{ "cells": [ { "cell_type": "markdown", "id": "dfc54822", "metadata": {}, "source": [ "# 4.42 Four Ways to Measure a Coupling" ] }, { "cell_type": "markdown", "id": "1f0e1fc8", "metadata": {}, "source": [ "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/qiskit-community/qiskit-metal/blob/main/docs%2Ftut%2F4-Analysis%2F4.42-Four-ways-to-measure-a-coupling.ipynb)\n", "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/qiskit-community/qiskit-metal/main?labpath=docs%2Ftut%2F4-Analysis%2F4.42-Four-ways-to-measure-a-coupling.ipynb)" ] }, { "cell_type": "markdown", "id": "85421f53", "metadata": {}, "source": [ "> 💡 **What you need.** NumPy, SciPy and matplotlib. Runs in seconds. Second of five notebooks reproducing Molavi *et al.* [1]; [4.41](4.41-The-package-mode-on-paper.ipynb) introduced the device." ] }, { "cell_type": "markdown", "id": "5a0934dc", "metadata": {}, "source": [ "An electromagnetic simulator never hands you a coupling constant. It returns eigenfrequencies, fields, or a network response, with the junction replaced by *something* linear — an inductor, an open circuit, a port. The paper compares four ways of turning such output into the bare coupling $g$ between a qubit and a package mode:\n", "\n", "| Method | Junction replaced by | Simulation | What gives $g$ |\n", "|---|---|---|---|\n", "| avoided crossing | variable inductor | eigenmode or driven | minimum splitting of two eigenfrequencies |\n", "| energy participation (EPR) | fixed inductor, detuned | eigenmode | fraction of the package mode's energy in the junction |\n", "| induced EMF | open circuit | eigenmode | voltage the package mode induces across the junction |\n", "| impedance matrix | lumped port | driven | circuit parameters fitted to $Z(\\omega)$ |\n", "\n", "Before running any of them on a 3D model (notebook 4.45), this notebook runs all four on the circuit they all rest on: two coupled LC resonators. Here every quantity has an exact answer, so each method can be checked to the last digit, and its approximations can be seen one at a time.\n", "\n", "**What you'll learn**\n", "\n", "- what the bare coupling $g = g_C - g_L$ is, and how the capacitive and inductive parts combine;\n", "- how each of the four methods extracts $g$, with the paper's formulas as code;\n", "- which methods also give the *sign* of $g$, and why none can separate $g_C$ from $g_L$;\n", "- how the Appendix D fit turns an impedance matrix back into a circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "colab-install", "metadata": {}, "outputs": [], "source": [ "# In Colab, uncomment to install the dependencies of the whole series.\n", "# Colab only (not needed locally): gmsh's Linux wheel needs system graphics libraries Colab lacks.\n", "# !apt-get -qq update && apt-get -qq install -y libglu1-mesa libgl1 libxcursor1 libxft2 libxinerama1 libxfixes3 libxrender1 libxext6 libfontconfig1 > /dev/null\n", "# !pip install -q \"quantum-metal[skfem]\" pymetis" ] }, { "cell_type": "code", "execution_count": 1, "id": "0351b73c", "metadata": {}, "outputs": [], "source": [ "import sys\n", "import urllib.request\n", "from pathlib import Path\n", "\n", "# The solver code shared by tutorials 4.41-4.45 lives in docs/tut/resources/package_modes/.\n", "RES = Path(\"../resources/package_modes\")\n", "if not (\n", " RES / \"package_modes.py\"\n", ").exists(): # e.g. in Colab: fetch it next to the notebook\n", " RES = Path(\"package_modes\")\n", " RES.mkdir(exist_ok=True)\n", " urllib.request.urlretrieve(\n", " \"https://raw.githubusercontent.com/qiskit-community/qiskit-metal/main/\"\n", " \"docs/tut/resources/package_modes/package_modes.py\",\n", " RES / \"package_modes.py\",\n", " )\n", "sys.path.insert(0, str(RES))\n", "\n", "import package_modes as pm\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy.linalg as la\n", "\n", "TWO_PI = 2 * np.pi" ] }, { "cell_type": "markdown", "id": "82d3e75b", "metadata": {}, "source": [ "## 1. The circuit\n", "\n", "The equivalent circuit of the paper's Fig. 3: a package mode $m$ and a qubit $n$, each a capacitance in series with a geometric inductance $\\delta L'$, shunted at its port by a lumped inductance $L'$. The coupling runs through a capacitance $C_c$ and a mutual inductance $M$. The junction is $L'_n$; the package-mode port is shunted by a tiny $L'_m$ that barely disturbs the mode. The values below are the ones the paper fits for the corner qubit (0,0) (Sec. III D), so this circuit *is* that qubit and its package mode.\n", "\n", "Since the port nodes carry no capacitance, each shunt adds in series with its geometric inductance, and the circuit reduces to two resonators with capacitance and inductance matrices (Eq. A3)\n", "\n", "$$\\mathbf C = \\begin{pmatrix} C_m + C_c & -C_c \\\\ -C_c & C_n + C_c\\end{pmatrix}, \\qquad\n", "\\mathbf L = \\begin{pmatrix} L'_m + \\delta L'_m & M \\\\ M & L'_n + \\delta L'_n\\end{pmatrix}.$$" ] }, { "cell_type": "code", "execution_count": 2, "id": "8a1f65c0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C (fF) =\n", " [[ 1.321e+02 -1.000e-01]\n", " [-1.000e-01 1.739e+02]]\n", "L (nH) =\n", " [[ 4.571e+00 -3.400e-04]\n", " [-3.400e-04 3.950e+00]]\n" ] } ], "source": [ "p = pm.PAPER[\"zfit_q00\"]\n", "Cm, Cn, Cc = p[\"C_m\"], p[\"C_n\"], p[\"C_c\"]\n", "Lpm, dLm, dLn, M = p[\"Lp_m\"], p[\"dL_m\"], p[\"dL_n\"], p[\"M\"]\n", "\n", "\n", "def matrices(Lpn):\n", " \"\"\"C and L of the two-mode circuit for a junction inductance Lpn (henry).\"\"\"\n", " C = np.array([[Cm + Cc, -Cc], [-Cc, Cn + Cc]])\n", " L = np.array([[Lpm + dLm, M], [M, Lpn + dLn]])\n", " return C, L\n", "\n", "\n", "Lpn = p[\"Lp_n\"] # 3.63 nH: the qubit sits about 0.4 GHz below the package mode\n", "C, L = matrices(Lpn)\n", "print(\"C (fF) =\\n\", C * 1e15)\n", "print(\"L (nH) =\\n\", L * 1e9)" ] }, { "cell_type": "markdown", "id": "fbabcb58", "metadata": {}, "source": [ "### Bare modes and the coupling\n", "\n", "Writing the Hamiltonian in terms of node charges $Q$ and fluxes $\\Phi$, $H = \\tfrac12 Q^T\\mathbf C^{-1}Q + \\tfrac12\\Phi^T\\mathbf L^{-1}\\Phi$, the diagonal elements define the *bare* resonators and the off-diagonal ones couple them (Appendix A):\n", "\n", "$$\\omega_k = \\sqrt{(\\mathbf L^{-1})_{kk}(\\mathbf C^{-1})_{kk}},\\quad\n", "k_C = \\frac{(\\mathbf C^{-1})_{mn}}{\\sqrt{(\\mathbf C^{-1})_{mm}(\\mathbf C^{-1})_{nn}}},\\quad\n", "k_L = -\\frac{(\\mathbf L^{-1})_{mn}}{\\sqrt{(\\mathbf L^{-1})_{mm}(\\mathbf L^{-1})_{nn}}},\\quad\n", "g_{C,L} = \\tfrac12 k_{C,L}\\sqrt{\\omega_m\\omega_n}.$$\n", "\n", "In the rotating-wave approximation the two channels combine into one exchange rate $g = g_C - g_L$. Both $g_C$ and $g_L$ scale as $\\sqrt{\\omega_n}$, so the $g$ that matters — the one the qubit would see *on resonance* with the mode — follows from the detuned values by Eq. (10),\n", "\n", "$$g = \\Big(g_C - g_L\\,\\frac{\\omega_m}{\\omega_n}\\Big)\\sqrt{\\frac{\\omega_m}{\\omega_n}} .$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "ca8f1fce", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "bare package mode wm/2pi = 6.4768 GHz\n", "bare qubit wn/2pi = 6.0726 GHz\n", "k_C = 6.598e-04, k_L = -8.002e-05\n", "g_C/2pi = 2.069 MHz, g_L/2pi = -0.251 MHz (paper: 2.07, -0.25)\n", "on-resonance g/2pi = 2.413 MHz (paper: 2.42 MHz)\n" ] } ], "source": [ "bare = pm.circuit_couplings(C, L)\n", "wm, wn = bare[\"w\"]\n", "g_exact = pm.g_on_resonance(bare[\"gC\"], bare[\"gL\"], wm, wn)\n", "print(f\"bare package mode wm/2pi = {wm / TWO_PI / 1e9:.4f} GHz\")\n", "print(f\"bare qubit wn/2pi = {wn / TWO_PI / 1e9:.4f} GHz\")\n", "print(f\"k_C = {bare['kC']:.3e}, k_L = {bare['kL']:.3e}\")\n", "print(\n", " f\"g_C/2pi = {bare['gC'] / TWO_PI / 1e6:.3f} MHz, g_L/2pi = {bare['gL'] / TWO_PI / 1e6:.3f} MHz \"\n", " f\"(paper: {p['gC'] / 1e6:.2f}, {p['gL'] / 1e6:.2f})\"\n", ")\n", "print(\n", " f\"on-resonance g/2pi = {g_exact / TWO_PI / 1e6:.3f} MHz (paper: {p['g'] / 1e6:.2f} MHz)\"\n", ")" ] }, { "cell_type": "markdown", "id": "40250e8a", "metadata": {}, "source": [ "This is the reference value. The paper quotes 2.42 MHz from unrounded fit parameters; the rounded values it prints give 2.413 MHz. Note that $M < 0$ here, so $g_L < 0$ and the magnetic channel *adds* to the electric one.\n", "\n", "## 2. Avoided crossing\n", "\n", "Tune the qubit through the package mode by sweeping the junction inductance, and track the two normal-mode frequencies. Near resonance they repel; the smallest separation is $2|g|$ (Eq. 6). The exact normal modes of the circuit come from the eigenvalues of $\\mathbf C^{-1/2}\\mathbf L^{-1}\\mathbf C^{-1/2}$ (Appendix A) — no rotating-wave approximation." ] }, { "cell_type": "code", "execution_count": 4, "id": "3c9c3cd1", "metadata": { "nbsphinx-thumbnail": { "output-index": 0 } }, "outputs": [ { "data": { "image/png": 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GDckER2hqERiC8ZBRQTQkD5GqmFtCiEOQN+7UqVOW/HHBwcGaEsNefqvTp0/rtpCQkBR7FHUgjYRtihCAelEHytjj3LlzxqVLlyzfUfbq1at2yyJFBdpuXT69ddoDaSBOnDiRJE8aQJ+hLnvnaXt8tBPtdQTSiyAfXFrLXLt2TdtinXbjypUrxuHDh5OVDQ8P17LWaVJMkCYF54oyALnfcMt1dL1sxwdSZyC3nCOuX7+ufWGbUgR9izaZxwW4Rlhn2++2IP0IFoB60Q6k6UiJ8+fPa5+ZHDlyJEkal7TUCVAnUgE5+v1gcZYLFy4ku6a2HD161OH4R/8hB6HZ18jL+NhjjyUpg/F0p2PYXj+Mj5Ry8yHPI3IA4joTklpc8Ce7hUxCCMntIGIXpjkEeThr6kVKHJjwbCOqMwuYTAFMzHdzndnJzp07VQMHU/LTTz+daceBJhAmYsyEgtlXCEktNNESQkgGAh8s5DYzfe7gS4apxWCmtk2BkRLwOYR5zl5UKska4FcLtwhTDwJTO0zwMDMjtUlmguuO6287fRohzsI0KYQQkoHAVwp+aPCbhH8lfBfhs4akwLYR0ymBfZ2ZkJ5kHohaRjAS5mqGTyCCnuCvOnv27BR9YTNqHPH6k/RAEy0hhGQSZl44OOg7M9NCdmPOyJGWJMJZWWd2aGXPnz+vAT6ZLdgRklFQwCOEEEIIyWXQB48QQgghJJdBH7x0RjlhCifkacoJ5hdCCCGE5FwQ8INk9Aj0uVN0PQW8dADhztkJ1wkhhBBCMgIk1kby+5SggJcOzMmx0dF0vCUkZ4D5fHtXrixfFi4i7kWKSIUli6mBJ4TkCDBFIRRLpvyREhTw0oFploVwRwGPkJxD+6efFt+/Fovr9eviExwsnmXLZneTCCHEaZxxC2OQBSEkz/H+J5+IX/16+jliy5bsbg4hhGQ4FPAIIXkOzC5xpXAR/Ry5dVt2N4cQQjIcCniEkDwHkg+/OO1H/Ry5ZYtlKipCCMktUMAjhOQ5MA2Yd506EufiIvFXr0rsyVPZ3SRCCMlQKOARQvIkLdq0kX0xMfo5cuvW7G4OIYRkKBTwCCF5knvvvVc2hIbo58itDLQghOQusl3Ai4+Plx9//FEGDhwoTz31lGxJRUTbokWLpHv37jJ58uRk23777Tet78EHH5QJEyZIdHR0sjJ79+6VESNGyP333y9jxoyR4ODgdJ8PISRn0KxZM4koV14/R2zdRj88QkiuIlsFPAhd7dq1k88//1zfprG89tprsnPnzjvue+bMGRXOtm/fLgcOHEiy7dlnn5Xhw4dLzZo1pVevXrJgwQLp3LmzTi1msnXrVmnSpImu69Gjh/zzzz/SsmVLiYqKypRzJYTcXfj6+sq0jRvExctLEq5dk9gTJ7K7SYQQkmFka6Ljjz/+WA4dOqRLUFCQrnv44YclIiLijlo/lHvvvffk66+/TrLt6tWr8u2338ovv/wi/fv313U9e/aUkiVLyrx58+Shhx7SdW+++aZ06tRJvv/+e/0OQRDTfkydOlUFREJIHsDdXRKrVBaXffs1H55XxYrZ3SJCCMn5Grxp06bJoEGDLMKdNsjV9Y5TcIwaNUqKFi0qTz75ZLJtFy9e1P+VKlWyrEN9RYoUkcWLF1s0h2vWrJG+fftayhQoUEDat28vf//9d4acGyHk7mflypXy1b+r9DPz4RFCchPZpsG7ceOGnDt3TurVqyfjxo2THTt2SIkSJVTga9iwYYo35J9++kn27Nljd3uVKlWkYMGCMmvWLLnnnnt03caNG+XkyZMqFJrmXeTBsp2oF/O7rVp162bvaA5LLNZzwhFCci5NmzaVN2OiLZG0yIfnzBRAhBByt5NtGrzIyEj9/8Ybb8iFCxfkgQceEHd3d73h/vnnn3b3gfl18ODBqvkrVKiQw/xWM2fOVAGvRo0a0rp1a3n00UfVvw7Z60FsbKzFB8cafDe32WPs2LGSP39+ywKBkBCSc4F237NGDYl1dZWEGzck9tix7G4SIYTkbA0eTKIAAt1XX32lnxHxChMrBCn4zdkCH7rw8HCZOHGiLgCaOWjSjh07poIhTLzdunWTU6dOyf79+zVoAsEUvXv3lnz58iU5NrSI1ly/ft2yzR7w23vppZcs33FcCnmE5Gxatmkje3//XRq6e0jElq3iVblydjeJEEJyroDn7++vfnIVbZyaK1So4DBVCgS3smXLJll38OBBqV27tgwdOjSJacXPz08FOxAWFiYbNmyQ999/X78j4AIaQJh5UafJ7t27pX79+g7b7OXlpQshJPeA6P3V83+ThrenLQscOCC7m0QIITk7yOKJJ55QrZvpywbt3MKFC9WcaoIoWaRDAeXKldO8d9YLtHLly5fXz6aAt3TpUkudOufkiy+qX54ZlIFy8PWbMmWKau3A8uXLNT0LTMCEkLxD165dZcz8+fo5cts2MazSKRFCSE4lW9OkvPLKK6o1gxYPWjjks6tWrZomJjaBlm3z5s2prhvBGxAIjx8/rn42yHMHvzmTDz74QOuuWrWqBmbs2rVLNXzw2SOE5B3g1uFTu5a4+PhIQnCwxBw9Kt5Vq2Z3swghJF24GAgby2aOHj0qp0+fljJlyqiwZTvbBGaYcCR4rVu3Ts2tCKiwBtpARObCp65OnToOI+NQ/+XLlzUpMqJ4UwO0hBAaQ0JCLP59hJCcB/x+S/04TRq6uUnRt96SwMGDsrtJhBCSLrnjrhDwcioU8AjJHcA1ZNETT8jLhYuIf4f2Uvqbb7K7SYQQki65I9vnoiWEkOymVatWsu32NIWR27bTD48QkuOhgEcIyfMEBgaKW+XKEuPmJokhIRJz+HCe7xNCSM6GAh4hhECL16aN7L8dQRuxKfWBXYQQcjdBAY8QQkRkzJgx0vmVV7QvIrZQwCOE5Gwo4BFCyO0ZbgJattC+iNy+Q4zbUxsSQkhOhAIeIYTc5rnPPpMoDw8xIiMlat9+9gshJMdCAY8QQm7j6eUlO2Jj9HPE5k3sF0JIjoUCHiGEWM1Lu/LyFf0cudn+nNiEEJIToIBHCCG3wYw5myMj9HPUrl2SGB3NviGE5Ego4BFCyG2KFSsmXuXLS5iXlwZZQMgjhJCcCAU8Qgix4tdff5XC7drp5wiaaQkhORQKeIQQYkWdOnWkYOvW+pmBFoSQnAoFPEIIsSImJkZem/mTfo7et18SwsLYP4SQHAcFPEIIscLLy0tW7tkjwT4+IomJErl9O/uHEJLjoIBHCCE2tGnTRrbF3MqHx3QphJCcCAU8Qgixkw9v6bmz+jliM+elJYTkPCjgEUKIHQFva2Skfo45ckTib9xgHxFCchQU8AghxIayZcvKxOnTxbVCBf0euXUr+4gQkqOggEcIIXYYOHCg5G/ZQj/TTEsIyWlQwCOEEDucOnVKZu/dp58jN9EPjxCSs6CARwghdkhISJDRv84Tw8VFYk+flriLF9lPhJAcAwU8QgixQ4UKFSR/8eJyLX9+/R6xZQv7iRCSY6CARwghdnBxcdFo2i23o2mZD48QkpOggEcIISkkPP7z5EmLBs8wDPYVISRHQAGPEEIc0KlTJ+n2yssiHh4Sf/GixJ0+zb4ihOQIKOARQkgK+fDeeO898a1XT79HbKYfHiEkZ0ABjxBCUuDQoUNyxNNTP0dsYboUQkjOgAIeIYSkwOrVq+WdeXP1c+SWrWIkJrK/CCF3PRTwCCEkBRBJuzs8XBI9PSXhxg2JOXqU/UUIueuhgEcIISlQvXp1yR8UJJcCC+r3yM000xJC7n4o4BFCyB3y4bVu3Vo2hYXrdwZaEEJyAhTwCCHkDjz44IPi3qC+fo7ctk2M+Hj2GSHkroYCHiGE3IH+/fvL6z/8IK758klieLhEHzzIPiOE3NVQwCOEECc4ceqUxFWpop8jNtEPjxByd0MBjxBCnODll1+W347+p58jNm1inxFC7moo4BFCiJPpUn45eEg/R+3cKYnR0ew3QshdCwU8QghxUsA7HB4mCQUKiBEbK5Hbd7DfCCF3LRTwCCHECerWrSv58+eXs4GB+j1i00b2GyHkroUCHiGEOIGbm5v069dPrpYood8jNtIPjxBy9+Ke3Q0ghJCcwtSpUyX+2jU52rKVxBw6JPHXr4t7oULZ3SxCCEkGNXiEEJIKwtzcxL1SJf0cwWnLCCF3KXeFBi82Nlb27t0rvr6+Ou8jpgZyhhs3bsjOnTulTJkyUuV2fiqThIQEOXLkiNy8eVO3ly5dOsn2w4cPy7lz55Ks8/f3l6ZNm2bAGRFCciO4r5QvX15mtm8vEPEiNm6U/N26ZXezCCHk7hPwfv75Z3nuueekaNGiKuBh+fXXX6VIkSIp7mcYhjz88MOycuVKefbZZ+XLL7+0bNuxY4dOLRQXF6eC3b59+6RVq1Yyb9488fPz0zIo/8cff0jt2rUt++HGTQGPEJKSHx7uEf9eu3ZbwNuk9yJnX0oJISRPCHj//vuvDBw4UGbOnCmPPPKIrtu0aZNcv379jgLeJ598Il5eXlKrVq1k2yDw1ahRQxYsWKA35IsXL+r3b775Rl5//XVLOQh98+fPz4QzI4Tk5nQp48eOlafLlpP4ixcl9tQp8SpfPrubRQghd48P3vvvvy9dunSxCHegWbNmaqZNiS1btsi3336rDs+OTLd16tRR4Q4UL15cSpQooeZaayIjI2Xjxo1y4MABNRMTQogzAt71sDCJM/3wNjJdCiHk7iPbNHgxMTGyYcMGNZVCIDt06JAKYTCTpkRISIiaZidNmiSFCxe2W2bs2LHy/PPPa31ly5aVZcuWqe8MNHvWrFq1Sq5du6Yavvj4ePn++++ld+/eKbYZi0loaGiqz5sQkrNp2LChFCpUSK4ULyYlDh1SM23ggAHZ3SxCCLk7NHgQrCBUbd++Xc2sr776qtxzzz36dnzlyhWH+w0dOlS6desmXbt2dVgGPjKoC4Lexx9/LHPmzJEBAwaoJs+ke/fucuHCBdm6daucOXNGhgwZooLjf//dmmvSHqgPiU7NxTZwgxCS+/H09JRLly5J8+HD9Xvkli1ixMdnd7MIIeTuEPA8PDz0/7p162T//v1qKj158qRcvXpVXnnlFbv7ICgC2rhOnTrJihUrdAkPD5ezZ8/qZzg7Y4HZ19vbW06dOqX1Isjihx9+UJOwtYBXsGBB/QwH6TFjxug+ixYtctjmN998UzWI5oLjEkLyHu7u7uJWubK45ssnieHhErVvX3Y3iRBC7g4BD+ZVpCWBSTTw9tQ/0Ir17dtXTbf2cHV1VfPIxIkTZdy4cbpcvnxZtm3bpp8h3J0/f14Fuscff1xvwgCaOwh0S5Yscdge1I12wFzrCAR15MuXL8lCCMl74B4TGBQkcdWq6nf64RFC7jayzQcPWrPOnTvL6dOnk6yH1g0pU0zgmwdtGcyuvXr10sWaevXqSZs2bSxpUoKCgjS4AvU4qjcxMVEiIiIkICAgyXFQBvNNEkJISlSuXFldTA57eUlNnZd2kxQeMYKdRgi5a8jWNCkffPCBRs0idUmLFi00Onbu3Lma3sRk/PjxsnnzZjXjOgPMrM8884y89dZbEh0dLRUqVFCzLky4//zzj5ZBwEXjxo1l0KBBUrNmTfXB+/TTT7Ut/fv3z7TzJYTkDnCfwUvn4vPnVcCL2r1HEsIjxM3/Vp5NQgjJ02lSkA4FQh386BAVizQmEOYQRGGC/HUQvByBm2zVqrfMJCYw4SKNyu7du2Xy5Mm6DsEcHTp0sPj/rV27Vt/Ap0+fLrt27VL/vDVr1qgDNSGE3AkEhP25ZYt4lColEh8vkdu2stMIIXcNLgYc10iaQJoU+A3ChEx/PELyFkjU3r59ezn43PMiy5ZJwUGDpNjbb2V3swghuZjQVMgd2arBI4SQnErLli01yKvkfffp94hNTHhMCLl7oIBHCCFpAO4cmFLRt0ljRI1J7LHjEnf5MvuSEHJXQAGPEELSCOaybtKhg3jXrHk7Xcom9iUh5K6AAh4hhKQR+MLs3LlToqpU0e800xJC7hYo4BFCSBpBhD/ybu6RW7FqERs2ipGYyP4khGQ7FPAIISSNYDYezK6z6NgxcfH1lYTr1yX60CH2JyEk26GARwgh6cyHt2rdOvFr2kS/R6xbz/4khGQ7FPAIISQdDB8+XJYvXy5+LVvp9/D169ifhJC8PVUZIYTkdMqVK6f/Y/PnFyRJidq1WxLCwsTNaq5rQgjJaqjBI4SQdPLNN9/I2B9/FE8IewkJErGJ6VIIIdkLBTxCCEknJ0+elClTpohfq1tmWvrhEUKyGwp4hBCSTtq0aSPnzp2T8MqV9Hv4unXCab4JIdkJBTxCCEknrVq1EhcXF1kfHCwuXl4Sf+mSxB47xn4lhGQbFPAIISSdFChQQOrWrSurN24U30aNdF0406UQQrIRCniEEJIBfPzxxzJs2DDxb33bD4/pUggh2QjTpBBCSAbQtWtX/R9TpKiIjJXIbdslMTJSXH192b+EkCyHGjxCCMkAEFQxfvx42XjqpHiULClGXJxEbN3KviWEZAsU8AghJANAkMX06dNl9pw54teqpa5juhRCSHZBAY8QQjJwXto1a9aI/+18eEiXQggh2QEFPEIIyUAB79ixYxJatqyIh4fEnTkjMSdPsn8JIVkOBTxCCMlAAQ+s3bZNfBveo5/DV69h/xJCshwKeIQQkkEUKVJERo0aJRUrVpSAtm11XfiqVexfQkiW42JwPp00ExoaKvnz55eQkBDJly9fRl4XQkgOJ/bsWTnesZOIm5tU2bhB3PLnz+4mEULykNyRLg1ecHCwLoQQQv7/BvzTTz9JmK+veFaqKJKQIOHr17N7CCFZSqoEvJiYGL1x3XfffRIQECAFCxbUBZ+7desms2bN0jKEEJJXiYiIkEcffVT+/fdfKzPt6uxuFiEkj+G0gDd79mz1KxkzZoxUqlRJvvvuO/nnn390wecKFSpYfE/mzJmTua0mhJC7lOLFi0vlypVvpUtp08aSLsWIj8/uphFC8hBO++C1bNlShbt27dppQk97oCq8tb733nuyPg+YJOiDRwixx5AhQ2TLli2yd/duOdqipSQEB0uZn2aIX+PG7DBCyN3lgweBrX379g6FO4BtKJMXhDtCCEkpXcr+/fvl+s2b4n9va11HMy0hJCtJU5DFsGHDZN68eQ63EUJIXqZNmzbSp08ffdv2N/3wVtMPjxByl6dJgabOw8NDXnrpJfn444/F1dU1yba8knmFJlpCyJ1ICA+X/5o1F4mLkwpLl4hX+fLsNELI3ZsmBcEVU6ZMkZ49e+oBCSGE/D9hYWGybt06cfP3t/jehS1fwS4ihGQJaRbw2rZtK9u3b5ezZ89KkyZN5OjRoxnbMkIIycH89ttv6ot38+ZNCejUSdeF/fNPdjeLEJJHSFei43LlysnGjRulZs2a0rhxY9XqEUIIuRVoAXcVaPECOrQXcXWV6AMHJPbceXYPIeTun4vWz89Pfv31V3nxxRele/fuGdMqQgjJ4eAFuHTp0poPz71QIfFt2FDXhy1fnt1NI4TkAdIk4E2ePDnJdwRWIMnxggUL5OWXX86othFCSI4F90Vo8SDgAZppCSF3vYCHJJ72wHRln3/+eXrbRAghuYIOHTqIr6+vxMfHS0DHDrouavduibt8ObubRgjJ5aTbREsIIcQ+mJN27dq14u7uLh5Fi4pPvXq6ntG0hJC7SsCDycGZhRBCyC0SEhLk0qVL+jmgc2f9z2haQkhm454e37uhQ4cmW0cIISSpS8uhQ4dk8+bNEtCxo1z55BOJ3LFD4q9dE/egIHYVIeTumckiL85aYQ/OZEEIuRM//PCDPPvssxIcHCz+/v5y8v4HJHr/fin67jsSOGAAO5AQcnfNZEEIIeTOIJIWZlrkDAX5unfT/yF//snuI4RkGhTwCCEkE6lWrZoUKVLEki4lf7dut5Ie79krMSdPsu8JIblTwMM0Pm+99ZY0bdpU2rVrJ7/88kuqTB+4eY4dOzbJ+piYGE3Xgvrq168vvXr1kiVLliTbf/HixdK5c2epV6+eDBo0SE6cOJEh50QIIbb58I4dO6bf3QsXFr8WLfRz6KK/2FGEkOwPshg2bJhT6yB4OcONGzdUsEO2dwhpyBf1zTff6PcWt2+AjtizZ49FsLtsk1PqhRdekEWLFmldyCb/999/S48ePVSg69Kli5aBwNe7d2+to1mzZvLFF19Iq1atZP/+/VKwYEGn2k8IIc4wc+ZM8fLysnzP37OnRKxbJyGLFknQc88y+wAhJHuDLCCMOQOixZwBjsd//fWXRpj5+PhY1iMpKPJGOSIiIkIaNmyoWrq3335b2rRpI19++aVle/ny5WXw4MEyZswYy7o6depo0tEJEybod8ydW716dZkxY4Z+j42NlWLFismrr74qb775plPtZ5AFISQ1wBfPzc1NEqOi5GiLlpIYGSll58wW3wYN2JGEkAyVO1KlwXNWcHMWmGOhAbQW7rRRKQh3YMSIEWp+xcwZEPBsad26tfq7REZGqlYQAuTJkyd1PQgPD5ft27fr/Lkmnp6eKgCuWrXKaQGPEEKcpXnz5tK+fXv54IMPxNXHR6cuC1mwQEIW/kkBjxCSe3zwrl69KtevX5eyZctqnij4ykFgmzdvXor7zZ49W7Zu3ZrilGjIzVe8eHF1bIaJFtq+iRMnqkkWnDt3TtO7oIw10OBhmyPg2wfp2XohhBBnKFGihKxevdryPX/vXvo/9K+/JDEigp1ICMk+AQ+m05UrVyZZ98orr1gWmDfDwsKcqgsmUYB9YD6dOnWqdO/eXYMd/ve//9ndB07K8K+DkGer9bPm/fffl3Xr1sm0adPk999/l3fffVdGjhwp69evt5hJTK2dNfCRwTk6Av56UI2aC3wFCSHEGRBogZdTWBaAb+PG4lm2rAp3IXaCwAghJF0YqWD27NnGwIEDk6xDFTVr1tSlaNGixldffeVUXZGRkYarq6sxePDgJOuHDh1qNGjQwO4+X3/9teHj42NUrVrVsnh5eRkFCxbUz/Hx8UZwcLDh5uZmzJgxI8m+ffr0MTp27KifL168qO1euHBhkjKPPfaY0bRpU4dtjo6ONkJCQizL2bNntR58JoSQlNi7d6/eL1auXGlZd23qj8bBqtWME337sfMIIXcE8oazckeqNHjQssGcagsiT7HApw7aNWeABq5WrVoSGBiYZH2hQoXUR84eAwcOlJ07d8qCBQssCwIqECGLz3Bejo6OVg0d6rEGxzHrhSm2VKlSyXwKN23apOZcR0DDB6dG64UQQpyhZs2aeh8yLQkgf5/e4uLhIdEHDkjUvv3sSEJIhpEqAQ/BCog8dQTyyR08eNDp+hBFO3fuXA2AAGfOnFEB8b777rOUgXm1Z8+e+rlAgQKa9856gdCFtCb4DIoWLaqCI3zuTHMx2gRTLRycTZ5++mmZMmWKHD16VL//+OOPagLG/LqEEJLRuLq6anCXdWCYe8GCEnA7ddNNJ1+OCSHEGVIVRXvt2rVkvm8IljDBNmjQnAXC1KlTp9QHD0Ia6nr44Yfl448/tpS5ePFiqhMQI1ADmkYIe0FBQXLlyhX17XvnnXcsZd544w0VKCEMwp8OvnfTp0/XthBCSGYAi4MtgQMHSOiiRRKyeLEUfnGkeBQtys4nhGRtHrwyZcrI/PnzNYeco+TDmDUCQltqiIqK0mTFiDKzDXy4dOmSbrd3YwQ4FlKhIGLWFphkEamLej08POzuj0hYlIHJ1lEZRzAPHiEkNeBls0+fPjJu3DhNrG5yeuAgidy+XQKffEKKvvoqO5UQkm65I1Um2o4dO8qHH37ocDtuWiiTWqD5QzoTW+HO9JdzJNwB7GdPuAP+/v6ahiUlwQ0dhPpTK9wRQkhqgUUBri7//vtvkvUQ7EDwL3MlwclMBIQQkmEmWswZi3x1bdu21STBVapU0Xxy//33n84QAQ3erl27UlMlIYTkKT88aO6QiN0a/3vvFc9KFSX22HH1xQuyMwUkIYSkhlRp8CpWrCgrVqxQcypMsQi4qFGjhiYQhn8etqWkbSOEkLwOplZExD4Sp5u4uLpK0NO3hLrrU3+UhODgbGwhISRPzmQB/7sDBw5ouhKkRcGCz0iTklKKEUIIIbcSHiMYDUmPrcnX7T7xqlpVEsPC5PqUKewqQkjWBFnghuTt7S0ZXTYnwyALQkhqQZ7O5cuXq6nWz88vybaw1avl3LDh4uLlJRX/+Vs8ihVjBxNCMjfIomrVqjqFmKMkxOaBv//+ey1LCCEkOUjI3qVLl2TCHXJy9hg9WqReXTFiYuTyx2PZfYSQzA+yQHoUzOeKOWcRZHHPPfdonjkoAJHKZNu2bTqRNoIwUJYQQoh94NaCrAOzZs2yZA/A/RXBF3NHjpT++/ZL2LJlEvbvKglo15bdSAjJ3Dx4YOPGjep3t2HDBjl79qy4uLhoDrmWLVtqkuKmTZtKXoEmWkJIWsCMFo0aNdJpy1q0aKFJ1xHEhoTrSA215fnnJWLGT+JeorhUWLhQ3AIC2NGEEEmN3JGqNCmgefPmuhBCCEkbmNYxICBANXYQ8MaOHasJ23HzRjLkP729pUupUhJ37pxcHDVKSk6YoC/ThBCSaVG0hBBC0oe7u7sGWcCtBdq7qVOnyv3336/bkHZq3PjxUuijD1FQwpb+LcFz57LLCSGpggIeIYRkU7oUuLx89NFHanLp3r27rn/hhRd0Du4527dLkRdf1HWXP/pYIjZv5nUihDgNBTxCCMkG+vbtK999953MmTNHXn31VZ2yEcAXb8CAARqAEfj4YxLQubMYcXFybsSzEn34MK8VISRzgizI/8MgC0JIesFUj5UqVZJly5ZJ165d5dy5c1KoUCHNToC5thNjYuTsk0Mkcvt2cStYUEpPmiQ+tWux4wnJg4RmRh482zlpkbOJEEJI2kGQxT///KNz1FqDRPEQ7vQm7eUlpb77Vrxr1pSEmzflzKOPSviGDex2QkjGC3iLFy+WKlWqSOvWrWX69OkSERGRlmoIISRPgzlp8cKM9Cgp4ZYvn5SZMUN8mzSRxMhIOTv0Kbn2ww9iJCZmWVsJIXlAwNuzZ4/mcapdu7a89NJLUrx4cRk6dKjerAghhDgfaIHZgZD4+E64+ftJ6Un/k/z9+ookJsrVLyfK6cGDJebECXY3ISTjgiwwk8W3334rFy5c0CnMTp06pcmOa9SoIZ9//rkEBwentWpCCMkTNGzYUPPfIV2KM8BcW+Kjj6T4Rx+Ki6+vRG3fISd79ZbLY8dK/I0bdvfBjBnw60stad2PEJJLomgxryKiv7DAjwQ3q2+++UbKlCnDKcsIISQFPDw8NNExfPFSQ4F+/aTioj8lulFD+fP6Nfn8iy/kfw0byflx4yT23PlMFfAwg9Gnn35q+X716lWZPXu2vtgvXLjwjubmrCQhIUE++eQT+fjjj+9YNiYmRn777Tc9tx9++EEO24lYjo6Olj/++EPL/PTTT3LDgVBtsn//fhk9erTWZ8u1a9d0Gxbb8vb6EOewmalySFYIeAcPHtR5aTFN2eOPP64CHcy2WE6cOCGfffaZPPvss2mtnhBC8gRwb7nvvvtSvd/URYuk7/r1sqNWLQkuUEAmnD8n9773nuxo11bODhsuIYsXS2Im+Edjqsp169bpZwgujRs3liVLlmjU7xtvvCF169aV69evy93Ae++9p4LqnQS8y5cvS82aNeX9999XwQtTyOE8vv76a0uZHTt26AwkP//8s57fzJkz9bmXknAOgW3MmDGa29BWWIb/OnIgYrtteQp4JCNI9VRlAPPNbtmyRYMs8NaGDOxmDicATd5TTz0lw4YNy5BGEkJIbuWBBx7Q/3///Xeq9qtfv76+aOPei2xXV5b+LQ37PyiTrl2X11avlvDVq8XFy0uMqCgJXb5CYosVE4+yZXXKM7jQ/PrrrxogBzMx0i2sWLFCfarvxF9//SWPPPJIsjYACEhw08HUa3g2QKiZMmWKw7pGjhwpBQoUkMzg33//VWEUOQbvJOBBAwnBbu/evWqFAohi/vDDD+W5557T72gnElMHBgZa9kNyapSBL2VKdOnSRQW6d955x7IOs5d069ZNtZ5pAecUGxubbD2OgZlSCEnTKIBgB/U0ImkdgZtIWFgYe5gQQu4ANGIQlFJDkyZNktxvi97XVeq1aSPBcXFSqHMXCf17qcSdPiNGfLzcmDJFjs+eLe7Fi0tUjRrSY95cKRAYKG07dpIZM2aooIC8WncS8CAYIpgOApFtGwCEIwTfnTx50rIOU7FNmzZN3nzzTfH09NQ6Jk6cKCNGjLB7DJT/8ccfU2wH/L07dOjgcDvMxo899phq23bt2iV3wlE+MeQbM0ECalsgSNmmuLHHk08+qcLs22+/rdcKGkIIlBA+0yrg2RO8oQHEMQjR8ZmWbrD2v0gJf39/9jIhhNwBmOXS+0IMEynMhaNGjZIiL46UwiNfkJhDh8SlYUPxql5dXM6fl/iLF+WLPXvEMyJcfioYKJ4rV8pTpUpJ7x3bJTEhQW7Omyee5cqJZ9lbOfhsWbp0qZoy4ZpzpzYAlHviiSdUwEM6GDwTEJAHAQ8uPJmhvYM2E8IdFvg3OiPgPfroo1quffv2qsDAVHGHDh3S2URsmTBhgppoUT4yMvKOwiiACf7pp5+WVatWSbt27VSrOXDgQBV47QGtoK0WzlZbh/40gWYRWlOYzOHXSUiaBTw4n+IN7oMPPkimGh40aJBUrVqVvUsIIU7Spk0bfUCnFQQIPPjgg2pWNDVj0BR516ghLp6eUnz0e1Klbl2J3LFTtvR/UPpWqSy+3j4Sf+mSuJw9K13d3GRuWJhcGvWepc7EsDA5O+JZKVa1qngUKybuxYrJ7wv+kA5Vq0rExo06q4ZbYKD+d/X0tNuGtAC/NuvAg9RiCmCmkOkMUVFR6ocHkzUCM+ADBw0bFnugDIQ7CLQItKhQoUKK9UNYGzx4sAqDjRo1UvM43Jx2794t6QVmcEx798wzz6g/PCHpEvDgkwBnWns3KTiTptaXhBBC8jLw4Xr33XfTtC80O/CDhtYJ6Vas/aGtcfXxEf+WLeRKTIxUGTpUKj/5pMRfvy4xR45IxenTxXXuXPFr3UpiT52WuNsBAQnXrklURIRE4bNhyPJjR+WH8xfkzO49SeqO9/GRF86dlTPR0TKvW3e5/sab4hrgL25+/nLzyhUtE7xggSQGFZaI8FuaypiTJyXW11dcvL21ba7e3uLi4ZEuE21cXJxqtvr3769aMLB161btIwiN8JmDz6EtUFYgFyHM5JhFBEDL+NBDD6kAZW3CtTZjw/QKf0RMN3cnUBZBGjBh16pVSxdHAh6UJWY7TODTaE8w7d27t9ZpbzvJ26RJwIM62Nb3AmDdBk6hQwghqQKRqDCtQUBJDSiPIA2YEyHclSxZ8o77IDE9tFXAvVAhcW/eXMJWrRLXgAApM2mSroffnmuhQlLs/TFSsmhRibt4SdZv2igeZ89Kk9atxQi+KfE3g3XqtLj4eBl57Kgci4mRGaXLSMDu3WJtbA6JjNT/l97/QMJcXeVi3C1T47lnRoinl1fSxrm7yyVXF7keHCwu7h7iAjOlh7v+189ubuLi6irXDh2SC6tXq+bQxcNTXDw99H+Cm6u80LmLuISFSdT+/eLi6ibxEDANQwXKyN17JCI+QVxQp5ubiBvqdZPdmzdLg+rVxfXyZYnDcdzdpWmtWmo2P7pvnwaTYB320f1u07ZtWxVGkT7FViCzBT7ryB8LQR6pxDKCIUOGqE/j8uXLNWUZIekW8BBFhNks4N9gDdZZO6USQgi5M15eXtK5c2d1lE+tcHfgwAH17XLkF2cLjoPgA6S5gg8YtFuINrVGhSmYeKtWlXxNm+q6jYcPSff+D0r5adMs5WJjYuSBvn3ldEy0rPjuOynu5SWJ4eGSEBau/xPDw8QfwSPTpol/y5biHRMjvlevipw4IS4w7bq4SGJUlM7MocTHSzERecbX7/8bk5AokhArEmPlgxa8V0L27LV7frZGSvebN2V9QoIM3rJVZMtWOQNhMy5O5ocEy/35C0gxDw8pevmyrIkIl4MdO4nX7aCJhTdv6AMy8bHH5YibmxyMjpZqXl63gipuC3u/nDktZby85Ey79rcEP2sh0M1NLl+6qHWd6N1HBdPn3NylQeXK0uyfZXJq9Rq5dvqUbj/9+OPi4uIq124Hp5x99jnx9vISF1cXEVc3EVcXMRAI8+efcuHiRV333ZbN8ueGDfLXk0Mk+quv5JKWc9Xj6H83VxEXVxG32+vwGfW5uKj5Xr/rf5dbx8FnwfGwXpKVwb631pnr1Q/gVt3iqAz+46OrVf1WbbDsa1Umhf0sddvd73Y5c18Xc53YbL+9zXq9uU3XWe1rZ/9b/1Le383PT1z9rMZwThLwoLaGunnSpEnSvHlzXQfNHfI5YRshhJDUAb+11Ah4ENAQgYl7MVJumEDQg2bHEa+//romoUe6K2igIBzCp+xO0aBoG9KgWPPqa6/Jn0uWaBvmbN2atA3DntbPQevXq4BX6quJGmRRIjZW/AID5dvixTRgD2lVjLg4TeeSGB1t+Q/Bz9D/0WJER936j3JYYmPt/E+6LvH2f889e8TlxnXxrlPHsh0+et+dOC5typaVUn7+MszfX1bv2ycPnj0jrQIC5HJsrCwLDZWXChcR/9uasW2RkfLOpYtS19tHvF1dZGdUlFyIi5PxJUpIgoOEx/Ghofo/5nbS5Nq3FzlwQM3eMSEhuj5y0+Zb5W6Xj1i7VuJtrge0qtH7D0jIhYtyIz5exh4/Jvf4+Mi8eXOTlBtWKEjcTQGEZAtBzz4rhZ9Nux9qtgp48FdAMmP4jcB5FFFLuEHA0dP0eyDp550F+2TfmesSHxcvfv5++n4QFRkp7u5uag7AROMRkRHi5+ur1yEuNlZiY2PUXwRl4TAMtb2f7608WWGhoVqPp4eHvrVHR0VJwYIF8E4i4eFheoPXyGfDkODgmxLg76+aBbylo65ChQL1zSb8drRffviluIjcuH5NAvwDxNvHW8vCrFE4KEhcXV30mDg2ouVwz7l29aoEBPiLr4/v7dQMwVK4cGFxc3PVsgnx8VKoUCEte+XKFW1PgJ+floUzc5EihcXD3UNCQ0P0XIsWKaJtunzpkvj5+em5x8XF6nGKFi2q54qy8FWBaQr9cvnyJfH18ZHAwIKSEBen+xYrVlR8fLwlNCREfYTKlS2j9V68cF58vL2lSOEgbRuy+JcsUVz8/fy07Tdv3JDKlSrpC+X5c+fEy9NDShQvrhGJJ04cl1KlSkr+gHwSEnxTLl+5LDVrVFetxdkzZ8TdzVXKlikjhpEoRw4fktKlS0tgwQISGhwi586dldq1a4m7m5ucPXNay1SqWFFffvfu2aPtK1o4SM0zSElRp04dHQP4DM2OmcIIPj4lSpSQIkWKSGhoqBw7dkx9f6C5ga8THMWrVaumZZEDDOWKFSum86PCrwgPX4w1+CFhf3wHSMcATT7qRh0IvEI9SJOB6QtxrXAcAL8mXBc89GHKwne0D9cWTuq4zmg/QD2oA472uOY4TqVKlXR/lEPd8GMCaB/MmuXLl1eneLQfnwsWLKjO8Ti/Bg0aaFmcN8Y3nOETExO1XxAMgHNAWxHZicS2+L3g3ob7WeXKlXVf+Gbh2mCcor+xHT5PODb2Q3CBGViGejHOMPbM/kbUKX5HaA9+R9WrV7f0N+pEefT30aNHdT3ajt8M0pZgXwAtHX5DMMFiLMMkC7MhEvni9waTK44J0EcYp2gz+hvnguMClEOfo53z5s3T8QKftdOnT2u6FJwr0oHAEoM2HDlyRAVBnCfaZ44r1AmLDfoBbcAYgA8gxg5+N7hWx48f17rQDuRFRTtxzdGWL7/8UttiRtXi+qG/3fLn1+hUjBX0DfoA9dSu3VL7G+3EOZn9jTbgmDh3NacePWoZs+gD3Ku6hIeL+4oVEt6jhwQFBWl/J/z3nzw1frzUe+UVPa7v+fOy6MoVvbY4XqmICHmlbVu5t3VriQoPl8MHDshb5cvLk5cuyR8LF2rb36lfXzrfe69cOHNGfDw9pViRIhIbGSnHjx6VUsWLi5+Pj9TdvkOeXrZMSr/8soiRKOfOnBEPNzcpUriwxMfGSvn16+Wl/45KiUcfldCQYCm3d5+8fuqklOrbV65fvSquhuh9NzE+QZ6cOVOa1qsrRapVF+P6NXlq8WLL/Rr3clwvHy9vKdS+vVy7clny+QeIj5enbsM9pVDBgnpfDQsJ1ftT/vz59Bly4/p1vR96e3rpby4sLFQK5Muv9ykNOomLk4CAAD1OyM2bOpa9vDwlPjZOIsLDtQ24L+E4eFb5I4+gYegzxd3NXbw8PSUhIV4iwyP0OPgdxkZHS3xcnH5Hu/Fcc3N1EU93D/19RkdFipenl7YBzzXce3FcaHrxjMEYw73RuP3dA5pTF9F+QlmNJDYMiY+Hy4OLPl8k0dBj4jOeeTgO+kHrgab29uwhOOatMR5/+7OLHgeLvgQZhn7Gfz3o7e+q9cM6XX93SEAuBno3jeAmgxsCTgw3G/PGlVfADRw3QtyEHOVRSg99v9sgO89wTl/iGFcx9Ibm4+MlHq6uEhUZIYkJ8VI4KFDcXV3lzOlTUiiwoAQVCpSoiHA5cfyY1KtTW7y9veTk8eMSER4qTRo10pvryhXLpVKF8lK9WlW5eeO6rFi+TPr06imBBQrI1i2b5OzpU/LEY4PFw81Fvv1qotSrW1u6d+0ily+cl3Effyhj3ntXKlesIPPn/ixrVv0rs2fOEA83Vxk88BFp3rSxvPX6q3L29Gnp2L6NLFrwu7Rp2UK++PxT+eKLCZq3DCDCEEIZ5reGUAnhAEFbMCt+9dVXmkvNFFYQ1AVBAKksIKThxQBTTeFFE2koYFEwb29IKIsHxO+//64CGQQAzESAVBUwV8JRHkIWXhJg9sRv+59//tF9IThj3m2kufjzzz+lV69eKsBAAEEqDghxyGsGcB+AMz8c8ZE4uGPHjipEmZGlyCGHeyaAoIF1cKjHetMagv3RFhwLAhaAkIt2IdIWgiGEUQQPoL9QHudrzpQAYRl9g/5C2yDAoP2IssQMQ0iQu23bNq2zWbNmet/et2+fCkbIbwpNHfoLgjZeFrBgRgccp1OnTtpf5r0PQiLahSS+iOBEWfRXz549tS04h/jbD1ykSkF/IYIU0bbmffPhhx/W64/+ArhOiIRF3yxevFgDIyC0or+gmYSwi/4CENAxJpBPDj6I0EhCyMO5Pf/887oO/WWt2cR54Pzh9wgBEf2FOtAu9BeAAIlzQH/heHhZge85+gtKDPQnBFqA8Yr1WAdhFS8Z8IlDEAjOA8dDf5nBIWgb+gvnjBcqaGFxLIx5nLM5iwXGPPrHTEgNQWrOnDnaXxjzyFgBYRf9hTGPcY3+AngmT548Wc8XY75fv36qtUR/YcxjrJjzH2PMY1yhvzDmkZQZwjH6C2Me4xX9BTDmMbbRXxjzrVq10pcy9BfWY3/0F8CYx7HQX6gD/oeYDQT9hTGPc0B/AbzI4HzRXxjzeFlEbkj0F9qG9TnlHnE3yR3pEvDyOpkt4G06fl1Onr8soWFhUrp0GTHEkLNnz4m3ap8CJTY2Ts6dP69vrxiMaEdwcIiUKl1a30guXbwk7h7uEhhYSOITEuTcufMSVDhIvL199G335s1gKVW6lL5w4IEFXwaUxZvN+fPnpWBgIY3IC4+IkJs3b0rxEiX0bQY3CtSPNiQaht588+cvID4+vqpduHHzprYJN5mbwcGSkJAoBQML6nEu6Vt7gPj4+khMdIxux1s1/E9CQkP15lag4K2yV69d04cM2hATG6vnBu2Mq5ubhIeFS2xcnGo1UPbGzRvi6eWtZfGQCQkJlXz586tGJiIyUmJjYvU72g0tjLuHh/ZDXHyCXkdfP3+tNyoqWqJjYsXP31/PDecOR21ovOIToDGN1OPgTS4mNk4X9D3KRkfHiIE3S3cPSUhMlJiYWHGFE7eLi/Y/juXm7o4XSXVMv/UC6Kr7om689RmGi36/tUiewMvNRfy8PcTHw03cjHjx8XSX/P4+uj4uKkKCCuaTfH7eYsTFSEJMpFQuW0ry+bhL2I2rUsDXUyqXKy1+Hi5y9sR/UrNKBSkSVChHavDw0EeGAjyo8PC5kwYPx8TDBoIGzhdtAtCQQuNiavBwjAULFmiON2ie8HuFSRUCHR5MprCEhyR+56YGDwsemMgRh4ce2o4HLgQYU4NnakxxT4B2DS/6GO/QggHUhUcMtHJly5bVByyOAaHX7G98NjV4wL4Gr3aaNHhYZ2qdIcSaGjycCwQJXAvcM3C/w7W17m+cP9ph9repdUZ/Q9gwtc7YhusArTPGAvY1tc7ob5Q3tc44JsYCxh7uU2gTxiSuLepEm80xi3NB/2C72d+2Yxb1YlxjTGJc47jmmEV7cL5mf1PLH58lWv5cIeDB5w6LvcmWMfdfXiCzBTxCEhP/X9izFvwSEgyJT0yUBJgdEo0k/299ttmW8P/rbwmUSfe59T8xSR3W2+MSEm8vhsTGJ0psQqL+j7P6H5Pku5F8Pfa/vS+2ZxbeHq6Sz9tDCvp6SlCApwT5e1ktWOclhf29pFh+bynk5/n/DtfZDASsrl276sMeApMzMyQ4A+7H0EJYB2FAaFm0aJEKTHigQXthGwVqbz9CSPaS6QLeJ598on4beHuAJGyLqWrP7VDAIyRtQGiMjkuQyNgE/R91+3MUlrh4iYpN1HVRsfG3/ydKZFy8RMYkSFh0nIRGx9/6H3X7f3S8hMfcMm2lBmgNSxX0ub346v9yQX5StWiAlA70VdN1Vgt4AJoGUyNHCCFpkTvSFGSBBJDwG4BvBCGEpBYITn5e7rpkpNAYHh0vodFxEhIVJzciYuVaeMztJVauhcXIVfPz7fUQHo9eCdfFniawcpEAqVI0QGqWyCf3lC0oNUrkU7/CzARmIZj1KOARQtJDmu6uUO9jPj1CCLmbhMb8vh66lHaifEx8glwIjpZzNyPl3M0o/X/2RpScuBYuRy+HS3Rcouw7H6LLbzv/X+irU6qAtKgYJG2rFZZaJfJrtHhGAud1ZxIWE0JIhgt4iBhChAucgQkhJCfi5e4m5YP8dLGnDTxzI1KOXArTZc+5YNlx+qZqBreevKHLFyv+U5++zjWLSd8GJaVBGaShyBhhDw73CEjIKD88QkjeI00CHsKdkdAYYfeI2rG9qSEUnhBCcrI20BT+utTC3ApIwWXIiWsRKtyt+e+KbDh2Xc29s7ec0aVsIV95uHEZeaRJGQ3ySCtISdGnTx/NAWhGdRJCSGpJU5DFnaKqzHxMuR0GWRCSd0GU8JaT1+WPXefl7/2XNEgEBHi5y4CmZWX4vRXVXJzaIAskcIZgh2TAeIkmhBAT5sHLIijgEUJAREy8LN57USatOyHHbgdsBPp5ysudqshDjco4FY1rCnh4QUYiYPjhIZEwIYSkRe6ggwchhKQTRAM/2Ki0LBvZWiYPbiiVivhrFO/bf+yXB37YKGeuR6aqPkwDuWbNGkuWfUIISS1pFvAw5QiyriNBpgnmMkRGdkIIyYsgorZjjaKy9IVWMrpHDTXXYrrB+75aJ0v33ZrayhkwxRJmW8gr7i6EkLtEwMN8d5iDDtnWlyxZYlmPrOjwGyGEkLwMcuU91qK8LB3ZShqVK6hJmIfP3infrz7ulFYOaagwxRSmPyKEkCwT8EaNGqWTUmPiY2v69+8vU6dOTVNDCCEkt4HZMX4e2lQea15Ov3/y92EZ9/fhOwp5mCMWc69iTkxCCMmyNCmYXPm+++7Tz9YpUuAUjEmbUwsm/F27dq1OLN+pUyed0NkZMAn10qVLdco0TIJtMmnSJImNjU1WHpFpbdu21c+rV6/WNATWIO/Uww8/nOr2E0KII9zdXGV0z5o69dkHfx2U/605Id7ubvJixyq6/fDhwzqRvW0y+S+++EKmTJmi97m7Zb5cQkgu1+BhMuyzZ8/qZ+sbz8aNG1M9MfWYMWOkevXq8scff+jSokULOXXq1B33i4mJkX79+snrr78u8+fPT7LtyJEjetM0ly1btqi/4NatWy1lfvnlFzUnW5c7efJkqtpOCCHO8mTL8jKqew39PHHlUfl56xn93KhRI/nss8+SlH3qqadk5syZek9C2hRCCMkSDd4jjzwizz77rEybNs0ibK1YsUKGDx+eqiTHMPF++OGHqr3D7BgAgqMzZomXXnpJmjdvbnfb+PHjk3z/9ttvVaB79NFHk6yH5u+bb75xur2EEJIenmhZXsKi43UWjFEL90uVov4yaNAgFfAmT56sZY4dO6b3Rqx77bXXNJq2atWq7HhCSOZr8CCUBQYGqgMwhDGYVLt3764C1zvvvON0PZ9//rk88MADFuEOoM6yZcumuB80ff/++6/u7wzwC+zRo4cUK3YrI73J5cuX5ccff5TffvvNopEkhJDM5Pn2laRrrWISl2DIsFk7ZdjzL2luq0WLFun2iRMnSvHixWXEiBE6axDcSQghJEsEPG9vb5k7d66aQvGmOX36dDl48KBqyTw9PZ2qAykAdu/eLe3bt5ddu3apEAZ/OviepAQEMWgKZ8+erT57d2Lnzp1a/9ChQ5Ntg78gbp7fffedVK5cWSZMmJBiXdBU4kZsvRBCSGqAW8vnD9SVykX85WpYjPxvZ6gMGTJEXzTBwoUL5a233hIvLy/Nh4d5v5kPjxCSJVOVZQTI7wRtXceOHeXChQvSuHFjnYMxLCxMli1blszpGCQkJGh+KGgL4XtnmlmxzlF6FrwF480Yfn3WE3dv375d6tevL25ubvodUcGPP/64bN68WX1i7DF69Gj1GbTFmYzShBBizb5zIdL7uw2SkGjI6HZFZWi3ZhIfH6+WBtyvIODByoBoWlhMCCEkNBUzWaRJwLuTafSVV165Yx03btzQqFWYICBUIS0ABDjk1wsKCpI///wz2T4Qwp5//nl5//33LcLauHHjVPuGgAsIc9ZBH9HR0WrqGDlypLz33nt3bBNurKgfb8+ONHhYrDsaQioFPEJIWhi/7Ih8/e8xKeTnKYU3fSH/LF0qH330kcN7ECEkbxOaCgEvTUEWs2bNSvIdfnhIcowD16pVyykBD2+kEPCQ0BPCHYA2DSZb2/pNypUrJwMHDkwSVQaBCwlBEQULWdVawIPJA2164oknnDovmJeDg4MdbscbNRZCCMkInmtXWZbsuyjHr0ZI277PS2x0tLz44otJyrz77rs6QxDSphBCiLOkScCD75wtyDs3bNgwqVSpktP19OnTR33krIG/XMWKFS3fV61aJZcuXdL8dK1bt9bFmvXr1zs00cKvr0uXLsmywUNTCBOI9XEQyQv/Put8eoQQkpl4urvK292qyxPTt8ufJw1Z8etf4uPjk6QM/JKRCgo+wsyHRwjJ9Llo7Wm/xo4dq1GpzgJTK1IC9OrVSz799FM1s0LQ+uSTTyxlEEwBk0VqOXHihAZQ2AuugKYPwuXgwYP1WDDtdu3aVdOoINqWEEKyirZVi0irykESm5CoM13YgkAL+CzjnkYIIVku4JmaMTgFOwv846AN7NChg1y5ckVvZEePHlW/PBOYcJF3zxEPPfSQ+u3Zmx0D/nQIyLAFJmFoDrENJlmkZUEeP0QD8w2ZEJKV4J4DLR68Sxbvuyj/XQ5Lsh33N5RBPjxCCHGWNAVZ/PXXX8nWwQ/u+++/V+c/pDvJC6TG2ZEQQlLimdk7ZMm+S9Kzbgn56uH6SbY1aNBAateuLTNmzGAnEpKHCc3sIIv7778/2bqCBQvqmyYdgQkhJPWMaFtJBby/9l6QkR0qS4XC/z8nN3J1Fi5cmN1KCHGaNAl4SD9CCCEk46hZIr90qF5EVhy6Ij+sOS6f3l/Xsq1p06bsakJI9vngEUIISTvD29yK7F+w+4LciIi1rIcnDdKn2HOPIYSQDNPgOTsHLHAmJx4hhBCRBmUKSu2S+WXf+RD5ZdsZeabNrbRTCLJAyigEhdkLHCOEkAwR8JC6BNGvmEIHEagAiY7j4uJ06jBz+i9AAY8QQpwDgtyjzcvJK7/ukVmbTstTrSqIu9stQwuyDGDaRUIIyTQTbbdu3TR3HXIzIa0JFnzGOrxdYp5XcyGEEOI83esUl0A/T7kQEi3LD/5/2ikkdD958qSmgCKEkEwR8KDBQ0qUIkWKWNbhM9ZhGyGEkLTh7eEmDzW6NfvOz9vOWtab+T6ZD48QkmkCHqYOw/Q5tmAdthFCCEk7/W8LeOuOXpULwbfutUFBQZoupXHjxuxaQkjmCHgdO3bUab727t2r0V1Y8HnQoEHSqVOntFRJCCHkNmUL+UnTCoGCNPS/7Thn6Zfhw4dL1apV2U+EkMwR8CZPniz+/v5St25dnRjb29tbPyOr8qRJk9JSJSGEECsebHhLi/frjnOSmHhrwqFr167p3NwXL15kXxFCMn6qMpNDhw7JwYMH9XONGjWkevXqkpfgVGWEkMwiKjZBGn20QsJj4uXnoU2lWcVCcvXqVfV3njVrlgwYMICdT0geIzQVU5WlK9ExBLp+/frpkteEO0IIyUx8PN00ohYs3H1e/2O6MrxMr169mp1PCMkcAW/Hjh3y3HPPacoUE0yEHR4entYqCSGEWNGzbgn9v3T/JYmNT7SkS2EkLSEkUwS8xYsXa8j+9evXZcmSJZb1SHb85ZdfpqVKQgghNjSpUEiKBHhJSFScrP3vqiXhMXKPXrhwgf1FCMlYAW/UqFHy008/yZw5c5Ks79+/v0ydOjUtVRJCCLHBzdVFut020y7ae8Ei4MF6kpCQwP4ihGRskIWvr69Gc+G/q6urJCbeMh3APBsYGCixsf8/SXZuhkEWhJDMZteZm9Lnu43i6+kmO97pqL55hJC8SWhmB1kUKFBAzp49a5k70WTjxo1SqlSptFRJCCHEDvVKF5DSgT4SGZsgKw7dmroM5tlffvmF/UUIyVgB75FHHpFnn31W558FMTEx6pc3ZMgQGThwYFqqJIQQYge8RPeocyvY4s89t8y0a9eulYcffpgzBxFCMlbA+/DDD9UUW7p0aTXPIulx9+7dpXnz5vLOO++kpUpCCCEO6HE7mnbNf1clIiZe/fBMQY8QQjJMwMPMFXPnzpUjR45ooMX06dM14TFMBp6enmmpkhBCiAOqFQuQMoG+mioFQl7x4sWlSpUqzIdHCHGIu6QB3FwwVQ5uMFgIIYRkrpm2c82iMnndSfnnwCW5r3Zx5sMjhGS8Bg9Rsjdv3kzLroQQQtJA55rF9P+/h6+oJg9J5mvXri3x8fHsT0JIxgVZfPbZZ5KOaWwJIYSkggZlCkqQv5eERcfLphPXpWfPnuoW4+6eJkMMISSXk6Y7w3///SfLli3Tm0u1atWS+d0tWLAgo9pHCCEEb+OuLtKxRlH5eesZNdPeW6WwBAcHazaDWrVqsY8IIekX8CpXrqwLIYSQrAN+eBDwlh+8LB/2qiWvvvqqbN68Wfbt28fLQAhJm4A3a9YsS447zDdLswAhhGQtzSoWEn8vd7kaFiO7zt7UdClTpkzRmYWCgoJ4OQghqffBGzRokOWzh4eHs7sRQgjJILzc3aRttSL6+Z8Dl5kPjxCSfgGvcOHCsmvXLmeLE0IIySQzLVh24JJODVmhQgVZs2YN+5oQkjYT7TPPPCMNGjQQX19f/Y7ZKxwRHh7ubLWEEEJSQZuqRcTDzUVOXY+UE9cipEuXLhIVFcU+JISkTcAbPXq09O/fX44fPy49evRQnzxCCCFZC3zwmpQvJOuPXZNVh6/It99+y0tACElfFG316tV1efvtt6V3796p2ZUQQkgGAT88CHhIejykVQWJi4uTyMhIyZ8/P/uYEJL2RMcffvhhWnYjhBCSAbS7HWix9eQNCYuOk/r166uVhRBC0iXgEUIIyT7KB/npEp9oyPqj16Rhw4YMtCCEJIECHiGE5EDaVr2lxVt5+IqmS9m9ezfnCCeEWKCARwghOdhMu/rIFWnVurXODb5+/frsbhYh5C6BAh4hhORAGpcPFD9PN7kWHivhHoFSunRp2b9/f3Y3ixCSk+eiJYQQkr14urtKq8qF5e8Dl2TVkaty6NAh8fPz42UhhCjU4BFCSA430646csUi3MFUSwghFPAIISSH0qZaYf2/91yIHD59QcqWLStLlizJ7mYRQu4CKOARQkgOpUiAt9QueSu58d4r8ZKQkCCrV6/O7mYRQu4CKOARQkgOn9UCrP7vqqZLWbNmTXY3iRByF0ABjxBCcjBtqt4y0yLhcavW98qOHTskNDQ0u5tFCMnrAt5///0nffv2lQIFCkiJEiV0uh3Mq+gMr732mri4uMjIkSOTrPf399f1tsvzzz+fpNwXX3yhPive3t7SqFEj5pAihOQ46pYqIPl9PCQ0Ol6K1WwiiYmJsnHjxuxuFiEkLwt4J0+elGbNmklgYKCG+GPx8PCQbdu23XHff/75RxYtWiSVK1dOti08PFwjycxl5cqVuv7++++3lJk6daq8/fbb8u2338r58+elXbt20qVLFzlz5kwGnyUhhGQebq4u0rJSkH4+GeWtufA6derELickj5OtAh4ErJIlS8qkSZOkePHikj9/fl3XvHnzFPe7dOmSDBkyRGbNmiW+vr53PA6EuSpVqkjr1q0t6z777DOto3v37lKoUCEZN26cahG///77DDk3QgjJKlpXuSXgrT16TWrWrCmurtlunCGEZDPZdheAGQEauIceeihVNyNo5AYNGiQjRoyQe+65547lg4OD5ffff5ehQ4da1t24cUOOHDkibdq0sayDCRffadoghOQ0Wle55Ye352ywrFi7UZo2baqWDEJI3iXbBLwrV67oDQgm2ZYtW4qPj49UrFhR3n//fYmPj3e4HzRtsbGx6n/nDLNnz1Zh8tFHH02iAQSFC9+6KZoUKVLEss0eMTEx6rxsvRBCSHZTPL+PVC7iL4mGyIlIT9myZQtfVgnJ42SrBg98+OGHMmrUKLl+/bpMmTJFAx+wzh7bt2+XCRMmyMyZM53W+sE826tXr2TCnCPtIDR5jhg7dqyakc0Fcz8SQsjdpMU7Fu4hRYsWZT48QvI42SbgQeByd3eXAQMGqEMwfOnatm0rjz/+uPz6669299m8ebNcu3ZNI1/NyNg9e/bIxIkT9bOt5m/Xrl26WJtnQbFixfT/1atXk6zHd9wYHfHmm29KSEiIZTl79mw6eoAQQjJewFt39Jq0Zj48QvI87tnVAzDNNm7c2K4WzZF27tlnn9XFmnr16qnv3JdffmlXe1e+fHnp0KFDkvWI2q1ataqsWrVKU7SYx0UGePj3OcLLy0sXZ0BGeWfTvRCS2t+Om5sbO40koUn5QPFyd5WLIdHStXkH+eOVZyQiIsIyRy0hJG+RbQIeeOONN1SD16dPH2nRooX6jUyfPj2Jfx0iXaG5Q+h/aoiOjpY5c+bIyy+/bNfs+sorr8gLL7ygqVGQquWTTz7RgIxhw4al+7zgW3ju3DlO+k0yBYznUqVKab5HQky8PdykcflA1eD5V2qkqaQ8PT3ZQYTkUbJVwOvRo4fmoYNW7vTp01KmTBk1g0L4Si+InEUQBEy+9oDgiO3Dhw+Xy5cvS+3ateXvv/9W8296gOYOwh1MzjBDp+TTR0hqgaYZrgQYY8gBSU0esebeKoVVwNt9OVZeeqIdO4eQPIyLgScGSRMQEBFsAX+8fPnyWTSHSOBcrlw5jQwmJKOJioqSU6dOqfsBZmEhxOS/y2HS6Yu1aqr9uGG8bNm4Tj799FN2ECG5WO5wBLNhZhLU3BGOLZLVIFVKsXzeEhOfKJuOXVHf5MjISF4IQvIgFPDyAOvXr08WSZwTQYqcyZMnS24C12XTpk3Z3QySi14szVkt4oMqa6AXfJgJIXkPCnh5AAR95IaULkiOjXyJuQlcF0Q6EpLR6VIO3jB0GkZkByCE5D0o4BFCSC6iZaUgcXUR+e9KuDRt10XWrFmT3U0ihGQDFPDyCIilGT16tM5RichizMcLDh8+LNWqVZPq1atL69atdTYRa9Muoo0/+OADadKkiezcuVPrQeQzcg82b95cPvvsM4fpYGBSxfbHHntM9x8zZoxGGYOffvpJj4uJ0bt166bHsp7lBMdA4mu0q2fPnsnqPnHihOY33LFjh0Zeo646dero3MbHjh2zlENibExTh/PGNHg4H9MkimCFd955R9Pk4Fjz5s1L0ZT6/fffa95E5G9EMu61a9fqfq1atUrSfqTbQWR4o0aNNAUQknGbQAOJ/jfbY913qWkPIY4o4OspdUoV0M+NegyW559/np1FSB6EAl4WcfHiRdm3b5/l+8GDBy1mU0TeQngKCwvT70jbYi0UHDlyRNPIAPjUoCwiaFLDypUrNUnzN998o0IWBB2ASMwFCxbIH3/8oYIctps+OzDtIi8hEqUiaTSELUwlh+2IzIMAt2zZMt3myKSKuYMhwKHsn3/+qYKbmSIHx4Wg9MQTT8jAgQNVwAHjx4+X//3vfyq4oV2YqcR2yjrsj/bec889+gBDXZh3GMKWdbLqwYMH64wpOC+kFMH5mCbRp59+WtdBcINgBQF427Ztds8F1wr+fyNHjtQ0Pmjz559/rtPXPfzww0nmOoZACwH6u+++0/ZAEIXQZ24DZntwXUxS0x5CnDHTXnULkn79+rGzCMmLIE0KSRshISFQv+h/k6ioKOPgwYP635r33nvPKFmypOV77dq1jeeee04/Hz16VOtZtWqVfv/000+NggULWso2bdrUePLJJ/XzhQsXtOxff/3ldDuXLl2qxzMJDw83vLy8jLi4OCMmJsZ46623jGbNmhnVqlUzAgMDja+//tqyX4MGDZLUVbduXaN8+fJG1apVdSlevLgxePBgu8d9/fXXLedo1nfvvffq57NnzxqPP/641o96vL29jX379um2OnXqWPrCtr5OnTrpuRw5csSyfseOHUa/fv10P9Tl6elpJCYmGtHR0Xqe+G9Sq1YtY/ny5XruHh4elvPAgj6fMGGC3XPp3LmzMXfuXMv3KlWqGBs2bLB89/X1NSIiIrQ/3d3djdDQUMu21q1bGwsWLLC0JzIy0rKtZs2aqW6PozFGiMnWk9eNsq//ZTR4f5kx79f5xsKFC9k5hORSucMR2ZroOC8B7Yz1m/Qvv/wiAQEB+hmzEsDUiMS1ptYJ8/OaQOtk5jsLCgrSshUrVkzV8a3z5SAJM6aDi4mJUW0RtESYyQN1f/zxx6pRNEGyZmugZYTmqkaNGnbrTum4BQoUsKRswIwhVapUUU0dZmTo1auX5bjQHGI6OUdRgmi3NTDhvvXWW6r1graubt26qqVEfZjWy3p6OeQPAtAWwjwKDSLKmBQpUsSpc8E+tt9jY2N1PmS00Xp6KJw3tIZoN9pnnR8R29LaHkIcUa90AfHzdJPrEbEy5dfFEnvlpF1XB0JI7oUm2iyiePHiOluGCQSk0qVL62cIbw0aNLAIfEWLFlUhxQTz5pozbODhj7KmoOIsEOJME/GsWbNUQIQQcubMGfWPgymxYMGCsm7duhTrge/db7/9pqZd+L1hKVGiRIozisCcDOEFplwcC+C4MN02bNhQ/eTgU2dy7733qlkWwpK940+aNEn3xfR1MFljfwjPmJcYvnDw4QPoI/Q72gtw/qbJE30Nn72FCxdq/5rn4kiwdBYIfZUqVZIZM2bo96NHj6qTO/zxsA3X/Oeff9ZtMMNndntI3sTDzVWaVCiknwvXbq1uFdYvboSQ3A8FvDxCrVq11G8M2kLMzwvNGcC6H374QQVIOP6bWkRHwPcO/mTQ9pmCCHzfHAEtHQQXCK3QPELLBl588UXVKOC4aA+EIhNoEzEbCI6B+m01DxAAZ86cKb1795a9e/dqQAMEVpwbfNqs59/EeUJ7CsHqySef1DZDg2kKuvDxM4+DBf6N6eXHH3+UUaNGaXsgjCOYwuxXCKfwGcQ2BG5YC/2Z1R6SN2lR6VY+vAj/Uircbd26NbubRAjJQjhVWSZNVXY3TSMF8+DNmzdVqECwB8yuMBWawHSI+U1Lliyp2jA4+kNzZL2fLTCjnj9/XjVzxYoVs5garXnjjTd0/auvvqqBI7aaPvQfjo32IIgEQqB1n+HYCNSAwIb+RBvNtgFsw/4Q3rANplhch//++08FSxNoArEd5uUWLVpo5DDyg1lHtmI7gMBpb4o5zP0KDadpesU1Rn+ZwiQ0dRAyYfoG6Bf0D0ysthO+m+2BdhH14nxModOZ9tyNY4zcfRy5FCadv1wr3h6ucunbQfLyiy/Iu+++m93NIoRk0VRl9MHLA0AoMQUTCBW2QDAyhThrnzvr/WyB3xy0Yc4AocyeGdd6cJomaGsgUGFx5A9o7Z9mvc1auJs/f75qDeEfB6EJGkhr4Q7gu+06W2yFXAhX1thqPuGHZ08wBhCuzetgr4wz7SHkTlQp6i+FA7zkaliMDBz5rtSqVYadRkgeggIeyTRgeoVwl5107NhRzdPwXSxTpkySAAZCcjN4yUDS4z92nZeyTTpLn87VsrtJhJAshAIeyTRsNW7ZAVTZqQ1IISQ3+eFBwFt/9JrUkX9U01yhQoXsbhYhJAtgkAUhhORSWlS6Zerfdz5E+g983BLBTQjJ/VDAI4SQXErx/D5SsbCfJBoidTr047y0hOQhKOARQkguplXlW64S+ao0lg0bNmjuSEJI7ocCHiGE5IF8eNc9CutMMpjLmRCS+6GAlwfADA7jx4+XnAKm61q8eHF2N4OQXEGTCoHi5uoiF8MTpHXX3smm+iOE5E4o4OUBkHB3+fLlklPAjBfmtGq2LFiwQBdzGrRFixZlcesIyVnk8/aQuqVuRZKPGPOVTvdHCMn9UMAjOYpy5crpAjCNF+ZzJYSkDPLhgXVHr8quXbvoh0dIHoB58PIQS5culX/++UeqV6+u86BiWq0zZ87ovKlIioq8df3795d77rlHy0OLtmzZMk0UvGTJEp3zFXm0MKcltGeYHQLzwbZu3drhMTG36urVq3VOVkzHFRAQIF26dJEZM2bobBDmvnPnztVZKzp16qTfExMTdY7cQ4cOSdeuXXUfcOrUKf2PGTagvUMi5WPHjul8tX379s2CXiQk59GycmH56t9jsubwJflmQHfZvHmTNGnSJLubRQjJRKjByyIwByw0TtYL5hM15xa13WY9yfyRI0eSbbtx40aqjg+hbOrUqVKpUiWZMmWKvPbaa5Ypx2Cyuffee3V6LAhJmFfVNO1+9NFHMn36dKldu7YmDIZQBUEPU49hZoghQ4ao0GiPadOmyYsvvqiC3JYtW+SZZ56R/fv367ZNmzbpnLEm27Ztk4MHD1q+T5w4UduBYzz++OMWU+zu3bt1QVswvRnqRvttpw4jhPw/9UoXEF9PNwmNNSRfmer60kUIyd1Qg5dF/O9//5MxY8YkWTdgwACZNWuWTjhvas2swYT14LHHHpPNmzcn2TZz5kwZOHCg08fHvK/z5s1TrR2EOMzX+tlnn+lE9xDsVq1aJTdv3lTNGD6bc6ti25w5c1TDB8aNG6eaPlMADQoKkt9++006d+6c7JjfffedTJ48WacLA6dPn3a6vdDkmYEhECa///576dGjR5J5aOvUqSPe3t7aP4QQx3i6u0qT8oGy6shVqdK6h+bDe/3119llhORiKOBlEU8//bSaEa2BSdKccB6BBY6ABi0iIiLJOtMPzVlQHsKdKTBBeAwLC1PN2Pvvv6+aOGjpLly4IKGhoZb9MK2RKdwBCKP33XeflCxZUr+npD27fPmyagxNrD9b12ktzJpUrFgxyX6XLl1K1fkSQpKnS4GA512mrqxb8K3Ex8eLuzsfAYTkVvjrziKKFy+uiz2ghYKPmiOqVq2a7uPv3btXgoODpUCBAmoOhYkTWj2YSocNG6am1ISEBNW6WWMriEEIhDDmjNYM7YYpCAIg6l6/fr08/PDDFuH27Nmz+hn1wYRcunRpy77r1q3T9Tg+6qhWLflE6V5eXuoHSAi5My0r3wq0uCz5pGiJkuqCATcHQkjuhAJeHgGm2LZt26pmDCbYL774QtcjeGHQoEFqAoYPHIIbUuLzzz9X8yn87kztHvZv3759srKjR49Ws+rChQtVmLOuG2Zi7HPgwAHVCtrm5oIw2rRpUzXFom1osy0NGzZU/zwEXiDYg0EWhDimatEACfL3kmvhMfLzkg1StuyteWoJIbkTCnh5AGjd4MOGaFgISzDJ1qhRQ7d1795dtWWHDx+W+vXrq2AFjaK538svv5ykLmjSUHbjxo2qAYCWzTTX2tKiRQtNYwKNIfzlENxhLZzBjw8BE/A/vHbtmkbZggceeED9ExEhi2PBj69YsWK6DYKcCaJrkRAZkbYMsiAkZfAy1rJSIVmw+4JsOHZNqgW6WtxECCG5DxfD1vmJOA181WDqDAkJUXOnGRGL6FgIHKagRG7xxhtvaFDGK6+8wi5JBxxjJK38uv2svDp/rxT3iJZDXz8p169f1xcpQkjOlTscQQ0eyTKgmaPQS0j20fx2wuNLcd4SGhVn0aATQnIfzINHsgw8SGrWrMkeJySbKFnAR8oV8hWYbfJVasB8eITkYijgEUJIHtTilW3ciQIeIbkYCniEEJKHaF7xVvSsW/HqOh0h3bAJyZ1QwCOEkDxEswq3BLwbiT6yZc/BZLkuCSG5Awp4hBCShyjk7yXVigXo522ng6nBIySXQgGPEELyGM0r3vLD+3zmIo1uJ4TkPijgEUJIHqNFpdtmWvcgWbFihU4lSAjJXVDAyyPcuHFDpxezBtOD/f7779nWJkJI9tC4fKC4ubpIqOEt4YmeOuMMISR3QQEvj/Daa6/Jjh07kqzz8PCQRx55RKccI4TkHQK8PaROqfy3Ple6h+lSCMmFcCaLTAYpCKLiMtf84ePhlmIk3PHjx2X+/Ply8eLFJOtdXV11jtcTJ044nE+WEJJ706XsOhMsJRu0kzVr1shLL72U3U0ihGQgFPAyGQh3NUYlNY1mNAff7yy+no4v5W+//SadO3cWHx8fOXfunDz22GPqdwOCg4PF398/U9tHCLk7Ay2+XXVcvMrUkZkTns7u5hBCMhiaaPMAR44ckRo1auhn+OG5u98SBg8cOKD/a9euna3tI4RkPfeULSie7q5yPTJersbwUUBIbuOu0OD9+++/uvj6+qpPWLly5Zzab/PmzTJr1ixp27at9OvXL1X1zp07V9atW5ekfIkSJeStt96SjDafQsOWmeAYKREQECCHDh2SCxcu6HlfuXJFrl27puc6YsQIi8AHJk2apH1mzZAhQ6RDhw6Z1n5CSNbj7eEm95QpKJtOXJeh73wujzQqpb91QkjuIFtf2xCa//DDD6vwBV81LH369JGDBw86FRWK/ebMmZNMUHOm3lWrVsmGDRukWrVqlqV8+fIZfo7wjYP5NDOXO2Wif/HFFyU0NFT69+8v77//vnTv3l26du2qmrvRo0cnKVu/fn3p3bt3kiUz+oUQcvekS7lk5Je//voru5tDCMktGryvvvpKbyp79+61CBEjR46UyMjIO+77+OOP69vmvHnz0lxvxYoV5dlnn5XcTtmyZWXJkiWW702bNpUPP/zQbtlGjRrpQgjJ/TTThMf/SUJgBVk7/0NJTEzU4CtCSM4nW3/J3333nQwYMCCJhsjPz08KFy6c4n4Q4G7evClvvPFGuuo9duyYpg/56KOPZO3atek+H0IIyUkgVYqfp5vEiLuEexTQl2JCSO4g2wQ8mAwhYLVo0UJ++eUXefXVV+WLL77QKM+U2L17twpkM2fOtPum6Wy9MGsWLVpUChQooL5pXbp0keHDh6d4bCQGRv3WCyGE5FQ83FylSYVbZlr/ig00XQohJHeQrQIeGDt2rPz888+qXVu/fr1UrVpVfePsERERoX5kENhgdkxPvQgwQEQp/n/77beydOlS+eGHH2T58uUO24w68+fPb1lKly6dzl4ghJDsz4cHmvV+jPPSEpKLyDYfPER2AiTYXbhwoWU9AgDeeecdDYKwBRGzly9flo0bN+oCMAvD6tWr1ZcOpltn67UVzu69915dB2GwY8eOdtv85ptvJkkGCmGSQh4hJKfnwwMnw92kcNFi2d0cQkhO1+BBA1aqVCmN2rQG30+dOmV3n+bNm2twgHXkq5eXlxQsWFA/w+yalnpNYmNjJT4+3uF2HCtfvnxJFkIIyclUKxYggX6eEhmbIINeeEdTKhFCcj7ZGkWLNCYrV65UoQq52JDeBN+thTOkQYFgBlMq0nrYJuWdMmWK1K1bN0k07J3qxXr4mrRv396yz08//aTaQcz4QAgheQVXVxdpVqGQLN53UZbvPSPNli2T6tWrZ3ezCCE5OYoWJlNoxSCgPfHEEyqAXb16VSZMmGApg6S7EPIysl5o+saPHy+NGzfWdCsQ9IYNG6Y+dq1bt87w8ySEkLuZZrf98IJqtVCXF0JIzidbNXjwl0N6Eghxp0+floceekjatGkjnp6eljJId2KtabPnFwd/u9TU6+bmpnnhkBJg165dauKFf1/x4sUz8WwJIeTuDrSIy1dK1s7fzHx4hOQCsn2qMghbjoIaAKYhSwlE1aalXlCnTh1dCCEkL1M+yE+K5/eWiyHREulbVPbv3897IyE5HKYszyPA7/DixYtJ1iFrPXIAEkLyNnBbMc20XR4bKUFBtyJrCSE5Fwp4eYRPPvkk2byzcXFxUqZMGZ0VhBCSt2lxO11KYuHKUqJEiexuDiEkp5toczuGYYgRFZWpx3Dx8dE3cEdcv35dPv/882TpDxCIghs51iMFDSEk79K80i0N3r5zwTLqw3Ey+q3XOC8tITkYCniZDIS7Iw3uydRjVN25Q1x8fR1unz9/vjRp0kSKFSsmwcHBqsn78ssvdVt0dLSmkrFl3759aqZh4AkheYPi+X2kQpCfnLgWIZ/P+EMe6NUtWVoqQkjOgSbaPAAihRs1aqSfkQIBDtQA/neYjaNGjRrJ9kGewOPHj2d5Wwkh2Yfph+dXgfPSEpLToQYvk4H5FBq2zD5GSiCYIjw8XP9Pnz5dtXYAc/ref//94u/vbymLqdwOHDigaWZOnDghu3fv1kjmmjVrZuo5EELujmnLZm85IwWqNJHVq/9KkkCeEJKzoICXycA3LiXzaVaAZM59+vSRv//+W15//XX55ZdfpGrVqhpgYZtEGpG2hw8f1lk9MAMIpm+rV69etrWdEJL1Grw4v8KyZssu5sMjJAdDAS8P0KxZMxXcILDB3+6xxx7TCFoPD49kZTHNG5ZvvvlGBbuWLVtmS5sJIVkP5qStXjyfHLoYKu0eelqioqLEz8+Pl4KQHAh98PKQJtE6mMKecGcNEkAzVQIheY8Wt7V4FZp1oXBHSA6GAh6xC+bkrVChAnuHkDyaLmX1oUvq1kEIyZlQwCOEEGKhcflC4ubqIhfD4mTw8JGay5MQkvOggEcIIcSCv5e71C6ZXz9H+peSgwcPsncIyYFQwCOEEJKE5rf98HzL1dPcmYSQnAcFvEyCZg3CsUVyerqUgIoNZBUFPEJyJEyTksEgOhURq1evXpXChQunOEcsIWl5ccDYwri6UyQ0IWmlYdlA8XBzkTjv/JK/ZEV2JCE5EAp4GYybm5uUKlVKzp07J6dOncro6glR4Q5jDGONkMzAx9NN6pUuINtO3ZQOjzzDTiYkB0IBLxPA1F+VK1fWZMKEZDTQ3FG4I5lNs4pBKuCtPnhemgTFM20SITkMCniZBB7AfAgTQnIqzSoUkq9WHpXle8/IjSVfyK/z5mV3kwghqYBBFoQQQpJRv0wB8XR3lURPf1m76wgDxwjJYVCDlwGRsqGhoRl1PQgh5K6hbhFP2XLyhkT4FpVt27ZJtWrVsrtJhORpQm/LG85k6nAxmM8jzSCQonTp0mmvgBBCCCEklZw9e1aD7VKCAl46SExMlAsXLkhAQECmpEOBpA4BEhcyX758klfgeeed681rnXeudV693nnxnPPqeYdmwTlDJxcWFiYlSpQQV9eUvexook0H6Nw7SdAZAQZKXvmBWMPzzjvwWuct8uL1zovnnFfPO18mn3P+/LemErwTDLIghBBCCMllUMAjhBBCCMllUMC7i/Hy8pL33ntP/+cleN5553rzWueda51Xr3dePOe8et5ed9k5M8iCEEIIISSXQQ0eIYQQQkgugwIeIYQQQkgugwIeIYQQQkgug3nwMpGQkBA5fvy4FCtWTJMSOkNERIQcPnxYAgMDpXz58km2hYeHy+7du5PtU7duXU227Gw9mc3p06f13HFc23alNCvIpUuXpFKlSlKgQIEk27Zs2SJxcXHJ9ilSpIhUqVJFP588eVLOnz+fZLuPj4/cc889khXExsZqf/v6+up5u7m5ObXfvn37JDIyUpo0aeIwmfaBAwc0uWXNmjXt1utMmczixo0bcurUKSlZsqQULVrUqX1iYmJkx44d+ruoUKGC3TJIIH716lXdbjuGMLbQb7bgWuOaZzboZ4w3/MbQPj8/P6f2w/jEfvZ+r0ePHpXLly8nWYcyKGvv94W+qVq1qtO/r4wA1w1jHMcsV67cHZOsmuzZs0d/vw0bNkyy/vr163Lo0CG7+9SpU8eSR2zjxo06xq3BbwxjLiu4du2anDlzRhPYFi5c2Kl9kOj25s2bUrFiRYfjA9vxfChevLjDc3GmTGaN8WPHjul9DWPcmd8VrvGRI0f0Hli2bFm796E7lcH4Qn/b5nyrXbu2ZAVRUVHaPjyD0D5nJjAIDg7W3zVy4tqOD/Tjhg0bku1TuXLlZPdL9A3u4wjQwJSAGTJ5AqYqIxnL2bNnjQcffNAICgoyGjRoYAQEBBitWrUyzp8/n+J+P/30k+Hv729UqVJF/3fo0MEICQmxbN+2bRsmnzOaNm1qtGjRwrIcOHAgVfVkFosXLzZq1KhhVKpUyahZs6bh4+NjvP766ynuExMTY/Tv31/LVq9e3fD29jY+++yzJGW6deuW5HybNGmi/fDiiy9ayrzwwgtGwYIFk5RDvZlNXFyc8dZbb+m1rlevnlGiRAmjbNmyxvLly1Pc78cff9TyaHOhQoXsltm7d69RsWJFo3jx4kbJkiW13p07d6a6TGZw7Ngxo0ePHkaRIkV0jPv5+RmdOnUyrl275nCf69evG6+++qr2ka+vrzFixIhkZf755x+jfv36ej516tTRctjHGvQtrr/1tcZy+vRpI7P59ddfjcqVKxtVq1bV8Yrf1wcffJDiPps3bzZ69eqlYwTt3rRpU7Iyjz76qFG4cOEk5/Pkk08mKRMREWF0795d+6RatWr6/3//+5+R2URHRxuvvPKKjlNcm2LFiumYW7duXYr7ff/993ofwBjHuLRl1apVya5hmTJltI+OHDliKefl5aX3FetyP//8s5HZ4L7asWNHPV+cN/ob1zE0NNThPgsWLNBzLlWqlFG7dm39XYwZMyZZuXHjxum9zrznPfLII0ZsbGyqy2QGs2bNMsqXL6/HxTMkX758xvjx41O8h5v3QJw77kMYH6tXr05VGdCvXz/tb+tr/eyzzxqZTVhYmB4nMDBQ72f4LeL8d+zY4XCfw4cP6z0Q4xv3ctwLevbsaQQHB1vKREVF6XjGWLA+p0WLFiWpa82aNXre+J2gj2rVqmWcOHEi3edFAS8T2LBhgwo7Jrgh1K1bN0WBA4PF3d1dH/zgxo0b+iAZOnRoMgHv5s2b6aons5g8ebJx8uTJJP2A9toOZmtGjx6tA/vMmTP6fcmSJYaLi4sOeEf8/vvvWu+ePXuSCHgQBLOa8PBw44svvjAiIyP1e2Jiogou+NEnJCQ43O+NN97Qmwf2tSfgYV88xDFmUCcYOHCgUaFCBRUqnS2TWaxYscL4999/kwhvEOyffvpph/tAGMVD68qVKyqk2xPwvvvuO2PXrl2W71u3btWH29SpU5MJeNkB2nfu3DnLd/zO0ZaUhB38LjBmDx06lKKAN2DAgBSPPXLkSKNcuXLG5cuX9TuEHPxWrPsrM7h69aqeNwQ9EB8fbzz22GP6kE6Jl19+Wa85BGB7Ap498JLQrFmzJOsg4KV0D8ks/vrrL2Pjxo2W7xcvXtSXk5ReWr/88kvj4MGDlu/4jeB+/NtvvyX57bi6uup/gHsmHuofffRRqspkFl9//bWeq8ncuXN13Dp6ccQzBu0yBV/cl5577jm9B0JwcraMKeCldA/JLE6dOmVMmzbNct+EIN23b18VRh2BMfnnn39avuN3iWft448/nkzAS+n+gPOHQPnSSy/pd7QBShnb30FaoICXRTzxxBNGy5YtHW7H2w3e+mxvFnhrNG+spoCH/7ipQ7hISz1ZBX7E0Mz98MMPDsvgjR3CjjUNGzbUB54jIMg1btw4yToIeHjbhtB09OhRfQhlF/PmzdMHb0pv+iaOBLy1a9fqtd6/f79lHbQaWGdqB50pk5XghggNkzM4EvDsgd+N9U3TFPDwMgMh3xSuswNo1XCtf/nllzuWxbhMScBD/23fvl3f3G1fDvAdD0MIyNbggYKxn9XgBdLDw8OpFwlnBTxoYCHUmC+n1gIehGTc9yBsZift2rXTl6jUAG2MtbUBmjjbZwGEd2i0UlMmq8ALGcYtBF5nwT0J+2zZsiVVZSDgDRo0SK81hC7zxTU7mDBhglGgQIFU7YNnGX6TtgIe7g/4bUPQtWXOnDmGm5tbEusHBHvsh5fC9EAfvExk27Zt6je3a9cu+fPPP2XmzJkOy6KMrb9Y48aN1T/rv//+S+KD0LdvX/XrgG/GM888I59//rm4u7unup7MwPSPwmTIP/30k/rI9e/f36H/Fnxb7LV3/fr1Dn2z/v77b/nhhx+Sbfv333/l0UcfVf8k+Ad9//330qtXL8kK4K9y8eJFPZ/3339f3nzzzXT5R+E6whcDPnUm6Ev4JWFbhw4dnCqT2WzatEn9VuAnuXbtWvnjjz8ytH74ucFPq2vXrsm2YR3GPfr8pZdeko8++ihj/FbuAMbtwYMHdaxPmjRJ/Sd79uyZ7noXLVqk4whjHL/vyZMnS8eOHXUb/Bzhj2X7W2nUqJFe66wAvknwE0RbPvjgAxk9erTlvpMRTJs2Tfz9/eXBBx9Mtu21115THzjcw9q1aydTp05VH86sAPci+B9ifMNHCvdbZ4GfIfyz4FtsguvVqVOnZPe8L7/8Uu+buG84UyYzwT0U1xtj7ttvv5U2bdpYxqKzzz7cg1Py/3ZUZu7cueq3Cb9s+JDjWrdu3VqyggMHDug1g0/shAkTdJynhu3btye51ibPPvus+lGiT3Gv+N///qfnBnCt4dNaqFChJNfa3AZ/vLRCAS8TGTt2rD58cFEhaDhypDcfGtYPamBecGwDBQsWlBUrVkj79u31+9atW/Uzyr377rtO15OZnDhxQt544w39kUDg+eSTT5IFTZiY7bEe2OZ3R22dPn26Ovw+9NBDSdbjpo/j4qYPh2xkE4dgiR9I9erVJbP57bffZOHChXr+cLZ94IEH0lUfzt+2X2z7xpkymQ36GdcaztEDBgyQevXqZWj9I0aMUCHiqaeesqyDczIcl5s3b67fV69eLV26dNEb6HPPPSdZ8RCAAI+HIM4dD930Bnf06NFDxo8fr9cuPj5eXn75ZenXr5/s379fypQpk+JvZe/evZIV/Pzzz/LPP//oiyUeYr17986wumFNgoD3yCOPJAtK+Oabb+SJJ55QYQCBKhDs8SKHtmQ2CQkJel/BiwaES4xDZ+8nOKehQ4eq4/2gQYMs6+39bq3v0RDenCmTmeC+iRdVCPQQKHENPD09ndoXzzwI5MOGDXMYlOKoDIT7KVOm6DMDAR74/ffp00dfqJwN4koP06ZNU4EeAh4CnOy9WDoC7V61apXej0wwZlEnxitePiHsQ1AePny4CrLA3rXG9fXw8Ej/fTxd+j/iFPCZg2Ml7OqOgDoeanlrdu/erWpaaz8QW2CegQNyeuvJDOCDBxPt9OnT7W6HCh7tgt+dNXDohh+ZLVDXw0ThjD8hTFrwa/j444+NrASm4ddee83Inz9/igEHdzLRfvjhh+rwawv8FUeNGuV0mawCpjP4md5///0ZZqKFuQMO3imZeaxNnM2bNzeymmXLlqmPFZzr02OitQU+QPjtwPctpd/wkCFD1Ck8K4FZFtcOvy9n3BCcMdGiH3F+KTm1Wwe6oCz8PrMSBMnB/IY+d4bhw4frb3vfvn1J1sOFBq401mD84JwuXLjgdJmsAseF6dwZt49Lly5pABJ8KR25BDlTxgRuSDBfInAwK4mOjjYGDx6s49YZ16Y//vhDXRacCXqCuwHuGQg8AcOGDdOAMtvfGFw/Jk2alI6zMAzmwcsC8DaCN7mVK1fqW4k9EJJtm+bD/I43eEfgrcZ6v7TWkxlAw9KiRQtZunSp3e1IHYO3FHvttdfWNWvWqPYAfXkn8OaEN0PbujMbhP3DXAjzHcyXaQXXEeYRmNZNYCaCxsjsG2fKZBVBQUHy+OOPO7zWqeWdd95R0xDM8aa5IiVsfwdZBd7GobXMqPM2we8CGnvznHCtgbO/lcwEGtUXX3xRNZhId5MRwAzXoEEDXe6EqcmBKTsrwf0KWmpnrjU0yfPmzdN7fq1atZJsc3SPhrsFUj85WyargPUJrh/4LabElStX1JICUzqsGfbmY3WmjDXQ5sJsn9W/bS8vL3n++ec1JZGjVD4mcL+CRWnixIlJLA0pjV9o6dEX5rXGWIbG18T8nt7fNgW8TADqfFvgW4N8PrhxA6i9oQrGf/NBgXxP1jmA8AOAOcDMf2Sv3uXLlye5gThTT2ZhLWgADGL461irn2HCNB8K6It7771XfyAm0dHRanqx5+8BFTjU5vA7ssW2b3BcqNltb65Zda2B9Xlv3rxZzRLOgpsghNS//vrLsm7JkiXap6aJ3pkyWX3e1ueM/FAY4/DRSw2jRo2Sr776Sh8ozZo1u+OxYZK39yDNaNCvEKCtwXiFr5D1ecOUBx+i1JgBUY+tGRg3efOc8JKIPHLWvxW8RMAclBrfqMwc4zCbp+VBjBeSBQsW2H1xs3fsZcuWqUncUQ7FrBzjuM9ijFvn6YRgMGfOHHWnsZfHENcL9zjrl33co/F7NvPCOVMmM8DxbHOOoh+Qo9T6vCH0WOeihLCPtsFNAmPU29s7Wd13KoPj2ipA4NuLcX433McTExP1Wlvnq8S9F2Zl+OvB7Ors+IX/HfrBvNYYR9YKAVxr5AqEgiRdpEv/R+zyzDPPaE6d+fPnq/kRqnZPT081x5nATGNtroG6FiYumJmg7n3//fdVNW1t+kFYOdT+qBfrYQ5DCgnbfEN3qiezTJMwFSNf0t9//62RpJ07d9bIP+ucVjDtWEeC4fzRN0ipsHDhQqNr164aWWubCgbfYbL65ptv7B4f6UKQP2/p0qWaUgMpO5CbCFGOmQmuxX333admaJgw0L7SpUsbXbp0SRIBBpPte++9lyTHFkLnn3/+ed2Gz1is24vIO6RGQPg+TBRFixbVsWWNM2UyA0S64ZphjCFVCD5jnFlHQOJaWEeCwWxunifGCqJG8dk6/cInn3yipgn8N8tisY4URooORBTi2Eg/gqhq5KBClFpmgvxWyGc1ceJEzdeHNCX33nuvmsSR+9IE6U7uuecey3eknMA5IJIO/QEzDr6b+yBNAtIx4P6A3w6izjGG8Bu2zntmmoPfffdd/T3j2DB1ZXYUMcZ27969dXyhDYjKxzkj4tEaXH/rHJZIkYLzhEsFypvX0tbkZUb528vViZxsiMyeMWOGjifkRIQp7PPPPzcymz59+hhvvvmm3peQEgP3LpwjfvMmGAO4pmZaEZRHGaQasR6/iPg2gWkZJljkUEOaDbjZIFIYKYFSUyYzgPkX9020H9d69uzZmq4D4xHRtCbIB4jxZ45f/C5gzsQ+1udtmtGdKYM0Iyjz1Vdf6e8L91KMm/bt26eYciojmDhxovHQQw/peMOxMY5hXrfORYlzwLWGidVMgYNrgnuh9flYu1F8++23xgMPPKD1QhbAMxy/YbMOE5SBWxLGE37/uJ9lhHuRC/6kT0Qk9t7IETELVX5oaKhGCcHJ0jrIAk6jUOciCq9GjRq6DuY2BCUgEgcSPt5ord/OrevFmwGia2AKMM03JneqJ7PAmw2ccaGhwxs23l7xVmPtRPvFF1/oW9kvv/xiWYfvX3/9tQZlIEDk9ddfT6ZthDbn448/1jc/e0EbUHejDhwbmlK8+aB/nXUMTg/r1q3TiGGo8xHkAcdcvNVZv2ljHQIv4CwOcI72Mpzj+ppRZXhjxPjAOeNn2q1bN+1P63qdKZMZ4G37xx9/VA0yNHTQpjz55JNJgixwXREsAG0GTA0oZ28cYl/0H8B4thcV2rRpU0v0ovWx8caPMQOtiflGnJlAW4cxjhll4AiNqNann35azakmiLzDWIDG2Xwb/+yzz5LVhesEk59tvdAYQLONsWIbpQo3BUSHQxuCvkYAgLOzK6QHaEhnz56t7UQ/IygE0fzWs1kg0hJO82YAlKNrOX/+/CQRsOY9Ak799kB0/KxZs1Q7aN5L7Wl2MxpoVfHbgpYU4wyzD+Beat6vzX5BoBF+f7jXwk0BlgNbENGOqGMT9OO4ceNUEwbTL8avrWXCmTKZAQIB4B4BDR3utTgm7qXmzCLgrbfeUusT7rmwTCA4xlGgYatWrZwqY1pe8DtAcBHcPtBvgwcPdnrWlPSwePFiNavjOYRAOYzv7t27W7ab9y/85rAeUe4zZsxIVg80b9DS2daL5yPudRhD9evXT7IPxhdMvND6wjyMZ4V1YE5aoYBHCCGEEJLLoA8eIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIXkQJOC+0xyLWQUSq5rzMmZm0lokT0Vi6PSABMNoL3FMeuZgxlRwhw8fzpTuRaJZTLlFSF6BAh4heRBkWs+K2QBs5yqGkGU7eQ4ytn/33XeZemwct3bt2irYpof//e9/GZJh3gSzAWBWm5wE5tqFoGsPnEvv3r3TXDdmsxg/fnyq9oHAjXl7bcFcyLjuJsePH9cxbzvvLyG5FQp4hORBMJ2b9ZRLWcHOnTtVyIKWxhpM31OkSJFMPTamzsOUZpk9hVtqwdRjDRo0kJwCpomrU6eOLFq0yO52TB+HKevSAoS0L7/8Ut59991U7QeBe9SoUcnWL1iwQMdbfHy8fm/evLlUrFhRp9ciJC9AAY+QPAjmRZ46dWqSh+vZs2eTlLl+/bocO3bM8h3zSZomLmxLydwF7QnmlTS1dZhr0TRtQssDzQrmFgVjxoyR+++/P1kdaA/2sdX4Xbt2TbUxplYQ877eyfSKBzvmP/bz87PM1wxNFIBGB3Vgrmd74DwdnSvmHb1x40aSdegnzGdpC8qhT6zntkRZnB/6A4t5HJTD9wMHDuj52hISEiJHjhzRzxCYUd5R+9H3uI44nj1wLdHPjva3Bm3C8RwJpZg3FvPRpgXMsYs5STFvsb2+RP/Z69fUgLliMc9qek31hOQIDEJInuPXX3818ufPb/n+9NNPG/369UtS5osvvjBq1qxp+d6tWzddGjVqZJQpU8bw8/MzWrVqZYSEhFjKXLx40ejatavh4eGhZUqXLm2sXLnSOHHihFG+fHlIakaNGjW03rffflv3adGihfHee+9Z6tizZ49uz5cvn1GoUCGjbNmyxr///mvZPnbsWKNq1arGgw8+aBQrVswICgrSMnv37nV4vtu2bdNj37x5U79PnjzZKF68uPHkk08aRYoUMYoWLarLxo0bLftERUUZffv2Ndzd3Y1SpUoZlStXNu6//35trwna8fXXXyc5Vq9evYwRI0ZYvp85c8Zo166d4enpqf2Bfli/fr2eJ/rIxcVFzxfLuHHjdJ8hQ4bod/QVrlOdOnWM/fv3W+qcOXOm9s3w4cONwoULaz/g/5o1ayxlEhMTtV/9/f2NEiVKaD1mn4MLFy4YHTt2NAICAoxy5crpdttzsQX9hvOIjY1Ntg3rBg0aZKQVnOuECROS9SXGU5MmTbTvMOaaN29uuY4A1wPX0ZZp06bpNY+Li7Osu3Lliq7bunVrmttJSE6BGjxCiNOsWLFCvvjiC9V4QbsCLZtp8oImqmfPnqpVg6YFZeBwD21b+fLl5aefftJyO3bsUE3Qhx9+mKx+aJEeeughqVevnmqWoL164IEH5MEHH0ziPwftFfypcBwsdevWlddeey1VVxL7FS9eXLVm+Ny1a1d5/vnnLds/+eQTNSufOHFCzxMapj/++CNVx8D5oF5PT08NJEGfQcsFzR9MndAmYZupwXv99dd1v8mTJyfR4LVp00Yee+yxJHWjf/z9/S3t79u3r4wYMcKyHb5sEydOlL///lu1pfCbg6navFa9evWSSpUqWQJHVq9eLW+99Za2zxG4drVq1RIPD49k23B+zzzzjKTHFxHX0ZaVK1fKp59+ahlvCJbAeVkDjazZh+ZiaoitKVy4sJQqVUo2btyYpnYSkpNwz+4GEEJyDhDgWrRooZ8DAwOlS5cusnv3bv0OYW7btm36oC5UqJCuK1mypAwdOtTp+iFkILp31apV4u5+6/b0wQcfqMAzf/58eeKJJ3RdiRIlZOTIkfoZ5SAAvvLKK6k6Fwg7o0ePFhcXF/0OwRLnB/Odq6urHvPVV1+V0qVL6/b27dtLt27dVLByFggnENKWLl2qfo+gXLlyyYQ1e6AdEN4gvHTu3Fm++uorNc2a9eC8ISSjreDhhx/WNsMkC6ER5SGwmtcLQtnbb7+tnyHgbN++XYNbTDM49mnZsqX6rrVr185umyDwOjLP4lpjSQsQ2kBQUFCybejz1q1b6+eCBQuqwGyOOROMF9Nkbe0mYA8IeYymJXkBCniEEKeBYGUNfNpM3zo8YL29vaV69epp7lH4iuEBXLRoUcs61Fm5cuUk/oDQvNm2A1qg1IDADuugC9QB4QgLgAbINhAFgRpr1651+hjoEwi7ppDoLNOnT1dtHjSA6A/TDxFtMgU81AuhzLr9EAqhQcV+0HbVr1/fbv0QonHu9gTNKlWq2N0HwQp79+51SjhNLeZ5mH1/pzFne62hvZwyZUqyPoTPnS3wIfTy8sqglhNy90IBjxBi0WJZY0YfOgsEMURZYrFnwnMGPLztBQNAaDEDJLICtB+LbVvQjtT0G/rEUXCDI86dOydDhgyRefPmqeACEBBStWpVp4MD0HZo9mzbaytQweTqrLADTSQCUlIT9YvACGh6sR+OY6+/TIEdfYVzb9iwoWQWEJQRUASXAUJyO/TBI4Solsg2lxjMcakBPnF4gMIcaQ0EPoAHuPV3e0DjFB4eLlu3brWsg+8VBBxH2qjMANot+MjB9GeN7XfbfoNwt2/fPst3pOaAkGXr12bdJ7aCNDSVpo+ctak3NcB8i0jpv/76y+5xYbaFls+eT6E9LZopDJr94gzQssGnbvjw4Wp6hRbTkWkUAinGz+bNmyUzgUYVptu2bdtm6nEIuRuggEcIUT8nPFzhvL5lyxZNOPv777+nqmfgW/bcc89pHjT4gsEnDwEZL730kiXfHTRH06ZNUyHInhM8TKCPPPKIDBw4UHOtIagDKVQgrNx3331ZeqWQjw0+asjNBp+1p556KtnsH927d1fTIPzW1q1bp+22TuWB80F/DBgwQE2G6BMEDJi+cDCHQphDn5hpUpC7DcET8CmEoPvDDz/IO++8k+r2jx07Vq8hfBXXr18vv/32m8WXDWljsB4pTeCrh2uO7f369VPNoSMBD0IagmasgxkQTGMP+PhBoMQxECADoRLrHPHoo4+mesylFpzjvffemyQVCyG5FZpoCSEqQCFPHAQzPGQhCCA6dsmSJZbeKVu2bDLfN3yHxs0EAh0ElLlz58qPP/6oTvsfffSRboOpbubMmTJp0iQVihDQgCAB20TH2O+zzz6TcePGqXYLEaSmQGRqzRD9aU2+fPlSTNxsm+gYbYHJ0xqYgFHGDFqABm3GjBkqYEGAQ462zz//PImQAuEVGi+sRxsgjOJcihUrZimD88UMGDh3mGtxPu+9955ug6CBvsC2CRMmqIAI3ztoQSGgQTiCMDZ79mwV+EwtaIECBaRatWopniMEmQ0bNmg0LYQ51GM9YwiOB3PonDlz9DxxHQYPHpxEc2gNrjP6CMEo1uCcEaxiCwJunn76aUtkLIJF8BLgCNSLepAsuWPHjpYxZ+2PCdC31iZWtNtecAcCMtAfplkYYwm5HxG5TEhewAW5UrK7EYSQrGXWrFmaEgPmT0IyAwh+SNsCcyjMwRDKoO1z5IcH/vzzTxWmIeRnNDBXIxIbmlRC8gIU8AjJY8Cs9uabb6rfU2abxEjepXHjxpr2xtfXV8cc0t1As0sIyRoo4BGSx0BONZgokciXvkiEEJI7oYBHCCGEEJLLYBQtIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQkgugwIeIYQQQojkLv4PjTKjDuA6/asAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "avoided crossing: |g|/2pi = 2.4131 MHz at L'_n = 3.152 nH\n" ] } ], "source": [ "Lsweep = np.linspace(3.05e-9, 3.25e-9, 801)\n", "modes = np.array([pm.circuit_eigenfrequencies(*matrices(Lj)) for Lj in Lsweep]) / TWO_PI\n", "split = modes[:, 1] - modes[:, 0]\n", "k = np.argmin(split)\n", "g_ac = split[k] / 2\n", "\n", "# the bare frequencies along the sweep, for reference\n", "bare_sweep = (\n", " np.array([pm.circuit_couplings(*matrices(Lj))[\"w\"] for Lj in Lsweep]) / TWO_PI\n", ")\n", "\n", "fig, ax = plt.subplots(figsize=(7, 4))\n", "ax.plot(Lsweep * 1e9, bare_sweep[:, 0] / 1e9, \"k:\", lw=1, label=\"bare package mode\")\n", "ax.plot(Lsweep * 1e9, bare_sweep[:, 1] / 1e9, \"k--\", lw=1, label=\"bare qubit\")\n", "ax.plot(Lsweep * 1e9, modes[:, 0] / 1e9, color=\"tab:blue\", label=r\"$\\omega_-$\")\n", "ax.plot(Lsweep * 1e9, modes[:, 1] / 1e9, color=\"tab:red\", label=r\"$\\omega_+$\")\n", "ax.annotate(\n", " \"\",\n", " xy=(Lsweep[k] * 1e9, modes[k, 1] / 1e9),\n", " xytext=(Lsweep[k] * 1e9, modes[k, 0] / 1e9),\n", " arrowprops=dict(arrowstyle=\"<->\"),\n", ")\n", "ax.text(\n", " Lsweep[k] * 1e9 + 0.004,\n", " modes[k].mean() / 1e9,\n", " f\"2|g|/2π = {2 * g_ac / 1e6:.2f} MHz\",\n", ")\n", "ax.set(\n", " xlabel=\"junction inductance $L'_n$ (nH)\",\n", " ylabel=\"frequency (GHz)\",\n", " ylim=(modes[k, 0] / 1e9 - 0.012, modes[k, 1] / 1e9 + 0.012),\n", " title=\"avoided crossing (cf. paper Fig. 5)\",\n", ")\n", "ax.legend(fontsize=8, loc=\"lower left\")\n", "plt.show()\n", "print(\n", " f\"avoided crossing: |g|/2pi = {g_ac / 1e6:.4f} MHz at L'_n = {Lsweep[k] * 1e9:.3f} nH\"\n", ")" ] }, { "cell_type": "markdown", "id": "8b2ae13e", "metadata": {}, "source": [ "The avoided crossing gives only $|g|$: the splitting is the same for either sign.\n", "\n", "## 3. Energy participation\n", "\n", "Now fix the junction so the qubit sits well below the mode (the paper uses about 0.2–0.4 GHz), solve for the package-like normal mode, and ask what fraction of its inductive energy sits in the junction (Eq. 7):\n", "\n", "$$p_{mn} = \\frac{E_{\\rm junction}}{E_{m,\\rm ind}} = \\frac{\\tfrac12 L'_n I_n^2}{\\tfrac12 I^T\\mathbf L\\, I}.$$\n", "\n", "A detuned qubit borrows a small piece of the mode, with an amplitude proportional to $g/(\\omega_m-\\omega_n)$ — so the participation is $\\propto g^2$, and Eq. (8) inverts it:\n", "\n", "$$g_C - g_L\\frac{\\omega_m}{\\omega_n} = \\frac{|\\omega_m^2-\\omega_n^2|}{2\\sqrt{\\omega_m\\omega_n}}\\sqrt{p_{mn}} .$$" ] }, { "cell_type": "code", "execution_count": 5, "id": "2e075b17", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "participation of the junction in the package mode: p = 3.066e-05\n", "EPR: g/2pi = +2.3133 MHz (exact +2.4130)\n" ] } ], "source": [ "def normal_modes(C, L):\n", " \"\"\"Frequencies and node-flux vectors of the normal modes (classical, exact).\"\"\"\n", " w2, Phi = la.eig(\n", " la.inv(C) @ la.inv(L)\n", " ) # (C^-1 L^-1) V = w^2 V, fluxes share the same vectors\n", " order = np.argsort(w2.real)\n", " return np.sqrt(w2.real[order]), Phi.real[:, order]\n", "\n", "\n", "w_modes, Phi = normal_modes(C, L)\n", "package = np.argmax(\n", " np.abs(Phi[0]) / np.linalg.norm(Phi, axis=0)\n", ") # the mode living on node m\n", "qubit = 1 - package\n", "I = la.solve(L, Phi[:, package]) # branch currents of that mode\n", "p_mn = 0.5 * Lpn * I[1] ** 2 / (0.5 * I @ L @ I)\n", "wm_d, wn_d = w_modes[package], w_modes[qubit] # what an eigenmode solver reports\n", "\n", "\n", "def g_from_participation(p):\n", " \"\"\"Eq. (8), then Eq. (10) to move to resonance.\"\"\"\n", " lhs = abs(wm_d**2 - wn_d**2) / (2 * np.sqrt(wm_d * wn_d)) * np.sqrt(p)\n", " return lhs * np.sqrt(wm_d / wn_d)\n", "\n", "\n", "sign = np.sign(\n", " I[1] / I[0]\n", ") # the relative sign of the junction current fixes the sign of g\n", "g_epr = sign * g_from_participation(p_mn)\n", "print(f\"participation of the junction in the package mode: p = {p_mn:.3e}\")\n", "print(\n", " f\"EPR: g/2pi = {g_epr / TWO_PI / 1e6:+.4f} MHz (exact {g_exact / TWO_PI / 1e6:+.4f})\"\n", ")" ] }, { "cell_type": "markdown", "id": "4f0bf7c1", "metadata": {}, "source": [ "EPR comes out 4% low, and the whole deficit has one source. Eq. (8) is derived for a qubit whose only inductance is the junction (Appendix B), but the qubit branch also carries its geometric inductance $\\delta L'_n$ — 9% of the total here. The package mode stores energy in both, and counting only the junction's share undershoots $g$ by $\\sqrt{L'_n/(L'_n+\\delta L'_n)}$. Count the whole branch and the method is exact:" ] }, { "cell_type": "code", "execution_count": 6, "id": "fd3b4243", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "EPR with the whole qubit branch: g/2pi = +2.4131 MHz\n", "sqrt(L'_n / (L'_n + dL'_n)) = 0.9586; ratio found: 0.9587\n" ] } ], "source": [ "p_branch = 0.5 * (Lpn + dLn) * I[1] ** 2 / (0.5 * I @ L @ I)\n", "print(\n", " f\"EPR with the whole qubit branch: g/2pi = {sign * g_from_participation(p_branch) / TWO_PI / 1e6:+.4f} MHz\"\n", ")\n", "print(\n", " f\"sqrt(L'_n / (L'_n + dL'_n)) = {np.sqrt(Lpn / (Lpn + dLn)):.4f}; ratio found: {g_epr / g_exact:.4f}\"\n", ")" ] }, { "cell_type": "markdown", "id": "e5e7513a", "metadata": {}, "source": [ "EPR, like the induced EMF below, returns the *sign* of $g$ through the sign of the junction current relative to the mode. On a finite-element model the geometric inductance is not a separate element but part of the field around the junction, so the same shortfall appears there — the paper notes that EPR tends to come out slightly below the other methods, and notebook 4.45 returns to it.\n", "\n", "## 4. Induced EMF\n", "\n", "Open the junction ($L'_n \\to \\infty$). Now the qubit carries no current, its mode moves to zero frequency, and the package mode is alone. Its field still reaches across the junction gap and induces a voltage there — through the capacitive divider $C_c/(C_n+C_c)$ and through the mutual inductance (Eq. C1). With the mode normalized to energy $E_m$, the coupling follows from classical circuit theory (Eq. 11):\n", "\n", "$$g = \\frac{\\omega_m V_{n,\\rm open}}{2}\\sqrt{\\frac{C_n + C_c}{2E_m}} .$$" ] }, { "cell_type": "code", "execution_count": 7, "id": "43af12b0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "voltage across the open junction for 1 J in the mode: 2.5269e+03 V\n", "EMF: g/2pi = +2.4130 MHz (exact +2.4130)\n" ] } ], "source": [ "# Open junction: only the package branch carries current. Excite it with energy Em.\n", "Em = 1.0 # joule\n", "wm_open = 1 / np.sqrt(\n", " (Lpm + dLm) * (Cm + Cc * Cn / (Cc + Cn))\n", ") # Eq. (A15) with the qubit branch open\n", "Vm = np.sqrt(\n", " 2 * Em / (Cm + Cc * Cn / (Cc + Cn))\n", ") # peak voltage on the package capacitor node\n", "Im = Vm / (wm_open * (Lpm + dLm)) # peak current in the package branch\n", "V_open = (\n", " Cc / (Cn + Cc) * Vm - wm_open * M * Im\n", ") # capacitive divider minus the EMF of M (Eq. C1)\n", "g_emf = wm_open * V_open / 2 * np.sqrt((Cn + Cc) / (2 * Em))\n", "print(f\"voltage across the open junction for 1 J in the mode: {V_open:.4e} V\")\n", "print(\n", " f\"EMF: g/2pi = {g_emf / TWO_PI / 1e6:+.4f} MHz (exact {g_exact / TWO_PI / 1e6:+.4f})\"\n", ")" ] }, { "cell_type": "markdown", "id": "7130b819", "metadata": {}, "source": [ "No qubit mode, no detuning, no sweep: one solution of the package mode gives every qubit's coupling at once, as long as each qubit's capacitance $C_n + C_c$ is known. That is why the paper calls this the most efficient method for a large array, and notebook 4.44 uses it for all 100 qubits. The voltage carries a sign, and so does $g$.\n", "\n", "## 5. Impedance matrix\n", "\n", "The last method treats the two junction positions as ports of a driven simulation and fits the circuit to the resulting impedance matrix. Here the \"simulation\" is the circuit itself, Eq. (12), sampled at 0.1 MHz from 6 to 7 GHz as in the paper." ] }, { "cell_type": "code", "execution_count": 8, "id": "bae61c14", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = np.linspace(6e9, 7e9, 10001)\n", "w = TWO_PI * f\n", "Lp = np.diag([Lpm, Lpn])\n", "dL = np.array([[dLm, M], [M, dLn]])\n", "Z = pm.circuit_impedance(w, Lp, C, dL)\n", "\n", "fig, ax = plt.subplots(1, 3, figsize=(12, 3.4), sharex=True)\n", "for a, (r, c_), name in zip(\n", " ax, ((0, 0), (1, 1), (0, 1)), (\"$Z_{mm}$\", \"$Z_{nn}$\", \"$Z_{mn}$\")\n", "):\n", " a.semilogy(f / 1e9, np.abs(Z[:, r, c_]))\n", " a.set(title=f\"|{name}| (Ω)\", xlabel=\"frequency (GHz)\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2b5813b7", "metadata": {}, "source": [ "Two poles — the qubit near 6.07 GHz and the package mode near 6.48 GHz. $Z_{mm}$ barely sees the package pole: its port is shunted by 1 pH, so a zero sits only ~0.6 MHz above the pole. That is why the frequency grid must be fine.\n", "\n", "The fit follows Appendix D. A lossless network is a sum of poles plus a linear tail from everything above the band (Foster's form, Eq. D1/D4),\n", "\n", "$$Z(\\omega) = \\sum_\\mu \\frac{2j\\omega\\,\\omega_\\mu}{\\omega_\\mu^2-\\omega^2}R_\\mu + j\\omega\\,\\widetilde{\\delta L} .$$\n", "\n", "Each residue is a rank-one matrix $R_\\mu = \\sigma_\\mu\\sigma_\\mu^T$, whose entries are the mode's zero-point flux at each port (Eq. D14). Stacking the $\\sigma_\\mu$ gives $\\widetilde{\\mathbf L}$ and $\\widetilde{\\mathbf C}$ (D7), and undoing the tail (D3) returns $\\mathbf C$, $L'$ and $\\delta L'$. `pm.fit_impedance` implements these steps." ] }, { "cell_type": "code", "execution_count": 9, "id": "93c2c399", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "poles: [6.07254746 6.47685364] GHz, relative rms misfit 2.0e-13\n", "\n", " fitted true\n", " C_m (fF) 132.000 132.000\n", " C_n (fF) 173.800 173.800\n", " C_c (aF) 100.000 100.000\n", " L'_m (pH) 1.000 1.000\n", " L'_n (nH) 3.630 3.630\n", " dL'_m (nH) 4.570 4.570\n", " dL'_n (nH) 0.320 0.320\n", " M (pH) -0.340 -0.340\n", "\n", "impedance matrix: g_C/2pi = 2.069, g_L/2pi = -0.251, g/2pi = +2.4130 MHz\n" ] } ], "source": [ "fit = pm.fit_impedance(w, Z)\n", "print(\n", " f\"poles: {fit.poles / TWO_PI / 1e9} GHz, relative rms misfit {fit.rms_error:.1e}\\n\"\n", ")\n", "rows = [\n", " (\"C_m (fF)\", fit.C[0, 0] + fit.C[0, 1], Cm, 1e15),\n", " (\"C_n (fF)\", fit.C[1, 1] + fit.C[0, 1], Cn, 1e15),\n", " (\"C_c (aF)\", -fit.C[0, 1], Cc, 1e18),\n", " (\"L'_m (pH)\", fit.Lp[0, 0], Lpm, 1e12),\n", " (\"L'_n (nH)\", fit.Lp[1, 1], Lpn, 1e9),\n", " (\"dL'_m (nH)\", fit.dL[0, 0], dLm, 1e9),\n", " (\"dL'_n (nH)\", fit.dL[1, 1], dLn, 1e9),\n", " (\"M (pH)\", fit.dL[0, 1], M, 1e12),\n", "]\n", "print(f\"{'':>11} {'fitted':>9} {'true':>9}\")\n", "for name, a, b, s in rows:\n", " print(f\"{name:>11} {a * s:9.3f} {b * s:9.3f}\")\n", "gC_fit, gL_fit, g_z = fit.couplings()\n", "print(\n", " f\"\\nimpedance matrix: g_C/2pi = {gC_fit / 1e6:.3f}, g_L/2pi = {gL_fit / 1e6:.3f}, g/2pi = {g_z / 1e6:+.4f} MHz\"\n", ")" ] }, { "cell_type": "markdown", "id": "ba5a8d5f", "metadata": {}, "source": [ "On noise-free data the fit returns the circuit exactly. With simulated data the individual $g_C$ and $g_L$ are not meaningful, the paper warns: moving the package port from one wall to another changes both while $g$ stays put. A distributed package mode has no unique \"coupling capacitor\" — only the combination $g$ is physical.\n", "\n", "## 6. Side by side" ] }, { "cell_type": "code", "execution_count": 10, "id": "07d9c3e3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " method g/2pi (MHz) rel. diff\n", " avoided crossing 2.4131 0.00%\n", " EPR 2.3133 -4.13%\n", " induced EMF 2.4130 0.00%\n", " impedance matrix 2.4130 0.00%\n", " exact (Eq. 10) 2.4130\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = {\n", " \"avoided crossing\": g_ac\n", " * np.sign(g_exact), # magnitude only; sign copied for the plot\n", " \"EPR\": g_epr / TWO_PI,\n", " \"induced EMF\": g_emf / TWO_PI,\n", " \"impedance matrix\": g_z,\n", "}\n", "ref = g_exact / TWO_PI\n", "print(f\"{'method':>18} {'g/2pi (MHz)':>12} {'rel. diff':>10}\")\n", "for name, g in results.items():\n", " print(f\"{name:>18} {g / 1e6:12.4f} {(g - ref) / ref:10.2%}\")\n", "print(f\"{'exact (Eq. 10)':>18} {ref / 1e6:12.4f}\")\n", "\n", "fig, ax = plt.subplots(figsize=(6.5, 3))\n", "ax.barh(list(results), [abs(g) / 1e6 for g in results.values()], color=\"tab:blue\")\n", "ax.axvline(abs(ref) / 1e6, color=\"k\", ls=\"--\", label=\"exact\")\n", "ax.set(\n", " xlabel=\"|g|/2π (MHz)\",\n", " xlim=(0.9 * abs(ref) / 1e6, 1.05 * abs(ref) / 1e6),\n", " title=\"qubit (0,0), two-mode circuit\",\n", ")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "89eee512", "metadata": {}, "source": [ "Three methods are exact on this circuit; EPR is 4% low for the reason found in Sec. 3, and exact once the whole qubit branch is counted. (The avoided crossing agrees to 0.01%: the counter-rotating terms that the rotating-wave picture drops shift the splitting only at order $g^2/\\omega$.) On a 3D model, discretization error adds to these — notebook 4.45 runs the same four methods through a finite-element solver.\n", "\n", "## Where to go next\n", "\n", "- **4.43 Mesh and solve the 10 × 10 processor** — build the device in Quantum Metal, mesh it with gmsh, and find the package eigenmode with an open-source Maxwell solver.\n", "- Move the qubit closer to the mode: set `Lpn = 3.3e-9` and watch the EPR estimate drift as the perturbative assumption $|\\omega_m-\\omega_n|\\gg|g|$ weakens.\n", "- Flip the sign of `M` and see $g_C$ and $g_L$ now partly cancel." ] }, { "cell_type": "markdown", "id": "611068f3", "metadata": {}, "source": [ "## References\n", "\n", "1. R. Molavi, E. Forati, Y. Zhang, A. R. Klots, J. Atalaya, B. W. Langley, D. A. Timucin, M. Nazari, G. Khan, Z. K. Minev, A. N. Korotkov, M. H. Devoret, \"Extracting electromagnetic bare mode couplings in large superconducting quantum processors,\" [arXiv:2609.22442](https://arxiv.org/abs/2609.22442) (2026).\n", "2. Z. K. Minev, Z. Leghtas, S. O. Mundhada, L. Christakis, I. M. Pop, M. H. Devoret, \"Energy-participation quantization of Josephson circuits,\" *npj Quantum Inf.* **7**, 131 (2021). [doi:10.1038/s41534-021-00461-8](https://doi.org/10.1038/s41534-021-00461-8)\n", "3. C. A. Balanis, *Advanced Engineering Electromagnetics*, 2nd ed. (Wiley, 2012) — LSM modes of a partially filled waveguide.\n", "4. C. Geuzaine, J.-F. Remacle, \"Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities,\" *Int. J. Numer. Methods Eng.* **79**, 1309–1331 (2009). [doi:10.1002/nme.2579](https://doi.org/10.1002/nme.2579)\n", "5. T. Gustafsson, G. D. McBain, \"scikit-fem: A Python package for finite element assembly,\" *J. Open Source Softw.* **5**, 2369 (2020). [doi:10.21105/joss.02369](https://doi.org/10.21105/joss.02369)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.14" } }, "nbformat": 4, "nbformat_minor": 5 }