{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Improving energy estimation of a Fermionic lattice model with SQD\n",
    "\n",
    "In this tutorial we implement a [Qiskit pattern](https://docs.quantum.ibm.com/guides/intro-to-patterns) showing how to post-process noisy quantum samples to find an approximation to the ground state of a Fermionic lattice Hamiltonian known as the single-impurity Anderson model. We will follow a sample-based quantum diagonalization approach to process samples taken from a set of ``16``-qubit Krylov basis states over increasing time intervals. These states are realized on the quantum device using Trotterization of the time evolution. In order to account for the effect of quantum noise, the configuration recovery technique is used. Assuming a good initial state and sparsity of the ground state, [this approach is proven to converge efficiently](https://arxiv.org/abs/2501.09702).\n",
    "\n",
    "The pattern can be described in four steps:\n",
    "\n",
    "1. **Step 1: Map to quantum problem**\n",
    "    - Generate a set of Krylov basis states (i.e., Trotterized time-evolution circuits) over increasing time intervals for estimating the ground state\n",
    "2. **Step 2: Optimize the problem**\n",
    "    - Transpile the circuits for the backend\n",
    "3. **Step 3: Execute experiments**\n",
    "    - Draw samples from the circuits using the ``Sampler`` primitive\n",
    "4. **Step 4: Post-process results**\n",
    "   - Self-consistent configuration recovery loop\n",
    "       - Post-process the full set of bitstring samples, using prior knowledge of particle number and the average orbital occupancy calculated on the most recent iteration\n",
    "       - Probabilistically create batches of subsamples from recovered bitstrings\n",
    "       - Project and diagonalize the Fermionic lattice Hamiltonian over each sampled subspace\n",
    "       - Save the minimum ground state energy found across all batches and update the avg orbital occupancy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: Map problem to a quantum circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will create the one- and two-body Hamiltonians describing the one-dimensional single-impurity Anderson model (SIAM) with ``7`` bath sites (``8`` electrons in ``8`` orbitals). This model is used to describe magnetic impurities embedded in metals.\n",
    "\n",
    "Then we will create the ``16``-qubit Trotter circuits used to generate the quantum Krylov subspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "n_bath = 7  # number of bath sites\n",
    "\n",
    "# hopping matrix for the bath\n",
    "hopping_matrix = -np.diag(np.ones(n_bath - 1), k=1) - np.diag(np.ones(n_bath - 1), k=-1)\n",
    "\n",
    "# eigenvectors that diagonalize the bath (non-interacting system)\n",
    "spectrum, eigvecs = np.linalg.eigh(hopping_matrix)\n",
    "\n",
    "V = 1  # hybridization amplitude\n",
    "t = 1  # bath hopping amplitude\n",
    "U = 10  # Impurity onsite repulsion\n",
    "eps = -U / 2  # Chemical potential for the impurity\n",
    "\n",
    "impurity_index = 0\n",
    "\n",
    "Ur = np.identity(n_bath + 1)  # Single-particle transformation to diagonalize the bath\n",
    "indexing = np.arange(n_bath + 1, dtype=int)\n",
    "indexing = np.concatenate((indexing[:impurity_index], indexing[impurity_index + 1 :]))\n",
    "for i in range(n_bath):\n",
    "    eigvec_i_extended = np.zeros(n_bath + 1)\n",
    "    eigvec_i_extended[indexing] = eigvecs[:, i]\n",
    "    Ur[:, indexing[i]] = eigvec_i_extended\n",
    "\n",
    "# Place the impurity in the central qubit\n",
    "qubit_ordering_imp = (\n",
    "    [i + 1 for i in range(n_bath // 2)]\n",
    "    + [0]\n",
    "    + [i + n_bath // 2 + 1 for i in range(n_bath // 2 + 1)]\n",
    ")\n",
    "\n",
    "Ur = Ur[:, qubit_ordering_imp]\n",
    "\n",
    "# One body matrix elements in the \"position\" basis\n",
    "h1e = -t * np.diag(np.ones(n_bath), k=1) - t * np.diag(np.ones(n_bath), k=-1)\n",
    "h1e[impurity_index, impurity_index + 1] = -V\n",
    "h1e[impurity_index + 1, impurity_index] = -V\n",
    "h1e[impurity_index, impurity_index] = eps\n",
    "\n",
    "# Two body matrix elements in the \"position\" basis\n",
    "h2e = np.zeros((n_bath + 1, n_bath + 1, n_bath + 1, n_bath + 1))\n",
    "h2e[impurity_index, impurity_index, impurity_index, impurity_index] = U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will generate the quantum Krylov subspace with a set of Trotterized quantum circuits. Here we create helpers for generating the initial (reference) state as well as the time evolution for the one- and two-body parts of the Hamiltonian. For a more detailed description of this model and how the circuits are designed, please refer to [the paper](https://arxiv.org/abs/2501.09702)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ffsim\n",
    "import scipy\n",
    "from qiskit import QuantumCircuit, QuantumRegister\n",
    "from qiskit.circuit.library import CPhaseGate, PhaseGate, XGate, XXPlusYYGate\n",
    "\n",
    "n_modes = n_bath + 1\n",
    "nelec = (n_modes // 2, n_modes // 2)\n",
    "\n",
    "dt = 0.2\n",
    "Utar = scipy.linalg.expm(-1j * dt * h1e)\n",
    "\n",
    "\n",
    "# The reference state\n",
    "def initial_state(q_circuit, norb, n_alpha):\n",
    "    \"\"\"Prepare an initial state.\"\"\"\n",
    "    for i in range(n_alpha):\n",
    "        q_circuit.append(XGate(), [i])\n",
    "        q_circuit.append(XGate(), [i + norb])\n",
    "    theta = np.pi / 2\n",
    "    beta = -np.pi / 2\n",
    "\n",
    "    q_circuit.append(XXPlusYYGate(theta, beta), [n_alpha - 1, n_alpha])\n",
    "    q_circuit.append(XXPlusYYGate(theta, beta), [n_alpha - 2, n_alpha - 1])\n",
    "    q_circuit.append(XXPlusYYGate(theta, beta), [n_alpha - 3, n_alpha - 2])\n",
    "\n",
    "    q_circuit.append(XXPlusYYGate(theta, beta), [n_alpha - 1 + norb, n_alpha + norb])\n",
    "    q_circuit.append(XXPlusYYGate(theta, beta), [n_alpha - 2 + norb, n_alpha - 1 + norb])\n",
    "    q_circuit.append(XXPlusYYGate(theta, beta), [n_alpha - 3 + norb, n_alpha - 2 + norb])\n",
    "\n",
    "\n",
    "# The one-body time evolution\n",
    "free_fermion_evolution = ffsim.qiskit.OrbitalRotationJW(n_modes, Utar)\n",
    "\n",
    "\n",
    "# The two-body time evolution\n",
    "def append_diagonal_evolution(dt, U, impurity_qubit, h1e_rot, q_circuit):\n",
    "    \"\"\"Append two-body time evolution to a quantum circuit.\"\"\"\n",
    "    num_orb, _ = h1e_rot.shape\n",
    "    for i in range(num_orb):\n",
    "        q_circuit.append(\n",
    "            PhaseGate(-dt / 2 * h1e_rot[i, i]),\n",
    "            [i],\n",
    "        )\n",
    "        q_circuit.append(\n",
    "            PhaseGate(-dt / 2 * h1e_rot[i, i]),\n",
    "            [i + num_orb],\n",
    "        )\n",
    "    if U != 0:\n",
    "        q_circuit.append(\n",
    "            CPhaseGate(-dt / 2 * U),\n",
    "            [impurity_qubit, impurity_qubit + num_orb],\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate ``d`` time-evolved states that specify the quantum Krylov subspace. Here, we have chosen ``d=8``. The error from sampling Krylov basis states converges with increasing ``d``. Note that the particulars of this problem instance allow for an efficient compilation of the one-body evolution using `OrbitalRotationJW`; however, in general, one could use Qiskit's [PauliEvolutionGate](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.PauliEvolutionGate) to implement the Trotterized time evolution of the full Hamiltonian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the initial state\n",
    "qubits = QuantumRegister(2 * n_modes, name=\"q\")\n",
    "init_state = QuantumCircuit(qubits)\n",
    "initial_state(init_state, n_modes, n_modes // 2)\n",
    "init_state.draw(\"mpl\", scale=0.4, fold=-1)\n",
    "\n",
    "d = 8  # Number of Krylov basis states\n",
    "impurity_qubit = n_bath // 2\n",
    "circuits = []\n",
    "for i in range(d):\n",
    "    circ = init_state.copy()\n",
    "    circuits.append(circ)\n",
    "    for _ in range(i):\n",
    "        append_diagonal_evolution(dt, U, impurity_qubit, h1e, circ)\n",
    "        circ.append(free_fermion_evolution, qubits)\n",
    "        append_diagonal_evolution(dt, U, impurity_qubit, h1e, circ)\n",
    "    circ.measure_all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Gn2tRVXICtUdPtuuYQG0kmi83ouuAiHYfR0RERPZYwBK10+AFSWg2GGGs1UO3cjP6zRyPxqo6m33Cxg9D+ISWK55H/r4Nve9LaD3mh83fwmI2o6u2p91xzlRcXIxx48a5LB4REZGzdboCNjZ5M86cb7ipPsK6+3ba9WS3JD6DhsoasdOw49ujG+4ryHJqDFPdZRguXETXARGImpUIL5USkMnQa9oo/LhtDwDgzM5DOLPzkMNjLGYzBqROaj3OVeLj410Wy1Pk5+fDYDDcVB8qleq669YSEZHzdLoC9sz5BlTVNoqdhsdqqKyBsUYvdhqiOP7P7QCAU1/us2m3Fq/tOcb6tSt50pO4XMVgMMBoNIqdBhER3SDexEUkcaWlpWKnQEREJCgWsEQSN3bsWLFTkIwrV66InQIREaETTiEg6mwqKyvFTsEj/Pjjj9ixYweOHTuGpqYmdO3aFbfffjvGjBkDX19fbNq0CWfPnsWCBQvETpWIqNPziAI2NzcXmZmZUKvVCAwMRFpaGqZMmSJojOExwZh5V18888ZeLH40Fnt1F7BjzxlBY0hJF5UCo16dh2aDEfUVlTj6jzyxU7opPkEa3PqnWdD06YEv739B7HQEVV5eLnYKbs1kMuFvf/sbiouLkZCQgNmzZ0OpVKKyshI7d+7ERx99hLi4OBw+fBgvvCCtnw0iIk/l9gVsRUUFVq9ejcLCQshkMoSGhmLlypWCxzlwpAoTR4XhhcdiofbzZvH6K3refRt+2nEAJ/P2Ytzfn4bsva9gafbcP682Vtfj26ffwfj3fi92KoJLTEwUOwW3ZTabsXz5ctTX12PlypUICAho3TZw4EBMmDABy5cvx7fffou5c+ciMjJSxGyJiMjK7QvYnJwczJ07F0qlEhaLBSEhIThy5Ajef/99fP/99/jDH/6Avn372h1nsVig19vfLW8xm9uM9f7WcpRvS0bUvZ9cNyeL2Yz6+vqOn4wEWCwWAIBfaDDO7j4MoKX48+mmhuH8RVHz6uiYWM/F3dzIuVg1NTXZtZWVlSE6OtqmTcifX6OpJaZ1tQO9Xg+T0Vuw/q+NI0QM8//eB/bu3YtTp07htddeg7+/v91+mzZtwpEjRzB9+nRs2bIFEyZMgFwub+2js74PEBEJTa1WQ9aBJSbdvoA1GAytHzbZ2dmIiIjAhAkTMGHCBPz1r3/F2bNnHRawer3e5mpKK+1bgJfaYazMRSMw5cl8/HnBcDyyeHebOVVXVzvuuxNY0f0eaORKXD5bBb+wYFSXnIBPNzUaRV5aq+oGxsR6Lu7mRs7FKj093a6tqKgItbW1Nm1r1qy5of4dUSh9sGjpCmi10Zj/fCbCw8NhMgq/VJ01DoCbjpGdnQ2NRoPt27dj8uTJbRavX331FV544QWEhYVh586dOHToEG699VYAnft9gIhIaHV1ddBoNO3e3+0L2NTUVKSkpGD9+vXQaDSIjY0FAGzYsAFeXl64/fbbHR6nVqtRV2f/tKM+U7egus5k1/7/Zg7Elq9P4ZuD59A3XI059/fHe585njsYFBSECgd9dwafxz8FU+0lnPxiL+JfSccto2Jw/sBx0acPBAcFoa68Y2NiPRcAkCu8cFtGGgIH9sRtr6Rj7/PCFXgddSPnYuVoyayEhARERUXZtGVlCffQB6OpCVlrN+HYsTKs+mArTp8+DaXCOVdgs9ZuAoCbjlFQUIDa2locO3YMCxcutNt+dfFqnTYwZswY7N+/v7WADQoKcvgeQ0REHadWO7642Ba3L2C1Wi10Oh0AICMjA/3798c///lPfPDBB5g6dSp0Oh0GDx5sd5xMJnNYycvkjlcOW/XR0dZ/r9ty/ZteZHJ5h35LkBLr5f0rBhO+XfSOyNn8oq3x/rVjrMymZux5LlvotG7IjZyLlbe3fVGn0+kQExNj0ybkz2+jseUXQutVTLVaDR+lQrD+r40jRAy5XA6ZTIZ7773X7nuh0+nsilcAGDZsmM2VbHknfh8gIhKb2xewV9PpdEhOTkZ0dDRSU1PFTofII3AZLcf8/Pzw29/+1q590KBByMzMRGBgoE37wIEDXZUaERH9Co8qYDdu3Ch2CkQeJykpSewUPIpMJrMrXomIyL3wSVxEEldYWCh2CkRERIJiAUuCGv5iKnpOvQ0DH7sHABD/ajq6Rkci8q6Rdm1WXaMj4RcW3Pr16DceR0D/MADA7W8vQNSsRAx9OhkAEHnXSMQ8fi9inrgXAVHhrjotj1ZTUyN2CkRERIJiAUuCUQT4wctXiZN5e6GODEHsMymoO3EWF8tO4dSX++zarIKH9IE6MqT16/1L/4lhz83EgNRJOFNYgu9yCuDlq0TE5BHoNW00jqzeiu8/3onoR4R9GptUzZgxQ+wUiIiIBOVRc2CFENbd1y36kKLuwwfgYtlPAIATnxRi4od/wsa4x1q3X9sWNLQvon47AZq+oWi6ZEDv+xOgW/UZLv10HsfX5UObfjd2PvI6AOBQ5seYtv0v2D5jGQDAWHsJ6p4huBm+Pbrd1PHOInReeXl5mDdvnqB9ejqVSuWw3WKx4LKhEb4+PmhobISfyqfNhbXb6oOIiJyv0xWw//2EN7Q4i7daBVP9ZcgVXhi8IAm7Hn8Lw56dgQMZHzhsqy45gT0lJ9Av5Q5c+ukCzu050tqX/sdzuHTq59avzaZm6H+ohOHnX5Yxslxp+6lq7XFfgXBroboz6xOy6BeTJ0922N5oNGHJ8nX4wxPT8NrfPsSShdOdsiQYERHdHE4hIMHUV1TCv2cIhj37EErf2YLK3YfR3GBEjzGDHbbdrJstYDuL2bNni50CERGRoDrdFVhynurDFYh5bBp2z1/R2vbfrJalzyr/rbNrs/p+4y67vi6dvoB9L66zads5J7P137eMjsHpncUCZC19GzZswPz588VOg4iISDC8AkuCOvbeV1B0tX+uvNDk3l4o/2in0+NIgclk/+hkIiIiT8YrsCSoCweOuyTO2cISl8SRgqFDh4qdAhERkaB4BZZI4kpKWOwTEZG0sIAlkri4uDixUyAiIhIUpxCQS/gEByBqViIMP9eiquQEao+ebNcxgdpINF9uRNcBEe0+joiIiKSt0xWwscmbceZ8w031Edbdt93ryW5JfAYNle73KE/fHt1csg7q4AVJaDYYYazVQ7dyM/rNHI/GqjqbfcLGD0P4hJarhEf+vg2970toPeaHzd/CYjajq7an3XHUPsXFxRg3bpzYaXRK+fn5MBgMN3y8SqVqc81aIqLOrNMVsGfON6CqttFl8Roqa2Cs0bssnrsx1V2G4cJFdB0QgahZifBSKQGZDL2mjcKP2/YAAM7sPIQzOw85PMZiNmNA6qTW46jj4uPjxU6h0zIYDDAajWKnQUQkOZ2ugCXXOv7P7QCAU1/us2m3Fq/tOcb6Nd0YPomLiIikhjdxEUlcaWmp2CkQEREJigUskcSNHTtW7BToGs3NzaipqUF1dTWam5ttttXU1PDhE0REv8LtpxDk5uYiMzMTarUagYGBSEtLw5QpU8ROi8hjVFZWip0C/c/58+exY8cO7Nq1C3p9y9x4X19fjBs3DpMmTYK3tzeWLVuGqVOn8uYtIqLrcOsCtqKiAqtXr0ZhYSFkMhlCQ0OxcuVKp8QaHhOMmXf1xTNv7MXiR2OxV3cBO/acETRGF5UCo16dh2aDEfUVlTj6jzxB+3c1nyANbv3TLGj69MCX978gdjrUhvLycrFTILQ8UGL58uUYMmQIFi5ciAEDBkAmk+H777/H9u3b8dxzz0GlUmHEiBGYOHGi2OkSEbk1t55CkJOTg7lz50KpVMLb2xshISGoqqrCW2+9hUWLFuHIkSOCxTpwpApVFxvxwmOx0Ph7C168AkDPu2/DTzsOoOiPa/Cb4QMg8+oieAxXaqyux7dPvwNjbeddZcETJCYmip1Cp/fDDz/gzTffxNy5c7Fo0SLExMTAy8sLXbp0wYABAzBz5kyoVCro9XqMHj0acrlbvzUTEYnOra/AGgwGmM1mAEB2djYiIiIwaNAgHD16FLt374a3t3ebx1osltY/0dm0/68/R97fWo7ybcmIuveT6+ZlMZtRX1/frnOwWCyt//YLDcbZ3YcBtBR/Pt3UMJy/2K5+hGaxWNp9Dtce545u9Hykpqmpya6trKwM0dHRNm1Cfq+MppaY1tUO9Ho9TMa2X5s3G8cVMYQ6F+v7V25uLhITEzFmzBi7faqqqrBs2TKMGDECXbt2xaZNmzBw4MDW4/lzTUSdgVqthqwDy2W6dQGbmpqKlJQUrF+/HhqNBrGxsQCAlJQUREVF4eDBg4iKinJ4rF6vR0BAgP0G7VuAl9rhMZmLRmDKk/n484LheGTx7jbzqq6udty3Ayu63wONXAkAuHy2Cn5hwaguOQGfbmo0irg+bFUHzuFqV5+PO7nR85Ga9PR0u7aioiLU1tbatK1Zs0awmAqlDxYtXQGtNhrzn89EeHg4TEbh11q2xgHg9BhCnUt2djZMJhOKi4uxfPlyu+3W4nXIkCFIS0vDpUuXsGXLFpw5cwZhYWEdeq8hIvJkdXV10Gg07d7frQtYrVYLnU4HAMjIyED//v3xxRdfoLS0FD/++KPDD2srtVqNujr7Jzf1mboF1XX2d/j+v5kDseXrU/jm4Dn0DVdjzv398d5njucOBgUFocJB3458Hv8UTLUtV3NOfrEX8a+k45ZRMTh/4DgszVfa1YczBAcFoa6840+2uvp85Aov3JaRhsCBPXHbK+nY+7xwRVFH3ej5SI2jJbMSEhLsftHLyhLuKWxGUxOy1m7CsWNlWPXBVpw+fRpKhXOujmat3QQATo8h1LkUFBRg9+7d6NWrF37zm9/YbLu2eJXL5dBoNBgwYACOHz+OsLAwBAUFOXwfIyKSGrXa8cXFtrh1AXs1nU6H5ORkREdH4+677/7V/WUymcNKXtbG3LJVHx1t/fe6Lde/6UX2vw+a9rj6cvgVgwnfLnqnXcc5W1vfn/YcZ2U2NWPPc9lCpnXDbvR8pMbRtBqdToeYmBibNiG/V43Gll8I/f39AbS8CfkoFYL1f20cV8QQ6lzkcjmio6MRHBxst+0///mPTfFqNXPmzNarrvIOvNcQEXUmHlPAbty4UewUiDwSl9ESV2BgIAIDA+3ap02bBgB2c7769u3rkryIiDyZxxSwRHRjkpKSxE6BHOjIzQpERGSLa7UQSVxhYaHYKRAREQmKBawbGP5iKnpOvQ0DH7sHABD/ajq6Rkci8q6Rdm1WXaMj4Rf2y7y60W88joD+YQCA299egKhZiRj6dDIAIPKukYh5/F7EPHEvAqLCXXVa5CZqamrEToGIiEhQLGBFpgjwg5evEifz9kIdGYLYZ1JQd+IsLpadwqkv99m1WQUP6QN1ZEjr1/uX/hPDnpuJAamTcKawBN/lFMDLV4mIySPQa9poHFm9Fd9/vBPRj/AxvJ3NjBkzxE6BiIhIUJ1uDmxYd1+36MOq+/ABuFj2EwDgxCeFmPjhn7Ax7rHW7de2BQ3ti6jfToCmbyiaLhnQ+/4E6FZ9hks/ncfxdfnQpt+NnY+8DgA4lPkxpm3/C7bPWAYAMNZegrpnCG6Gb49uN3W8s7hrXu4gLy8P8+bNEzuNTkmlUjlst1gsuGxohK+PDxoaG+Gn8nE4J7at44mIOrtOV8D+9xP3uqHFW62Cqf4y5AovDF6QhF2Pv4Vhz87AgYwPHLZVl5zAnpIT6JdyBy79dAHn9vzyOF39j+dw6dTPrV+bTc3Q/1AJw8+/LGJvudL2k8ja474C4dYPJdewPlWKXG/y5MkO2xuNJixZvg5/eGIaXvvbh1iycLpTlgUjIpIqTiEQWX1FJfx7hmDYsw+h9J0tqNx9GM0NRvQYM9hh28262QKWPM/s2bPFToGIiEhQne4KrLupPlyBmMemYff8Fa1t/81qWfO28t86uzar7zfusuvr0ukL2PfiOpu2nXMyW/99y+gYnN5ZLEDW5Ek2bNiA+fPni50GERGRYHgF1g0ce+8rKLr6Oz2O3NsL5R/tdHocci8mk/2jk4mIiDwZr8C6gQsHjrskztnCEpfEIfcydOhQsVMgIiISFK/AEklcSQl/cSEiImlhAUskcXFxcWKnQEREJChOIXBTPsEBiJqVCMPPtagqOYHaoyfbdUygNhLNlxvRdUBEu48jIiIi8iQsYN3M4AVJaDYYYazVQ7dyM/rNHI/GqjqbfcLGD0P4hJarakf+vg2970toPeaHzd/CYjajq7an3XHUORUXF2PcuHFip0FOkp+fD4PBcFN9qFSqNtesJSJyRyxg3Yyp7jIMFy6i64AIRM1KhJdKCchk6DVtFH7ctgcAcGbnIZzZecjhMRazGQNSJ7UeRxQfHy92CuREBoMBRqNR7DSIiFyKBaybOf7P7QCAU1/us2m3Fq/tOcb6NRHAJ3EREZH08CYuIokrLS0VOwUiIiJB8QoskcSNHTtW7BRIBGazGUePHkVNTQ28vLzQr18/dO/evXX7t99+ixEjRkChUIiYJRHRjXH7AjY3NxeZmZlQq9UIDAxEWloapkyZInZaRB6jsrJS7BTIhZqbm/HFF19g+/btaG5uRo8ePWAymfDjjz9iyJAheOCBB1BaWoovvvgCvXv3RmhoqNgpExF1mFsXsBUVFVi9ejUKCwshk8kQGhqKlStXip3WDfMJ0uDWP82Cpk8PfHn/C2KnQ51EeXm52CmQizQ3NyMrKwsXLlxAamoqbr31VnTp0gUAUFNTgx07dmDJkiXw9vbG0qVLWbwSkcdy6zmwOTk5mDt3LpRKJby9vRESEoJbbrkFu3btwpAhQ8ROr8Maq+vx7dPvwFirFzsV6kQSExPFToFc5IMPPsDFixexbNkyjBw5srV4BYBu3bpBoVBAoVDgypUrNtuIiDyNW1+BNRgMMJvNAIDs7GxERERAp9Ph5MmTGDly5HWPtVgs0OvFLxQtFovYKThksVhQX18vdhoksKamJru2srIyREdH27QJOfZGU0tM62oHer0eJqO3YP1fG8cVMVx1LkLEsb5H6vV67Ny5E6+88gp8fX3t9tu8eTO++OILLFmyBF9++SW++uorpKent/bB9wMiEpNarYasA8t/unUBm5qaipSUFKxfvx4ajQaxsbHYsmUL/P39ceTIEeTn57e5+LZer0dAQICLM7a3ovs90MiVYqdhp6q62i2+PyQsa0FytaKiItTW1tq0rVmzRrCYCqUPFi1dAa02GvOfz0R4eDhMxkbB+r82DgCnx3DVuQgRJzs7GxqNBrt370a/fv0QERFht4+1eF28eDF69uyJSZMmYenSpZg1axZ8fHxQzfcDIhJZXV0dNBpNu/d36wJWq9VCp9MBADIyMtC/f3889NBDAFqWBrrek2PUajXq6sR/EtXn8U/BVNtylUWu8MJtGWkIHNgTt72Sjr3PC1dEdFRwUBDqysX//pCwHC2ZlZCQgKioKJu2rKwswWIaTU3IWrsJx46VYdUHW3H69GkoFc65apm1dhMAOD2Gq85FiDgFBQVoamrCmTNn7K60A/bFKwD06dMHAFBVVYXw8HAEBQW5xfslEXVearW6Q/u7dQF7NZ1Oh+Tk5Navf+0Kkkwm61Al7yxXXw43m5qx57lsEbP5hbt8f0hY3t72RZBOp0NMTIxNm5Bj32g0AQD8/f0BtLwJ+SiFX5rJGscVMVx1LkLEkctbbmVIT0/HlStXbLZZLBaYzWab4tUqOzu7dQktuVzO9wMi8igeU8Bu3LhR7BSIPBKX0eoc5HJ5azFrJZPJMH36dIf7K5XuN7WJiKi93HoVAiK6eUlJSWKnQEREJCgWsEQSV1hYKHYKREREgmIBSyRxNTU1YqdAREQkKBawRBI3Y8YMsVMgIiISlMfcxOWpfHt0EzsFh9w1LxJeXl4e5s2bJ3Ya5CQqlarNbRaLBZcNjfD18UFDYyP8VD4OFwq/Xh9ERO6IBayT3Vcg3HqbRDfC+rQnkqbrrYfdaDRhyfJ1+MMT0/Da3z7EkoXTnbIsGBGRq3EKAZHEzZ49W+wUiIiIBMUClkjiNmzYIHYKREREgmIBSyRxnN9IRERSwwKWSOL4jHsiIpIaFrBEEhcXFyd2CkRERIJiAUtEREREHoUFLJHEFRcXi50CERGRoLgOLJHExcfHi50CSUB+fj4MBsNN9aFSqa67bi0RUXuxgCWSOD7IgIRgMBhgNBrFToOICACnEBBJXmlpqdgpEBERCYoFLJHEjR07VuwUiIiIBMUpBEQSV1lZKXYKJFEWiwVlZWU4cOAALl++DJVKhbi4OAwaNAgymQxVVVXYvHkzHnnkEXh7e4udLhFJiNsXsLm5ucjMzIRarUZgYCDS0tIwZcoUsdMi8hjl5eVip0ASdPz4caxduxbV1dWIj49HUFAQ9Ho93n77bfj7+2P69OnYuHEjBg0ahC5duoidLhFJjFsXsBUVFVi9ejUKCwshk8kQGhqKlStXip0WkUdJTEwUOwWSmCNHjiAzMxMPPvggJk2aBKVS2bpt9uzZ2LZtG95++20MGTIEc+fOhVzO2WpEJCy3LmBzcnIwd+5cKJVKWCwWhISEoKioCNu3b0dUVBQefvhhBAYGOjzWYrFAr9e7OGMicTU1Ndm1lZWVITo62qatvr5esJhGU0tM62oHer0eJqPwfy62xnFFDFediyfFMZvNLX0ajVi+fDkefvhhjB8/3m6/uro6FBYWYvDgwSgrK0NDQwP8/f1b+xDyZ4+IpEOtVkMmk7V7f7cuYA0GQ+ubZnZ2NiIiIuDr64uAgABcvnz5un+W0uv1CAgIcFWqRG4hPT3drq2oqAi1tbU2bWvWrBEspkLpg0VLV0Crjcb85zMRHh4Ok7FRsP6vjQPA6TFcdS6eFCc7OxsajQb/+c9/EBgYiDvvvNNun6qqKmRkZGDQoEGYO3culi1bhsLCQkydOhUAUF1dzfdlInKorq4OGo2m3fu7dQGbmpqKlJQUrF+/HhqNBrGxsZg0aRImTZqEgwcP4v3338eCBQscHqtWq1FXV+fijInE5WjJrISEBERFRdm0ZWVlCRbTaGpC1tpNOHasDKs+2IrTp09DqXDO1cSstZsAwOkxXHUunhSnoKAATU1N2L17NyZMmGB3peTa4lUulyMxMRFbt25tLWCDgoL4vkxEDqnV6g7t79YFrFarhU6nAwBkZGSgf//++Prrr7F//3788MMPbRavACCTyTpUyRNJgaM7vXU6HWJiYmzahHxtNBpNAND6Z2K1Wg0fpUKw/q+N44oYrjoXT4pjnceq0WjQr18/m22XLl2yK14BoHfv3jbTvORyOd+XiUgQbl3AXk2n0yE5ORnR0dEO/3RFRI5xGS0S0qJFi+za/Pz88Lvf/Q7Dhw+3uWErLCwMf/zjH12ZHhF1Eh5TwG7cuFHsFIg8UlJSktgpkMTJZDKMHDlS7DSIqBPh2iZEEldYWCh2CkRERIJiAUskcTU1NWKnQEREJCgWsEQSN2PGDLFTICIiEhQLWCKJy8vLEzsFIiIiQXnMTVxEdGOsT2EiuhkqlarNbRaLBZcNLQ9I8FP5tPk0nev1QUTUESxgiSRu9uzZYqdAEjB58uQ2tzUaTViyfB0AYMnC6U5Z05aI6GqcQkAkcRs2bBA7BSIiIkGxgCWSOJPJ9Os7EREReRAWsEQSN3ToULFTICIiEhQLWCKJKykpETsFIiIiQbGAJZK4uLg4sVMgIiISFAtYIiIiIvIoLGCJJK64uFjsFIiIiATFdWCJJC4+Pl7sFIjaLT8/HwaD4ab6UKlU1123log8HwtYIonjk7jIkxgMBhiNRrHTICI3xykERBJXWloqdgpERESCYgFLJHFjx44VOwUipzObzWKnQEQuxCkERBJXWVkpdgpEN+XUqVPYsWMHjh07BpPJhK5du2LMmDG4/fbboVKpsGXLFpw8eRJPPfWU2KkSkYu4fQGbm5uLzMxMqNVqBAYGIi0tDVOmTBE7LSKPUV5eLnYKRDekqakJf//737Fv3z6MHj0aM2fOhI+PDyorK7Fz50589NFHGDFiBIqLi7F48WKx0yUiF3LrAraiogKrV69GYWEhZDIZQkNDsXLlSrHTIvIoiYmJYqdA1GFmsxkrV65ETU0NVq5cia5du7Zui4mJQWJiIt5++23s3r0baWlp6NWrl2i5EpHruXUBm5OTg7lz50KpVMJisSAkJAR+fn544YUX0LVrV9xxxx249dZbHR5rsVig1+tdnDGRuJqamuzaysrKEB0dbdNWX18vWEyjqSWmdbUDvV4Pk9FbsP6vjeOKGK46F6nFESKGdS7r/v37ceLECWRmZsLf399uvy1btqCkpAQPPPAAtm7disTERMjl8tY+hPwZJyLnU6vVkMlk7d7frQtYg8HQ+maWnZ2NiIgI5OTkoLm5GTKZDAqFos1j9Xo9AgICXJUqkVtIT0+3aysqKkJtba1N25o1awSLqVD6YNHSFdBqozH/+UyEh4fDZGwUrP9r4wBwegxXnYvU4gA3PzbZ2dnQaDTYsWMHJk+e3Gbxum3bNixevBgRERHYtWsXDh061HpBo7q6mu//RB6mrq4OGo2m3fu7dQGbmpqKlJQUrF+/HhqNBrGxsTCZTBg2bBiSk5Px6KOP4h//+IfDY9VqNerq6lycMZG4HC2ZlZCQgKioKJu2rKwswWIaTU3IWrsJx46VYdUHW3H69GkoFc65ype1dhMAOD2Gq85FanGAmx+bgoIC1NXVobS0FPPnz7fbfnXxap02cPvtt2Pfvn2tBWxQUBDf/4k8jFqt7tD+bl3AarVa6HQ6AEBGRgb69++PcePG4dVXX8UPP/xw3bl9MpmsQ5U8kRR4e9sXDjqdDjExMTZtQr42Go0mAGi9UqZWq+GjbPuvIzcbxxUxXHUuUosjRAzrNIBp06bZzHsFgCNHjtgVrwAQGxuLqqoqmz74/k8kbW5dwF5Np9MhOTkZPXr04I1cRB3AZbTI0/j6+uJ3v/udXfvAgQORmZmJbt262bRrtVpXpUZEbsJjCtiNGzeKnQKRR0pKShI7BSJByGQyu+KViDonPomLSOIKCwvFToGIiEhQLGCJJK6mpkbsFIiIiATFApZI4mbMmCF2CkRERIJiAUskcXl5eWKnQNRuKpUKSqXS7j+FQoGmK2Z4e7f8X6FQONxPqVRCpVKJfRpE5GQecxMXEd0Y61OYiDzB5MmTHbY3Gk1Ysnwd/vDENLz2tw+xZOF0pywJRkSegVdgiSRu9uzZYqdAREQkKBawRBK3YcMGsVMgIiISFAtYIokzmUy/vhMREZEHYQFLJHFDhw4VOwUiIiJBsYAlkriSkhKxUyAiIhIUC1giiYuLixM7BSIiIkGxgCUiIiIij8J1YIkkrri4GOPGjRM7DSK3kp+fD4PBcMPHq1SqNtesJSLnYwFLJHHx8fFip0DkdgwGA4xGo9hpENEN4hQCIonjk7iIiEhqWMASSVxpaanYKRAREQmKBSyRxI0dO1bsFIg8xpUrV3Dx4kXU1taiubnZZlttbS0fDELkJtx+Dmxubi4yMzOhVqsRGBiItLQ0TJkyRey0iDxGZWWl2CkQub2qqirs2LEDX3/9Nerr6wEAfn5+GDduHCZNmgRvb29kZGRgypQp/AwicgNuXcBWVFRg9erVKCwshEwmQ2hoKFauXCl2WkQepby8XOwUiNyaTqfDm2++iUGDBmHBggWIjo6GTCZDeXk5duzYgd///vfw9fVFXFwcJk2aJHa6RAQ3L2BzcnIwd+5cKJVKWCwWhISE4NSpU/j444+xb98+3H333Zg1a5bYaRK5tcTERLFTIHJbJ0+eRFZWFubMmWO33JxWq0X37t1x9OhR1NfXY8yYMZDLOfOOyB24dQFrMBhgNpsBANnZ2YiIiMDIkSMxcuRIPPLII0hJSWnzWIvFAr1e76pUidxCU1OTXVtZWRmio6Nt2qx/IhWC0dQS07ragV6vh8noLVj/18ZxRQxXnYvU4rgihlDnYv1s2bRpE+68806HayVXV1cjIyMDcXFxCAoKwqZNmzBw4MDW44V8HRF1dmq1GjKZrN37u3UBm5qaipSUFKxfvx4ajQaxsbEAWv7cExUVBYVC0eaxer0eAQEBLsqUyD2kp6fbtRUVFaG2ttambc2aNYLFVCh9sGjpCmi10Zj/fCbCw8NhMjYK1v+1cQA4PYarzkVqcQDPGZvs7Gw0Nzfj4MGDeOutt+y2W4vXgQMHIj09HZcuXcJnn32GM2fOICwsDNXV1fyMIRJQXV0dNBpNu/d36wJWq9VCp9MBADIyMtC/f38AwN///ncsXbr0useq1WrU1dU5PUcid+JoyayEhARERUXZtGVlZQkW02hqQtbaTTh2rAyrPtiK06dPQ6lwzhW4rLWbAMDpMVx1LlKLA3jO2BQUFOCbb75BZGQkunfvbrPt2uJVLpdDo9EgOjoax44dQ1hYGIKCgvgZQyQgtVrdof3duoC9mk6nQ3JyMgBg1apVv7q/TCbrUCVPJAXe3vYf6DqdDjExMTZtQr42Go0tywr5+/sDaHkT8lG2/deRm43jihiuOhepxXFFDKHORS6XY8CAAXjkkUfstv3nP/+xKV6tHnroodbXjrWoJSJxeEwBu3HjRrFTIPJIXEaLyLHAwEAEBgbatd9zzz2wWCx2N2z17dvXVakR0a/wmAKWiG5MUlKS2CkQeRSZTNahm0mIyPW4HgiRxBUWFoqdAhERkaBYwBJJXE1NjdgpEBERCYoFLJHEzZgxQ+wUiIiIBMUClkji8vLyxE6ByO2oVCoolUq7/xQKBZqumOHt3fJ/hULhcD+VSiX2KRB1aryJi0jirE8uIqJfTJ482WF7o9GEJcvX4Q9PTMNrf/sQSxZOd8qyYER0c3gFlkjiZs+eLXYKREREgmIBSyRxGzZsEDsFIiIiQbGAJZI4k8n06zsRERF5EBawRBI3dOhQsVMgIiISFAtYIokrKSkROwUiIiJBsYAlkri4uDixUyAiIhIUC1giIiIi8iidbh3Y2OTNOHO+4ab6COvui/9+kiRQRkTOVVxcjHHjxomdBlGnk5+fD4PBcFN9qFSqNtesJerMOl0Be+Z8A6pqG8VOg8hl4uPjxU6BqFMyGAwwGo1ip0EkSZxCQCRxfBIXERFJDQtYIokrLS0VOwUiIiJBdbopBESdzdixY8VOgYiuYjabUVZWhpqaGnh5eaFPnz7o3r176/aioiLExcVBoVCImCWRe3P7AjY3NxeZmZlQq9UIDAxEWloapkyZInZaRB6jsrJS7BSICMCVK1fw5ZdfYvv27TAajbjlllvQ1NSEkydPYujQoUhKSkJZWRm2bNmCpUuXIiwsTOyUidyWWxewFRUVWL16NQoLCyGTyRAaGoqVK1c6JdbwmGDMvKsvnnljLxY/Gou9ugvYseeMU2IRuVJ5ebnYKRB1es3NzXjrrbdw7tw5/Pa3v8Xw4cPh5dXyEVxdXY0dO3ZgyZIl8Pb2xksvvcTilehXuHUBm5OTg7lz50KpVMJisSAkJASHDh1Cfn4+1Go17rvvPgwfPlyQWAeOVGHiqDC88Fgs1H7eLF5JMhITE8VOgajT+/DDD1FdXY1ly5bBz8/PZltQUBD8/Pzg7e2NK1eutBa2RNQ2t36VGAwGmM1mAEB2djYiIiLg4+OD+vp6GAwGhIaGtnmsxWKBXq+3b/9ff468v7Uc5duSEXXvJ9fNy2I2o76+vp1nQeQ6TU1Ndm1lZWWIjo62aRPy59doaolpXe1Ar9fDZPQWrP9r47gihqvORWpxXBHDk75n1s+vy5cv41//+heWLl1qV7wCwLZt27Blyxa89NJL2L59O7766ivMmzevtQ9+3lBnoFarIZPJ2r2/WxewqampSElJwfr166HRaBAbG4uDBw9i1apVKC8vx6effoqnnnrK4bF6vR4BAQH2G7RvAV5qh8dkLhqBKU/m488LhuORxbvbzKu6utpx30QiS09Pt2srKipCbW2tTduaNWsEi6lQ+mDR0hXQaqMx//lMhIeHw2QUfq1laxwATo/hqnORWhyAY3O17OxsaDQafPPNN+jVqxd69eplt4+1eP3Tn/6E3r17Y9KkSViyZAlmz54NHx8fft5Qp1FXVweNRtPu/d26gNVqtdDpdACAjIwM9O/fHzKZDC+//DIaGxvx8MMPt3msWq1GXV2dXXufqVtQXWeya/9/Mwdiy9en8M3Bc+gbrsac+/vjvc8czx0MCgpChYO+icTmaMmshIQEREVF2bRlZWUJFtNoakLW2k04dqwMqz7YitOnT0OpcM6Vsay1mwDA6TFcdS5SiwNwbK5WUFCApqYmnD592u6vIIB98QoAvXv3hkwmw4ULFxAREYGgoCCHn2VEUqNWO7642Ba3LmCvptPpkJycjOjoaMyYMeNX95fJZA4reZnc8dK3qz462vrvdVuuf9OLTC7v0G8JRK7i7W3/QavT6RATE2PTJuTPb6Ox5RdCf39/AC1vQj5K4Zf/scZxRQxXnYvU4rgihid9z+T/+7yZM2cOrly5YrfdaDTaFK9Wq1evhlKpbO2DnzdE9jymgN24caPYKRB5JC6jRSSuLl26oEuXLnbtDz74oMP9fXx8nJ0Skcfjk7iIJC4pKUnsFIiIiATFApZI4goLC8VOgYiISFAsYIkkrqamRuwUiIiIBMUClkji2nPTIxERkSfxmJu4hBLW3dct+iBylby8vNZF0YnIdVQqVZvbLBYLLhsa4evjg4bGRvipfBwu4n69Pog6s05XwP73E97QQp2L9YlCRORakydPbnNbo9GEJcvX4Q9PTMNrf/sQSxZOd8qyYERSxSkERBI3e/ZssVMgIiISFAtYIonbsGGD2CkQEREJigUskcRxDh0REUkNC1giieNz1ImISGpYwBJJXFxcnNgpEBERCYoFLBERERF5FBawRBJXXFwsdgpERESC6nTrwMYmb8aZ8w031UdYd1+uJysBWxKfQUOl+z1m1bdHN9xXkCVYf/Hx8YL1RUTuJz8/HwaD4ab6UKlU1123lsjddLoC9sz5BlTVNoqdBrmBhsoaGGv0YqfhdHyQAZG0GQwGGI1GsdMgcilOISCSuNLSUrFTICIiEhQLWCKJGzt2rNgpEBERCarTTSEg6mwqKyvFToGIXMxisaC8vBz79u1DQ0MDfHx8EBcXh5iYGMhkMtTU1CA3NxepqalQKBRip0vUYW5fwObm5iIzMxNqtRqBgYFIS0vDlClTBI8zPCYYM+/qi2fe2IvFj8Zir+4Cduw5I3gcck9dVAqMenUemg1G1FdU4ug/8sROSTDl5eVip0BELlReXo61a9fi559/Rnx8PLp27Qq9Xo8VK1ZArVZj+vTp+OSTTxAdHQ0vL7cvA4gccuuf3IqKCqxevRqFhYWQyWQIDQ3FypUrnRLrwJEqTBwVhhcei4Xaz5vFayfT8+7b8NOOAziZtxfj/v40ZO99BUvzFbHTEkRiYqLYKRCRixw7dgyvvfYakpKSMGXKFPj4+LRuS01Nxeeff45Vq1YhJiYGjz76KORyziQkz+TWBWxOTg7mzp0LpVIJi8WCkJAQ6HQ6vPPOO7h48SIef/xxDBw40OGxFosFer39HeYWs7nNeO9vLUf5tmRE3fvJdfOymM2or6/v2MmQ27FYLK3/9gsNxtndhwEAjdX18OmmhuH8RdHyutGfr6amJru2srIyREdH27QJ+fNrNLXEtK52oNfrYTJ6C9b/tXFcEcNV5yK1OK6IIbXvmRBxzP/7XDOZTHjrrbcwe/Zsh7+4Xrp0Cbt378bAgQPx3Xff4fLly1Cr1a198HONxKRWqyGTydq9v1sXsAaDofWFmZ2djYiICGzbtg0vvfQSSktLsWbNGrz55psOj9Xr9QgICLDfoH0L8FI7PCZz0QhMeTIff14wHI8s3t1mXtXV1Y77Jo+yovs90MiVAIDLZ6vgFxaM6pIT8OmmRqOIy2tV3cTPV3p6ul1bUVERamtrbdrWrFlzQ/07olD6YNHSFdBqozH/+UyEh4fDZBR+qTprHABOj+Gqc5FaHIBjI0ac7OxsaDQa/Oc//4FGo8GECRPs9qmpqcGyZcsQHR2NRx99FBkZGdi1axemTZsGgJ9rJL66ujpoNJp27+/WBWxqaipSUlKwfv16aDQaxMbG4rHHHsN7772H5ubm6048V6vVqKurs2vvM3ULqutMdu3/b+ZAbPn6FL45eA59w9WYc39/vPeZ47mDQUFBqHDQN3mWz+Ofgqm25erHyS/2Iv6VdNwyKgbnDxwXdfpAcFAQ6spv7OfL0ZJZCQkJiIqKsmnLyhLuQQlGUxOy1m7CsWNlWPXBVpw+fRpKhXOuWGWt3QQATo/hqnORWhyAYyNGnIKCAjQ1NWH37t2YMGGC3VWsa4tXuVyOxMREbN68ubWADQoKcviZSeQq1r8GtJdbF7BarRY6nQ4AkJGRgf79+6OxseU31MbGRixYsKDNY2UymcNKXtbGfJ9VHx1t/fe6Lde/6UUml3fotwRyT1e/yV8xmPDtondEzOYXbf3stoe3t/0HoE6nQ0xMjE2bkD+/jcaWXwj9/f0BtLwJ+SiFv6vZGscVMVx1LlKL44oYUvueCRHHOo9VrVajX79+NtsaGhrsilcA6N27N7p27WrTBz/XyJO4dQF7NZ1Oh+TkZERHR0Or1YqdDpHH4DJaRJ3DokWL7NpUKhUeeughjBw50uaGrdDQUCxevNiV6REJymMK2I0bN4qdApFHSkpKEjsFIhKJTCZDfHy82GkQCY7rZxBJXGFhodgpEBERCYoFLNF1DH8xFT2n3oaBj90DAIh/NR1doyMReddIuzarrtGR8AsLbv169BuPI6B/GADg9rcXIGpWIoY+nQwAiLxrJGIevxcxT9yLgKhwp5xDTU2NU/olIiISCwtYojYoAvzg5avEyby9UEeGIPaZFNSdOIuLZadw6st9dm1WwUP6QB0Z0vr1/qX/xLDnZmJA6iScKSzBdzkF8PJVImLyCPSaNhpHVm/F9x/vRPQjwj9hDgBmzJjhlH6JiIjEwgKWqA3dhw/AxbKfAAAnPimEdu5d+C6noHX7tW1BQ/ti1OuPom/KHRj42D0Y9fqj8I/ojiZ9A46vy0fY+GGo+LRlfeFDmR8j7o+/xf6l7wMAjLWXoO4ZAmfIy5POY3GJiIgAD7qJSyhh3X3dog9yf95qFUz1lyFXeGHwgiTsevwtDHt2Bg5kfOCwrbrkBPaUnEC/lDtw6acLOLfnSGtf+h/P4dKpn1u/Npuaof+hEoaff3nAgOVK20+JuxnWJ/0QkTSpVKo2t1ksFlw2tCw/6afyafNJR9frg8gddboC9r+f8I5sap/6ikqETYjDsGcfQuk7W3Dh4HcIGRGNHmMGI3TcULu2yn/rbiqeswrY2bNnO6VfInIPkydPbnNbo9GEJcvXAQCWLJzulDVticTQ6QpYovaqPlyBmMemYff8Fa1t/81qWc7t6mLV2mb1/cZddn1dOn0B+15cZ9O2c05m679vGR2D0zuLBcja3oYNGzB//nyn9E1ERCQGzoEluo5j730FRVd/p8eRe3uh/KOdTunbZLJ/dDIREZEn4xVYouu4cOC4S+KcLSxxWt9Dhw51Wt9ERERi4BVYIokrKXFecUxERCQGFrBEEhcXFyd2CkRERILiFAKiDvIJDkDUrEQYfq5FVckJ1B492a5jArWRaL7ciK4DItp9HBEREdljAUvUToMXJKHZYISxVg/dys3oN3M8GqvqbPYJGz8M4RNarnge+fs29L4vofWYHzZ/C4vZjK7annbHOVNxcTHGjRvnsnhERETO1ukK2NjkzThzvuGm+gjr7ttp15PdkvgMGiprxE7Djm+PbrivIMupMUx1l2G4cBFdB0QgalYivFRKQCZDr2mj8OO2PQCAMzsP4czOQw6PsZjNGJA6qfU4V4mPj3dZLCKSrvz8fBgMhpvqQ6VSXXfdWqL26nQF7JnzDaiqbRQ7DY/VUFkDY41e7DREcfyf2wEAp77cZ9NuLV7bc4z1a1fik7iISAgGgwFGo1HsNIgA8CYuIskrLS0VOwUiIiJBsYAlkrixY8eKnQIRdWJms3Mek02dW6ebQkDU2VRWVoqdAhFJ1E8//YQdO3agrKwMJpMJAQEBGDNmDMaMGQOVSoXPP/8cFRUVeOqpp8ROlSTG7QrY3NxcZGZmQq1WIzAwEGlpaZgyZYrT4w6PCcbMu/rimTf2YvGjsdiru4Ade844Pa6n6qJSYNSr89BsMKK+ohJH/5Endko3xSdIg1v/NAuaPj3w5f0viJ2OoMrLy8VOgYgkprm5GdnZ2dizZw9GjRqFlJQUKJVKnDt3Djt37sSHH36I2267Dfv378fixYvFTpckyK0K2IqKCqxevRqFhYWQyWQIDQ3FypUrXRL7wJEqTBwVhhcei4Xaz5vF66/oefdt+GnHAZzM24txf38asve+gqX5ithp3bDG6np8+/Q7GP/e78VORXCJiYlip0BEEmI2m7Fq1Sr8/PPPWLFiBbp169a6bfDgwUhMTMRf//pX7Nq1C4888gh69+4tYrYkVW5VwObk5GDu3LlQKpWwWCwICQmByWTCwoULERwcjMWLF+Pw4cNYv349LBYL5syZA61W67Avi8UCvd7+bnnLdebivL+1HOXbkhF17yfXzdNiNqO+vr5jJycRFosFAOAXGoyzuw8DaCn+fLqpYTh/UdS8Ojom1nNxNzdyLlZNTU12bWVlZYiOjrZpE/Ln12hqiWld7UCv18Nk9Bas/2vjuCKGq85FanFcEUNq3zNPGhvrXNbi4mIcP34cr7/+OjQajd1+eXl5OHToEB544AFs27YNEydORJcuXVr76Kyfn3R9arUasg4sMelWBazBYGh9gWRnZyMiIgKRkZFYuHAhcnJyAADvvfceXn75ZTQ3N+Pll1/GX/7yF4d96fV6BAQE2G/QvgV4qR0ek7loBKY8mY8/LxiORxbvbjPP6upqx313Aiu63wONXInLZ6vgFxaM6pIT8OmmRqPIS2tV3cCYWM/F3dzIuVilp6fbtRUVFaG2ttambc2aNTfUvyMKpQ8WLV0BrTYa85/PRHh4OExG4Zeqs8YB4PQYrjoXqcUBODbuGge4+bHJzs6GRqPB9u3bMWnSJIfF6+eff47Nmzdj8eLFiIyMRGFhIQ4dOoThw4cD6Nyfn3R9dXV1Dn+m2uJWBWxqaipSUlKwfv16aDQaxMbG3nBfarUadXX2TzvqM3ULqutMdu3/b+ZAbPn6FL45eA59w9WYc39/vPeZ47mDQUFBqHDQd2fwefxTMNVewskv9iL+lXTcMioG5w8cF336QHBQEOrKOzYm1nMBALnCC7dlpCFwYE/c9ko69j4vXIHXUTdyLlaOlsxKSEhAVFSUTVtWlnAPfTCampC1dhOOHSvDqg+24vTp01AqnHMlKWvtJgBwegxXnYvU4gAcG3eNA9z82BQUFECv1+Pw4cN47LHH7LZfXbxapw2MGTMG+/btay1gg4KCHH42E6nVji8utsWtClitVgudTgcAyMjIQP/+/VFbW4t3330XBw8eRFFREebMmYOMjAwAQFpaWpt9yWQyh5W8TO545bBVHx1t/fe6Lde/6UUml3fotwQpsV7ev2Iw4dtF74iczS/aGu9fO8bKbGrGnueyhU7rhtzIuVh5e9t/OOl0OsTExNi0Cfnz22hs+YXQ398fQMubkI9SIVj/18ZxRQxXnYvU4rgihtS+Z540NnK5HGazGVOnTkVgYKDNtmPHjtkVrwAQGxuLCxcu2PTRWT8/SVhuVcBeTafTITk5GYGBgVi2bJnNtiFDhoiUFZHn4TJaRCQUX19fzJ492649Ojoar7/+OoKDg23atVptm/eqEN0Mty1gN27cKHYKRJKQlJQkdgpEJHEymcyueCVyJj6Ji0jiCgsLxU6BiIhIUCxgSVDDX0xFz6m3YeBj9wAA4l9NR9foSETeNdKuzaprdCT8wn75zX30G48joH8YAOD2txcgalYihj6dDACIvGskYh6/FzFP3IuAqHBXnZZHq6mpETsFIiIiQbGAJcEoAvzg5avEyby9UEeGIPaZFNSdOIuLZadw6st9dm1WwUP6QB0Z0vr1/qX/xLDnZmJA6iScKSzBdzkF8PJVImLyCPSaNhpHVm/F9x/vRPQjzn9CmxTMmDFD7BSIiIgE5bZzYJ0lrLuvW/QhRd2HD8DFsp8AACc+KcTED/+EjXG/LLVybVvQ0L6I+u0EaPqGoumSAb3vT4Bu1We49NN5HF+XD2363dj5yOsAgEOZH2Pa9r9g+4yWG/qMtZeg7hmCm+Hbo9uv7yQCofPKy8vDvHnzBO2TiDoflUrlsN1iseCyoRG+Pj5oaGyEn8qnzQXp2+qDqKM6XQH73094Q4uzeKtVMNVfhlzhhcELkrDr8bcw7NkZOJDxgcO26pIT2FNyAv1S7sClny7g3J4jrX3pfzyHS6d+bv3abGqG/odKGH7+ZUF+y5W2n6rWHvcVCLcWqjuzPumHiOhmTJ482WF7o9GEJcvX4Q9PTMNrf/sQSxZOd8qSYERX4xQCEkx9RSX8e4Zg2LMPofSdLajcfRjNDUb0GDPYYdvNutkCtrNwtOQNERGRJ+t0V2DJeaoPVyDmsWnYPX9Fa9t/s1qWQ6v8t86uzer7jbvs+rp0+gL2vbjOpm3nnMzWf98yOgandxYLkLX0bdiwAfPnzxc7DSIiIsHwCiwJ6th7X0HR1d/pceTeXij/aKfT40iByWT/6GQiIiJPxiuwJKgLB467JM7ZwhKXxJGCoUOHip0CERGRoHgFlkjiSkpY7BMRkbSwgCWSuLi4OLFTICIiEhSnEJBL+AQHIGpWIgw/16Kq5ARqj55s1zGB2kg0X25E1wER7T6OiIiIpK3TFbCxyZtx5nzDTfUR1t233evJbkl8Bg2V7vcoT98e3VyyDurgBUloNhhhrNVDt3Iz+s0cj8aqOpt9wsYPQ/iElquER/6+Db3vS2g95ofN38JiNqOrtqfdcdQ+xcXFGDdunNhpEBG1S35+PgwGww0fr1Kp2lyzlqSj0xWwZ843oKq20WXxGiprYKzRuyyeuzHVXYbhwkV0HRCBqFmJ8FIpAZkMvaaNwo/b9gAAzuw8hDM7Dzk8xmI2Y0DqpNbjqOPi4+PFToGIqN0MBgOMRqPYaZCb63QFLLnW8X9uBwCc+nKfTbu1eG3PMdav6cbwSVxERCQ1vImLSOJKS0vFToGIiEhQLGCJJG7s2LFip0BEdNPMZjPq6upw8eJFXLlyxWbbxYsX+dCWTsbtphDk5uYiMzMTarUagYGBSEtLw5QpU8ROi8hjVVZWip0CEdENq66uRkFBAXbu3Im6upabef38/HDHHXdg4sSJUCqVWLZsGRITEzF16lSRsyVXcasCtqKiAqtXr0ZhYSFkMhlCQ0OxcuVKl8QeHhOMmXf1xTNv7MXiR2OxV3cBO/acETRGF5UCo16dh2aDEfUVlTj6jzxB+3c1nyANbv3TLGj69MCX978gdjrUhvLycrFTICK6IUeOHEFWVha0Wi2efPJJaLVayGQylJeXY8eOHfj9738PPz8/DB48GHfddZfY6ZILudUUgpycHMydOxdKpRLe3t4ICQmByWTCwoUL8fLLLwMATp06ZfO1UA4cqULVxUa88FgsNP7eghevANDz7tvw044DKPrjGvxm+ADIvLoIHsOVGqvr8e3T78BY23lXWfAEiYmJYqdARNRhp06dwhtvvIFZs2bh2WefxdChQ6FQKODt7Y2BAwciNTUVfn5+qKurw7hx4yCXu1VJQ07mVldgDQYDzGYzACA7OxsRERGIjIzEwoULkZOTAwB2X7fFYrFAr7cvrCz/69+R97eWo3xbMqLu/eT6fZvNqK+v/7XTac3Dyi80GGd3HwbQUvz5dFPDcP5iu/oRmsViafc5XHucO7rR85GapqYmu7aysjJER0fbtAn5vTKaWmJaVzvQ6/UwGb0F6//aOK6I4apzkVocV8SQ2veMY2PPWgfk5uZi3LhxGD9+vN0+tbW1WLZsGQYPHoyQkBBs2rQJMTExrcfz88DzqNVqyDqwXKZbFbCpqalISUnB+vXrodFoEBsbe8N96fV6BAQE2G/QvgV4qR0ek7loBKY8mY8/LxiORxbvbrPv6upqx307sKL7PdDIlQCAy2er4BcWjOqSE/DppkajiOvDVnXgHK529fm4kxs9H6lJT0+3aysqKkJtba1N25o1awSLqVD6YNHSFdBqozH/+UyEh4fDZBR+rWVrHABOj+Gqc5FaHIBj465xAM8Zm+zsbFy5cgUHDhzAG2+8YbfdWrz2798fjz/+OC5duoTPPvsMp0+fRnh4eIc+o8l91NXVQaPRtHt/typgtVotdDodACAjIwP9+/dHbW0t3n33XRw8eBBFRUUYMGCAzddtLdKuVqtbJ3tfrc/ULaius79T8f/NHIgtX5/CNwfPoW+4GnPu74/3PnM8dzAoKAgVDvp25PP4p2Cqbfmt9OQXexH/SjpuGRWD8weOw9J85VeOdp7goCDUlXf8yVZXn49c4YXbMtIQOLAnbnslHXufF64o6qgbPR+pcbRkVkJCAqKiomzasrKEewqb0dSErLWbcOxYGVZ9sBWnT5+GUuGcqzxZazcBgNNjuOpcpBYH4Ni4axzAc8amoKAA3377LcLCwnDLLbfYbLu2eJXL5dBoNNBqtTh69CjCw8MRFBTk8POf3Jta7fjiYlvcqoC9mk6nQ3JyMgIDA7Fs2TKbbdd+7YhMJnNYycvamCOz6qOjrf9et+X6N73I/veCaY+rL4dfMZjw7aJ32nWcs7X1/WnPcVZmUzP2PJctZFo37EbPR2q8ve0/NHQ6Xeuf1qyE/F41Glt+IfT39wfQ8ibko1QI1v+1cVwRw1XnIrU4roghte8Zx8aeXC5Hv379MGfOHLtt3377rU3xajVjxozWAkjegc9o8lxuW8Bu3LhR7BSIJIHLaBGRp+nWrRu6detm1z516lRYLBa7G7b69u3rqtTITbhtAUtEwkhKShI7BSIiQchksg7d6EPSxTUniCSusLBQ7BSIiIgExQLWDQx/MRU9p96GgY/dAwCIfzUdXaMjEXnXSLs2q67RkfALC279evQbjyOgfxgA4Pa3FyBqViKGPp0MAIi8ayRiHr8XMU/ci4CocFedFrmJmpoasVMgIiISFAtYkSkC/ODlq8TJvL1QR4Yg9pkU1J04i4tlp3Dqy312bVbBQ/pAHRnS+vX+pf/EsOdmYkDqJJwpLMF3OQXw8lUiYvII9Jo2GkdWb8X3H+9E9CN8LG9nM2PGDLFTICIiElSnmwMb1t3XLfqw6j58AC6W/QQAOPFJISZ++CdsjHusdfu1bUFD+yLqtxOg6RuKpksG9L4/AbpVn+HST+dxfF0+tOl3Y+cjrwMADmV+jGnb/4LtM1pWbTDWXoK6Zwhuhm8P+0n17sBd83IHeXl5mDdvnthpEBG1i0qlcthusVhw2dAIXx8fNDQ2wk/l43A+bFvHk7R0ugL2v5+41w0t3moVTPWXIVd4YfCCJOx6/C0Me3YGDmR84LCtuuQE9pScQL+UO3Dppws4t+dIa1/6H8/h0qmfW782m5qh/6EShp9/WcTecqXtJ5G1x30Fwq0fSq5hfToOEZEnmDx5ssP2RqMJS5avwx+emIbX/vYhliyc7pRlwcgzcAqByOorKuHfMwTDnn0Ipe9sQeXuw2huMKLHmMEO227WzRaw5Hlmz54tdgpERESC6nRXYN1N9eEKxDw2Dbvnr2ht+29Wyxq4lf/W2bVZfb9xl11fl05fwL4X19m07ZyT2frvW0bH4PTOYgGyJk+yYcMGzJ8/X+w0iIiIBMMrsG7g2HtfQdHV3+lx5N5eKP9op9PjkHsxmewfnUxEROTJeAXWDVw4cNwlcc4WlrgkDrmXoUOHip0CERGRoHgFlkjiSkr4iwsREUkLC1giiYuLixM7BSIiIkFxCoGb8gkOQNSsRBh+rkVVyQnUHj3ZrmMCtZFovtyIrgMi2n0cERERkSdhAetmBi9IQrPBCGOtHrqVm9Fv5ng0VtXZ7BM2fhjCJ7RcVTvy923ofV9C6zE/bP4WFrMZXbU97Y6jzqm4uBjjxo0TOw0iIreRn58Pg8FwU32oVKo216wl52MB62ZMdZdhuHARXQdEIGpWIrxUSkAmQ69po/Djtj0AgDM7D+HMzkMOj7GYzRiQOqn1OKL4+HixUyAicisGgwFGo1HsNOgmsIB1M8f/uR0AcOrLfTbt1uK1PcdYvyYC+CQuIiKSHt7ERSRxpaWlYqdAREQkKF6BJZK4sWPHip0CEZFHMJvN+O6771BTUwMvLy/06dMHwcHBrdv37t2LYcOGQaFQiJglAW5awObm5iIzMxNqtRqBgYFIS0vDlClTxE6LyCNVVlaKnQIRkVszm8346quvkJ+fj4aGBtxyyy1obm7GqVOnEBsbi/vvvx/fffcdcnNzsXTpUoSHh4udcqfndgVsRUUFVq9ejcLCQshkMoSGhmLlypVipyUInyANbv3TLGj69MCX978gdjrUSZSXl4udAhGR27py5QpWrFiBn376CTNmzMDIkSPh5dVSHlVVVWHHjh1YsmQJvLy88OKLL7J4dRNuNwc2JycHc+fOhVKphLe3N0JCQmAymbBw4UK8/PLLAIB//etfeP311zFv3jycOHFC5Izbr7G6Ht8+/Q6MtXqxU6FOJDExUewUiIjc1kcffYRz584hIyMDo0ePbi1eASA4OBgajQZeXl4wm82cOuBG3O4KrMFggNlsBgBkZ2cjIiICkZGRWLhwIXJycgAAEyZMwIQJE/DXv/4VZ8+eRd++fe36sVgs0OvFLxQtFovYKThksVhQX18vdhoksKamJru2srIyREdH27QJOfZGU0tM62oHer0eJqO3YP1fG8cVMVx1LlKL44oYUvuecWzEiWOtMxoaGrBjxw689NJL8Pf3t9svLy8Pubm5ePHFF/Gvf/0LX375JR599NHWPvg5Khy1Wg1ZB5b/dLsCNjU1FSkpKVi/fj00Gg1iY2Md7rdhwwZ4eXnh9ttvd7hdr9cjICDAiZm2z4ru90AjV4qdhp2q6mq3+P6QsNLT0+3aioqKUFtba9O2Zs0awWIqlD5YtHQFtNpozH8+E+Hh4TAZGwXr/9o4AJwew1XnIrU4AMfGXeMAHJurZWdnQ6PR4N///jciIiLQp08fu32sxevzzz+Pvn37okuXLnjppZcwa9Ys+Pr6opqfo4Kqq6uDRqNp9/5uV8BqtVrodDoAQEZGBvr374/a2lq8++67OHjwIIqKivDdd9/hgw8+wNSpU6HT6TB48GC7ftRqNerqxH8S1efxT8FU2/Lbolzhhdsy0hA4sCdueyUde58XrojoqOCgINSVi//9IWE5WjIrISEBUVFRNm1ZWVmCxTSampC1dhOOHSvDqg+24vTp01AqnHP1JWvtJgBwegxXnYvU4gAcG3eNA3BsrlZQUICmpiacPn0aWq3Wbvu1xSsA9OrVC3K5HFVVVYiMjERQUJBb1BlSoVarO7S/2xWwV9PpdEhOTkZgYCCWLVvW2h4fH4/U1NTrHiuTyTpUyTvL1ZfDzaZm7HkuW8RsfuEu3x8Slre3/Zu5TqdDTEyMTZuQY99oNAFA65/f1Go1fJTCzxOzxnFFDFedi9TiuCKG1L5nHBtx4sjlLbcApaamtk4nuJrBYLApXq3eeecd+Pj4tPbBz1HxuHUBu3HjRrFTIPJ4XEaLiMixq2/YutqDDz7osF2lUjkzHeoAt1uFgIiElZSUJHYKREREgmIBSyRxhYWFYqdAREQkKBawRBJXU1MjdgpERESCYgFLJHEzZswQOwUiIiJBufVNXFLg26Ob2Ck45K55kfDy8vIwb948sdMgInIb17sZy2Kx4LKhEb4+PmhobISfysfhAvu8oUtcLGCd7L4C4dbbJLoR1qfWEBFRi8mTJ7e5rdFowpLl6/CHJ6bhtb99iCULpztlWTC6OZxCQCRxs2fPFjsFIiIiQbGAJZK4DRs2iJ0CERGRoFjAEkkc52kREZHUsIAlkjg+q5uIiKSGBSyRxMXFxYmdAhERkaBYwBIRERGRR2EBSyRxxcXFYqdAREQkKK4DSyRx8fHxYqdARNQp5efnw2Aw3FQfKpXquuvWdlYsYIkkjg8yICISh8FggNFoFDsNSeIUAiKJKy0tFTsFIiIiQbGAJZK4sWPHip0CERGRoDiFgEjiKisrxU6BiIj+x2Kx4MSJE9i7dy8aGhrg4+ODuLg4DBw4EDKZDBcvXkRubi5mzZoFhUIhdrpuy+0K2NzcXGRmZkKtViMwMBBpaWmYMmWK2GkReazy8nKxUyAiIgAnTpzA2rVrUVlZiZEjRyIwMBB6vR7Lly+HRqPBgw8+iE8++QR9+/aFl5fblWhuxa2+OxUVFVi9ejUKCwshk8kQGhqKlStXip0WkUdLTEwUOwUiok7v+PHjePXVV3HvvffirrvusnnM98MPP4y8vDysXLkSWq0WTzzxBORyzvK8HrcqYHNycjB37lwolUpYLBaEhITAZDJh4cKFCA4OxuLFi1FaWoodO3bg1KlTSE9PR0xMjMO+LBYL9Hq9i8+ASFxNTU12bWVlZYiOjrZpq6+vFyym0dQS07ragV6vh8noLVj/18ZxRQxXnYvU4rgihtS+Zxwbaccxm80AAJPJhDfffBMzZ850uCRWQ0MDvvnmG0RHR+P777/HpUuXoNFoWvsQ8j3bXanVashksnbv71YFrMFgaB3s7OxsREREIDIyEgsXLkROTg4AYNCgQTh69Ch2794Nb++2f6D0ej0CAgJckjeRu0hPT7drKyoqQm1trU3bmjVrBIupUPpg0dIV0GqjMf/5TISHh8NkbBSs/2vjAHB6DFedi9TiABwbd40DcGzEiJOdnQ2NRoO9e/fCz88PkyZNstvn4sWLWLZsGfr27YsnnngCL7/8MgoLCzFt2jQAQHV1daeoZ+rq6lqL9vZwqwI2NTUVKSkpWL9+PTQaDWJjYx3ul5KSgqioKBw8eBBRUVEO91Gr1airq3NitkTux9GSWQkJCXavk6ysLMFiGk1NyFq7CceOlWHVB1tx+vRpKBXOuSqStXYTADg9hqvORWpxAI6Nu8YBODZixCkoKEBTUxMKCwuRmJhod4Xx2uJVLpcjMTERubm5rQVsUFBQp6hn1Gp1h/Z3qwJWq9VCp9MBADIyMtC/f3/U1tbi3XffxcGDB1FUVISamhqUlpbixx9/dHi1yUomk3WokieSAkd/ldDpdHZTbYR8bTQaTQAAf39/AC1vQj5K4e+ctcZxRQxXnYvU4rgihtS+ZxwbacexzmP18/ND3759bbY1NDTYFa8A0KtXL5tiTi6Xs55xwK0K2KvpdDokJycjMDAQy5Yts9l29913i5QVkefhMlpEROJatGiRXZtKpcKDDz6I+Ph4mxu2QkND8dJLL7kyPY/ktgXsxo0bxU6BSBKSkpLEToGIiK4hk8kwevRosdPwWFyjgUjiCgsLxU6BiIhIUCxgiSSupqZG7BSIiIgExQKWSOJmzJghdgpERESCYgFLJHF5eXlip0BERCQot72Ji4iEYX2aDBERudbVj4u9lsViwWVDywMS/FQ+bT6F6np9dGYsYIkkbvbs2WKnQETUKTl6bKxVo9GEJcvXAQCWLJzulDVtpYxTCIgkbsOGDWKnQEREJCgWsEQSZzKZfn0nIiIiD8IClkjihg4dKnYKREREgmIBSyRxJSUlYqdAREQkKBawRBIXFxcndgpERESCYgFLRERERB6FBSyRxBUXF4udAhERkaC4DiyRxMXHx4udAhEROVF+fj4MBsNN9aFSqa67bq27YQFLJHF8EhcRkbQZDAYYjUax03ApTiEgkrjS0lKxUyAiIhIUC1giiRs7dqzYKRARkRsym81ip3DDOIWASOIqKyvFToGIiFzs7Nmz2LFjB44dOwaTyYSAgAAkJCRgzJgx8PHxwRdffIHy8nL83//9n9ip3hC3K2Bzc3ORmZkJtVqNwMBApKWlYcqUKWKnReSxysvLxU6BiIhcpLm5GWvXrsW///1v3HbbbXjggQegVCrx888/o6CgAB9++CHi4+Oxd+9ePP/882Kne8PcqoCtqKjA6tWrUVhYCJlMhtDQUKxcuVLstIg8WmJiotgpEBGRC5jNZrzzzjs4c+YMli9fjqCgIJvtEydOxN/+9jfs3LkTDz/8MPr27StSpjfPrQrYnJwczJ07F0qlEhaLBSEhITCZTFi4cCGCg4OxePFiAMCuXbvw1FNP4fDhw232ZbFYoNfrXZU6kVtoamqyaysrK0N0dLRNW319vWAxjaaWmNbVDvR6PUxGb8H6vzaOK2K46lykFscVMaT2PePYMI4QMaxzWQ8dOoSjR4/i9ddfR0BAgN1+X375JQ4ePIikpCRs27YNkyZNQpcuXVr7EPKzoaPUajVkMlm793erAtZgMLQOQnZ2NiIiIhAZGYmFCxciJycHAKDT6XDy5EmMHDnyun3p9XqHg0ckZenp6XZtRUVFqK2ttWlbs2aNYDEVSh8sWroCWm005j+fifDwcJiMjYL1f20cAE6P4apzkVocgGPjrnEAjo27xgFufmyys7Oh0WiwY8cOTJw40WH988UXX2DTpk14/vnn0bt3b3zzzTcoLi7GiBEjAADV1dWi1k11dXXQaDTt3t+tCtjU1FSkpKRg/fr10Gg0iI2Ntdtny5Yt8Pf3x5EjR5Cfn9/mortqtRp1dXVOzpjIvThaMishIQFRUVE2bVlZWYLFNJqakLV2E44dK8OqD7bi9OnTUCqcc7Uia+0mAHB6DFedi9TiABwbd40DcGzcNQ5w82NTUFAAvV6PkpISzJ0712771cWrddrAmDFjsHfv3tYCNigoSNS6Sa1Wd2h/typgtVotdDodACAjIwP9+/dHbW0t3n33XRw8eBBFRUWt0whKS0uv+8QImUzWoUqeSAq8ve3fAHU6HWJiYmzahHxtNBpNAAB/f38ALW9CPkqFYP1fG8cVMVx1LlKL44oYUvuecWwYR4gYcrkcFosFU6ZMsZv3WlZWZle8AsDQoUNx7tw5mz48qW5yqwL2ajqdDsnJyQgMDMSyZcvstgv5J1AiKeMyWkRE0qdSqfDwww/btQ8YMACvv/46goODbdq1Wi20Wq2r0hOc2xawGzduFDsFIklISkoSOwUiIhKJTCazK16lgE/iIpK4wsJCsVMgIiISFAtYIomrqakROwUiIiJBsYAlkrgZM2aInQIREZGgWMASSVxeXp7YKRARkROpVCoolUq7/xQKBZqumOHt3fJ/hULhcD+lUgmVSiX2aXSI297ERUTCsD5NhoiIpKmtZUUbjSYsWb4Of3hiGl7724dYsnC6U5YEEwOvwBJJ3OzZs8VOgYiISFAsYIkkbsOGDWKnQEREJCgWsEQSZzKZfn0nIiIiD8IClkjihg4dKnYKREREgmIBSyRxJSUlYqdAREQkKBawRBIXFxcndgpERESCYgFLRERERB6F68ASSVxxcTHGjRsndhpEROTh8vPzYTAYbvh4lUrV5pq1HcUClkji4uPjxU6BiIgkwGAwwGg0ip0GAE4hIJI8PomLiIikhgUskcSVlpaKnQIREZGgWMASSdzYsWPFToGIiCTMbDZDr9ejvr4eV65csdlWX1/vlAfquN0c2NzcXGRmZkKtViMwMBBpaWmYMmWK2GkReazKykqxUyAiIgmqqanBv/71L+zcuRO1tbUAAH9/f9xxxx2YOHEilEolMjIycOedd+Kee+4RNLZbFbAVFRVYvXo1CgsLIZPJEBoaipUrV4qdFpFHKy8vFzsFIiKSmGPHjuGNN95AVFQUHn30UWi1WsjlcpSXl2PHjh149tln4e/vj4EDB+Luu+8WPL5bFbA5OTmYO3culEolLBYLQkJCYDKZsHDhQgQHB2Px4sX47LPPsH37dkRFReHhhx9GYGCg2GkTubXExESxUyAiIgk5ffo0MjMz8bvf/c7uMyYmJgZhYWH47rvvcPHiRdx5552Qy4WfsepWBazBYIDZbAYAZGdnIyIiApGRkVi4cCFycnIAAL6+vggICMDly5fRpUuXNvuyWCzQ6/UuyZvIXTQ1Ndm1lZWVITo62qatvr5esJhGU0tM62oHer0eJqO3YP1fG8cVMVx1LlKL44oYUvuecWwYxxUxhDoXa422efNmjBkzxuEFkosXLyIjIwMDBw5Ejx498OmnnyImJqb1+LY+f9RqNWQyWbtzcasCNjU1FSkpKVi/fj00Gg1iY2Pt9pk0aRImTZqEgwcP4v3338eCBQsc9qXX6xEQEODkjIncS3p6ul1bUVFR69wkqzVr1ggWU6H0waKlK6DVRmP+85kIDw+HydgoWP/XxgHg9BiuOhepxQE4Nu4aB+DYuGscwHPGJjs7GxaLBfv27cPrr79ut91avPbu3RtPPvkkLl++jM8++ww//fQTIiIiUF1d3WZtVldXB41G0+5c3KqA1Wq10Ol0AICMjAz0798ftbW1ePfdd3Hw4EEUFRXBYDBg//79+OGHH9osXoGWSr6urs5VqRO5BUdLZiUkJCAqKsqmLSsrS7CYRlMTstZuwrFjZVj1wVacPn0aSoVzriRkrd0EAE6P4apzkVocgGPjrnEAjo27xgE8Z2wKCgqwZ88e9OjRA6GhoTbbri1e5XI51Go1YmJicPToUURERCAoKKjN2kytVncoF7cqYK+m0+mQnJyMwMBALFu2zGbbnXfe+avHy2SyDlXyRFLg7W3/xqTT6Vr/fGMl5Guj0diyPIq/vz+AljchH6VCsP6vjeOKGK46F6nFcUUMqX3PODaM44oYQp2LXC5Hnz59MGfOHLtt3377rU3xavXggw+2FqdyuVywzx+3LWA3btwodgpEksBltIiISCjdunVDt27d7NrvvvtuWCwWuxu2+vXr55Q83LaAJSJhJCUliZ0CERFJnEwm69BNWDeLT+IikrjCwkKxUyAiIhIUC1giiaupqRE7BSIiIkGxgCWSuBkzZoidAhERkaBYwBJJXF5entgpEBGRBKhUKiiVSrv/FAoFmq6Y4e3d8n+FQuFwP5VKJVguvImLSOKsT2AhIiK6GZMnT3bY3mg0YcnydfjDE9Pw2t8+xJKF052yLNjVeAWWSOJmz54tdgpERESCYgFLJHEbNmwQOwUiIiJBsYAlkjiTyfTrOxEREXkQzoElkpARI0bYtb3zzjvo2rWr65MhIiJyEl6BJZI4Fq9ERCQ1LGCJiIiIyKOwgCUiIiIij8ICloiIiIg8SqcpYIuLi3H//fejtLQUH3/8Mf7yl78gPz9f7LSIOoX9+/fjxRdfxHPPPQez2ey0OFe/zp1l27ZtePXVV/F///d/TosBAIcPH0ZWVhaefPJJXLlyxWlxNm7ciHnz5jmtfwBYvnw5/vznP+PTTz91apwTJ05g6dKlePPNN50ap7CwEMuXL0dCQoJTHxSydetWLF26FOnp6airq3NKjLy8PLz88st45plnYLFYnBIDsH1tZmVl4c0338T777/v1DjvvvsuHnzwQcFjXBvnlVdewR/+8Ads3LjRqXE+/vhjvPbaa3jnnXecFqOpqQmPPPIIPv/8c0FjXBvnd7/7HZYvX46jR4/ecH+dpoCNi4vD/fffDwD48MMP4efnJ25CRB7uQs1FHCn/EcdOnAIAfPfDaQBA2YlTdkXqpk2bsGTJEsTGxqKkpKRDcU6e+dkmDgAcO3EKP/xUabfv1a/zjrBYLDj2/Um7czl24hTOV9Xa7Dtt2jT88Y9/RGNjY4fjNDQaHX7Pjp04hUuXDTb7DhkyBBqNBjU1NZDJZB2KU1VT1+bYXLlqbPbt24fAwEAEBAR0+FyA9o9Nt27d4OXlBaPR2OEYFosFZSdOOfye/XzN2Kxdu7Y1VkeLseuNjf5yg82+48aNw7x58xAfHw9/f/8Oxamqbd/YAICPjw8uXLgAAFCr1R2Kc6qNsam4ZmwKCgrw+9//Hr6+vh1+bV53bC7U2Ox79Wvz3LlzePrpp3HkyJF2xTF0YGyujpOWloZevXq1+3zaGptjDsbm6jjPP/88FixYgLKysnbFOXX2vOOxOXXWbt+r49xxxx04d+4cunTp8qsxrjc2564zNqtXr8YDDzzQrvMAWp7A1ebYXGp7bEJCQnDp0qV2nUtbOk0Be60nn3wSW7ZsETsNIo+lVCiw6YtCbNi2EwCQ+9VuAMAPpyshlwv31mIyNeGD3O2tcQBgw7adaDB0vBhqi0wmw09nz9udy+avdsPb2361wddeew1z587tcBwfhTf+vV9nF2f33v9C5aO023/evHmYOHFih6++KRXeyP1yt12cip8q0eWqsfn6669x5MgRFBcX46effurw+ZiaHI/N5Qbb4j41NRXPPfcciouLO3w1uSNjc/nyZdxzzz3w9/dHcXFxh+L4KBX49oD92BQWHXI4Nh9//DEeeuihDsUA/jc2X9mPzYlTZ23GBgCOHj2KN954A6NGjerwlaqm5iuOx+aaX5SeeOIJvP322/jhhx/g7e3doRgymQynKy/YnUvuV7vh5eB1c/VxHaFUKvCfg6V2cXbtcTw2N8pHocDmr76xH5uTZ+zG5mo///wzsrKy8Oyzz7YrTnNzM3IcjM21v8Re65ZbbsHy5cuh1+t/NYZMJsOZc1X2Y/NlIby8HBeNNTU1+OGHH7B9+3bs3LnT4T7XUii8sefgEbs4X//n+mPz5ptv4o9//COys7PbFceRTlPAWgclJycHI0eOxJKlL6Nv375ip0XksTT+vkiacrtNW3BgAKbeEW+37/Tp07F06VKUlJRg6NChHYrTv3c4RsXF2LTFDeqPmKhedvte/TpvaGiw2349ExJuRWj3IJu2exMTEBhge+XrlVdeQVlZGf7zn/90+CqfXC5H8tQ7oLjqw71LFzkemjYBXbrYvh1/+eWXyMzMxP79+6FSqToUR+1gbIICA3DPnbZj89xzz2HhwoWIi4tDREREh2IAQP9e4Rh96yCbtmEx/TFoQG+btm3btuHPf/4zFArFDV1xGT86DmEhwTZt0yaMRrdrxiY1NRVr1qxBSUkJoqKiOhRDLpMh+e5rxkbeMjZeDnLev3+/w3WXf43azxcPTBlr0xYUqME940fZ7RsSEoLXXnsNhw4dQs+ePTsUp2/PUIwZPtimLXZgXwyO7mPT1tzcDIvFgsGDByMmxvZ11h53jhqGsFuuGZvxoxDUVWPTdvVrs2vXrnjrrbcwaJDtz05brGOjVPxSYMvlMjw0bbzd2FwdJy8vD8XFxfjss8/aFcffT4UH7rIdm25dNZjmYGyscT744ANMmzYN3bt3x+7du9sVp09kKMaMGGLTNlTbF0O09jXJ1eezbNmy1tdRe9wxKhbht/zGpu2e8aMQHGj7FxdrjC+++AIvv/wyHnzwQYwfP75dMVrGZpzd2My8d7xdoXz1ufz5z3/GCy+8gNtvv/3aLttNZnHmpBc3dehIOTZ8/jWGRPfBb+9LFDsdIo+24fOvcehIOeRyGebPTrL7MBOCqakZb6/bhAs1dQgMUOP/5kyHj7J9b+Id8XNVLd5+PxfNzVcQE9ULs+6f2OGrRe1xQHccn35RCACYljgaCbe274O8oz7J24WDpd9BLpfhyVn3I7zHb379oA5qamrGynW5uFBzEV01/liY9qBTxuZ89UWsXLcJzc1XMLB/L8xOcs7YHCz9Dp/k7QLQ8mE/ZsTg6x9wgz79ohAHdMchl8nwxOz7ENGju+Axmpqb8fa6zThfXYsAtR8Wpj0o6BVLqwv/G5um5ivQ9uuJ1AcmOWVsrJ/dADD1znjcPnLIrxxxYzZ9uRv7D5dBLpPh8Vn3ITLUOWOz6v3N+LmqZWz+L+1B+DpjbGouYuW6XDQ1NSO6byQenj7ZKWPz36Pf4+P/XYW9+47bMPa2jl2ouBEuuwL7448/4tZbb8WsWbMwaNAg/OMf/8DDDz+MuLg4vPrqq6irq0NKSgomTJiA8ePH4/vvvwfQcoXgzjvvRFxcXOul5l27dmHkyJG48847MWfOnA7lYTab8a//tPxpqcc1V1uIqOPum5iArhp/JCbc6pTiFQAU3l5IuedOdOkiR8rUO5xSIAFASHAgpowb2XIlZvJYp7zRA8Ctg6IwsH8v9OsZZnd1WUjTEkejq8YfE0bf6pTiFQC8vb0wY5rzx6Z7UFfcdcdt8PdV4YEptzttbOJi+mNQVG/07RmK0cOd84sFANwzYRQCA9QYPzrOKcUrAHh7/TI2yVPvcErxCgC/CeqKu++Mh5+vD6ZPcd7rJnZgPwwe0Ad9InsgwUm/WADAPePj0S1AjTtHDXNK8QpYx6blCnLy3Xc4pXgFgN9064qpd8bDT+X8sRkS3Qe9I3o47Ze+a7nsCuyPP/6IhIQEnDhxAhcvXkTPnj1x8uRJBAcHY8CAAUhOTkZsbCweeughlJSUICMjA59++ikuX74MPz8/GI1GDB48GEeOHMEzzzyDe+65B5MmTYLZbHY4385iscBoarJrP3zsBHLzv4FKqcDCtAehdNKbLVFn8nNVLYK7BVx3npgQKs9XO/0XT7PFgvNVtbjlN92cGudyQyOar1xBgNq5N5RybDrusqERzc0uGpvAALvpI0JzxdhYLBacu1Dj9DgNhkaYmprRVdOxm+c6imPTcQ2NRphMTTc8NkqFd4cKbJcWsHPnzsW//vUvAEDfvn1x4sQJAMCgQYMQERGBixcvQqls+S3Ey8sLBQUFeOONN/DZZ5+hS5cuKCkpwZEjR2A2m/H666+jtrYW48ePd3gzhaHRiKUrhF+ig4iIiIiE9dL/PdyhvxK0fZugE1xdWV9bZWu1Wtx+++1ISkoCAJhMJtTW1uK9997D4cOH0dTUhAEDBsBisSAoKAirVq2CxWJBVFQUkpOTodHYThgnIiIiImlyaQF7PS+99BIef/xxvP3227BYLJg6dSqeeeYZDBw4EGPGjIFWq0VQUMvl7zfffBPbt2+H2WzGxIkTHRavPkoFlix8pPVrs9mMVR98hpraekwYHee0yd9ERERE1DFXr2TQHp1mFYIzP1dh9fqt8O7SBc89PpNzX4mIiIg8VKcpYAHg0mUDzlXVoF/PMLFTISIiIqIb1KkKWCIiIiLyfJ3mSVxEREREJA0sYImIiIjIo7CAJSIiIiKPwgKWiIiIiDwKC1giIiIi8igsYImIiIjIo7CAJSIiIiKPwgKWiIiIiDwKC1giIiIi8igsYImIiIjIo7CAJSIiIiKPwgKWiIiIiDwKC1giIiIi8igsYImIiIjIo7CAJSIiIiKPwgKWiIiIiDwKC1giIiIi8igsYImIiIjIo7CAJSIiIiKPwgKWiIiIiDzK/wdsjs+++vZOqAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 867.599x581.933 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuits[0].draw(\"mpl\", scale=0.4, fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2740.49x581.933 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuits[-1].draw(\"mpl\", scale=0.4, fold=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: Optimize the problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we have created the Trotterized circuits, we will optimize them for a target hardware. We need to choose the hardware device to use before optimization. We will use a fake 127-qubit backend from ``qiskit_ibm_runtime`` to emulate a real device. To run on a real QPU, just replace the fake backend with a real backend. Check out the [Qiskit IBM Runtime docs](https://docs.quantum.ibm.com/guides/get-started-with-primitives#get-started-with-sampler) for more info."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime.fake_provider.backends import FakeSherbrooke\n",
    "\n",
    "backend = FakeSherbrooke()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will transpile the circuits to the target backend using Qiskit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.transpiler import generate_preset_pass_manager\n",
    "\n",
    "# The circuit needs to be transpiled to the AerSimulator target\n",
    "pass_manager = generate_preset_pass_manager(optimization_level=3, backend=backend)\n",
    "isa_circuits = [pass_manager.run(c) for c in circuits]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: Execute experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After optimizing the circuits for hardware execution, we are ready to run them on the target hardware and collect samples for ground state energy estimation. Here we use ``SamplerV2`` from ``qiskit-ibm-runtime`` to simulate noisy samples taken from the ``ibm_sherbrooke`` backend. We then combine the counts from each of the Krylov basis states into a single counts dictionary and plot the top 20 most commonly sampled bitstrings. Note the Hartree-Fock bitstring (`0000111100001111`) was the most commonly sampled bitstring.\n",
    "\n",
    "***Note: [Qiskit Aer](https://qiskit.github.io/qiskit-aer/index.html) is required to simulate samples from transpiled circuits.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
    "\n",
    "# Sample from the circuits\n",
    "noisy_sampler = Sampler(backend, options={\"simulator\": {\"seed_simulator\": 24}})\n",
    "job = noisy_sampler.run(isa_circuits, shots=500)\n",
    "\n",
    "# Combine the counts from the individual Trotter circuits\n",
    "counts = Counter(job.result()[0].data.meas.get_counts())\n",
    "for i in range(1, len(job.result())):\n",
    "    counts += Counter(job.result()[i].data.meas.get_counts())\n",
    "counts = dict(counts)\n",
    "\n",
    "plot_histogram(counts, number_to_keep=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4: Post-process the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will transform the counts into a bitstring matrix and probability array for post-processing.\n",
    "\n",
    "Each row in the matrix represents one unique bitstring. Since qubits are indexed from the right of a bitstring in Qiskit, column ``0`` represents qubit ``N-1``, and column ``N-1`` represents qubit ``0``, where ``N`` is the number of qubits.\n",
    "\n",
    "The alpha particles are represented in the column index range ``(N, N/2]``, and the beta particles are represented in the column range ``(N/2, 0]``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_sqd.counts import counts_to_arrays\n",
    "\n",
    "# Convert counts into bitstring and probability arrays\n",
    "bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we iteratively refine the samples using configuration recovery and approximate the ground state at each iteration\n",
    "\n",
    "There are a few user-controlled options which are important for this technique:\n",
    "\n",
    "- ``iterations``: Number of self-consistent configuration recovery iterations\n",
    "- ``n_batches``: Number of batches of configurations used by the different calls to the eigenstate solver\n",
    "- ``samples_per_batch``: Number of unique configurations to include in each batch\n",
    "- ``max_davidson_cycles``: Maximum number of Davidson cycles run by each eigensolver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting configuration recovery iteration 0\n",
      "Batch 0 subspace dimension: 3721\n",
      "Batch 1 subspace dimension: 3721\n",
      "Batch 2 subspace dimension: 3721\n",
      "Batch 3 subspace dimension: 3721\n",
      "Batch 4 subspace dimension: 3721\n",
      "Starting configuration recovery iteration 1\n",
      "Batch 0 subspace dimension: 4356\n",
      "Batch 1 subspace dimension: 4489\n",
      "Batch 2 subspace dimension: 4624\n",
      "Batch 3 subspace dimension: 4356\n",
      "Batch 4 subspace dimension: 4096\n",
      "Starting configuration recovery iteration 2\n",
      "Batch 0 subspace dimension: 4489\n",
      "Batch 1 subspace dimension: 4624\n",
      "Batch 2 subspace dimension: 4489\n",
      "Batch 3 subspace dimension: 4356\n",
      "Batch 4 subspace dimension: 4624\n",
      "Starting configuration recovery iteration 3\n",
      "Batch 0 subspace dimension: 4624\n",
      "Batch 1 subspace dimension: 4489\n",
      "Batch 2 subspace dimension: 4356\n",
      "Batch 3 subspace dimension: 4489\n",
      "Batch 4 subspace dimension: 4761\n",
      "Starting configuration recovery iteration 4\n",
      "Batch 0 subspace dimension: 4624\n",
      "Batch 1 subspace dimension: 4761\n",
      "Batch 2 subspace dimension: 4761\n",
      "Batch 3 subspace dimension: 4624\n",
      "Batch 4 subspace dimension: 4761\n",
      "Starting configuration recovery iteration 5\n",
      "Batch 0 subspace dimension: 4624\n",
      "Batch 1 subspace dimension: 4624\n",
      "Batch 2 subspace dimension: 4356\n",
      "Batch 3 subspace dimension: 4624\n",
      "Batch 4 subspace dimension: 4761\n",
      "Starting configuration recovery iteration 6\n",
      "Batch 0 subspace dimension: 4356\n",
      "Batch 1 subspace dimension: 4356\n",
      "Batch 2 subspace dimension: 4761\n",
      "Batch 3 subspace dimension: 4761\n",
      "Batch 4 subspace dimension: 4225\n",
      "Starting configuration recovery iteration 7\n",
      "Batch 0 subspace dimension: 4356\n",
      "Batch 1 subspace dimension: 4225\n",
      "Batch 2 subspace dimension: 4225\n",
      "Batch 3 subspace dimension: 4356\n",
      "Batch 4 subspace dimension: 4624\n",
      "Starting configuration recovery iteration 8\n",
      "Batch 0 subspace dimension: 4356\n",
      "Batch 1 subspace dimension: 4489\n",
      "Batch 2 subspace dimension: 4624\n",
      "Batch 3 subspace dimension: 4489\n",
      "Batch 4 subspace dimension: 4356\n"
     ]
    }
   ],
   "source": [
    "from qiskit_addon_sqd.configuration_recovery import recover_configurations\n",
    "from qiskit_addon_sqd.fermion import (\n",
    "    bitstring_matrix_to_ci_strs,\n",
    "    solve_fermion,\n",
    ")\n",
    "from qiskit_addon_sqd.subsampling import postselect_and_subsample\n",
    "\n",
    "# Set a seed for reproducability\n",
    "rng = np.random.default_rng(24)\n",
    "\n",
    "# SQD options\n",
    "iterations = 9\n",
    "\n",
    "# Eigenstate solver options\n",
    "n_batches = 5\n",
    "samples_per_batch = 450\n",
    "max_davidson_cycles = 200\n",
    "\n",
    "# Self-consistent configuration recovery loop\n",
    "e_hist = np.zeros((iterations, n_batches))  # energy history\n",
    "s_hist = np.zeros((iterations, n_batches))  # spin history\n",
    "occupancy_hist = []\n",
    "avg_occupancy = None\n",
    "for i in range(iterations):\n",
    "    print(f\"Starting configuration recovery iteration {i}\")\n",
    "    # On the first iteration, we have no orbital occupancy information from the\n",
    "    # solver, so we begin with the full set of noisy configurations.\n",
    "    if avg_occupancy is None:\n",
    "        bs_mat_tmp = bitstring_matrix_full\n",
    "        probs_arr_tmp = probs_arr_full\n",
    "\n",
    "    # If we have average orbital occupancy information, we use it to refine the full set of noisy configurations\n",
    "    else:\n",
    "        bs_mat_tmp, probs_arr_tmp = recover_configurations(\n",
    "            bitstring_matrix_full,\n",
    "            probs_arr_full,\n",
    "            avg_occupancy,\n",
    "            nelec[0],\n",
    "            nelec[1],\n",
    "            rand_seed=rng,\n",
    "        )\n",
    "\n",
    "    # Create batches of subsamples. We post-select here to remove configurations\n",
    "    # with incorrect hamming weight during iteration 0, since no config recovery was performed.\n",
    "    batches = postselect_and_subsample(\n",
    "        bs_mat_tmp,\n",
    "        probs_arr_tmp,\n",
    "        hamming_right=nelec[0],\n",
    "        hamming_left=nelec[1],\n",
    "        samples_per_batch=samples_per_batch,\n",
    "        num_batches=n_batches,\n",
    "        rand_seed=rng,\n",
    "    )\n",
    "\n",
    "    # Run eigenstate solvers in a loop. This loop should be parallelized for larger problems.\n",
    "    e_tmp = np.zeros(n_batches)\n",
    "    s_tmp = np.zeros(n_batches)\n",
    "    occs_tmp = []\n",
    "    coeffs = []\n",
    "    for j in range(n_batches):\n",
    "        strs_a, strs_b = bitstring_matrix_to_ci_strs(batches[j])\n",
    "        print(f\"Batch {j} subspace dimension: {len(strs_a) * len(strs_b)}\")\n",
    "        energy_sci, coeffs_sci, avg_occs, spin = solve_fermion(\n",
    "            batches[j],\n",
    "            h1e,\n",
    "            h2e,\n",
    "            max_davidson=max_davidson_cycles,\n",
    "        )\n",
    "        e_tmp[j] = energy_sci\n",
    "        s_tmp[j] = spin\n",
    "        occs_tmp.append(avg_occs)\n",
    "        coeffs.append(coeffs_sci)\n",
    "\n",
    "    # Combine batch results\n",
    "    avg_occupancy = np.mean(occs_tmp, axis=0)\n",
    "\n",
    "    # Track optimization history\n",
    "    e_hist[i, :] = e_tmp\n",
    "    s_hist[i, :] = s_tmp\n",
    "    occupancy_hist.append(avg_occupancy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first plot shows that after a few iterations we estimate the ground state energy within ``~.1 mH`` (chemical accuracy is typically accepted to be ``1 kcal/mol`` $\\approx$ ``1.6 mH``).\n",
    "\n",
    "This example is small enough that we are able to explore the full Hilbert space, as seen in the print statements above. Remember, the full Hilbert space is dimension ``(num_orbitals choose nelec_a) * (num_orbitals choose nelec_b)``. So for this problem: `(8 choose 4)**2 = 4900`. The subspace sizes above are close to this value, which means we are very close to performing a full configuration interaction (FCI) calculation.\n",
    "\n",
    "The second plot shows the average occupancy of each spatial orbital across all batches' solutions. We see that with high probability each orbital contains one electron."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact energy: -13.42249 Ha\n",
      "SQD energy: -13.42237 Ha\n",
      "Absolute error: 0.00012 Ha\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "exact_energy = -13.422491814605827\n",
    "min_es = [np.min(e) for e in e_hist]\n",
    "min_id, min_e = min(enumerate(min_es), key=lambda x: x[1])\n",
    "\n",
    "# Data for energies plot\n",
    "x1 = range(iterations)\n",
    "yt1 = list(np.arange(-13.5, -13.1, 0.1))\n",
    "ytl = [f\"{i:.1f}\" for i in yt1]\n",
    "\n",
    "# Data for avg spatial orbital occupancy\n",
    "avg_occupancy = occupancy_hist[min_id]\n",
    "y2 = avg_occupancy[0] + avg_occupancy[1]\n",
    "x2 = range(len(y2))\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n",
    "\n",
    "# Plot energies\n",
    "axs[0].plot(x1, min_es, label=\"energy\", marker=\"o\")\n",
    "axs[0].set_xticks(x1)\n",
    "axs[0].set_xticklabels(x1)\n",
    "axs[0].set_yticks(yt1)\n",
    "axs[0].set_yticklabels(ytl)\n",
    "axs[0].axhline(y=exact_energy, color=\"#BF5700\", linestyle=\"--\", label=\"FCI energy\")\n",
    "axs[0].set_title(\"Approximated Ground State Energy vs SQD Iterations\")\n",
    "axs[0].set_xlabel(\"Iteration Index\", fontdict={\"fontsize\": 12})\n",
    "axs[0].set_ylabel(\"Energy (Ha)\", fontdict={\"fontsize\": 12})\n",
    "axs[0].legend()\n",
    "\n",
    "# Plot orbital occupancy\n",
    "axs[1].bar(x2, y2, width=0.8)\n",
    "axs[1].set_xticks(x2)\n",
    "axs[1].set_xticklabels(x2)\n",
    "axs[1].set_title(\"Avg Occupancy per Spatial Orbital\")\n",
    "axs[1].set_xlabel(\"Orbital Index\", fontdict={\"fontsize\": 12})\n",
    "axs[1].set_ylabel(\"Avg Occupancy\", fontdict={\"fontsize\": 12})\n",
    "\n",
    "print(f\"Exact energy: {exact_energy:.5f} Ha\")\n",
    "print(f\"SQD energy: {min_e:.5f} Ha\")\n",
    "print(f\"Absolute error: {abs(min_e - exact_energy):.5f} Ha\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
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