvMDva6qrtu7DcUwX8C+XxuF+F1N0Yd81SRh0Ziy6JJwXjMkXR7q90oa284WmNXsKphZp+q4nFdIySXW1d0rL/GRLWUkLQDgSXQgswT7ROhI4CrtfuYZ9ovLquRtvuHi6bL80VzcTZw7iN4IxeeNwY2ytE4t1jX9PLdg9FRLsE8Dt3XRYkkWLKuRrIz12Zf8hasuPRvANJB8TCLcGLlPIO5FcLyvrn5vo8SmKcvAKR6LF2MUF5wOtwP011VWJ1jrxYSH4kSY4xKXbn1WmRZ+0Mytu2heV21eFxN8LPFzkzREjSJvQmdEeunved64kezAij11rRWTYOQ2jK8v3PbtkBdSWfxS3fit5vuzdOVIZg2T6l7KivmLUB7uHnNT/o7GP941gTG7em+211ok5mqBteiHFuS60t3XRblicu6hCPu0EhM7HPp+6A7s+hnfQ4un//gOv/OC3h7jThw9Vu3SgrUmt++HZZZdv8x/1InaNjY6RTJlximr+Qmiuyz15BYVCdyGEQEoLM5U0MomeDqQ8x5kSss/8a7nvjgIttSzfzZC11VImVneap5fG5CmwI1BYjH0e2l+kfjY7g0fb2DWIsammumrHdI9VIfFUvpuTfENM+ZYSujP0pE1+tDQmxywbqrShTQCHY/+NbWopK+kYq20r+wdVw2L/NOmLbg7kFLE6D/vNsQu4PxiTnU564JWAD7h1X6aqOx+2SwVcm3QVnKpJ8y232VcN3BuMyaxVrLMpbWi7GCFu1d0et+b2FQoBZjrVbWZSGaS8pqWs5M5cz3c6mxyBHcA48gOvXF83w5PJy5a6CDvah61fGpPHDje+Z24Qdxb6+ajPk72tbG8KozfJjSddJ7883PaU/YuoLT8XQTM+TyEel74jvSZjShLpTqT8tKys/8tEj1NRlANLPCSOExAGLsKu/fSChGrggWBMWs7F0qnY5wQJ4J6a6qr1g7fTWieOxa791AG07csWc6tCYvs0H1NyXThLCZtTevLeed/+kfNQH8MHI5IjufAdSNSWuxC04fccg2eIcpSGCb3JbUhOkpX1b45m25PNMzeIfxb4OcfvYciQQjoDHX08d9J1u7ZMdYJdncO9tqtCIpbv5uM+V/bzIEvC1pTec+9Rkeul2FE7JM2uRULfATYP7iRT2tB2qeZy/8ZTMKVgqK5xZiZNuqfjLaScO7ATyGjFQ6JEwFeBc7GzJJ+V8EPgX3fPXznPbfateN/rv7iqkL4ZATf+/mL3loSkgdFn8I6E04IxmfX/i/N3OY1dgxizsP+GJbAFeOu4bf/MP65z9Y1TfRRn25YlYXuSrRJm78n59UBOoOIqhPimEFoRQkhpmS7gYaT8RktZSdvebF/Zf6iAxf5pvwpY5BKORPOxgxYe4NaLN6zsAM4RcClQKKEN+G0wJt8ew31+GXi6prrqwb3ZTmlDmxv4CEKcC4CU/wH+0lJWMurCQ6tConO6P3udDXvzsDnl6rt33re+g11Yq797ycDvM4Bx2cxo48wimZfrBMyyYGs3b510nTxstOONh8Qc7JNOATwdjMlXRrsNZd8QteWzETybtS2eZUF3sgMp3yMr63e7UFAURdkTq0Li60IQCbjI9+roArvWQZ9Bp2HR9sTMZcs35Z94AXaHgyeBf9RUV6UmdtSwKiTap/ly3+kH2JKg6+75K48Cumuqq/ZZ5xBRW34IggfR9cPwuorRtP75nD1kjF4kF8nK+tZ9tf/x0lonDhWCJwp8zPR50PtffykhlUF2JdgmJUsWVch1e7L9eEicqgsemOLN/rvty2D0GdzYMn/lV7Cn88zErrMx01kOYedUym52BjE2rz/hkmZP4bSjNVf2mdep7o5OK5O6qqWsZI9uEKwKie8KwbV5Lgo99q2HHX9TCbzP/2Pulx8wNO+6hVvuvfuorie+JOBaTdhBBksigDskfD8Yk1tGu2+nwOkh2MGLw4BDT9t0R9m8zEtn+nMEgQA6UmzPWFwcjMlH9uCwgR0ZLLdrLveH3YGCgv5p2FJKrEyKdG93B9L6aEtZyX/2dB/K/kMFLPZPB0zAAiAciRYAV87offHQ095uvNStUejT7bsdhkU6aZCQ8EcJXwzG9qy1Vb94SMx7uei0Kr/R9fbs3udvD8bks2N0GHtlJHd4nDsBb98z79vL2dnBxDXg+x3/vmzmd2+YVWzl7J8uJWzupP2Od1bOqKmuMsKR6HTsO0JZu4jEQ+JIAb8TsNij23dF0hamlDwn4dOjLQo6WGlDWzHwLuxAyNqWspK9KRh2UBK15dX43F/G58neejeVMUmmfycr6q8Zx6EpinKAiodEyCW4udhL4eDPMSmh1yC5RZvx6oOHf/7XwF011VWvTsQ4+zl3lOcACy947af1M7Xuudnaa4J9kdiZonVpTJ48HuMTteUacB6CShCHAx1IeTPwJ1lZn7PGwP6ktU7MFoJfAu/zuLAAMgaahMek5AuLKuRedbNaFRL3+HTel+fevT5J2kR2pXlHwknZprg4F+3T2DWIMSPpKzrijXnnlnunzsx5nmVmUqR7uv7ecvmJH3C25wVOBl4cLqs4HhJXuQS12f6megyRbhdFj/7ziIr39U8rioeEhh1g0IFNY925Y1VI/L7AwxW5pk8BdKRFz3MFZ/7yhWnnrWZn5tGOZeAUk2xKG9rKNJfnl56C4iEzWCzTINW1fbuTwaK63x3gVMBi/3RABSwA/nTlguNnJF7+7xS3UeAZ9EY4YE5c89KYvGpPth8PifkCGoTgeI+OD5AZk6QleUPClcGYXDMGh7HHVoXE7/LdXOFzDZ0aCdCbIZUw+OHSmFw53PaeuUG8Na2A2bnmbmZMeKszf/Oft4R/hT01RQf+DcQGpz6CHewR8FiBh+keDTHwbkjarhi+XcLSPQkClTa0zUKInwMXaC6PCQjLSGvAg0h5bUtZyevDbEJxiLryNykIHEqu+UVSQmffdllZP238RqYoyoHIqVe1odjLUa4snzlSwraU6O7Ri079QGP7Ht0x31tOkGImsNBZioHukzbfVTC/9+nKIs/uF4b9OlN0py0+HYzJ5vEa78GktU5Mw76Q17CnAG0ai+3GQ8Ij4HYhuNDvIt8lcFkSkibthsU2CRcGY/Ll0W73klsee5fpL/q3r2hazs9Qy8hgbn/r5Xkv/u167AyOkwALaMFuOdvjLL011VU7pk84f1OvT/FyWLbzOGlPvei04IRgTL412mPYE/GQ+Faei+8EctRbA9iWEl1rppVe/3rhyZ3srO8yUJLdp1Ltsrx44sdavQVTj82VwZLu7eo1U4lwS1nJr/f8qJT9wb4MWIja8v4pUfnYf4/bhihorOyB0fzeJqRLyGjN7nvxG3lu8gYHK8CufFzgJn+7xSXxkPhBMCZfGs224yFxtIBHCzxMG3ihjRt/xmRKZ5p/xUPigmBs4tp8SvhRb4aPunWK9SFOmAwLEnYb2PoRbvBXiRTfyvdnr8Ddl6I7Y7m/DzwFXI39x3oM8LVwJLoFuyXZRmdpL4U/FHiY7tV3TQUUArw6CA9Tu9L8mZ1dUUaktKHtMIR43O3Pn6l7/Xr/L0hKiZlOfjjT131GaUPbGS1lJWrayUhI/LmTNbF/aWL/eG9QFGXSW6gLirIFK8B+ywm4ZIBMRxnwrXEbGRCORKdid5hYiJ3ingCew55yuvGI7qeFAWf3Grwnz7XrnXgpoc8gmbFYC/x1PMd9MFlUIbeRowPLnnIyDJbHQ+LIvgyfFbBAwnYJtwMP7Wn7TcOT9zqW5ZJSMtTd/36WaUghrZeBduyMnpnYdVne7Sw7hCPRBNAL9Myfdv6skvZ/5uta9uEJAT4XgT6DMuBHWVccW79PGIT9LoqyHbZhgbTklkVb7vrJdb/8fxIgHIm62L2Nb/8yA7ugaz5O0dq0Jy+gSTknV7ACwOX155np1OWAClgooyZqy4uBK4AvYReA7rdB1JbfCNwmK+s7JmBoWS1bvuJVYG1zU+OHBj1+D7CwuanxyIkY11iY9Bcl8ZAICPiwT8+eXWCf7JDfm+E67P9YIybgtgIP0wZfaAO4dSjyUtyZIhYPiXkT1Ts6GJPr4iFxdUeS3+a5KfLq9meglJAwMXsMLQnWx86OyXdGsj0Jv+pL8wWPi1meIeLgyTRWKsPWAlf7zTXVVclwJPoccCHwCDAFuyDoEdh3PMS0vpe9CO1Ej2Zl/WT26KAJZsZDYvGoMlaEuMMdKJzl8vq0XR8WuLx+IYQ2I93b2Yzd1kwZjqAdS05hqMhXP0uCfdKuKMpBxplucDp2Z4AO4CFZWb83qeOzdG3YMCm6QMfO5tvnwpFoITszKQ7FLqT4AvAPYENNddWA6aVVxEPioqTBrUmD9/td+HWBx5Q7pqT+Q8In97aAoDJxgjH5KhAZq+21lJW0l97x7ONWJn2+7sneOdVI9nVIdyBSU131JPDXcCT6LuxzrVuw/0/mD7HkeY3eRfoIbiroArewa8KMi2BMvrEqJO7tyfCRfDeBwUELS0JXmi4JXxt4Pu1kj7Q7y5AGtgXuzZ99rNS0q4FAzgEJAcjB2RuKMixRW34hcCcQwK2D28XOAvXGPDJmLXC9qC3/mKysv3+Ch3tQmPQBC+AwXWAMV/DKraFndP+54Uj0fJw+24OW9OB/X7xh5VGa4ARPjpMptwa6RpFhcSawekyOaA8EY/LOeEg835PhGz0ZSrEjzWZa99/730Mv3dbuO6L77BFua1GF3N5aJ5Z29PEvj4uigJdCTdidRvpSdGRM3pGS9y2qkEmAmuqqDuBPztNfB/4HEI5E/cCceZ3/vdqrW57hfkdenaK3tRnLwpFoN/bvo/930v99ZmBl79KGtrlC0xbpHm/WYJXu8QrRp80rbWg7vqWs5PkRvgQHL8kvSGeux+/NPrc2nUkj+e04jkpRlElA1JZfheB7aJoPXXNjSQPTtERd+S+RfFdW1o+oTlQ4Ei3CCWwffkjpWYu33euB3E+1JNIS+rB1ieIhcRJ2QEUATwZj8skRjikAnICdTXEE9oDWAw9j1wzIWigzGJNJ4NJ4SMzqM/iEgMOk3dLxT8HY2ExPUA4w0vpGurfrPV599xb3AJlEb0paZltLWcmO/7811VX/wzm/cgxZeyEeWrlFanyS3adS7MICq917aF44Ej0ceHNgi9xcWuvEVOAKTfBuCQkp+Qtw/6IKOezzJXwqZdrnzAE3xW7NbiOSMjESGXolfDsYk6MuMuoEETuBztKGti1IqQ2bwWJkpC/RroUj0SuB17ADHDOx67E1jmb/orb8XdjvHSawWlbWvzHaY1D2D06w4l5cuiDgEWiDLkE8LoFlQV/aj2HeK2rLP6iCFvve/hCwSEuGvzsjJRjCrWNPOejvuZ3r+ORLxWcev7DnEZ8QuRMnfDpTeiyWsBcBi9KGtqnA1QjtLMBEWvcAjS1lJSOeaxWMyeeAT4JdPCkYsz887otES4Hzw5HoizXVVd0j2daiCrm+tU7MT2UozRiUA9OBtyzJjYzwg6mmuioBrI+HVq7ThqkKDSAEotN76GLsIMVQZDgS7Q9epItmLVrcO/tEf64PJADd6y80Ej3nAqMOWIja8gLgCoS40onEb0DyU+A/B+gctVtIG1/H7fLjGmKOlWFCKtMF3DjuI1MUZcKIuvIoulZBnrdwlxM0S0Ii9RUM812itvyS/vdFZyrFxdjz7d3YQYC5ztci59lb3yh416OLtt59lSnJy5XY1WvqiSdnfFy7x/48e7KmumqXeffxkHiXgD/qgtle3U4PT5t0rQqJ7RIuC8bk44O36RQxPA47k6I/pfdl4C7ghZrqqlEVqHQ6kt0wmucoB6eWspI1pQ1tK1Jd2/7g8vp9utfvE0JgGQZGsrfDMo0XkPJDw29pSI8YFoYlyVqOyp6uJHqfn3Xu28Cngd5wJLoeWIedRbRb1lRrnRBCsFIIrvN78Hpc+KSERJqPZ0x6W+vEhxdVyKdyDSwYk+l4SFxsSM7oTvN14F2mcLm2+454tch4o+y8P6Ve3cNj3qGlrCRZesfae8x0coXL6x/yFZBSYiT7OvN7Nv8Uu1veJ7DfC7YAD4Yj0ZOc1yFnQU5RW34GglvQxCzcuheJJGMaoq78KSRXqMDFgcWZBnInLl2Q59XIdv2haZDn1ehNWRjmnaK2fM5kmx5yoJnURTfDkahwWcl5F75a88R0jzElV5HInjR9CZNwMCbrBzxfx26J6h1qOe2thtK5mQ1fzXeTs5JzwoCN+uG3P3zYp+uATcCWXVNGcyu9Y+1XgW+6vAGv5vb4QGKmUz1mOplByqv3tKVVPyfT4YvAaxdvWPln7KkaU4G3gbX7eipLPCROcQkemOJjSq71OlJ09OJbcf9R33gY+/fSv3iH+vebc06/ODXjmM+6A/k5CzgZiV6pbd9449xX/vMz7KkM78Luw56z7oioLV+K4C94XH48rgDCSTNJZTowrZeQnCcr6ztH+jrsL0Rt+XEIHsTtKsDrzkMT9kVJOtNHekdbvAktNKsoyvgRteUnoIlHKPAXDXmCJiX0JrswrKu+snnWXdj1jD6HHZh4CfvmgIX9+bgR+27m6zXVVb0Aq0LiOrfG9wo9FAy1+aSB0W2IZ+6eV/Vl7Ln7RdgZDE8Cay/esPI4AQ8WeZg6uFuH06GjQ8JFwZj8bzgSdTvjWwgc64xtI3ZNiuf6x6Qo42HAzarLAD+wHmnVAP9pKSvZ43OzVSHxTbfG17P9TSUMMr0ZHm6Zv/Jc7LajC5zlEOwL+Fewgxcv1lRXdQE8c4P4rlunojhv921mDGjvpV1KzlxUIUd1c8jJ8Pg08Nua6qoxucAvbWibhxBPeAumTNVcu54iSikxEj1JI5V4qOXyhRc4YwgAX8aeAvYs9usA9nnyBuz3sdcHFje1zxHFXeR5i3e5wSMlZEyLRGozklNkZf2bY3FMyp4bq6Kborb8OqCWQv/umRVDsSzoSkigQlbW/3xP9ztWnBoW64DLBv3oD8CCyVbDYtJ2CXFeyIXNTY09zr/PwC4UqWNHPa9sbmrc6LSKOgE4E5h9ytt/Wnhk8vn3F3qGnq9mWtCeol3CEcGYHHH7onhInKALVk8d5kK7PSW624rfd/tLU87agp3tYWD32n4L+wRtE7B5qCBG6R1rrxWa63vewuJCIXb9zy8tk1TX9k5pWctaykr+MdJxD+Wr3/jOwpKtf/vx3O4173YJ6dIFwrSQpqRTQiQYk38afit7blVIrC/2cnS2wmrO7+gtCYf3Z4YMp7ShbYnmcrd4C6fm/P2ku7b3TH3jqb9M2f7SJuA92GmUq4CHsH83bw++myBqy49H8DD5/ikMFQlLZtKk0q1ITj8QMy1EbXne/JT3x296Mh9OapYOdCD5DXDrgRikURQlO1FX/jt8nivwurOfoRkm/u70xs9vmfFb7EJ4J+DcrQQewE45H7LWhdPV4BZd42N5LgrdGjviw30GiZTJmxLeG4zJLc7n/9HYdYmOAdIfeKX66qmu1LyhCm+DHbToSIvX7z7q29chtOOwg96bgLXA2prqKvWephxQ4iGhCWh0abw/z0Wha9e/qb6UyWvO31THwOc5mVHHYgcv5mJ3Xtk00/3K2xdMu+32Qwqzd8NJZqCrj/tPuk5eNJqxOjcPvwY8XFNdtWr0Rzu00oa2xQjxN93t9etef6EQAss0pJHs7ZSW9RhSXtJSVrKjHpczVe1C4G/OQ/OwM6/mY9fHyACvAi91aMYrt0zf+gwF/llDniMCpA2LROo+WVH/wbE6JmXPjEXAwukGsh63Po8837BZ4zv0JiUZ82XgmIm+XnCus7PVrXltfw5YTPSUkA7gg81NjW8uW75iBVAdjkTrgPdiF3d8Gbjdn+nYmDb5V3eaU/LcBPpT4KS0Kw53pel0il6NqtdyMCafWxUSb2RMpmTrsW5aYFqy5/jt/7r2pSlnuYFZ2MXIZmMXCDsFp55EOBLdJYjx+tylneQfstJbsHuwAkBoOp78KUWp7u2/Km1oO3ZPo+3xkBAXQ4WuiWChVwYGpt0aFlO709y0KiTmLY3J6j3Z/khIuLIzxb1F3t2rwZsWdNi/o6tHGqxwPGyZRo9lGlM0fej/qtIyMU2jN+0t+DT2tJYrsU+kLeB87P/j0uls8pazbBIzxfek31Oc9YPI5/aQMY7BtJZgBz4OKF/ZPKsP+67C1TXVVfdN9HgURZlQ5+PO1ccD0DWSQh5iIh/QERux53L3Z7Pl7NIUjEkZD4lPGxbNXWm+jZ39ANAu4WfAb4Mx2QvgzLN/EXgxHIkWH9Xx6EddZGZmC1aAXWtKE9q0uV1rznyt6JR7sIMUW0d26Iqy/wnGpBUPiUszFhd3pvkW9nQHCWyT8BPg98GY3K14dk111XbgMeAxJzv3aGDBMYGnPufz4Ms1A9frAgGnt9aJGYsq5OaRjrWmuspc+ZUvbp7f8UhZPLTyNGAzcNfgYMpoOdNujjDTyY+YmfSngAKQ65Dyhpaykv8NXt8JXMYGPPQ/4H8DWhofjR28uOAlb+o4TdcLrFyp3W5dIyHOFLXlM2Vl/YiK3iuT2jRgPu5RXhq7XYKMOR87s33YOkzj4L/s3m3r+9jXr/utCQlYLFu+ogT4HXBxc1Pj2+FI1F80Zbq/t7vzVOAD2OlasZrqKqeYVRXxkDgvZVKVMvmcy5lVZEiElGyQUBGMyYf3ZCwSruhM868iL1MG31sacKF9ZTAmraBde+E1ZwEgHIl6sN/oDsUOYhwOLAY0X2Lbiekph/lEjrQizeVCaPo0aRonA2ucbbqcbbxdU121cQSHcYEu+HixR+5WldmlQbGXwu0pvh4PibucOhhjLhiTD8dD4sPtaa1ZFwT8upUngJRJZ8YiLeFTwZj8+2i22VJWIksb2j6b7m7/o7dwapHQdj1jlZZFqqu9Cym/1HBtqQGlb4cj0RpgCfAMdr/uQ7B/N/1LSVJYXk3yQdOda0Y14HNPoS9VyQEYsMB+XQqx0yAVRTm4Dd/HQwikkJm6Ge88ISvr+wPPI2416UxN/LuzEA8JMdx0xZrqqo54SAi/a/hzFb9m+ku23vPGl351939GOiZF2Z85fz8tzjKiv6mBnDpkbUDbMzesXOF14cm1vhDg0jHSBsdgBx2GFQ8Jt4BfnIO41KvjcbnxWhaJpMkNq0KiScKXgjGZteDtcFrKStLYQYjYcOtm4xR7f9tZVocjUc+TeX2/trx67g4jzgtCxjgVuGdP969MGvkAWetWZLNz/QImR8Bia3NT4y6fzcuWr6hABSxGbR5wK7Bs7lELesOR6EXA4nQqeYHL5X4I+HlNddVurY2cN7RvxUMimrFYjF3t9xWnHdUeC8bk0/GQuLAzxZ90jWKfbk8PSZl0GBYJJ1jxQLbnOymwrzsLAM4c2pm9hYd9X3Pn6Mbg0FxuX962DZeGI3+Zgf0H817suY7/cIqGDe5wkho4/UTAt/Lc2fteCwF5Lgp6MnwFex7hPhGMyfhXv/Gdby/Y/uCRx3asBtCkXYH93mBMjrjmx0AtZSV/L21ouyrZue1m3e116x5vAYCZSffXALm2paykuX99Z/7hfwZsov9DqD8YpD+S17PI0vg8Qvhy7lzTADFvT8a9H5iPPbXpteFWVBTlwDPgruLC4umujg7DPDTnnSXTAmgfEKzYK2NeW0mMoDq3ohzA9uZvSkByJE82pe79b9dF598RiR6JnXougB8M7PDWz5m2crdX56x89y431Px5En9PhrKUydx4SHxwlNm3+1RNdVX6p3XlXSO6RLKPaQTFDpT9gJ2lP9o/o53rj6jpgbJnJiJgcQ/Q2NzU+HI4Er0EOKZ9++buRF9PACjPNge2nxO4+O9YDigYk0/EQ2K+YfHeHouzsGtqPAH8c0/eRJ32aG+UNrRtcNtFQnKfR0nL0o1UAPsi8njs1L5twEnYKbe7CUeiBk7w4kNCe7dbyz1Mj45GhveP9lhGIh4SxUDeI4de4ZL+o2a/MO28266+6aEXxmr7LWUlfyltaLvXTCeXmZn0BQBI60GgaeD8xJGoqa4yRW35y8gh5ugMJiVuKcxwJOqvqa5KOHOrPaOtLL83WuuEH7hUE3wIcFmS1cBvF1XI7Xu56aOBV3O18lMUZXIqbWjTsediH4f9OfCPlrKSF0fy3HAkOg27Pd9C7Gl0fccmvHc87k58HZc+dNFNgFSmz+mgNK42++e/NCv1SjoPy5trvZRJB/bntqIoo2RJ7kym+aDPTWGOdTBNy3oteeJLwHnAUdhTt78WjkT767n1T73tuBg+6NI4I9/Nbtm/QkC+m4ApeW/G4gNMtgwFycNkjE/hcWV9PZASkTG1WRn3unEcmbLvbAM2kDHm4XGNPP6dMST238HenpcrOUxEwOJK4FfLlq+4de5RC+5+4/WXDzeNzF3Ah5qbGnMGK/YlJzL9sLOMlXuNVKLS5QtkLRoppcTMpI326cd++7bKj2137nqdjl1/4e/AC2TpcoLTUUMg5XAZTAKwhB4IR6KnYWccvLO3F97xkPiIgKgGRwiB+d5Nt/u6PDPX+zMdTVC1N5veTUtZSQq4w1n2iqysbxd15a9imCcN2drTIVJG37t6fRuxP4wLsP9eOsOR6PcGVpLOJh4SRwDLBMySdgZOUzA28nmfrXXiI0Jwi8+Nx+smXwApg/MTaf7vmTpx/UkV8icj3ZYzngLgVEN4fMWHfvJdHb45e9WdRlGU8Vfa0HYZQvxMc3m8uttdKKU0zVSyp/SOteuQcllLWcnAbL8jgHOwU8ZPwA5SzMYOcrwA3A+8/Hher4XFEhLps/F7ArsELaSEtJEhY7wG3DJexxmORA8DzuLQsuMuevXHPRmzryBbrSnDAtOiE3hkvManKAeYlrRB0jApzHZa1JskJYS85Qc/+NEd4Uj0z8CngCR2PaxDsd9fznRWT6T1vKuL9N6sRTyFgICLwq40/8dkC1jAXRjmr7EssnaLMEwKTG37ivZpHw9Hok9jB2q8wNaa6qoN4zhWZQzIynopastvJGPW5vy9D2RZkDEBfj7RBTcPdBMRsHgcqAB++9or6z4A/BH4XHNT4wGXmt5SVrKm9I61b5rpVLHu8Q75lm2m+jLAAy1lJdthx1y6R8OR6LNAwrkDnjPNaFVo5WbT4shctYEyFqT1wGZ2FqIkHIl24AQv2Dl1omOo1L7d9ylqXYKr8j12xXewgy/55tsn9Vo8Eg+Ji/e0rsi4kKwkkb6NfF/hkHcUTRNpGL1Flv8a7LsI12HP/2oFVoQj0eeAF4bq4R0PiXwBf9TgLJ+LPF3gMiXphMF3V4XEXRI+E4zJnMG51jpxrib4/dQCigb+Xj1ufHk+fB09fOuZOpE+qULeMNyhxkOiWECdgI+4NSyPSIuzNt3qRcql8dDKzwRjcrfiVIqiTD6lDWuvFrr+U2/BlMIBNX1cLl9esZVJnZru7fpvaUPbu1vKSjaFI9EZ2G38CrDfwwzsYpargJcGZlfVAKK2/CNkjJvJmB/B4/Kjax4saZLOdCPl00gukZX1e9wubiScgP1RwFnO123AXcIy7uo0+VeRZ/cC2QPamq7Y1y28FeVAtahCZlrrxMfae7i7MECxx7Vzar4loS9JKpHmRSntYn411VXJcCT6a0A4hXIBCEeieTg13dxW4tvunE3p7YK52JnFk4qsrE+L2vLP0ZP8Lfm+wt0uXg0T+lLb3Zbro9hNAlZgT3l/C7gLO4ijAOvWLCkErtQ0Pi0lBULwpmXxM+DuBYtXD3vzb5zdBlxPX9pPnlfLWc9CSuhLW0ACuH2cxnfQmrC2psuWr/gD8ChwPXY/aIBXmpsaPzpuAxoHpQ1t8xHiEXeg4BDd4xPC+c8vpYWR7Esbyb6NSHlqS1lJx57uIx4SX/Lp/LAgS9tXgI4UnRmLFXfPX3kfdhrwLOz5y7Ocpb+4UIqdAYz+r5sHntzGQ+LDLsHtxd6h218ZFnSk2CZhbn/l98lI1JX/FE27Gr+nEN3pCWbfTbRIpjuRXCgr658ACEeis4DPYxeE9WJ3iBHYNSCeA56vqa7qjoeER8BjARcn+F14B9+o7MnQlzJ5SML7c51cP3ODWD8ln6Oz3VG0LNjaTbuUHLaoYvdK4P2cYMUTARdz/S7c/eOR0j7R70rTLuGiYEw+PoqXTlGUcVba0FaAEBt9RdOLsxVyNpJ9ptW97b756+6JYWfqHY/9Pv4A8Iea6qrUcPsRteUzgcsQHIlkM/BHWVm/T0++nUDF8dgFkw/FTi1/CDsobAHEQ2KRgD9qgplenQIBImXSZUraJVwejMlH9+UYFeVg0FonFmuCG4ET3C6klMiMiQAapeTriypGfk63KiTap/koHu6ab1uSjqUxmbN9/UQRteUfR/ArXLoHl14EQNpox7K2OUHcNoBwJDoHWIl9Dr0Zu5jp6prqqhFn1R6I1q1Z8l4haPH7dX/ArwU0TWAYkt4+szOdtrZIydIFi1dv2tv9jEVb036itvxC4F5cuiDg0YbMtLAsO1hhmBL4gKysz1rrcDw519lrm5saPzTo8Xuwr7+PnIhxZTOa39u4BiwOVqUNbYcjxI+B92u62wCJZRoa8Aek/GZLWUnX3mw/HhJ5Ap7Od3Okz8Uu8Wwpoc8gmTBYI2FptuKX4Ug0n53Bi/5AxnTsi3IJbMUJYHzo5e/9eorHPHFwV5WButP0Jk2+HIzJm/bm2PY1UVv+IQQrgWMQwkBKHfgrku/JyvqXB67rTAvpramussKRaAB7/vgJ2FF1Abx+xlu3HXVY+pWKQo9TbXgQKaEzTWfG4uPBmByywn5rnVjk0vn3tAJyfoB39tGTTPO5RRXyD9nWWRUSvw+4WBFwM+R9Die4tEnCnMlU9EpRlF2VNrR9UfcGfuTJK8gamJZSkmp/Jzl3/QMVnkzvk0AndgCgs6a66plxG2wO4UhU7y8aHY5Edew6TWdif968AqwGXs6W6RcPicXYwRiAp4DHVWaFooyt1jpxOHAM9gX4mlw3RrJZFRIPFXpYkqslcdqEbaav9e9HfuPMmuqqfZrBtadEbbkLeD9wMnYR/AeBxwdPAQhHokHs97HXsd/TirCn3j1UU1315uDtOvXfrtLgEsAj4WkJtcGYHLMacBNp3ZolRwnBk9Omuqe6huianUiaZleX8bKUnLC3mRZjGbCAHUGLO4EAbt1uXdp/UzNjSGcaSB9wyWQJVuyPVMBikiptaCvCLnZoAc+3lJWMWfHGeEhMF3CPJjjW76JYEwhTYiYMuqXkYQmhYEyO6o/Y6XZyCDsDGbN8mc4jznv951+f4TNzdthw0nT/uzQmT8+13mQhasvzsTvPtMvK+lEVonR6mS8ATrjo1R/dMMOVmD7Ee/MOaRM6M2LV3fOqlgG+AYsf8J1ZeOcFxxe1VRQFsmfMACRSsLF7xh/v2fb5e7E/SPvTEBNA34Wv/NDjtZKvT/Nl7yAD0JGiI2OxYrRtZxVFGT+ldzz7F09+4Ud1d87ak6S62rdZRvoDLWUlky5rKhyJLsV+r7wNu3X3Gew8qV9dU131xgQOT1GUMRQPiYtcGk3FnqHPQaSE9rTo+d+UC/78cvEZL2FPuX20prpqvy9eOCAYuwSYhn1u9hDwWk11lYyHxCUCbvG58Hp1/ALIWJh99jn73RI+tafd9fYVUVs+DbuLoRt4TlbW5wysvPj0kpsL8l2fCgT0rCGr9o5MVyplXblg8eq/7s3YxjpgASBqy4uBTwLXYjdF6LcB+Dlwm6ys7xyLfR2sRvN7m4gaFgetlrKSTuw7QmMuGJNbgdPjIVHSm+EK7ADDqxJ+F4zJl4d5+pCcaSD9FZ8B+Pcn3LNdmF/EvsDOyrlez93DehKRlfU99Lc0GiWnl3kr0LoqtLLelbOTuT1n08J1CvYUk4EMINljTpluSSHtxJbsLInsNqZMAS7FbodrYBfAAmDd1PcdcXL7fboQuRMnfDrFhsXF2EVeFUWZnKxh3hImhKgtLwA+iB3c3grcIyvrd6u75HQnORdox65j5cNOm374YE+bVpQD1P2mxb+6M1xY4CZv8BTZ7gw9liXvfzO/5AvAqcB7gFOcGmGPDJWVsL9wssieDkeiz2BfkJ2F3XTg9T9duSB5qOCXxV6K9AGviUtD9+kUd2e4JG3SB3xuAoa+G1FbPh3BbxCci8sFAg3DNERd+etIPisr6x8b/Jx1a5ZoQrDM79dy5NdAXkAvzGSsrwB7FbDYF2RlfQfwc1FbfiMwFbseVDewXRXYHH8qYHGACcZkGxDeV9vXpbHdApeU5KxFY0jo9hwinNa164ENkzXdb6wN99oAaNJIYFfcT2JnRCT7O4+01q2cmjH4xHDbSWboONy37pt08hIQBJ50fuQHAlOTG8/RkB8bbrzOPnLftlUUZcKEI1Hdd9TZz2bcng/oHq8/23pSSiwzo2PX1dmnRG25C0ENgitxu3Q0EcCSfWQMU9SV347ky7Ky3nDGX4D9uXQKdjbFw8B9NdVVHft6nIqiTIxgTMp4SITSJj/cZnK1R0fTBX5TkkibWMDNEiLX/+QnJhAPR6KPACdh38X/TDgSfRW788/6wVPEShvaXEApQqsEeSiIDqR1M9DQUlYyaWqnOTV4nnWCMEcDS6ekN9UUenYNVvQTAgrc5G03WR4PiZXBmHx7nIe863hqy6cheBKf5zA8LtcuJ6WGOYXe1H2itvzDsrI+PuipeUIgxTAnwy6XQErmjP3Ix44TnNjmLMoEUVNClFFbFRJ/yHdzqc9F1nei9hQd6wre+93npl+QwM72kMAb2MGLl4BNI+lGMlBpQ1sedou+Quw5gg+3lJVMqroLq0Liv0Ue3pOtWCZA0kD2ZPjL0pj8eLZ1nrlB/CnPy0fzfEPXnkhlkJ19PH/SdfLEbNuIh8QRmuCZqd7cRa960vQl7Hojv8m+lqIo4y0ciXpwpk4Yumf6Kws+eJ23+JA8keWmlZHsMzKJnjtaLl/4qX05LlFbLhD8FbfrPPyevN3aoCbSvWSMBz+75ZAr8y39vcAi4FjsAO1mIAPcVFNd9dYQm1cU5QATD4kAdh2I6diZWH/PNk05HIlq2FPHzgTmYL9nPAK01VRXmaUNbYchRFxzeaa7fIEiTdeRloWRSvSa6WQfUr6/paxkn2Qz760HQ675LmE+Oc1Hca71ejN2Z7mlMXn9OA1tSKKu/A58nk/gdQ99g9u0oCex+ZiEd05p15RTsTOVD3Hp5twrP/rgr2bNdHtzBS0Mw2J7e2btMYtWl+zNOPfFlBBl31NTQpR9SkJVT4b3uzSmDFWroc8gbVq8OL/zkbqrbn5YhiPRQuzI8jHYH0DvA3rCkehL2AGMl51pFUMqbWjzIMTPEOIy3e0VCM0lzUzaMo1kacPaSEvZwtv2yYHuAQnf7zW4o0gbuoOKlNBr0C2hOud2JNf0pjhZwtyAF482oLtHMo3sTrJFSkpzbSMYkxtXhcRzGYv3Zit6ZUlImqSBrIU7FUUZX04R5NOwMxK8QJvLTDdKxLOprvZ6T0Fxoabv/PiWUmKmk2Ym0bMJKb86DkO8EE07e7dgBdi3CP2ePGFaZ7/gTd5wSiKvFbtI3U+wC/gFsKewqWkginKQcIITd45kXScr4flwJPoCcAR2xsVHgHOv+/aPnuLYD97qySs8Qvf4dpyBCk3H43LnWV5/Xqq7/f7ShrZFLWUlk64mjoZ5pFsbfnKfS8MDZL0hNR5EbXkRgg/hcWW/VtQ10HX/bMPzJ+xpE+uBFw1T35gxXM+k0/I9Xm/2gEVfwkpYFreM+eCVA44KWCijFozJl+Ih8YGOFHd7dXw+F/ka9jSQPoN202K9hAv6K7fXVFd1AWuANU4hov7q00dj33mzwpFof/bFeuCd/uyL0oY2N0L8S/f4F7sD+YEBkdo8yzRJ93T8vPSOtbNbLl/4w/F8DXK4x7D4R3eGC/Pd5GsD3qctCZ1p0feOb96zjx1a1hvMsZFFFbKztU6c0pfiB30pVrg0LCEgY+IC7pOSry6qkK8PNxgJ5V1p4sVeigcHlywJnSm6ge8GY3KP6ncoipKb09WiBDur4KFgLPvfbTgSnY5diPIk7OLMTwGP1VRX9Rf2aixtaOtLdW3/haa7Aprbk4eUppFKpkA+hZSXtZSVbN3HhwSCb+LzFGWdsyYE0ufJf7Sgd+Epibwr+6e7OXqdRVEUJSvnPPA14LVwJHoI8N6OKfO/oLvdMwcGKwbSXG7c/vyiTKLnK0DleI53hHotOXzAQkrocU/LC0eic4HX+9s7j0Y8JARwFHZh47eCMfnOKDexGJduDTvH2eMqeM6fKDy1L++vwH+A/9VUV8l1a/7xZle3uGea212kabtvwzAsEgmzD7h1lONSDkJqSoiyx5wUvxUafErad8xelvAzYPVI28yFI9H+zinHYLcH9WAXtXkJWL/+uA+fq/nyqj35RUMW8JTSItmxrRNpLWopK3l1DA5rr8VDQhdQBXzBraHpArchSRsWGUtoP7znqG+9idCOA/5fTXXV/4bbXmud8GG3T9WA9Ysq5KiqEsdD4j0C/p9bw+/V7ekhGZO+PktjU97xf39q5rLlgy4oFEXZS/GQWCrgFl0w1a3jR2KlLDJS0iqhLBiTO+7+hSPRw7HvIh6HfTH/GPBkTXXVkJ2kShvaBNDfcSMF/LulrGTYAOZYEbXl7RQFinOeyEoJnX2dsrK+eLzGpSjKge3Dd6xd4ymYcrLmGnK2LADSskh2bt3ecvnCaeM4tBGJh4RbwKapPqYNcQ2/w/aU6Hp66gcaXys69R3sqXQvY58XbxgQwM62DwFcIeA7mqBIE1imxCUlz0v4ajAmHx5unOFIVNw2detHt/rl78jzFeVcOW1AIvV7WVG/21TEF59e8mVNE98pLHAVeTwCIQRSShJJy+ruNjql5OIFi1cPO57hqCkh+yfV1lTZLznZF0dgBy+OkXDIy8eVXuuaMnPKwPTnwZx5279ouXzhpIqmx0PCA5yNnSb3DrAqGJOmMz+zFDu75N6a6qonxmEsGnChgIsBr4TH18y45IE3C951OXaV/n/v6zEoysEiHhLnanBnkZeigZlNUkLKxOrJsNkQrlP+Nu9b+djT5I7Antf9CPbdqUkdQBxFwKJDVtZPGb+RKYpyICu9Y+0mX/Ehs4Yr5pho39yFlNNaykom3XvpqpD4vlenMt9NYKjDSJvIrjQvPzFz2bGb8k+cjX1T72jseh4CezrdS86yceDnRTwkhIB6l8aKfDcF/Z8/UkLGgu4MnZbkmmBMxgbv17mBeJSzzNvsyhz6h2nby61Cvz/ne31fqpe0USkr628e6sfr1ixZogmqJJwmBIaUaMCfpaR6weLVG0bymg1HBSz2TypgoRwQPv2TPxy2dfZJz/umzCjItZ5lmqS6tj/fcvmJJwx83KmdUVRTXTXqO4+itvxkBN9Ech4CDehDchNwo6ys3zLa7Q0WjkQFcCFwOvDPmuqq1QDxkCgCzmdnYdF/78te3OFI9GzsO7U311RXbdpX+1GUg4WTYfXWFC8z9CGTliFhYL3DtGf/fcSX/gJsxA5UrBttIeLxFI5EXdjB5IU3T9/yk64C91xyVRc2TOhNPiIr6s8crzEqinJgK71j7Xpv4bSjNT37e4+UkmT75r6jn7/raE2ab2O3UPbXVFdtH+l+RG25Dlj7on2lk2Vxv1vntHwXAX1AUCFpYvVm2CrhzGBMvjTweeFI1I+didwfwCjAnmr4Ck4A4+INK890Ce4o9g5dR82SsD1Jp4QFd89f2QMciROgwL65JoG3nW2+8tOZ7/yGgOccstTcxJLQ3deBZI6srM851W/dmiUu7C52vQsWrx7TgvkqYLF/UgEL5YBQ2tBWJDTtFV/xITnv0EnLJLP97bfnv9ByHfZdyhR2Rfq5wBbgV6O5EBC15V9AE9fj8xTi1gVC2G/K6UyaVKYDydmysv75vTk22BG0CAJn+zMdj5+/se7jwCVeHU0TeAyLRMYiDXxn6T7q4OFktVyD/SF1s9M7XFGUPRQPiVKPxu1FXrKm0UoJW1Na79qp55/5hfr7nhnP8Y2G8/5wFLAQ+6TCC7x9X0FH3rP56W+T7xu6joWU0JvswrAulZX1fxvXQSuKcsAqbVj7TZcv8G13ID9rK3YznYTtbzx35Ev/aMa+INewa2F8J9e5oKgtnwVUIrgK8CARCFYj+Z6srH90LI/jps+e7Q1k2psO633uTDeGDkhLogPNElYGYzJnByXn/HEGO4MXRwD6ha/VfGqG1nNErlhyb4b0q56j//Hf2Zc/6Ty0FSdAAbxaU12148JR1JYfh+Bh8nxTcQ3aqOW8z5vW12Vl/a9H+RKMKRWw2D+pLiHKgaJLSpmWlkm2Nn4AZjotNTP1LHbk9mTgPcBM4C3s+eBl4Uh0K/abcv/SPdQHl6gtPwtNXE+Bf9cTcU2Az+PBpc+gN/lPUVs+T1bWp/bm4Jz9/+ebXw2bS976XZPPxbQ8F94Bu/U6hTF/vCokZi6Nye/uzf6yjMEMR6L/D/gMsAQY3EtbUZRREHC+V88erAC7kYZXszILt90/G5jQgEU4EtUGFnRzToSPwC4UegJ2V49twKPAszXVVVt+WlsusAiSSL8va1tT03oIuG88j0VRlAOd/I2R6vuK7vV5h5oqLC2LTF9PJy7/p7GnTnweO+C6BfhKOBJ9HngeeG3gDRpRW74Qwb/xuovxuN1own4vM8z3k0i/V9SVXy8r6n8yVkfx4tRz3gW0tlkfvPoDr1R7seu3bQrG5IjOK53zx3ec5eFwJOrxZTqP8Zi9X8vR0wMAn45nWnLjScA3gVecwvhDkpX1L4ja8nPoTd6FphXhcU1BAIbVTcbIIPlGtqkgijKWVIaFMqnZ0XT/t9yBAt9QP5dSkurc1iEtc2lLWUkb7Ki0/xns6PNq7MDcdOx0t/7IR5pdAxhbga0/nfnOnwh4z86Z6tyb6iZjlMvK+l1agTrz/44BnhpNRkc8JL7k1flRoQf/0Mdop/BZcHIwJl8Z6XZHIxyJvg97Lv1NF29Y2YXdTksHXgzGZPu+2KeiTBatdaIA+IQQLJSSLuAviypk62i3E45EXRe9+uNbp2p9l/uGOWnsStORMrksGJNjloFQ2tDmAy5BiJORJEH+DXispaxkyPejcCT6QaAYaAQOxT6xPxF7SlonsNZZ3h78niZqy10Ifgpcgdulo4kAluwjY5jAHUgqZGX9pJs/rijK/q20oe19CO3P7kB+se7xif5CjlYmTaavu1NK61stly/8BUA4Es0DLsd+H8vHvptbDCSAdcDzfyvseP15f/Il8nyzd8siAPskrDvRiSU/Jivr/7W343cy174EvFFTXfXnvd1ev3hI5Gvw+jQ/xbnWc6aFvLo0Jo8a6bZFbbnAvql1EQIfkqeAv8jK+iELQ4+3fZlh4RQxnYb9/6cH2DbSxgJKbirDQjmAyJ8bqcSVQtOP1L1+18BCS1JKMr2dPVJaf+0PVgDUVFdtDUeiddiFLV+oqa56Fuw7icAU7Dee6QOWYwB/QlhuTXKGNbj/52BeV4EwzC+GI9F7ARN7OsXJ2NM7erHvmGZGcnROgaRwnmvoYAXYd2MDbvJ6M1QC145ku3tgVSDTvujd7zQ3CVjk0jABDAvXqpD4p4QvB2Ny4z7at6JMiNY6IYTg20LwZZ8bt9tFQEpkIsUXn7lBvCElFy+qkK8NfE44EnX1FzlzshFmYc//nQcc8UrBKf5A90N9PmQg236lhIx9b2/YLkEjVdqwthwhrtfdXpfm9hQgJUYq+QVpGdtKG9o+3FJW8tyg41iEXRT4ReyT56nY71/PAm3YJ9NZT8qcYMR1orb8W6SND2G/l24F7pGV9d1jdVyKoigDtZSV/Lu0oe2MTF/3tzN93RcLIUwppQt4DClXtpSVPNK/bk11VS+wY0ptOBJ9APs9+3jsDLJF+aZ2PC5X4ZDBCrBPwvzeIvqS3wVGFbCIh4QOfFzY2QxzAT4kXFteKjr9mdcLFn1pVAc+vF4JpiXtpOBsDDufbt1oNuzU8njIWQ4K8ZAoBq7A/nycP+BHG+IhcSNwWzAmOyZgaAcllWGhTHqlDW3TEOLPQmiLdK+/QGiabhlGwkwn0sBvkfJrLWUle1XAJxyJBh4P9By/uqD3n7IoUJxzZcsi0JnaWr5lxi+dRw7FrpnRgX2ibwKW8zXn94FMu/vc12/80SE+a8i2rf1MC7anxbq751UtAlJjXZwvHhLFCLHGr8vD81y4+uNCTlcD2bOzCNT6sdyvokykZ24QP3TrfL44j4LBpRhSGazOPjZLyeJFFXKTE5y4ADgJ+6R1HnZ9hwB2gPI14OUpiY1vnPXW756e4mOqnuWkMWVCd5oHl8bk+8biOEob1n5R6Pr13oIphULbNeBqZtKkezq2IeXpLWUlL4Uj0anY0+Y+D7iBVuC/2MGTVwdOD1EURZnMShvadOw7330tZSUjulE0UDgSPeQXh2z+R6rAc1LWgAXYJ0NdfZ1IDh9pQDYeEh4B97k1Tgm4KXA7b82GBT0Z0WdYco2E80Y6DWQkVoXEjwMuKgJusvZ97UjRkbH4WDAmD5jucGOdYREPiQuBO4GAVwevbk98lNjnxCn7hkMf8LFgTN6/t/sba8uWr7gQ+AbwbuzrjrXAT5qbGu9atnzFNOwirY83NzVeOOh5XwFqgIubmxrv2dfjVEU3lQNSaUPbfOASEFNBvgzEWspKcvajHg1RW+5D8A6FgcKcLZwyJq7e1MPXbZ75SexpE/nYFzJzsU/6H3ce17GLPQ3+fsdjBal3Cs5+8ze/PsRn5eyEYlrwthHYev+RX/slYADd2KlpPTm+7x3pxceqkIgF3Hwk4Br6Q85ps/XC0pg8YaifK8r+prVOzNEEa6cXUpTtz70vhdWV0Br+8M53aoBzgfdjByafB97ALlL2MnY2wsDWciFNcHOxh8LBnULSJnSl2SbhvcGYfHFvj6O0oa0AIV73FU0vGhys6Gemk9Ls2vrI/Bfuvg04DPu8q9D52os9j/n3ezsWRVGU/Y2o+3wb+b6FZGvr1L9eV6LzQ+2FVxyb8m0CFmBn7P4yW7HyVSHxG6/O5dnal/ZkSCQNmpfG5BV7fxS2eEjMEPBMoYeZHp1d9iol9BmkEgZrnBtQB8wF4FgGLJxgxb0eDVHgQRsqW8WS0J3GSltI4IOTKWixbPmKK4HfAU8Bt2NfM1wIWM1NjZc461QAtcD5zU2N/3QemwJsAB5pbmr80HiMVU0JUQ5ILWUlG4AxK3o0mKysT4q68v+QMUvx5PjTSGc6DeSPa6qrXu5/KByJtmLftVwAtI40UOBMCfmpKSnIdjcWIG1hadL6F9CM3coq31kKsAMl+cDgLA0ZjkR7yR3U6D7r9d94psAFfj17RN6jI3TBrHhInBKMySezraco+wsBXwh4hz6R7Of3oHUmxCc8IvFGWvoz2MEJE/h7TXXV49meF4zJWDwkrPYUv3Rp+Lw6hRJk0qDDkrwj7bsyex2scHxS9/jd2YIVAJrbKzKaa3HCP+V2f6K9GVhfU12VdqbJzR6jcSiKouyP3sSSC8mRYIGUCEt6Dk973gWswC7s/jpQEY5EtwPbsYsTbwe2n/L2n4xD4RPZghUAeS78SYMPx0NiajAmR9xyNZdgTG6Oh8RZXWn+4dIo9rso1gQYFrLPEF1SyqckfPhAClaMJWcayJ0eDVHoQcv2u9MEFHrQuuygxZ3xkJgzGaaHLFu+YiZwI3aR7GBzU2P/jZT6ZctXzBmw6i+BzwE/XrZ8xbubmxol8C3sjNHrxnPMI6UCFooykKSKRHopLq2YoS4A0oaFYW4F7h34sDNF47/OMmLBmJTxkPh5wuA7+W6yFBaFPoNul0xGa6qrsrZTdQo55bEzkJE/6PsZ2Gns+ewsPsqm/BMWzOh82y1E7s8vn4vingwfAFTAQtnvCcEZniwZRQPWwa1bfecU/+Ev53/t9TXOtJCpQNaq6v2CMfnneEj89cX891QFjI6FM/tefAR4MBiTT43RITiD1M7U3Z6s9TIAhBAIty/x+lHnvNBSVvJs/+NOYPXNMR2PoijK/kTKOlKZ03DrxVnXyZhYQv7DL7XvY9fAuAo7Q20N9mfCTOw7xT6Abs8hC93JFzy5zquEsDt2JExKgd+P0dEQjMmX4iExP2NxvpHm0wKmdnhmsuGQ966q+MVfxrzb3AHmCiBQ4EHkupkB9u8v34O2PUkA+CTw83EY33Auxz7H//6AYAUAzU2Nbwz4PuNM/7gHWLFs+YpHgC9iTxvZMJ4DHikVsFCUAWRlfauoLf8U3Ylb8brz8LjdCOz8r1Smh4yxFcnZsrJ+yBTAPfTzpMEVumCeT8c9uENgV5puKWkMxmTWYAXYLUqxL6RyXkw5F11+nIDG9MQrH9OQFw83SAEipefPDkeinprqqvQIjktRJqVwJCoum+nSJcM3sRBIeYjnjS7YEZjcNopd6S9OWfpm2pXfWlNd9Zc9HO5unODkLGCO5+gLZ5OXc0aZQ4KdHaIoiqLs9ACmuYm0UYBniEIWlgWJdCeS7zifAZvCkeiPAY9T1BPY5dxq6oy+9Z9zCfnh4XasafgxmTKGxwJAMCYt4H5n6S+y/OFwJJpfU13VM9b7OxA43UC+5NVzFy0dSBfg1SFlcm08JG6cBJkrS7E/7OPDrdjc1HjvsuUr7ge+jx14exv4wb4d3p5TAQtFGURW1v8/UVv+JMnMl0hlViAJIHgLSQ3wp7Fu4xSMyd54SJzem6Gpz+A0n06+JnAZFr0pkwxwo4Sqsdqf84Hb5yyb46GV/zAEEXafUrKLlCUSGwsWzQC+EY5ENwEbsVMiN6oPQGU8xEPiXQLCwCnYF9/3SrgxGJPDZgmEI1EXcCRwHLBgQ6KkJ+B5OulxDZ3ZBPZ5qmnPUX11FGPUgcsFRATMvnBjrVtCbzy08mjgV8GYHNXfinMSXATMcZbDsKdxuAAz0L1pXXfe1FN0jy8/2zaklFhGRsfuYKQoiqI4ZGW9JWrLzyGReoiMMROvuxBds+8YpY00qUwfkjJZWb/j/bOmuirDoG5wA8+t4qGVa0ydPuxaQVkZFr0S3tkXxzVI/xTEBdi1DZTdTQPme3NNDRqCR0OkTOZjZ9qM5obGvnAUsLW5qXGkdTy+jH1ecCSwbBTPG3cqYKEoQ5CV9W8AX3eWfc6Z+3ZRPCSO6DMoxe4T/irw12BM9uZ46ljsu3VVSGw1LKZk6+hqSciYMrnNf1QFdurjEdjpj2cAOHM4N7IziLF1bzuZiNpyDViE/YH/pqysVx1KDlLxkNAF3KoLLg64KHJrdjGxlMmxfQafWxUS31wak78c/LxwJOrHblu8ADga8ALtwLNvpY5+4JjM06vyLHzZaq31pkgi+fWiCjl8KoY9TreAe90aZ+S5ybf/nkxMC3/CIJo0uToeEqfnmq8cjkQ92J2H5gxY+oMR7djFPtdiT+V4u2Pa0RpG+mOWaeRr+tAf6UayLwP8taWsRAUWFUVRBpGV9e+I2vITyZgfwbC+CvJwoA/JH4Bfycr6t0e5yb+nzdwtRqWEhKXr/5p73fR7ItES4Nl91aWpprqqLxyJvoZ93qYCFkPLBxhhcsUOA36/BUx8wCIPGM1N1a1AAnvsLw+z7oRSAQtFmUSCMbkR+MV471fCZzvT/LXYQ9HgizdLQmeKLqDq6zfc/jp2QOJJgHAkWggcjh3AOAK75aMA+sKR6OvsDGC8NbCLQi5OoKISQRhNs8semRairnwTkq/Iyvr7xuSglTFX2tA2FztAkAKebCkrSYzFdgXc4NG5pMBN3sApUwENj8+FpyPFD+Ih8U4wJv8cjkSLsQMUx2EXpNWAt4CHsXvPb+4PprXWifL2Hn5dnEfRwERgKaE3RSqR5kU5ihRJAT/w6rw3f9A4dQ3yPfh0gyN7M9wJnAM7siems2twYoa9KVLOuJ/GDlK8MTD9eKDShrYVqa72Zm9BcZHm2lmWQ0qJmUpkjGTvG0j55ZEeh6IoysFGVtZnsAubN+/ttoIxmVgVEr/oTlNZ6CF/cD0EKaE7Q4+h+RqTrsJ24GPAueFI9FHg6cHTblvrhAv4kCb4mrRrkSWR/FnCzxdVyI0jHNbzwAXhSNRXU101ppnCB4gecCZPjoK18wkjane7j/ViTxcdqR9i17RbB/wU59xkMlJtTRVFASAeEhcL+L1Xx+PV7Uhz2iKRNEgD31sakz8dbhvhSNSLnbLeH8CYA3iw2yq9xc4Axus11VW7pZ6J2nKB4I+49A/i9+TvUvjUMKEv1YklvyIr62/Z6wNWxkxpQ9upCPELIcSxmsstpZTSMjIa0IiUX20pK9njNMN4SEwTsGGaL3v7UdOCbWl90z1HffO7CG0W9nSRV7A/hNfVVFdlrevSWicuEoIbdY2pbh23JbHSdmjtTim5dlHFyDKc4iHhF/DmVB9Tct1R256ic8300i+8XrhYw/5b8WGfI23BCUw4y9bR3G0rbWhbghC/EZo2W3N5XEhpmZkUwD+R8pqWspIxqUKvKIqiDC8eEpqAWzTBR/PcFHmc05m0BX0ZOk3J3yVcFoxJKxyJzgLeCyzEDlY/DjxeU13V21onpghB3ONibsBLoVu3L5KTaTJ9KfosyRcXVcg7hhuPE8yvAO6sqa5q20eHPSHGoq2pU8NivVdnXqFn5IkWXWlkyuRl4JiJrmGxbPmKu4EPAvnDTe9YtnzFe4DHgCh21s3dwCXNTY1/3ecDdYzm96YCFoqi7BAPCR+wXMCHBOgWrAZu2dN2TU7bxP4pJP1Lf4XALQyogwG0/3TG2x/Hpd1Cnq+Aoa5OLQndfZ1ITpSV9aq7wSRQ2tB2NkL7qye/qFhzuXeU1pbSwkj0JY1U34tIecaeBi3iIXGt38WP8914c623LaX3/G/K+d99pfj0vwEv1VRXpUa6j9Y6IbCnH83DTo98aFGFHNXdknhIXOTR+GORl+Jc6/VmsF7ynnD/U7NCDewMTrw1mvHmUtrQdiL2CUAaeLilrGSiU1QVRVEOWvGQOEPAN4DTnYeekPad7YcHX+A6QYXTgcWAJrBaL5v5/e8W+K2FAe/uXa0sC7b10GlZfGhRhVw93FjCkehn89LbEu97/cYnsD/rXpvoi+yxMBYBC4B4SFwH1E7zIUZSeNOUsD2JBCqCMTnhXUKWLV/xNeBHwAeamxr/nmM9gd3VcBZwXHNTY9+y5StWY5+vn9jc1DguhfVH83tTU0IURdkhGJNJ7PZavx+L7Tl3iDc5y3+dFPhidp1G8m5n9R6v1L6Y8nmGDlaAPVnQ6w6QzHwRiIzFGJU9V9rQ5kGIZm/hlOLB9ROE0HAH8n0gjzVSie8BX+n/WTgSnQGcBtw/MPV1QGvegv7lfe5p5xSwLWewAsAjTLlw233rv1D/92eHW3ewRRVSYk+9eHq0z+1nCn2KJsxhP1N1gXZY73PPX1pd9cc93VcuTtvSUb8GiqIoytgLxuSjwLAdQwBqqqs6gPvCkWgcOPUo3zPLNE0cO1SwAkDToMhPUWcfPwLOzLXteEgsuFDPX+G2Eqe6BL0SNEvSFw+JHwO/dDqLHOxuA67vTuMvtCckZyUl9KSxsAM/t4/T+IZzB3aR/m8tW77iHwNbmy5bvmLOgNamVwGnApcNyMT4BvAQdnvTn43jmEdEZVgoijKhnMKIc3o0c/7N07f+xSoO+HM+wbSgJ7FOVtQfNz4j3Lda68RU4GpN8GFAl/CYlNywqEK+Mlb7iIfEkcJOBf0oduHJlyX8GLgnGBtZQcmhlDa0Ldc9vt948ouyVkKXlkWyc+v22RsfPa6g+y0PdsprKXYGwCogwM4ARYBda15Z79n0hyXzMuvPDbjIUhrT1pmiPW0RCsbkP/f0eEYjHIn6sANvc4EjDu96+ozF2+9ZMc1jBnI9rydDMmHwlWBM/mo8xqkoiqLsn565QftDoV+u8HmyryMlbO2iw5Icu6hCbhlqnXhIvEfAfQUepng0dtwTMi3oydCTsXhQwkf216DFWGVYAMRD4kLgXo+GyPeg6UMELUwnWJG2u4h9IBiTD+zNPsfSsuUrrgF+AzyBHUgxgAsAmpsaL1m2fEUxdteYl5qbGt876Ln3YAe+jm5uatzn2Zkqw0JRlP1GTXVVAlgvass3IUQKu495dkLgkqIwbFfVfhvY1j/XPxyJHoodNV4A3FpTXTXkh/dk0VonyoTgRr8Hr8+NDwEZg3f3JrnymRvE7VJynXP3f4/FQ+JKAXUBN3k+HZcADIuZfQa/z1i8Gg+Js/d0yg9C+6ju8eVs2yY0DV0ID3av703YhVmLsT8wZwId2NOCerCLVvUvPUDfzL71JyQFqwKu7L3qLQlpS+hb/Ec9MuC4NeB8AV/D7hCSBGLSvpM02orvhCPRAuyMoLnO15nYwZUeYOOb+QtvWbTlrg+ZFoFsXUekhKRBCmga7f4VRVGUg4tAHp7t82THOgI0DeulnpPedUck2oFd/+i1/p/HQ8IjoKXYu3snOF2DQg/53RnOSZl8EZjwaQ0TLRiT98dD4oNpizu3Jwl4dbt1qSb6zzWQKROwMysumUzBCoDmpsabli1f8SZ2l8MfYgcsngVqnFWi2MW+PzTE0/8PO9N0JfClfT7YUVABC0VRJotekAa5+oABmCaFpr4Nu6o2QCYciXYD87ELGL4JxBmj9lLxkPAAHxFwHoCEB4G/BGNyr2oOtNaJD+kaN07Np2hgbVG3jsvvoaijlyszJr3sxdSXeEicrQnqpngpGviSunUo0ilKGJzQm+Fv2MW+snKm8hRi9xmfCkwBpnqOuXAB+TnjFQBITc90F855oKD7rYexMysWYc/T/VdNddUw7Wqr1q4KiZeSBot9LnbrkC4l9GRIbA4cvfa/sy+76rFI9O8Xb1i5RcC/XBpHB1wUuzQnWGDytYTBl+Ih8ZlgTGatBO8c71R2DVBMdX7c38L3v87X7f1dR+Kh6/+vK01dsZfCLFXhe4E/5GprqiiKoiiOrdYIblkYlu5b27vk09gtsV8NR6L/wa4TtvUs76GnzTTe8mdrWy8E5LnIT5t8NR4SNx4INS32lhO0mAN8MmVybcpk/oAfv4wd2LktGJOdEzPC3JqbGu8F7s3ys+uA67L87H+w+3nWZKACFoqiTAqysl6K2vJfk858DZ9n6ARIKSGZ6diuW58D1mAXDJoNnIgdsJDAO8BS4PhwJNpfP+Nt4O3BrcKG43ROudWj4/bqFAKkTD6RNvlFPCSuCcbknXtyrK11QghBXXHersGKfkJAcR4FW7oob60TP1xUsfNDMRyJBgBzJEUaBfyo0L1rsGIgvwt30uC4eEiccvf8lU8DRewMSuwITDhf+z8vJNAJbNczif9lMpnjdbc3a8KqlBLLNLWeojnxmi++f6vz8L+dZUQklPZk+K8pmeV34ek/HsOCPoPetMnjz009tww4HyhL63mfKBa98/Lc7ByXgLydbVBvjofEm8GYfAR2Kw7bH6DIZ+f/p5eA14CNNdVVWYtxBmPy1lUhcej2JF8NuMn36OgCSJvIPoNOS/KAhGtHetyKoijKwcuS3NyX4hyvO3sx54wJAvO1LvOQ7wCfxM5Y7MX+HDvZJY0yn3P+ko2ugSbwm5J5wIYxPIT9lpN5+vN4SNyIfR5UgJ39uV0FdcafqmGhKMqkIWrLpyL4HwHvbNyD7gdICcl0grTxEJKLZGX94OraJwCfwA5QPI19ATobmIEdMZbYWRdvs7MQ6NtDtVcFex6jJogVeygcnJJpSuhI0WVJPhmMybtGe5ytdWKRS+df0wp23LUfUneCRG9KfOUP71Td5Dz0HuxMj0ewiyP1hyLEgAVAnLLpjzMPS6x7aqqX4lyFoxIG8k3t0CdWzbnmXthRJ8LEnqqxfYilo6a6ygQobWibgdBe9BVPLxJZdmKmk6R7u+5tuXzhUOmHIxYPiWJhF+78rBDoSDQJ7dKuiH1LMCaNcCQq3rW5ZdlRva23TPNa+dm2lTahI6M/ds+8b38NO0BxOHZtDxM7Q2cjdoDi9T3pVx8PiaMFfBk7gKIDT0n4cTAmnxj1gSuKoigHpdY6oQnBS0UBjvS6d2+1KSVs76HLMLlqUcXuN1DCkah28cvf/U+xxzrLPczUkvYUWw2Lc4IxuXbsjmB8jGUNC2X8qLamiqLst0Rt+eEI7kPTZuN1TUEIMKVBKtMD8l9ILpOV9UNmF4Qj0eOAZcDfa6qrnnQe04FDsIMXs7GzMmbBjrvvnQwIYACbjt3+YPdx7fHXir0cni2N0rSgPcUmCXNyFaoKR6Ie7M4X+c7XvCVFf37/cYVrv14UIOtFNUAiDS92zHv8n+2f/Dt2quex2IGENuyL66xm9Tw/67Stf75smsfMuY+MBVuMQOt9R37tM+wMSnT11wUZTukda7+v6e5rPQXFBYODFpaRIdXdvt1pa/riSLY3HKc2RTH28XcNvtOxKiRuzXdzhc+VvY+6lLAlpSf/M+dzP+3xHPICOwMUb9ZUV+1xEVJFURRFGUutdWKeEDwU8DLN78GrO1Mc0wb0JOg0Jb886Tr5zWzPXxUSN+a5KfcPMaWyn5SwLUmnhKOCMdm+b45k31EBi/2TKrqpKMp+S1bWvy5qyxdiWqeRSH8SxHSkfAm4WVbW5+ycUVNd9UI4Eq3HLoTY/5iJMyUEp22lMwVgKjunlMzGbrMZAEjp+TM0TSt2admv2XUNXBr+jf7jrwxHomvZNSixIzgBDJ4uIbdlZs8xreeA3DEBy0IG9M5ngP+HXYz0fcAcYC07W1fKAcuOf+dnth6KZX4i5w6wi0h5zL4X+wM8oyblty0zYyY7tlzn8vo9msvtl1JippIdlpnpQcoPjVWwAsAJDmWtASFgnq5lD1aAPeXGLczepW/8Jva+P2X+N1ZjUxRFUZSxtKhCvtxaJ0r6knyxL0U5EEAihOBxS/L9RRXyP7meL+EXfQaX+/Ts2ZZp+1Rk9f4YrFAODipgoSjKpONM93jMWUalprpq6wjWsYCtzrIWdiksOXt27/PXeDUrd7cSwK1RlNb8y4DDsOeM9jhftwKvDnqs//vEuwv+4TdMPi7lzvZiQ0mm6SjUt/2qprqq1RnjY9j1OtprqqveHGZ461aFxGbDsotOZpMwaJdw83DHmk1LWYkEqkob2uqMZN8VCO1kkH1I+RfgXy1lJfu8TVo4Es3Dntox932eaYX5cvh6q1Ki6dLo2NdjUxRFUZS9sahCbge+C3y3tU5ogDzpupGlyAdjct2qkPhnT4YP5LsJDD7nMCzozLgS66aedcfSMR+5oowNFbBQFEUBnE4PnUBnPLTyWVyYDP8eaR7Ws/b+/80ovaG/U8TIVPU+c4No6klyRYF/6DauqQyWKXl9UYVsHTTGEc8vlfCd7jQ3DdW1AiBlYhkW24B/jXzsQ2spK2kH6rL9vLShLR+4AiEqsVtqZYC/ImVNtgyMcCTqB/Sa6qqeQY/nA0diBymOxJ7yA9C+2Tf/7uKebUd5dYqyjcWwwJJsDcbkxpEen6IoiqJMtEUV2aegZiPhspTJHRmL8/0uClwautM5qzttklpffMYP1k8JHheORM/D7t6l6gUok4oKWCiKouzuP0mTRMCFN1cGRJ+lZ56a+fFDgQvDkej/gE0j/aCXkspEmlOk5MQ8H/7+wp6WhEQKszfFZim5eG8OIhiTf1oVEovbU3w2302RW8MpCQIJg3TSYKuE8/Z1xevShrYjEGK17vFNc/kCAU13YU8bSVyVSfSGShvWXtdStvC2gc8JR6KFwKeBl50WbXPZGaCY5qy2DTuT5SHg1Zrqqq54aKVuwCfTJkWeIWbsOm1QuyRU7aPDVRRFUZRJIxiTaSAUD4njejNcK2Ah0GfBH4DYZ25alQpHomcAFwIF4Ui0pb+4tqJMBqropqIoyhBWhcQjBR5O8+oMOaEiZSK7Mlrb3fO+83XsD/987KkgbcD/aqqrhp0L2lonvAIqEVynCTwCpCnRgEYp+e6iCrl5LI4lHhLnCPgWcCogJSL5TuDo9UWpt9YHzN5jAcuCvwE3BWMjmE8xCqUNbTpCvOjJKzpK93h3r3JuWaS6tnVKy7qopazkMWdqzizgS9idXl6EHVkom7GLY74GvJatxWg8JI4R8FDAxVSfC7cm7EBFxoLeDF2m5NalMVkxlsepKIqiKPuzcCS6EPgo9o2A2Ejap08Gqujm/kl1CVEURdlL8ZA4QsDj+W4O8epo/ZkWUtrBip4MWyScEYzJl50invOAEuw3Xw92L/T/Ac9ma53az5mTelhiAwvSW5mKSR/wSDAmsxaX3Ivj0oDvI7Rr83TL49FxSyBtkkwYpCSEgzH527HaX2lDW6nm9t7uLSjOOkXDTKcwurc9dvTzd/0EO4viGOzXcSvwBHAfsKGmuqp3pPuNh8QMp7Xo1QJc0m7ZulbCd4Mxed9eHZSiKIqiHIDCkehRwHLsDMbG/imZorbcg32O4wVelpX1b0/cKHelAhb7JxWwUBRFGQPxkJgj4FfAUo9ut/RIm2jAIxI+H4zJVwc/x2ljugB4FzDfeXg9dubFuprqqswQ+zldwE2aYI5bwyXBStvJmA9I+NxYBi5WhUTEpREp8lAweLqLJaEjRacp+XQwtntP9z1ResezD3jyi87X3YObpewkpSTV/k7yyBfv+5rbSLyIfXdHYL+OxwF31VRXvbAn+4+HhAB8QDoYkyrFVVEURVFyCEeis4DLAONVTyp2Z3H7dQiuRuufV2rpIFuRVMjK+mcmerwqYLF/UgELRVGUMRQPiUOARc4/nwnGRjZVw+lecSJ28GIOkAKex868eLWmusqKh8Q5Gvyl0Euxe8DkE6cgVqY3wxsS3j0W7cbiIZEn4I2pPoq1LLU5TAvaU7wuYW6u2hbhSFTHbgMb4P+3d+/BcZXnHce/5+xKuyvLkgUYMLixMU1V0jgkKjRpZmNNJ5NyK06Cu2a7jRtnaNUhGZKYqg0qJUaTElPq1IydxlOFhrhOd7bauLQ2HqAkqQERgksEHdPQdfEttUOoLUsr29Jezp63f5xdvBaSdVtrJfL7zJzR7rk+xzsjeZ/zvM/rDdmoG2UJHfjVWx/0N12+2Padv2VSZuBEn3EL79+5ZvnRqdybiIiIVEZ7R+eCjOWu3XZx392ng9YlBGtD2GWlpk4BhrL9GG4167Y+X81YlbCYmybzuanppojIOFq7zXHg6ckeVxzCsBfY297ReTFeOeX78JIfpzr+7J7XboRtjYG3Tz1qWRDyU2MMi4ccHgY+Pb27AOC2gA//WMkKAJ8NPpv5r9dfv3ZXR+cBRiQgyl4HRjncBYaBodJiGdNnXHcxozTALDHGYIxbgzdLi4iIiFTRxg3rB/ybPruoUOu7lLrAuX/vLQtq/FBvN3F6+J+tTXcuNuu2vq169J0g1Ru28Bp91+NNTd/X3NKjp/0zTAkLEZEZsHHD+j5gT3tH5zPAFcD7lqV/FK3x2XV+e+xZykJ+aoYcVj6z2prf2m1OwVvVDbV4SYPasiVwvtcfDi5ZtaRwpH68WP22FcrbgVuAFylLPgCDI96XL8NAZuQsKSu378vZmaFHfTW1Y/awcJ0cYP1455r3jtpEU0RERGaOtenOGizuIFg72sMJj88Gvy9IvvAJIDljwc2AVG94Ad6Dors4O7wX4ECqN7wF2Nbc0jNQhdDGFInG1gKPlq06DRwCtgObk4l4tmzfDwGdwG/i9fg6jPdgrjOZiA+Mcb5yn0km4t8uO18TsAn4ePF8TwJ3JRPxijSPV8JCRGQGFb/QHwOOPbv6/kiolrrz7W9Z4PPZvpebbnxgV0fnUbzkw3nqFQCv0iEL5Mp+5gpWzRnX4MLoM5+UGGOyvzzw/D/+Yddzj03wts5nl+vkBgq5bMNYs4Tkz5xKY9z7KnAtERERmb5fw7bhfCWZALX+Bhw3wjsoYZHqDd8A7ADqggGbYNDGsiyMMWQy7rJM1t0EPJDqDa9qbul5qsrhjubLeImKRmAV8BDw63jNVIlEY9cDe/CSFF8BTgLXAmuAvwcGiud5trgOvGTEUeBrxfc/HHHNx4rX2ADkgS8BT0Sisd9IJuLT7h+mhIWISPVM6HewhXHn5fsO4w0vyTEiETHy/cYN653RzvPM6vv3Zi1uqvPTNLLhZokxkCtgLMwPJnkvo9q5Zrmzcvu+38qdSff4nVCTL1AXsn0+jDEUchk3P3T6FMa071yzvKpjYEVEROQttYz1H4VzWHB26vE5r5is2F1ba1uNDX7L5zv33yAY9FmFgiE96IRyOXd3qjd8yyxMWjyRTMRfAohEY1vxqmVvj0RjdycT8Z8Bf45XMfuhUjVFcd+/AN6qkk0m4geBg8VtfwkcSybi3xl5sUg09jGgFVibTMS3Fdf9BHgcL2HSPd0bUsJCRKRKDLyQL7Aq4Bu7ysIYKBQMy9Ivxj/zzR9Naxqx1m7z38+utvZnC1wX9I9epTHkkAV2tnabivWT2Llm+aGV2/dd42SG7nCyw18AFgAFYBfGPLRzzfKfVOpaIiIiMm0HKbh+jOG8iYtCIYcxP565sC6c4jCQHbW1ttW0wG9bY9y3z2fRtMBv9w84bi7n7kj1hhfPtuEhJclE3I1EY3uA64ClwM+A9wCvlicrivsOTvEyt+I9NPunsnVP4E2NuxIlLERE5rTvZAp8tc5QN1bVZc4FA3tbu01F5jw38MnTefa6hsuD/rMNOF0DQw6ZjMPrBj5biWuV27lm+SBeSeGmSp9bREREKses23rCevjOF3AKN1IzxtdFY7CyTtZn+LuZje6C+TRQ19jgt8ZKVpRYlkVjg98+fiJXB/wBsHkmApyiUg+OvuLPN4CWSDS2NJmIH67A+ZcD+5OJeKa0opgo2VfcNm1KWIiIVElrtzn17GrrvnSWBxoDNIxMWuQLcCrHSeM1farUNd94ZrX1gSGH+4YcPmVbuIBV7G3xDQMPtXYbTQsmIiLyi8xwN0PZD1JvNeEbUZRpDJzJnrk6Ezjy8fSCje0dnfdu3LD+cGlzcXaNpXh9t441t/TM6qbaxXjvCgZsRg4DGYvPZxEM2GSy7udTveEts2j2kMZINHYJXg+LCPAJvIqKVHH7FuC7wH9ForHdwFPAY8lE/OQUr3c5Xn8LItHY94CFwPXA/+FVc0zbeRuviYjIhbWi23y9YLinL0M6nbOGMw4MO9CfpT+d45CB1tZukxr/TBPX2m1OrOg2XzBwRcHwwYLhOgOLVnSb+5WsEBEREbNu62sYfpvTmZ9zJpMm73hPUjK5HIPDaQqFrt9JNz4IXAasbu/oXJTqDftSveF1lsVRv896qcZv9VgW/7v/5XB3qjd89XjXrKKLgauDwfG6jJ4r4O1/NXDRBYlqar4HHAdex2uC+X3gk6WNyUR8B3AT8BJej4lHgDci0dhXI9HYeE3dRxPA66EGXpJqMVCDN0wkOLVbOJcqLEREqmxFt9l675/+Sf+7+5+7YdngfwwAGQO7gedbu80Fy9i3dpssxYZKIiIiIuXMuq0vWZvu/CXyhZtxCqvBqsOYXuCbZt3WN9s7Oi3gB8CtPrvQlnf8N86vd5fPr/fPK1UqFGfX+N3BU85HU73hjza39LxSxVsaSz14Qz0mwz67/3zODrmots8B+4FTwOFkIv7myB2SifiTwJORaGwh8DHg80AH3ix2fzvJ62WB2uLr9wO+ZCJ+JhKNBYDMmEdNghIWIiJV1t7R6cffcNWrC2/ZtvaRvXuqHY+IiIgIgFm31QF2FpdzFKdqf6O9o/NbN7f2dtXXmQ80NvgD5V/8LcsiFPJZfr910cn+/O5Ub/hdzS09057qssJOg5dcmQz37P6zacjL3tIsIeNJJuLHgXgkGtuB9wBrNZNPWPwcr8qGZCJ+umz9pcVt06YhISIi1XcVXkmdZssQERGROeWPIk+bRQsHbm5o8AXGqlKoqbGprbXnATfPbHQT0gccyGTcSWUsst7+B4Cp9n+YFZKJeBavKuOyKRy+D/iVSDT21vCPSDRm4zXc3FeJ+JSwEBGpvvfg/bE8Xu1ARERERCbpGr/P8o/XsDIUshttm0/NUEwTVmyYuSWTdSkUJpazKBQMmawLsHkWNdwcVyQa+8jIXhXFJp3XMrVhwo/jPXS7vWzdTXh9QXZNNc5yGhIiIjKDItHYYeC9pbK59o5O+9jRQ3/l5HPvApYA7dWMT0RERGSS6qwJPAYv9nyov9DBTNE24IH0oBNqWuC3z9fPwhhDetBxgWHgH2YqwAq5F3h3JBpL4FWHXAbcATQAXyvtFInGlgEfLr6dB1wZicZKyaYfJhPxUnLjaeA5YEskGrsCyAP3AK8AOyoRsCosRESqa2lDw4IXfX7/V6odiIiIiMgUHHEc4xuvB0Q+7zrGVGaYQKU1t/QMAKtyOdf0DzjuWJUWhYKhf8BxcznXALcVj5tL/hp4Efg9vH4Vd+ENB/lIMhH/ftl+K4DtxeUSvIaapfcrSjslE3GDN3XqvwBfAr6M14j1pmQi7lQiYGuyzUVERGTqShUWeH0rvnXp5YsfDoXmLTxyKDWAV3mhCgsRERGZU/7nlfCexoaa1kBg9OfhxhiOn8ilXZdrm1t6jlTqul1dXXXANcBrbW1t056aPdUbvgGvMqAuGLAJBG3LtixcY8hmXFMcBjKEl6z4t+le7xfVZD43VViIiMy8ZcC3gdtDoXmLgNeqG46IiIjI1Lku69KD+QHHcd+2zRjD4KAzZAz/WslkxYXQ3NLzFLAY+GIm6x5Mpx36B/Kk0w6ZrHsQ+CJwpZIVM0c9LEREZt7jQHzJVc1vAnXAq8Ci6oYkIiIiMjXNLT0vp3rDt/WdzH83GLRrQ0FfvWVBPm8KZ4acU67LbmO4o9pxTkRxmMfmVG94C3ARMB9v6tKTc6nB5juFEhYiIjNvLfCNI4dSjy65qvnBjRvW5yLRWLVjEhEREZmy5paef0/1hhcPD7vRbNaNAUFj+E9j2Nzc0rO/2vFNVjE50VdcpEqUsBARmXl78UoKHzlyKLVinH1FRERE5oTmlp5h4NHiIjJt6mEhIlIFyUT8SeCnwOci0dgLwN8AfxyJxo5GorFAdaMTEREREak+VViIiMygZCK+tOz17xdffr060YiIiIiIzF6qsBAREREREZG5zKp2ADIppc9r3CamSliIiIiIiIjIXJTD+9I7v9qByKSUPq/ceDtaxmhmFhEREREREZl7urq6lgCXACeBfiDPBJ7cS1VYeMmKK4ETbW1tR8Y7QD0sREREREREZK76KXAG70vwRVWORSZmQskKUIWFiIiIiIiIvAN0dXXV4D2UV0+L2ckAuba2tsJED1DCQkRERERERERmHTXdFBEREREREZFZRwkLEREREREREZl1lLAQERERERERkVlHCQsRERERERERmXWUsBARERERERGRWUcJCxERERERERGZdZSwEBEREREREZFZ5/8BTSGWBgQomdAAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# First-order Trotter\n", "dt = 1\n", "trotter_routine = h_spin.get_trotter_step(dt, qubit_reg, trotter_order=1)\n", "\n", "circ = qtn.Circuit(n_qubits)\n", "circ.apply_gates(trotter_routine)\n", "circ.draw(figsize=(14, 14))\n", "circ.psi.draw(figsize=(12, 12), color={\"PSI0\", \"H\", \"RX\", \"RZ\", \"CX\"})" ] }, { "cell_type": "code", "execution_count": 5, "id": "bfb769ab", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:06:19.702426Z", "iopub.status.busy": "2026-04-03T04:06:19.702274Z", "iopub.status.idle": "2026-04-03T04:06:20.848699Z", "shell.execute_reply": "2026-04-03T04:06:20.847902Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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jpJdOgFlmDmtrd/H4sPVS7XPYq2s61XMjj4z5v4bj9++FZ3u6LiAULOcp5pDZvoMnny68dPH5wopMfwBApEeyNZspj+jyrldT9XJ0o5d+5gHElqMbWdyqWZun0SzNkoeIiLynelt90n0ZwH1zNR7fqZu36FgidWbxJ/nHNq3M/e1/UzXeEl3PZcZ6zT42kqkHiK3rXo2vVfSoOk+4A9ixMlj5egkdfflXuoa2F+v8s41kMrks27ujKD+JYhjGEICvAARk/p1to5hefCT4zPA4opFeAEBuZxOfp+YweO6bPU37tp4N277Rf10bfCGGcG/pBFZh00T6RhYvrL9oa9C0Ss0//bkz2D/wA4TDPaXpChmsr/0FP/5h/siaTvXcyiNT8/oH0WAsPAY9VMpjWhlkCzfx4su5/Zqi/ZHpkUzNZsojurzr1XRlObrRSz/zCC5H1Vncqlmb5yRZmiEPERH5Q/W2+iT7MoD75gPz5vGd0nkLjiX27iTmfv3NyurrZy8NKBtvia7nomO9VhgbydYUWTe8GF+r6lF68ZHgueEfYLXrI0ATOpdRBHA2mUwqe4y38q/zJJPJVcMwnoLklSi5h7G4XQzM1r5uFwPIPYxdrr0SxbQKV2qnNQMFfHZm7t3KWa3FJT1umtqhmqapYXFJv1x7pqy2Zm09N/LIWLgVjhd2tVmED75e2NWwcCt8ufrKDZH+AIBIj2RrNlse0eXtVFP1cnSjl37mAcSWoxtZ3KrplKeRLM2Sh4iIvKd6W61iXwZw31zB4zt18xYdS6TOLP5kN7JtHVdP5u8UXc9lxnrNPjaSqQeIretejq+dajaSJ4AOPGb/DLn8GpZXbotciaLsBArg0j1RGrlcZnJiBkDp8qKKys876ejKr2aufgqUHvcV6ghuwipdDlRR+XmrY33zb70fL8xNLqyPXboGoHSJUUXl5y9ToZXfv/9W3ZpO9dzIIyMxMlXKUKzKU/75/r3wyh8+evNTmf4AgEiPZGs2Ux7R5V2vpurl6EYv/cwDiC1HN7K4VbM2T6NZmiUPERF5T/W2+qT7suqfT/u+GVB/nO53j/zMIzqW6OjSv9cBvae6jhdjiXp5WnVsJFMPEFvXvRpf16vZeJ4YrIIOK6/Deqgv/vI3r0n3p1FNc2NZAKsA8ssrtw/dpKb8u31aADloMNPzmUM3WdICqH6O+iqA/Nra3cZqHq4nQziPbM3M9p0ja0r0Z7/mcT2SrCnKqzwnXodULsfyvK30fObQTZYa7aVETd/WS1E+9wdwztOqy5uIiHyielutYF8GcN98oB6P746dt9LxVrAzuOXGeEtkPZcY6zX92KiRmsetG56Nr51rynDKc5L+NKRpTqJMf/hqanJiZhQCj+YK6IGN/vNdb2Cv5u8PwNp+kLdLX3sCbn7yemrs0jXHmtWPYKpbs6aeW3lELSxfTSVGphxrVt+tWbQ/gHiPZGo2YR6x5e1Q04XlaNpFpPRY8O16j/sCYLpV08/1UpCv/QHq5mn00XK+5yEiIl+o3lar2JcB3DcD4PGdCDfGWx19+toj/9j3L9Z2sbtePRky67noWK8VxkYyRNcNz8bXDjUV5PH8EceuPJ3HTePTif6OAf0X/c90r4d79ANnsAoZM7r++Vb/7pr5O9nL5ZxqNlrPT1725yQ1/Zy3n3nK84+h/iO9zEael+5GTb+0W3/aLQ8REYlRva3mvqy5tVOPVB8rN8Gxt9Kxnt95VGvH8ZbbmuZKFKLTwo0dXqsdaByl3frTbnmIiEiM6m0192XNjT0iOj08OYkyOTEzDIWXlwHA7oY5sLtmfufAiwFYABq+tOZQzTr13MiTGJlyrNnopVue9KdOTdVZZObtd00iIiIionbgxrHyzte7Q7Vf53Gq58l4wsOxhOo8LTu+rlPTjTxucv0kSrkhSwAO3XxmcmJmtJHG7Jl7fet3t96EjUM3qdFjwXca+TsdazrUcyNP+U3lWDMxMjUq++byrD8ONVVnkZm33zWJiIiIiNqBG8fKuxvmwPrdrX8/brzl2XjCo7GE6jwtPb52qOlGHrd5cSXKEIDOkfiziIRjAEqPJCrfUXcIgHRT7D1EYUMfvNgDPVaKYGYtpOczeu2NlxqteUQ95XkqNXu6LiAULM3OKuZQvjOzdE0v+nNETaVZmiAPEREREdGp4saxcjFf7JYZb7k5nvB4LKE6T0uOr4+o6cb42lWunEQxDGMEQB8AdPT2xHc3I4iEY4hGeg9MFxnMxQ3DkKr9XOhH3V+E7vSuYxV6LIRw78ETW927/b1PbF5IGIaxpaJmbb3IYCy+k44qywMATz4djt+/F0YoGIUe6qn5XUGqptf9qa2pMksz5JH6Y4mIiIiIWpzqY+XnQj/qTnUuDuQHNi0Ax463vBxPeDGWUJ1H9XjU7/FWbR4TGZgBE6FOEx19+XONjK9rbCSTyeWTFqmm/Ok8hmEMAfgKQAAAzJ1QceOLweD5f/in/YWc29nE56k5DJ77Zk/TStPJsGHbN/qva4MvxPYXSGHTRPpGFi+sv2hr0LST1qxXz7ZRTC8+EnxmeFxdHhvF6x9Eg7Hw2P4by7QyyBZu4sWXc9I1vehPvZqqs/idh4iIiIjotFF9rGzD3ruTmPv1Nyurr5+9NHDseMvt8YSXYwnlYz03xqM+jx8reTojHUhp7wOa0nMURQBnk8nkqqqCyq9ESSaTq4ZhPIXylSg7q11xALM7hW9vLr1TyMIuBpB7GLscezS7IlN/M7TW/cXgnZ+bVuGKmbX2XzezFsxAAZ+dmXv3ifSF93qtAeEzZU4169XLPYzF7WJAWR4AWLgVjhd2tVkr+O3Tn6xiDoVdDQu3wpcvPl8QrulVf+rVVJmlGfLI/K1ERERERK1O9bHyZmitO3Vm8Se7kW2rUueoel6MJ7wcS6jOo3o86vd4qzbPoPZT7FgZrHy9hI6+/CtdQ9uLMnkcbKg8gQK49HWe6stlJidmVgHky99pqpbfSUfnfzUjdyOd8elEvx4JPkAWVno+c/Dv12BlI+sP/tb78YLsc6wdazrUU50HABIjU6sA8uXvxR2oef9eeP4PH70pXNPT/jjUVJmlGfLI/K1ERERERK1O9bHy+HSiv6NL/15nsCMCDWZ6PlN9c9dD9TwbT3g0llCdp6XH1w416+fR89ZD/b9/+ZvXTsc9UapNf/hqanJiZhTqHllk2kWk9Fjw7dqb3GgB5OwiUgBMFTWd6rmQBwvLV1OJkSnHmg3cfdqz/jjVVJxFat4+1yQiIiIiageqj5XNYn4vk/9mF3os+M5x4y2vxhNejSVU52nl8bVTTTfG125Tfk8UIiIiIiIiIqJ2JH3TGSIiIiIiIiKi04gnUYiIiIiIiIiIBPAkChERERERERGRAJ5EISIiIiIiIiISwJMoREREREREREQCeBKFiIiIiIiIiEgAT6IQEREREREREQngSRQiIiIiIiIiIgE8iUJEREREREREJOD/Acs54397Bld8AAAAAElFTkSuQmCC", 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Second-order Trotter\n", "trotter_routine = h_spin.get_trotter_step(dt, qubit_reg, trotter_order=2)\n", "\n", "circ = qtn.Circuit(n_qubits)\n", "circ.apply_gates(trotter_routine)\n", "circ.draw(figsize=(14, 14))\n", "circ.psi.draw(figsize=(12, 12), color={\"PSI0\", \"H\", \"RX\", \"RZ\", \"CX\"})" ] }, { "cell_type": "markdown", "id": "9df50ff4", "metadata": { "lines_to_next_cell": 2 }, "source": [ "## Trotter error: full unitary distance as metric\n", "\n", "Let us first use the distance of the full time evolution as a metric: $||U_{\\rm Trotter}^{\\dagger}(t_f) U_{\\rm exact}(t_f) - \\mathbb{1}~||$\n", "\n", "We define a function that collects the errors defined for given times $t$ in `t_list`, number of timesteps $n_{steps}$ in `ns_list` and Trotterization order `order`.\n", "\n", "NB: in this example we consider the Frobenius norm to define the error. Any other norm supported by `quimb.norm` can be used via the optional parameter `ntype`." ] }, { "cell_type": "code", "execution_count": 6, "id": "37516bea", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:06:20.850470Z", "iopub.status.busy": "2026-04-03T04:06:20.850316Z", "iopub.status.idle": "2026-04-03T04:06:20.854354Z", "shell.execute_reply": "2026-04-03T04:06:20.853641Z" } }, "outputs": [], "source": [ "def errors_trotter_slice(t_list, ns_list, trotter_order, ntype=\"fro\"):\n", " res = {\"t\": t_list, \"n_s\": ns_list, \"errors_lists\": [], \"durations_lists\": []}\n", "\n", " hamilt_matrix = h_spin.to_dense()\n", " id2n = qu.eye(2**n_qubits)\n", "\n", " for t in tqdm.tqdm(t_list):\n", " U_matrix = qu.expm(-1j * hamilt_matrix * t)\n", "\n", " errors = []\n", " durations = []\n", " for n_steps in tqdm.tqdm(ns_list, leave=False):\n", " st = time.time()\n", " circ = qtn.Circuit(n_qubits)\n", " dt = t / n_steps\n", " trotter_slice = h_spin.get_trotter_step(dt, qubit_reg, trotter_order)\n", " for _ in range(n_steps):\n", " circ.apply_gates(trotter_slice)\n", " U_trotter = circ.get_uni().to_dense()\n", "\n", " errors.append(qu.norm(U_matrix.H @ U_trotter - id2n, ntype=ntype))\n", " durations.append(time.time() - st)\n", "\n", " res[\"errors_lists\"].append(errors)\n", " res[\"durations_lists\"].append(durations)\n", "\n", " return res" ] }, { "cell_type": "markdown", "id": "f42fe949", "metadata": {}, "source": [ "We consider a sequence of evolution time growing like powers of $2$ as in QPE: $t_f = 2^kt, k = 1 \\dots 6,$ where $t$ is picked randomly in $[0,2\\pi]$. We vary the number of Trotter steps between $5$ and $200$." ] }, { "cell_type": "markdown", "id": "78276737", "metadata": {}, "source": [ "### First order Trotter\n", "\n", "Let us start with first order Trotter. The following cell should take a minute to run:" ] }, { "cell_type": "code", "execution_count": 7, "id": "acfa18e7", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:06:20.855728Z", "iopub.status.busy": "2026-04-03T04:06:20.855586Z", "iopub.status.idle": "2026-04-03T04:07:11.689979Z", "shell.execute_reply": "2026-04-03T04:07:11.689120Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "76efe340086e48bf88a8c889cec702f4", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/6 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (axl, axr) = plt.subplots(ncols=2, figsize=(12, 4))\n", "for i, t in enumerate(res[\"t\"]):\n", " axl.plot(\n", " res[\"n_s\"], res[\"errors_lists\"][i], \"-o\", label=rf\"$t_f=${t / np.pi:.2g}$\\pi$\"\n", " )\n", " axr.loglog(t**2 / res[\"n_s\"], res[\"errors_lists\"][i], \"-o\")\n", "\n", "axl.set_ylim(0, 3)\n", "axl.legend()\n", "axl.set_xlabel(\"$n_{steps}$\")\n", "axr.set_xlabel(r\"${t_f^2}/{n_{\\text{steps}}}$\")\n", "axl.set_ylabel(r\"$\\| U_{\\mathrm{Trotter}}U_{\\mathrm{exact}} - \\mathrm{Id} \\|$\")\n", "axr.set_ylabel(r\"$\\| U_{\\mathrm{Trotter}}U_{\\mathrm{exact}} - \\mathrm{Id} \\|$\")\n", "fig.suptitle(\"First order Trotter\");" ] }, { "cell_type": "markdown", "id": "e097664c", "metadata": {}, "source": [ "### Second order Trotter" ] }, { "cell_type": "markdown", "id": "8312f493", "metadata": {}, "source": [ "Similarly, we plot the errors reached with a second order Trotter formula, as a function of $n_{\\rm steps}$ (left, linear scale) and as a function of $t_f^3 / n_{\\rm steps}^2$ (right, log scale)." ] }, { "cell_type": "code", "execution_count": 9, "id": "da9ca484", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:07:12.135161Z", "iopub.status.busy": "2026-04-03T04:07:12.135013Z", "iopub.status.idle": "2026-04-03T04:09:09.515247Z", "shell.execute_reply": "2026-04-03T04:09:09.514407Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "67421a8e0506424f9d947e43e66838be", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/6 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (axl, axr) = plt.subplots(ncols=2, figsize=(12, 4))\n", "for i, t in enumerate(res2[\"t\"]):\n", " axl.plot(\n", " res2[\"n_s\"], res2[\"errors_lists\"][i], \"-o\", label=rf\"$t_f=${t / np.pi:.2g}$\\pi$\"\n", " )\n", " axr.loglog(t**3 / res2[\"n_s\"] ** 2, res2[\"errors_lists\"][i], \"-o\")\n", "\n", "axl.set_ylim(0, 3)\n", "axl.legend()\n", "axl.set_xlabel(\"$n_{steps}$\")\n", "axr.set_xlabel(r\"${t_f^3}/n_{\\text{steps}}^2$\")\n", "axl.set_ylabel(r\"$\\| U_{\\mathrm{Trotter}}U_{\\mathrm{exact}} - \\mathrm{Id} \\|$\")\n", "axr.set_ylabel(r\"$\\| U_{\\mathrm{Trotter}}U_{\\mathrm{exact}} - \\mathrm{Id} \\|$\")\n", "\n", "fig.suptitle(\"Second order Trotter\");" ] }, { "cell_type": "markdown", "id": "5ccf3bf7", "metadata": {}, "source": [ "### Number of steps required to get below a given error\n", "\n", "For the first order Trotter formula, since the error scales like $t_f^2 / n_{\\rm steps}$, to reach an error $\\epsilon$ requires a minimal number of steps:\n", "\n", "$$ n_{\\rm steps} = \\mathcal{O} (t_f^2 / \\epsilon) $$\n", "\n", "Since in QPE maximum evolution time is $t_f = \\mathcal{O} (2^m)$ where $m$ is number of phase bits, we get\n", "\n", "$$ n_{\\rm steps} = \\mathcal{O} (2^{2m} / \\epsilon). $$\n", "\n", "As shown on the plot below, the number of Trotter steps quickly grows to about $10^6$, which translates into at least as many CNOT gates. This is why in practice we use the second-order Trotter decomposition.\n", "\n", "Trotter error at second order is $\\mathcal{O}(t_f^3 / n_{\\rm steps}^2)$. Thus to reach an error $\\epsilon$ requires a number of steps scaling like\n", "\n", "$$ n_{\\rm steps} = \\mathcal{O} (\\sqrt{t_f^3 / \\epsilon}) $$\n", "\n", "Since in QPE the maximum evolution time is $t_f = \\mathcal{O} (2^m)$ where $m$ is number of phase bits, we get\n", "\n", "$$ n_{\\rm steps} = \\mathcal{O} (\\sqrt{2^{3m} / \\epsilon}) $$" ] }, { "cell_type": "code", "execution_count": 11, "id": "2b575e60", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:09:10.267313Z", "iopub.status.busy": "2026-04-03T04:09:10.267130Z", "iopub.status.idle": "2026-04-03T04:09:10.539510Z", "shell.execute_reply": "2026-04-03T04:09:10.538541Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "epsilon = 1e-2\n", "\n", "fig, ax = plt.subplots()\n", "ax.loglog(t_list, t_list**2 / epsilon, \"-o\", label=r\"first order $t_f^2/\\epsilon$\")\n", "ax.loglog(\n", " t_list,\n", " np.sqrt(t_list**3 / epsilon),\n", " \"-.s\",\n", " label=r\"second order $\\sqrt{t_f^{3}/\\epsilon}$\",\n", ")\n", "ax.set_xlabel(r\"$t_f$\")\n", "ax.set_ylabel(r\"$n_{\\text{steps}}$\")\n", "ax.legend()\n", "fig.suptitle(f\"Number of Trotter steps to get below $\\\\epsilon = {epsilon}$\");" ] }, { "cell_type": "markdown", "id": "1016318c", "metadata": {}, "source": [ "### Number of CNOT gates required to get below a given error\n", "\n", "Here we investigate the number of entangling gates required to run a Trotter time evolution within a given error bound $\\varepsilon$.\n", "\n", "The Trotter decomposition expresses the evolution operator as a product of exponential of Pauli strings. Let us describe the algorithm for the exponentiation of Pauli strings." ] }, { "cell_type": "markdown", "id": "ddcfe7de", "metadata": {}, "source": [ "#### Quantum circuit for exponentiation of Pauli strings\n", "\n", "The different terms in the Hamiltonian can be written as Pauli strings, i.e. using the Pauli operator basis:\n", "\n", "$$ H_\\ell = U_1 \\otimes U_2 \\otimes \\dots \\otimes U_n, \\qquad U_k \\in \\{\\mathbb{1}, X, Y, Z\\}, $$\n", "where $n$ is the number of qubits required to represent the Hilbert space.\n", "\n", "Here we present the algorithm to exponentiate $H_\\ell$, i.e. to encode\n", "$ e^{-i H_\\ell t} = e^{ -i t U_1 \\otimes U_2 \\otimes \\dots \\otimes U_n }. $ A mathematical demonstration of a similar algorithm can be found in Fleury, Lacomme, *Quantum circuit for exponentiation of Hamiltonians:\n", "an algorithmic description based on tensor products*, [arXiv:2501.17780](https://arxiv.org/abs/2501.17780).\n", "\n", "Let us first state the following two properties\n", ":\n", "* $ e^{-i t Z} = R_Z(2t) $ by definition.\n", "* $ e^{-i t Z_{i_1} Z_{i_2} \\dots Z_{i_M}} = CX_{i_1 i_2} CX_{i_2 i_3} \\dots CX_{i_{M-1} i_M} \\left( \\mathbb{1}^{\\otimes (i_M-1)} \\otimes R_Z(2t) \\otimes \\mathbb{1}^{\\otimes (n - i_M - 1)} \\right) CX_{i_{M-1} i_M} CX_{i_{M-1} i_{M-2}} \\dots CX_{i_1 i_2} $ (see [arXiv:2501.17780](https://arxiv.org/abs/2501.17780)).\n", "\n", "\n", "The algorithm proceeds as follows:\n", "1. First, apply basis rotations to bring all qubits into the $Z$ basis:\n", " * if $U_k=X$, apply a Hadamard gate $H$ to the $k$-th qubit.\n", " * if $U_k=Y$, apply a rotation gate $R_X(\\pi/2)$ to the $k$-th qubit.\n", "2. Then, apply a sequence of CNOT gates between $i_k$ and $i_{k+1}$ where $i_k$ are the indices of non-identity operators in the strings.\n", "3. Apply $R_Z(2t)$ to the last qubit on which a non-identity Pauli operator is acting.\n", "4. Apply the reversed CNOT sequence.\n", "5. Bring the qubits back to their original basis applying the inverse rotations.\n", "\n", "\n", "This algorithm is executed by the `rotation_gates` function from $\\texttt{qpe-toolbox}$ 's `hamiltonian` module." ] }, { "cell_type": "markdown", "id": "330b7c56", "metadata": {}, "source": [ "#### CNOT gate count\n", "\n", "Thus, the algorithm to implement a Pauli string exponential $\\exp( i \\theta P_1 ... P_K )$, where $P_i \\in \\{X,Y,Z\\}$ are Pauli operators distinct from Identity, uses $2 (K - 1)$ CNOT gates, where $K$ is the length of the Pauli string.\n", "\n", "For the Heisenberg Hamiltonian:\n", "\n", "$$ H = \\frac{J}{2} \\sum_{i=0}^{n-2} \\left( X_i X_{i+1} + Y_i Y_{i+1} + Z_i Z_{i+1} \\right). $$\n", "\n", "- One Trotter slice (first order):\n", "\n", "$$ e^{ - i H dt } = \\prod_{i=0}^{n-2} e^{-i X_i X_{i+1} dt J/2} e^{-i Y_i Y_{i+1} dt J/2} e^{-i Z_i Z_{i+1} dt J/2} + \\mathcal{O} (dt^2) $$\n", "is thus implemented with $6(n-1)$ CNOT gates (3 axis, for each axis a length-2 Pauli string).\n", "\n", "This gives a total CNOT gate count for the Trotterization of $U(t)$:\n", "\n", "$$ 6(n - 1)n_{steps} \\qquad \\mathrm{CNOT~gates}$$\n", "\n", "- Second order:\n", "\n", "$$ e^{ - i H dt } = \\prod_{j=0}^{n-2} e^{-i X_j X_{j+1} dt J/4} e^{-i Y_j Y_{j+1} dt J/4} e^{-i Z_j Z_{j+1} dt J/4} \\prod_{k=0}^{n-2} e^{-i Z_{n-2-k} Z_{n-1-k} dt J/4} e^{-i Y_{n-2-k} Y_{n-1-k} dt J/4} e^{-i X_{n-2-k} X_{n-1-k} dt J/4} + \\mathcal{O} (dt^3). $$\n", "\n", "Total CNOT gate count second order Trotterization:\n", "\n", "$$ 12(n - 1)n_{steps} \\qquad \\mathrm{CNOT~gates}.$$\n", "\n", "Note that the two neighboring $e^{-i Z_{n-2} Z_{n-1} dt J/4}$ terms could be merged, as well as the $e^{-i X_0 X_1 dt J/4}$ terms from neighboring Trotter steps, to reduce the total CNOT gate count. Here we only implement the most naive version of second-order Trotterization: in general, one should merge the two occurences of the last Hamiltonian term." ] }, { "cell_type": "code", "execution_count": 12, "id": "31295b90", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:09:10.540936Z", "iopub.status.busy": "2026-04-03T04:09:10.540787Z", "iopub.status.idle": "2026-04-03T04:09:10.842260Z", "shell.execute_reply": "2026-04-03T04:09:10.841585Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0.98, 'Number of CNOT gates to get below $\\\\epsilon = 0.01$')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.loglog(\n", " t_list,\n", " 6 * (n_qubits - 1) * t_list**2 / epsilon,\n", " \"-o\",\n", " label=r\"first order $6(n-1)t_f^2/\\epsilon$\",\n", ")\n", "ax.loglog(\n", " t_list,\n", " np.sqrt(12 * (n_qubits - 1) * t_list**3 / epsilon),\n", " \"-.s\",\n", " label=r\"second order $12(n-1)\\sqrt{t_f^{3}/\\epsilon}$\",\n", ")\n", "ax.set_xlabel(r\"$t_f$\")\n", "ax.set_ylabel(r\"number of CNOT gates\")\n", "ax.legend()\n", "fig.suptitle(f\"Number of CNOT gates to get below $\\\\epsilon = {epsilon}$\")" ] }, { "cell_type": "markdown", "id": "506da23a", "metadata": { "lines_to_next_cell": 2 }, "source": [ "## Fidelity as an error metric" ] }, { "cell_type": "markdown", "id": "7b817bed", "metadata": { "lines_to_next_cell": 2 }, "source": [ "In a QPE experiment, we are interested in the time evolution of an Hamiltonian eigenstate. Let us therefore consider the quantum fidelity as an error metric. Quantum fidelity is defined as $|\\langle\\psi_{\\rm exact}(t) | \\psi_{\\rm trotter}(t)\\rangle|^2$.\n", "We consider second order Trotter decomposition" ] }, { "cell_type": "code", "execution_count": 13, "id": "4e84a376", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:09:10.843784Z", "iopub.status.busy": "2026-04-03T04:09:10.843630Z", "iopub.status.idle": "2026-04-03T04:09:10.848060Z", "shell.execute_reply": "2026-04-03T04:09:10.847392Z" } }, "outputs": [], "source": [ "def fidelities_trotter_slice(n_qubits, t_list, ns_list, trotter_order):\n", " res = {\"t\": t_list, \"n_s\": ns_list, \"errors_lists\": [], \"durations_lists\": []}\n", "\n", " reg = list(range(n_qubits))\n", " h_spin = heisenberg_hamiltonian(n_qubits)\n", " hamilt_matrix = h_spin.to_dense()\n", " _eigvals, eigvecs = np.linalg.eigh(hamilt_matrix)\n", "\n", " psi0 = eigvecs[:, 0]\n", " psi0_mps = qtn.MatrixProductState.from_dense(psi0)\n", "\n", " for t in tqdm.tqdm(t_list):\n", " U = qu.expm(-1j * hamilt_matrix * t)\n", " psi_ref = U @ psi0\n", "\n", " errors = []\n", " durations = []\n", " for n_steps in tqdm.tqdm(ns_list, leave=False):\n", " st = time.time()\n", " circ = qtn.Circuit(n_qubits, psi0=psi0_mps)\n", " dt = t / n_steps\n", " trotter_slice = h_spin.get_trotter_step(dt, reg, trotter_order)\n", " for _ in range(n_steps):\n", " circ.apply_gates(trotter_slice)\n", "\n", " errors.append(\n", " abs(1 - qu.fidelity(circ.psi.to_dense(), psi_ref, squared=True))\n", " )\n", " durations.append(time.time() - st)\n", "\n", " res[\"errors_lists\"].append(errors)\n", " res[\"durations_lists\"].append(durations)\n", " return res" ] }, { "cell_type": "code", "execution_count": 14, "id": "b4e9c636", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:09:10.849468Z", "iopub.status.busy": "2026-04-03T04:09:10.849315Z", "iopub.status.idle": "2026-04-03T04:11:10.327159Z", "shell.execute_reply": "2026-04-03T04:11:10.326463Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "95b16abd6e9b4e9d9f7506edccae2d84", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/6 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (axl, axr) = plt.subplots(ncols=2, figsize=(12, 4), sharey=True)\n", "for i, t in enumerate(res2[\"t\"]):\n", " axl.loglog(\n", " t / res2[\"n_s\"], res2[\"errors_lists\"][i], \"-o\", label=rf\"t={t / np.pi:.2g}$\\pi$\"\n", " )\n", " axr.loglog(t**3 / res2[\"n_s\"] ** 2, res2[\"errors_lists\"][i], \"-o\")\n", "\n", "axl.legend()\n", "axl.set_xlabel(\"timestep $dt$\")\n", "axl.set_ylabel(r\"$1-\\text{Fidelity}$\")\n", "axr.set_xlabel(r\"${t_f^3}/n_{\\text{steps}}^2$\")\n", "fig.suptitle(\"Fidelity for second order Trotter\");" ] }, { "cell_type": "markdown", "id": "5f939d29", "metadata": {}, "source": [ "This ends our simple introduction on Trotter-Suzuki decomposition.\n", "For the reader interested in going further, we refer to [this paper by Andrew M. Childs](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011020) that gives a theoretical study of Trotter error with a focus on Hamiltonian simulation." ] } ], "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": "3.13.12" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "00994cbc123443588806d3a4abaf9af6": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "HTMLStyleModel", "state": { "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "HTMLStyleModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "StyleView", "background": null, 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