{ "metadata": { "name": "", "signature": "sha256:767a93e1f1634cd7d8066429f3654a5c885b89f63a447812a4a2394767f72ed2" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP lecture: Superconducting Josephson charge qubits\n", "\n", "J.R. Johansson (robert@riken.jp)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Introduction\n", "\n", "The Hamiltonian for a Josephson charge qubit is\n", "\n", "$\\displaystyle H = \\sum_n 4 E_C (n_g - n)^2 \\left|n\\right\\rangle\\left\\langle n\\right| - \\frac{1}{2}E_J\\sum_n\\left(\\left|n+1\\right\\rangle\\left\\langle n\\right| + \\left|n\\right\\rangle\\left\\langle n+1\\right| \\right)$\n", "\n", "where $E_C$ is the charge energy, $E_J$ is the Josephson energy, and $\\left| n\\right\\rangle$ is the charge state with $n$ Cooper-pairs on the island that makes up the charge qubit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### References\n", "\n", " * [J. Koch et al, Phys. Rec. A 76, 042319 (2007)](http://link.aps.org/doi/10.1103/PhysRevA.76.042319)\n", " * [Y.A. Pashkin et al, Quantum Inf Process 8, 55 (2009)](http://dx.doi.org/10.1007/s11128-009-0101-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Helper functions\n", "\n", "Below we will repeatedly need to obtain the charge qubit Hamiltonian for different parameters, and to plot the eigenenergies, so here we define two functions to do these tasks. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def hamiltonian(Ec, Ej, N, ng):\n", " \"\"\"\n", " Return the charge qubit hamiltonian as a Qobj instance.\n", " \"\"\"\n", " m = np.diag(4 * Ec * (arange(-N,N+1)-ng)**2) + 0.5 * Ej * (np.diag(-np.ones(2*N), 1) + \n", " np.diag(-np.ones(2*N), -1))\n", " return Qobj(m)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_energies(ng_vec, energies, ymax=(20, 3)):\n", " \"\"\"\n", " Plot energy levels as a function of bias parameter ng_vec.\n", " \"\"\"\n", " fig, axes = plt.subplots(1,2, figsize=(16,6))\n", "\n", " for n in range(len(energies[0,:])):\n", " axes[0].plot(ng_vec, energies[:,n])\n", " axes[0].set_ylim(-2, ymax[0])\n", " axes[0].set_xlabel(r'$n_g$', fontsize=18)\n", " axes[0].set_ylabel(r'$E_n$', fontsize=18)\n", "\n", " for n in range(len(energies[0,:])):\n", " axes[1].plot(ng_vec, (energies[:,n]-energies[:,0])/(energies[:,1]-energies[:,0]))\n", " axes[1].set_ylim(-0.1, ymax[1])\n", " axes[1].set_xlabel(r'$n_g$', fontsize=18)\n", " axes[1].set_ylabel(r'$(E_n-E_0)/(E_1-E_0)$', fontsize=18)\n", " return fig, axes" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "def visualize_dynamics(result, ylabel):\n", " \"\"\"\n", " Plot the evolution of the expectation values stored in result.\n", " \"\"\"\n", " fig, ax = plt.subplots(figsize=(12,5))\n", "\n", " ax.plot(result.times, result.expect[0])\n", "\n", " ax.set_ylabel(ylabel, fontsize=16)\n", " ax.set_xlabel(r'$t$', fontsize=16);" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Charge qubit regime" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 10\n", "Ec = 1.0\n", "Ej = 1.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "ng_vec = np.linspace(-4, 4, 200)\n", "\n", "energies = array([hamiltonian(Ec, Ej, N, ng).eigenenergies() for ng in ng_vec])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_energies(ng_vec, energies);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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QulxCqdfZ6If0/jT/LBShBmU8G/vY6Cuc31/ZE1kEJgXgb+G3ceLxeRBdHEXmkDOLuNHJ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8ViKmx5TakGXMexBWqnI/O6liZN6DUl7H95FoOmwpbHjsgCpu6zDR5tYauUGFTbvSktBZKS7Hc7\nACAmRl33JjWV3nzNm9t/rZEjqXGTWu7N+vX0ulAiTUrtdGR705AFvLxIiK1bZ/+15CDUpA4aZP+1\nevSgroOXLtl/LTls2WJfTaoxY8fS55daB1pKHTYAJNLXrlXmWgzR10zqvE6nQ7t27TB79mxs3LgR\n2dnZSE1NrTHzVlUuXwZYmqkrBdMGUrwKWze3mo1keD9sMH5OeHU5AddxbIGaDaTKy/nshA7QgY+7\ne3V2nCsJW55TkVu0oO8SkTy6wlZJtwOo3hiqQXIy8MQTyn2QqOneKHXYANCXd7Nm1MBJDZRIQxYY\nPpzGspgOp3cGd+5QNkK/fspcb8wY9dKRlahJFXB3V/dAS4k0ZIH27SlF8dQpZa4nhYoKytJQai1j\nxtDnCAud6p2Mu7s7unXrxs64H56FbePG1RvD/HzqKlq3rroxycVYEKan81lfC1SP+xEO4HicYSvg\nSo6tcSOsO3eoPworDeykIri2AL8p1QAJ2wdNBgHQgRav75XISE3YimLrVnJclHA7gGr35rfflLme\nFJQUgwCJ9LVrne/eKFWTaszYscCaNcpdTyxXrtDroWtXZa4XFkYp72rUDK9bR03JlJqvN3gwcPQo\nneo6GyWdQUC9QyChJlUJFx2grAK11nLgQPVsYCWIiqKaLxY61avEO++8o3YIBM/C9rHHqpvDCW4t\nj02KgJopvDw7tr6+VJojNPXicYatgLFjazDQWngVUca1qTwLdIDWIqS93rzJr2Nbrx51DBcaqJ49\na39ZnFpowlYkSotBd3faMDt7Y6hkTapA+/b0/ydPKndNMZw+TR/wbdsqd82xY0nMONu9WbuWnhN3\nd+Wu+fTT6oj0NWvodyuFnx81bHN291phTqpSWRoAdVa+csX5c4Z37qTOzErOK1VL2Cp92ACom0HD\nAO2Fz3C1KS7mMyURoCyos2fpv69dU+7gRQ3Cw6s/o3h2bIGaIp3n9F1jxzY3l5oZ8tikCKjp2PIu\nbI0d2+vX+V2Lm1t1bWplJXDhgiZsXRqhJlUpt0NAcDqdycGDtLlV8lRcp1NHRK1ZQ39DJU/FW7ak\nuoL9+5W7phiUFoMACY/Nm8mtcxaZmVSTOmSIstdVQ0Rt2QL07m1/53BjPD2pltvZNcNKH8wBQJcu\nVKLhzBFGQpaG0msRhG1VlbLXZZTtanZ/t0aLFvy6nNHRtJkqLeW3vlagc2faKwB8O7ZATWHLc/Oo\n0FCaw1tUxLdAB2o2j+Jd2Bo7tgcP0nuHV4Q62ytXSCfwenDSoAG9T0TOsn00he3OnXRy0aCBstft\n3ZveEFevKntda6xeDTzzjPLXFVJ4nZWObDA4bi3OFulXr9KHiT1zUs3RoAG52c7cxP78M6UhK91B\nMz6eap/z8pS9rjUc4QwCzhfpStekCri5OT/r5PhxSnFv3VrZ6z72GH2J//KLstdllM8//1ztEMzT\nooXaEcjHx4dc2osX+Re2fftStorBwLcYBEg0/f47ZQMUFJBA5BGdrlqk8zp+ScC4eRTPLidQnVad\nk0MHW6z0K5CDIGzPnqUMFF7R6ei75MoVUXd/NIXt6tXAs88qf10PD+c2k6msJIdYaWcQAJ58kjbQ\nv/6q/LXNcfo0ddNzxIeIkI7sLPdmzRoSCI5onvD0087NCnDU6ysoCOjTx3kjjIqLlZmTao4BA+h9\ncueO8tc2x759lGLkiI22s0X6mjX0Ox3h6j3i6chMwGt9rYCQjsy7sG3cmA56zp0j4cFzKvKwYcCy\nZdU1qfaOoFMTIR2Z5/pagLLisrLooOGHH+g54hUhfXffPqB7d/vm3auN0EDqzBm+hS0gKR2Z408E\nmZSWktsxdqxjru/MdOQDByi9IDpa+WvrdM5dy+rVJKAcscFt1YqaLx04oPy1zeGINGSB0aOps68w\nk9CRZGVRk6ehQx1zfWeKqO3bgY4d6XWgNN7e9EXurHFMwnvFEfTsSQLdGSOMDAbgxx8dc8gIVI/9\nUWuEkQb/wrZ1a9oU8i5sAXJtd+ygpn28jv0AyDwoLga++YZv5xkgp/Prr+lzkGfH1sOD9qIffkjm\nBCs1/nIQHNuUFOWz7pyNsWOrdFaUs9GErRW2baN0Tkd1OouNpU2hM5rJOCp1V8BZ6cgGA/0eR67F\nWenIjkpDFmjUiE7eduxwzPWNWbeOOhgrnYYsMHIklQUUFTnm+sb8+KNjX1/OSuGtqKDf46i1OHOE\n0dGjdBruqE1Q27a04TpxwjHX17AN78LWVRxbgPYmP/xAolbJpobOxs0NePddYOFCvsUgAEyfTgfv\n3boB48apHY19REQAn38OvPee2pHYR0QEjfnZvZveMzwjCFtXcGwlzLJ99ISto8Wg0EzG0XM6HZmG\nLNClC7UKd3QzmVOnKA35yScd9zuc1UzGkWnIAs4S6Y50ngGaCdm1KzV1ciRFRfQ7xoxx3O8YMoTq\nOYUxFI5i926q+3Nk7aKznHThsMFRzYWcnXWiURvehW3r1nQAk5vLt8sJ0GHrkSP8u5wAfW60aMG/\nsO3VC/jgA/ofrx1rBSIigP79+W62BFAGVp06QFoa/2tp1ozE4KVLQEyM2tHYh+bYWqC4GNi0ybEb\nXMA5m6l9+8i9i4py3O8QZls6ei3CYYMju2fGxNCHldAZ0lE4WgwC9Jw4Oh357l0Sao6ulRk3Dli5\n0rG/Y/NmOqRRcjSOKf7+5G47+kDLkam7AsIII+Ph7kpTVeW4XgfGaOnI6sK7yxkVRfPIIyL4ruUE\n6Llo2pTv+loBd3fgu++ACRPUjkRD4PXXybF1BZo0ofpaLy+1I7GPRo1oL9e4seMy75xFZKTWPMos\nSUlUZ6d0N2RT+vcnl1NoSe8IHO08Czi6WZEz0pAFHO10OjoNWSA8nE53d+503O8Q0pD9/Bz3OwBK\ne925U3Qbd1msWuV4AQUA48c7VqSXlVEdr6PfK56elHXw44+O+x2HDgEBAY5Pj3ryScoGOX3asb9H\nwzw8N14BKP7oaP4FukBsrGs4tgDQo4eyM+817CM2ln9XUKBxY/7TkAHKHIyI4L++FqDPYJGa6tES\nts4Sg97ewIgRjhOEQp2do51BgGo/srNpuLMjOHmS0qo7dnTM9Y1xdDqyM9KQBRwt0p3hPANASAgd\nBGzY4Jjr5+eTcFZ6NI45hg6les7btx1z/Z07aZPtjI2po0W64NY6esapTuecrAAN1+WJJ1xH2L7/\nPjlrGhoalvnwQ+C119SOQhmaNuW/vhYg91xkb6RHR9gWFQFbtzpmjqU5nnvOcZupvXtpc+uM+iU3\nNzoMWLXKMdcX3FpHb3ABcjmDgsgtcgTOEoMApVgmJpKLpzR37wKHDzuvZf+4cY57fSUm0nzpOnUc\nc31jfHyAp54i0eYInJGGLNCnD5CZCZw/r/y1q6qcl6UBkEhftUpLRxbJlClTUL9+fbRp08biff74\nxz8iKioK7dq1wwlXb841dCj/3VEFmjVzHcdWQ8NRPPYYv/ORTRk0COjXT+0olEGk5nl0hO2WLVQI\n7sg6O2P696fUVJHFzpJwlvMs8Nxz1E1R6Y2hweD8tTjKvXFWGrJARAQJ9e3blb+2kIbs76/8tc0x\nciSwf79jGi/9+KNzu0066vVVUkJ11c46OHF3JxHtiAOH/fupcdhjjyl/bXO0aUOvZUfX17sIkydP\nRlJSksWfb9myBZcuXcJvv/2GJUuW4DVXcTYsMXEiMGmS2lFoaGhoSOfdd4G4OLWjUIZXXhF1t0dH\n2DpbQHl40CZU6U1uRQU1qHHWBheguWQGA3DsmLLXPXGCrtuhg7LXtcZzz9Frobxc2euuWkUuqjPS\nkAWEAwelWbGCru0sAgKoq7DSjZdycii7YeRIZa9rjf79qcHB1avKXjcpCWjXzrmdWYV0ZKUPtJzR\nNMoYnY7W4oj3CiPMnDlTsWv17t0bISEhFn+emJiISQ+EXteuXZGbm4uMjAzFfr+GhoaGhkYtROqe\nR0PYFhbS/FpnpSELOMLp3L2bcuabN1fumrbQ6WgtK1Yoe90ffiCHyxlpyAKRkfS327VLuWsaDPS3\ncXaHxmeeoUyE+/eVu2Z6OvDrr5R+50wc4XSuWwcMGEDp587C05MOOJR2Op2ZhizQuTOlDR8/rtw1\nhTFlzjxkBEjYrllDB4MuyJAhQ5z2u27evInGRumsERERuHHjhtN+v4aGhoaGhiWcaC+pSGIite6u\nW9e5v7d7dxoxdPo0uS1KsHy5Oi3ux4+nPP0FC5QZ7l5ZScJWSYEplgkTSIgqtRk8fZrEZY8eylxP\nLKGhNAdv/Xrg+eeVuebKlSTMvL2VuZ5Yhg4FpkyhxktKuZKrVgFTpypzLSmMH08NWt55R5nrCf0B\nvvxSmeuJxbjxklIzpvfscfyYMnNERlJ9YXIy1Rxp2IXB5LBWZ+FwUhdrdHszAE48j9XQ0NDQ4Jyr\nAK5Je8ijIWyXL1du4y8F4xQ4JYRtYSF1j/3nP+2/llRiYmhDmpJC6Zb2kpJCAsZZdXbGPPMM8N57\nJBiUGGezfDk52mrMOZwwAUhIUO71vWKF8wUUQI2XRo4kV+2Pf7T/epmZNId33Tr7ryWVXr2ok/jZ\ns8q02Rfm8IaF2X8tqYwfTwdAn3yizOtbyNJQA+GzWBO2dhEeHo709PSH/75x4wbCw8PN3teQojXs\n0tDQ0NBQBkuHqMa4fipyRgZw4IBzxn2YQ+jIqcSIGcF5dvQcXksoWdOp1mEDANSvT2OMEhPtv1Zl\nJTlaaq1l5EhqipOZaf+1zpwhQda7t/3XkoOS3ZHXriUX2FkNsIxxc1O28ZJwcKIGrVvTSKb9++2/\nVnEx1VGrtZZnn6X3fEmJOr/fRRg5ciQSEhIAAIcOHYJer0f9+vVVjkpDQ0NDQ+NRELY//kgzZdXY\n4ALUkTMoCEhNtf9aaopBgITHunX2bwyLiyl9Vi3nBiCnUwmRvncvOWmPP27/teTg7w8MH06vc3tZ\nsYIOYtRwngGqh/3tN+DaNfuv9f33wAsv2H8duSg1YubuXUrfHTNGmbjkoNRM240baV51RIT915JD\nw4bUqG7LFnV+vwqUlJSgoKBA0mPGjx+PHj16IC0tDY0bN8ayZcuwePFiLF68GAAwbNgwtGjRAi1b\ntsQrr7yC//znP44IXUNDQ0NDQzI6g2mxDGfodLpa9T416NwZ+Mc/1E0/++gjaspjzwYgMxNo1Qq4\neVM9kQ5Q2/DXX7evEdfq1cA33zhmVI1YCgpont/ly/bVXr/0EqVTv/mmcrFJZetWYN48++bzVlVR\nU63EROXqweUwfToQHk4t6uVy8SLNYb1xw7ldqo0xGOj9+sMP9Bkkl0WLyJFXunGbFK5epVToW7eo\nOZZcRowAxo5Vd3TKN99QI8E1a6zezeb3CsMUFxfjwoULaNmyJby9vbF27VoEBARgpDO7g4Pvv6GG\nhoaGBnuI+V5xbcf2wgXa3Ko9w2ncOEqNtGfEjNrOs4AS6chqO88AEBhItYNr18q/RkkJOdjjxysX\nlxwGDiTxcemS/GscOEB/k7ZtlYtLDpMmAf/7n31O5/ff03OilqgFqL7++eep/tke1HaeATrwiIqy\n7yAqKwvYt8/5nelNGTOG1pGfr24cDuTll1/G/Pnz0aVLFwwcOBB37txBqhIZQxoaGhoaGozj2sJW\nqE1Tc4ML0MawZUtgxw7512BBDAK0MdyxA8jLk/f4u3cpfVetmmdj7B1htHkzpTZaaJziNDw8qCGW\nPQcOwrgiZ45eMkeXLhSDXPe5qorE4MSJysYlh4kTKR25tFTe49PSgOvXKUVbbSZOpAMHuaxaBcTH\n0+GJmoSE0EGnPQdajDNo0CCsWbMG58+fxzfffIOqqir0cHbHdg0NDQ0NDRVwXWFbVUWbdRbEIECu\ni9yNYVoa8PvvynQjtpeQEBr789NP8h6/ejU19VF7gwuQY3vuHIkHOag1eskcQs2wHKezrIw2+mo1\n9TFGpyPXVq7TuW8fvbbat1c2Ljk0b06115s3y3v899+zcTAHUOOlbduouZgcWO/igNAAACAASURB\nVHCeBV58Efjvf9WOwmEEBgYi+8HzFBUVhTfffNPpacgaGhoaGhpqwLywbdasGdq2bYsOHTqgS5cu\n4h944ACl7bKwwQUoHXnbNiAnR/pjhaY+LGxwARIe330n77EsHTZ4eQFPP02bbqnk5NBMTDWb+hjT\ntStQUQEcOyb9sdu2UZ1w06bKxyWH55+nAxA5TcoEt1Zt51ngxRflHWhVVdHBCQvOM0AHWkOGyGtS\nlpZGPQZYcJ4BYNgwisme1H2GSU1NRevWrTFz5kysWbMGt2/fVjskDQ0NDQ0Np8C8sNXpdEhJScGJ\nEyfwyy+/iH+g4BCwssEVNoZSu4saDLTBZcXtACilMC2NOthK4coVegxLcyQnTyb3RqrTuWYNrSM4\n2CFhSUank58V8N//svX6atKEDqQ2bpT2OGGcDCsuOkDNkvbsoRpTKezbR93U1WzkZYpcp5OFmmdj\nPD3JCbe3/plRGjVqhJMnTyI2NhYHDx7EqFGj0KtXL7XD0tDQ0NDQcDjMC1sA0jsrlpRQqiwLqZXG\nCCJKCgcPAj4+VMvJCl5eJB6kriUhgVIa7emsqjSdO9N6pM7pXLaMnk+WePFFOjiR4nRmZQG7dqk7\neskcQhMpKWzYAHTqBDRq5JiY5BAYSE3fpNY/s5S6KzBwIDmv58+Lf4zgPLO2FsFJV2K+OGPEx8dj\n27ZtGDRoEBYuXIjDhw9j7969aoeloaGhoaHhcJgXtjqdDgMGDECnTp2wdOlScQ/atIm6uzZu7Njg\npDJgAI3MOHtW/GOWLWMrtVJg8mTaGFZWirt/ZSWlL7/0kmPjkopOB0yZQn9nsZw9Sxt8lpxngFKJ\nO3QggSeW5cuBp54id5AlRo+mw4aMDPGPSUhgJ3XXGKkinUXnGSDH9fnnpa1l/34gIICdkhCBdu2A\nOnWAlBS1IxHN5MmTMXfuXCxdutRql+OoqChMnDgR/kYd9N3Umk2toaGhoaHhRBjJDbPMgQMH0LBh\nQ2RlZWHgwIGIiYlB7969a9zn/ffff/jfsbGxiP32W/YEFAC4u9PG+7vvgAULbN+/oICc53PnHB+b\nVNq2BerXB3buBAYPtn3/XbuA0FD2NrgAbdZjYoAvvxTX1Orbb8nxYSW10hhBpD/7rO37Ggy0ln//\n2/FxSSUggAT3Dz8As2fbvv+dO0Bqqs35pKrQrx8547/+CrRpY/v+iYnsOc8CkybRgc4//kGfZ7b4\n73/ZPJgDqlOr4+KQkpKCFMZFbkJCAhYtWoR+/fqh0uRAcdGiRahTpw6efvppeLKUEaOhoaGhoeFE\ndAaOJqjPmzcPAQEB+POf//zwtlrDeq9fJ9fqxg3A11eFKG1w8SLQpw85frY2IN9+S3WG69c7Jzap\nLFpEjsyqVbbv++yzQN++wPTpjo9LDqNGASNHkjC0RlkZEBFBIqplS+fEJoXiYorvxAmqVbXGkSOU\nrn/xIpvCIzkZ+NOfgJMnbd/3s8+A06ftG0njSObModeOmAOtQYNIdLFWSiHQuTPwwQfUM8Aa+fn0\nGkxLo0Mw1sjKovm816/XylgQMwTe2XTr1g2HrIzB+uWXX7BgwQJERUXh1VdfRWOVM5ZY/BtqaGho\naPCLmO8VpvOTioqKUFBQAAAoLCzE9u3b0caW4/Hdd9SohEVRCwCtWgGRkUBSku37suo8Czz3HLB1\nq+1Oz3fvUuddVjfqAKVWi+n0vHEjjXBhUdQC9LofN06cwBPqhFkUtQAQG0vjZU6dsn4/gwFYuhSY\nOtUpYcli0iRK+66osH6/q1fpUGL0aOfEJQexnZ5XrqQRZSyKWgAIC+Nqpm2zZs0e/vfdu3dr/bxL\nly5YuXIlMjMzERkZ6cTINDQ0NDQ02IBpYZuRkYHevXujffv26Nq1K4YPH45B1uoaKytps87yBhcQ\n10Tq3Dng2jWa+coqdepQGrKtTs/LlwPDhwN6vXPiksOwYdSx+eJF6/dbtsy2q6s2U6aQSLfWGKeo\niEbqsFiTKuDmRiLKVv3zvn0kzlnu/BodTXNtbR1offMNpcb7+DgnLjmMGwds2QLk5lq/H+uHDQBX\nM22NU4yPHj2K+Ph4PPPMM/jqq6+QlpYGAHB3d8cXX3wBX1YPdjU0NDQ0NBwI08K2efPmOHnyJE6e\nPIkzZ87gnXfesf6AnTvpFJ7FOk5jnnmGak7NnLo/hOU6TmNsOZ1CHSfLzjNAaeHPP299k3vzJnWp\nHjvWaWHJomNHqhXes8fyfdato9m3ERHOi0sOU6bQ7GNrnZ6XLAFefpld51ngpZdIuFqiooLeS9Om\nOS8mOdStS+nS1g60TpygVF/WGqyZMnQolzNthwwZghUrViA5ORlhYWE4a9SQ0M/PD506dVIxOg0N\nDQ0NDXVgWthKhgeHAKB6rhEjyMk0R2kpjftg3RkEaON6+zZw5oz5nx85Qu5g377OjUsOtjo9/+9/\nwNNPA35+zo1LKmI6PfPgPANAs2bAk09Sl2Bz3LtHXdBZdp4Fxo2jw4bbt83/fPNmoEULSnVnnWnT\n6EDBUq3LN9/Q60tMgyk18fSkUUTffqt2JDYpLy+v8W+9Xo+4uDiMHTsWo01S1+vVq+fM0DQ0NDQ0\nNJjAdYRtZiY5tizXcRpjbWOYmAg88QS7dZzGuLtT/aAlJ0pwa3kYN9G6NTmY27bV/llVFYlB1p1n\ngQkTqB7YXLrolSvUaGnECOfHJYepU+nQyhzff09p7nXrOjcmOQQE0MGIpQyHJUvYd2sFBgyg19ax\nY7V/VlREDeV4ODgB6G/+3XfU3Ith1q1bhzFjxmDJkiW4du0aANQY6WOMB+uZPhoaGhoaGg6AA7Uh\nkoQE4A9/YG8epyWEkUX799f+GQ+pu8ZMnUruc3FxzdsLC2n8yqRJ6sQlh6lTgcWLa9++bx/VPXbu\n7PyY5BAaCgwcSONyTFm2jISvt7fz45LDU09Rzflvv9W83WCoTkPmhWnT6BDItP75+nXg0CESvjzg\n5lZ9OGfKmjVAt27szRG3RHQ08NhjdKDIMO7u7jh8+DBeffVVtGjRAq1atcKhQ4ewevVq3LlzR+3w\nNDQ0NDQ0VMc1hK3BQJtFHtKQBXQ62pB//XXN23//ndJ3We6Kakrz5kCXLtSMyJg1a4AePYDwcHXi\nksNzz5GIvX695u2LF9Pri/U6TmNefRX46quaWQFlZXRw8sor6sUlFS8vOhwxPXA4cIAEoslca6bp\n1IkO33burHn7smXUzZ31NHdjJk+m9/iDzvUP4aUkxJiXXzZ/oMUQw4cPx40bN3Du3DksWrQIbdu2\nRVZWFsaNG4dGjRqhVatWmDZtGhISEnDr1i21w9XQ0NDQ0HA6XM2xNYdOp4Nh717amJw7x5fwyM6m\nmrpLl8hhA4D33qMUv//3/9SNTSqJicBHH1FzJYDEVOfOwPvvU6ooT7zxBnVw/uAD+vedO+ToXL3K\ndmdnUwwGinvp0mrx9+OPtIFPTlY3NqlcvUqvp+vXq8XfxInUKO5Pf1I3NqksWUL1tBs20L8rK6mW\neNMmoF07VUOTzJgxNNJHmE99/jyN0Ll+3facbpYoLSWH+cF8ahZnsO7Zswd9TXoVGAwGnD59GsnJ\nyUhOTsbevXtRUFAAnU6HSku9ApwEi39DDQ0NDQ1+EfO94hrCdsQIamL0+utqhyOdiRNptu3cuVSb\n1qwZOVFRUWpHJo2KCnJuN24ksXHwIDVluXiRj/paY86epRpCYXP+wQfAjRvMOzpm+eILSnEVOtj2\n7UvCnfXOzuYYMQIYNYrS9M0dCvFCURHQtClw+DCtYfNm4O9/p3/zxr59VEt74QLV28+YQY70Rx+p\nHZl05syh19XXX3MryiorK3HkyBFMmDABly9fVjUWXv+GGhoaGhps8ugI2/Bw2uCyPPvREpcv09iV\nY8dog7t9O7B+vdpRyePzz6lpTHIyiY/u3YGZM9WOSh59+tBs29mzgchImtvZtq3aUUknN5cOHH79\nlcZLxcfTfGSe3DSBbduAt98mAfjXvwIZGeZriHngr38FysuBd96h+bt//zvw7LNqRyUdg4E+v+bM\nIbE+ZAgdDPF22ADQ+yM6GjhxArqmTbkWZc8++yx+/PFHVWPQhK2GhoaGhpI8OsL2yy/JheKVDz+k\nzfqFC1Rrx1PNoDEGA7k3164Bp05R+mhwsNpRyePMGUpvv3GDXPS9e9WOSD5/+Qs5twDw8cf8pe4K\nVFWR8CgtpRTrxYvpueGR33+necORkdTk6x//UDsi+fz4I5VOlJVRXTcv3ZDN8fbbQF4edF9/zbUo\nO3nyJNqrPM9dE7YaGhoaGkry6Ajb4mI+3VqB0lKqrQsKIoHLU52wKeXlVHcXFQV89pna0diHwQD8\n9BOJp06d1I5GAwBSUoCSEnIGeWf8eMDfn2qgeX7PV1TQaLLGjWlOL2+lB8ZkZQExMdBlZzMjyubP\nn4+XXnoJ9evXl/X4u3fv4sMPP8S//vUvhSOzjiZsNTQ0NDSU5NERtnwvgTh/nkQhj+muphgM9D+e\nN7gaGo6mqsp13iOHDgGNGgFNmqgdif0sXAjdn//MzPdKQUEBXnnlFQwZMgQTJkyAu7u7qMcZDAb8\n9NNPWL58Ob7++ms0aNDAwZHWxGW+mzU0NDQ0mEDM94qL7Kr4517TesiMdO7Gw2HodK6zYdfQcBQu\n9B658XgECuqHqB2GIqwf1kLtEGoQGBiIhIQEZGdno2PHjvi///s/bN++HXl5ebXuW1hYiD179mDe\nvHno0KEDDh06hJUrVzpd1GpoaGhoaKiBSzi25ZXl8HDzUDsU2VQZqtDnuz7w8/TD9he2qx2OXRgM\nBry14y00CmyE2d1nqx2O3Zy4fQIhviFopm+mdigaAM5nnYdOp0NMaIzaodjNnF1zoPfR462eb6kd\nil0YDAa0+7odokOjsebpNWqHYxclFSVo8UUL3H7zNpNuY25uLr777jts2bIF+/btg06nQ3BwMHQ6\nHXJyclBZWYlu3bohPj4ezz//PCIiIlSLVXNsNTQ0NDSU5JFxbBNOJagdgl18deQrGGDA+bvnceTm\nEbXDsYs5u+Yg6XIS5u+fj/tl99UORzbX867j2bXPovd3vfHa5tfUDscuFqQuQPSiaEQviub6vWIw\nGDDup3Ho+k1XTE2ciqzCLLVDks2tglv4+ujXWHJsCf7fYc5mVpuw5bct0Ol0+DXjV/x8/me1w7GL\nZSeWoVMjduvp9Xo9Zs+ejR07diA/Px9paWnYtGkTNmzYgPPnzyM/Px/79u3D22+/raqo1dDQ0NDQ\nUAOXELbz9sxDaUWp2mHI4vfc3/H+nvexbOQy/KXHXzB//3y1Q5LN4qOLkXgxEbsn7Ua/Zv2w9NhS\ntUOSzZQNU9A4qDHSZ6fj1J1TOJ1xWu2QZJFbkov5++bjv0/9F58P/hzvJr+LssoytcOSxc4rO1FZ\nVYmrM6+ioqoCf9rOaXdnAF8e/hLPt30eOyfuxKepn2LDhQ1qhySbjw98jDm95uCbkd/gja1vIKc4\nR+2QZFFWWYZ/Hvgn3u39rtqhiMLLywtNmjRBp06d0KVLFzRv3hy+vr5qh6WhoaGhoaEaLiFs29Zv\ni8XHFqsdhizmJM/BH7v8EdGh0ZjacSoOph/EmcwzaoclmdKKUvx979/xw+gfEOoXir/2/CsWHlrI\npYg6dusYLt67iI/6f4QQ3xD8sesfsSB1gdphyeLro19jeKvh6N64O4ZFDUOruq2w6swqtcOSxYKD\nC/BmjzdRx7cO/jXkX9jy2xZcz7uudliSyS/Nx9LjS/Gn7n9CM30zLBmxBO/tfo/LtM391/fjdsFt\njHl8DHo16YURrUZg/j4+D+eWn16O6LrR6BrRVe1QNDQ0NDQ0NGTgEsJ2Xuw8fJr6KXci6lruNWy7\ntA0zu80EAPh5+mFm15n4eP/HKkcmnRW/rkCbem3QrkE7AMCTjZ5ETGgMfvj1B5Ujk86nqZ9idrfZ\n8HT3BAC82ulVbLq4Cel56SpHJo3SilJ8efhL/KXHXx7e9laPt/Bp6qfciahTd07hTOYZjH9iPABA\n76PH5PaT8a9Dzh1hogRLjy3FoMhBD+u2B0cOBgBsu7xNxajk8dH+j/BWz7ce9jiY03sOlp1chtyS\nXJUjk0ZFVQU+2v8R5vaZq3YoGhoaGhoaGjJxCWHbsWFHLkXUwoMLMbXjVAR5Bz28bXrn6Ui6lITL\n2ZdVjEwaVYYqfJr6aa0mOG/3fBv/PPBPVBmqVIpMOldyrmDnlZ2Y2nHqw9t4FVHLTy9Huwbt0KZ+\nm4e3DYocBDedG5IuJakYmXQWHFyAN7q8AW8P74e3zeo2C/89+V+uUl9LK0qx8NBCvNWj+r2i0+nw\nVs+38MmBT1SMTDqnM07jxO0TmNhu4sPbmgQ3wbCoYfj66NcqRiad1WdXo0FAA/Rp2kftUDQ0NDQ0\nNDRk4hLCFgD+2vOv+OTAJ9yIqLtFd7H89HLM7Dqzxu3BPsF4tdOrXG1yN6ZthL+nP/o161fj9rjm\ncfD39MfGtI0qRSadhQcX4uUnX0agd2CN22d1m4XvTn7HjRMlHDYYu7UAiai/9PgLPknl5/V1Necq\ntvy2Ba91qtnEKyIoAiOjR3Ilor4//T3a1GuDDg071Lj92dbP4lL2Ja6ax328/2PM/v/t3Xl4TNf/\nB/D3hBD7HkFCVCyJJQtqJyhRihb90tDNVq19jZ0ghEiLahUtqlqUqqgl1sSSkFhCEbuEiCXWRDbJ\nzJzfH/dHrcksd+bOxPv1PH0qmXvP/dyZe3Pmc8655zQeCbv8di/8flzTcVgYtRCZ6kyFItOPVmgR\ncDAAk1uwt5aIiMia5ZnEtm3VtihkWwhbL25VOhSd/BD9A7q7dkeFYhVeeW1E4xHYELsBiSmJCkSm\nv3mR8zCu2TioVKoXfq9SqTC++XgERgRaxdDXe+n38MfpPzCs0bBXXnMq4YRONTpZTRK19eJWFC1Q\n9JXGBkBKoq48uIJjN48pEJn+5kfOx0CvgShhV+KV18Y0HYNF0YusIonSaDWYFzEPE5pPeOU123y2\nGNVklNU0OFx9eBW7ruzCVw2+euW1uuXrwquCF3479ZsCkekv5HwICtsWRvtq7ZUOhYiIiIyQZxJb\nlUqF8c3GI/CQ5SdRaVlp+OHoDxjTdMxrXy9buCw+d/8cwYeDzRyZ/iKuR+B26m10c+322tc/qvUR\n7qffx8HrB80cmf6eNjY4FHV47etjm47FoqhFVjED99Pe2pcbGwApiRrZeCSCIoMUiEw/d1LvYO2Z\ntRjReMRrX69jX8dqkqhN5zahTOEybxzu2t+rP8Ljw3H5wWUzR6a/oIggDGow6IXHKJ739FlujVZj\n5sj0I4TArIOzMLnF5NfeK0RERGQ98kxiCwDdXLvhbvpdHLp+SOlQcrQiZgWaV26OmmVrvnGbMU3H\nYNXJVbiXfs+MkelvXuQ8jGky5tnkMS/LZ5MPY5uOtfgJsdKz03NsbACk2bfrla+HNf+uMWNk+juc\ncBg3Um6gu1v3N27T36s/9l7di6sPr5oxMv0tOLIAn9T5BOWLln/jNuOajsP8w/Mt+jEEIQQCIwIx\nvtn4NyZQRQsUxaD6gxAcadkNWrdTb2P92fWvHdnwVMsqLVG6UGlsPr/ZjJHpL/RyKLI12ehcs7PS\noRAREZGR8lRim88mH8Y0GYO5EXOVDuWN1Fo1gg8Hw6+ZX47bVSpeCT3celj0hEXn7p7DkRtH8IXH\nFzlu95n7Zzh5+yRO3T5lnsAMsDJmJZpVbpZjYwMATGg+AXMOzYFaqzZTZPqbGzEXoxqPemNjAwAU\nK1gMA+sPRFCE5fbaPsp8hGUnlmFss7E5bteySkuUtCtp0WvB7r66G5nqzFwTqKGNhmLd2XW4k3rH\nTJHpb8GRBehdtzfsi9i/cRuVSgW/Zn6YGzHXYkfQCCEw88BMTGoxCTaqPFUVEhERvZXyXG3+ucfn\nOH7ruMWuBfvn2T9RpWQVndZK9Gvmh5+O/YTkzGQzRKa/eZHzMLjhYBSyLZTjdgXzF8SIxiMs9vnB\nJ+onmBsxN9fGBgBo5dwKjsUdLXYG7phbMYhOjH5hVuc3Gdl4JNafXW+xyxj9ePRHdKre6dmyOG/y\n9DGEgIMBFptEBR4KhF8zv1wTKPsi9uhVuxcWRi00U2T6Sc5MxvITyzG66ehct+1SswuSnyRj/7X9\nZohMf+Hx4bifcR893HooHQoRERHJIM8ltnb57TC80XDMOTRH6VBeodFqMOvArNdOHvM61UpXQweX\nDvjx6I8mjkx/l+5fwj8X/slxOOLzBjUYhJ2XdyLuYZyJI9PfipgVqG1fG40dG+u0/bRW0zDzwEyL\n7LX13+8Pv2Z+uTY2AEC5IuUwwGuARd4r6dnpWBS1SKfGBgDoWqsr1Fo1/rloeTNwR92IwpWHV56t\nwZsbv+Z+WHp8qUU+hqBrYwMgjaDxa+aHGftnmD4wA8w8MBMTmk9APpt8SodCREREMshziS0grQW7\n+8puxN6NVTqUF6w7sw4l7UrCp5qPzvuMbz4eC6MWIj073YSR6W/mgZkY3mg4StqV1Gn74gWLY4DX\nAIubsOiJ+glmH5oNf29/nffxdvZGhaIVsPb0WhNGpr+YWzE4evMoBtYfqPM+Y5qOsche2xUxK9DY\nsTFq29fWaXsblQ2me0/H9PDpFtdrO/vQbIxuMhq2+Wx12t65pDP+5/Y/zI+cb+LI9PP4yWMsiFqA\n8c3H67zPp/U+xfXk6wiLCzNhZPrbF7cPCSkJ6F23t9KhEBERkUzyZGJbvGBxjGk6BtPCpykdyjNq\nrRr++/0xs/VMvWbfrGNfB02cmuDnEz+bMDr9nL93HqGXQzG88fDcN37OqCajsP7seovqtf35xM+o\nV74e3q30rs77qFQqTPeejlkHZ1lUr60+vbVPWWKvbUZ2BgIPBWJii4l67de1ZlcAQMgFy3nWNjox\nGsdvHscArwF67TexxUQsP7EcSWlJJopMfwuOLEC7d9rBrZybzvvY5rPFtFbTMDV8qsU0OAghMCVs\nCqa3mq5zYwMRERFZvjyZ2ALA4IaDcej6IZy8fVLpUAAAa/5dg4rFKqJN1TZ67zux+UQERQYhS5Nl\ngsj0N2P/DIxsPPKNS328Sbki5TCk4RD479e9d9SUMtWZmHNoDqa3mq73vq2dW8O+iD3WnVknf2AG\nOHHrBI7ePKp3AgUAo5uMxvqz63E9+boJItPfj0d/RMNKDfVqbAD+a3CYHj7dYmZInrRvEqa0nKJX\nYwMgrZvsW8cX8yIs47n0BxkPsDBqIaZ7T9d7X9+6vriXfg+7r+6WPzADhF4OxaPMR+hVp5fSoRAR\nEZGM8mxiW6RAEUxoPgFTw6YqHQqyNdmYsX+G3r21TzWs1BCuZV0tYq3Os0lnsTduL4a8O8Sg/Uc1\nGYXtl7bj3N1zMkemv+XHl8OzgicaVmqo974qlQrTWk3DrAOzLGKtTkN6a5961mt7UPle25QnKZgb\nMRczW880aP/ONTojv01+i1hmJiwuDHEP49DXs69B+09oMQErYlbg1uNbMkemv/mR89HNtRtcSrvo\nvW8+m3yY3mo6poRNUbzX9mlvrb+3P5+tJSIiymPybGILAAPrD0TM7RhE3YhSNI6VJ1fCpbQLWlRp\nYXAZU1pOwayDsxTvtfXf748xTcagWMFiBu1fwq4ExjYdi6nhyjY4ZGRnIDAiUK9na1/WtmpblC1c\nFuvPrpcxMv2duHUCx24eM6i39ilL6bX99vC36ODSAXXs6xi0v0qlgr+3v+K9tkIITNo3Cf7e/gYP\nd61YrCI+c/9M8eXL7qTewdLjSzG55WSDy/i49sdIz07HtkvbZIxMfyEXQqARGnRz7aZoHERERCS/\nPJ3Y2uW3w+QWkzElbIpiMTxRP8GsA7Mwo7VxM4O2qNICrmVdsfTYUpki09+/d/7FwesH8U3Db4wq\nZ/C7gxGZEInjN4/LFJn+lh5fioYVG8KrgpfBZTxNoqaFT0O2JlvG6PQzLXyawb21T5UrUg4D6w9E\nwIEAGSPTz920u/g++nujGhsAoGP1jihkWwh/xf4lU2T623ZpGx5nPTZ6uOv45uOx+tRqJKYkyhSZ\n/uYcmoM+dfugconKBpdho7KBv7c/poYp96ytVmgxJWwKZnjP4Lq1REREeVCer92/9PwSlx9cxv54\nZdZSXH5iOeqWr6vzUjI5md12NgIOBuDxk8cyRKa/qWFTMbbpWBQpUMSocgrbFsakFpMwOczwHiBj\npDxJQeChQIOeF3xZ23fa4p1S72D5ieXGB2aAA9cO4EzSGb1mQn6Tcc3GYdP5TTh/77wMkelvzqE5\n6FW7F6qWqmpUOSqVCjO8Z2BK2BRFGhy0QovJ+yZjZuuZRg93dSjqgL6efTHrwCyZotNPQnICVp9a\njQktdFuiLCcf1foIAPD3+b+NLssQf579E4VtC+ODGh8ocnwiIiIyrTyf2BbIVwDTWk3DxH0Tzd5T\nkPIkBQEHAwx+XvBlHg4eaPtOW3x35DtZytPH/vj9OHn7pNG9tU/19+qP8/fO4+C1g7KUp495EfPg\n4+IDDwcPWcoLbBuImQdmmr3BQQiBsbvHIqBNAOzy2xldXulCpTGu6ThM2Gt8EqOvhOQErDq5yqjh\nrs9rX609nEo4KTKb+IazG1AgX4FnszQba0LzCdh4bqMiz6XPPDATA+sPhENRB6PLUqlUCGgTgIl7\nJ5q9wSFbk42pYVMNnueAiIiILF+eT2wBoE+9PkjLSsNf58w7NDHwUCB8qvkYNdz1ZTNbz8SiqEW4\n+fimbGXmRiu0GLN7DOa0nSNLAgVIDQ7+3v7w2+Nn1gaHGyk3sOTYEsxqLV8PmGcFT7St2tbs645u\njN0ItVYt6+yuQxsNxYlbJ3Do+iHZytSF/35/DKw/EBWKVZClPJVKhaB2QfDf74+UJymylKmLLE0W\npoRNwey2s2VLoMoULgO/Zn7w2+MnS3m6OpN0BpvPb8a4ZuNkK7ODSwc4mxTc+gAAIABJREFUlXDC\n0uPmfaTix6M/omqpqmj3TjuzHpeIiIjM561IbPPZ5MO3Pt9i3O5xyFRnmuWY1x5dw9LjSxHQRt5n\nFt8p9Q76e/XHpH2TZC03J+vOrIMKKvSs01PWcvvU64MnmidmXTJnStgUDPQaCKcSTrKWG9AmAD8c\n/QEJyQmylvsmmepMjN87HkHtgmR9XtAuvx1mtZ6FUTtHmW3ypZO3T+Kfi//Ar5m8iZuHgwd8XHww\n95D5Jl/6Pup7VC9THe+9856s5Q55dwhOJ51GWFyYrOW+iRACo3aOwuSWk1G6UGnZylWpVAhuH4yZ\nB2biUeYj2crNyYOMBwg4GIDg9sHsrdVRaGgoatWqherVq2Pu3Ffvn/DwcJQoUQKenp7w9PTErFnK\nDJUnIiJ63luR2AJAm6ptULd8XSyKWmSW403YOwFDGg5BpeKVZC97YouJCL0capbJl9Ky0jB+z3gE\ntw+WfcIVG5UNFvgsgN8eP6Rnp8ta9utE3YjCzss7Mb75eNnLrlKyCgY3HIxxe+Tr3crJt4e/hXt5\nd4PWRc5N73q9kc8mH1afWi172S8TQmB46HD4e/ujVKFSspcf0CYAS48vxdWHV2Uv+2VJaUkIjAjE\nt+2/lb1su/x2mPveXIzcORJqrVr28l+2/dJ2JKQk4OsGX8tedr3y9dC5RmfM3C/PIxq5mbF/Brq7\ndjd4pu23jUajwZAhQxAaGorY2FisXbsW5869Ogy+VatWiImJQUxMDCZPVma+BCIioue9NYktAAS1\nC8K8iHkmn2E0LC4MEQkRsg7he17xgsUxs/VMDAsdZvJetYCDAWhRpYVRSxXlpEWVFmjq1BTzIuaZ\npPyntEKLoTuGYk7bOShhV8IkxxjXbBwOXT9k8ueGb6TcwLeHv0Vw+2CTlG+jssGiDoswce9EJGcm\nm+QYT22M3YhHmY+MWqooJ47FHTG6yWiM3DnSJOU/b/K+yfi03qeoWbamScr/2O1jlC5UGj8d+8kk\n5T/1RP0Eo3aNQnD7YIOXKspNQJsArP53Nc4mnTVJ+U+dSTqD30//Dv/Wxs20/TaJjo6Gi4sLnJ2d\nYWtri169eiEkJOSV7ZRek5iIiOhlb1ViW6NMDQxqMAijd4022TGyNdkYvH0wvvP5zujZg3PypceX\nUGvVWHVylcmOcfH+RSw7vgxB7YJMdgwAmNduHhZHL8blB5dNdoyVMSuRzyYfPnX/1GTHKFKgCILa\nBWHojqEmnRxn7O6x+KbhN0bPHpyThpUaomP1jvDfb7qEIDUrFWN2j8HCDguNnj04J6OajELs3Vjs\nuLTDZMeIuhGFrRe3Ymor063PrFKp8P3738N/vz+S0pJMdpygyCDUKlsLHat3NNkxyhctj2mtpmHI\njiEmS5CEEPhm2zfw9/aHfRF7kxwjL0pMTIST03+Pajg6OiIx8cXGYJVKhcjISLi7u6Njx46IjY01\nd5hERESveKsSW0AaxhuVGIXdV3abpPwFRxagSskqz5a2MJV8NvnwU6efMGHvBNxLvyd7+UIIDN0x\nFOObj0fFYhVlL/95lUtUxvjm4/HNtm9M8iX3btpdTNo3CYvfX2zy9St71u4J+yL2WBi10CTl77i0\nA1E3okwynPplc9rOwe+nf8eJWydMUv7UsKnwdvaGt7O3Scp/qmD+gljUYRGG7BhikiHvaq0aX239\nCvPbz0dJu5Kyl/+82va18Wm9TzFut2lGg1x5cAULjizAog6mf2RjUINBeJT5CGvPrDVJ+b/9+xvS\ns9PxVf2vTFJ+XqXLc8heXl5ISEjAqVOnMHToUHz44Yev3W769OnP/gsPD5c5UiIiysvCw8NfqEd0\nIqycIafwz4V/hMsiF5GWlSZrLJfvXxZl5pYRF+9dlLXcnAzfMVx8uflL2cv99eSvwuMnD5GlzpK9\n7NfJUmeJekvqiT/+/UP2sn3/8hWjQkfJXu6bPL0O4h7GyVpu6pNU4bzAWey6vEvWcnOyMmal8Frq\nJbI12bKWeyzxmLAPshd30+7KWm5Oem3sJcbsHCN7ufMj5ov3Vr8ntFqt7GW/Tkpmiqj8XWXZrwOt\nVis6rOkg5h6aK2u5OTmScEQ4zHeQ/TpISk0SDvMdRPSNaIP2zwNVo8EOHz4sfHx8nv08e/ZsERgY\nmOM+zs7O4v79+y/87m1+D4mISH661CtvXY8tAHxQ4wM0rNgQk/bKN7OwVmjR/5/+mNB8AqqXqS5b\nubmZ2Xom9sXtQ+jlUNnKvJ16G2N3j8UvXX4x2TN2L7PNZ4tlHyzDqF2jZB1muf3Sdhy5cQQzWs+Q\nrczcVCtdDWOajsFXW7+StQd6athUtKjcAu2qmW/Jks/dP0cpu1JYeES+HuhsTTYG/DMA896bh7KF\ny8pWbm4WdliI1f+ulnXStUv3LyEwIhBLOi0x24y7xQoWw9IPlmLg1oFIzUqVrdxVJ1fhduptjGxs\n+ueRn2rk2Ai+dXwxbMcwWcsdsmMIetftjYaVGspa7tugQYMGuHTpEuLj45GVlYX169ejS5cuL2xz\n586dZ3/boqOjIYRA6dLyzZ5NRERkiLcysQWA79//HuvPrpdtop+lx5YiIzsDIxqPkKU8XRUrWAwr\nuq7AgH8G4GHGQ6PLE0Jg8PbB6OvRV9b1d3XRyLERvnD/QraE8GHGQwzaOgjLPlhm0uedX2d0k9F4\nkPFAtol+9sfvx9oza002YdSbqFQqLP1gKQIjAmWb6GfG/hmoUKwCPnP/TJbydGVfxB7z283HFyFf\nyLLsl1qrxuebP8fUllPhUtpFhgh118GlA1pWaYkJeybIUt715OsYt2ccVn+42myNWU/NbDMTR28e\nRcj5VycoMsTG2I04dfsUZrY2z6zLeU3+/PmxePFi+Pj4wM3NDT179oSrqyuWLl2KpUul9Yc3btyI\nunXrwsPDAyNGjMC6deZbso2IiOiNTNtpbHrGnMLf5/4W1RZWE8mZyUbFEJsUK8rOKyvOJp01qhxj\nDN42WPTZ1MfocpYfXy7q/lhXZGRnyBCV/jKzM0W9JfXEryd/NaocrVYrevzZQwzfMVymyPR3/u55\nUWZuGXHh3gWjynmY8VBU/q6y2HZxm0yR6W/58eXCfYm7yMzONKqcyOuRonxQeXHr8S2ZItPP0+ti\n2PZhRpc1+8Bs0ebXNkKj1cgQmf4epD8Qlb+rLLZe2GpUORqtRrT9ta0IOBAgU2T6OxB/QDjMdxCJ\nKYlGlZOYkigc5juIyOuRRpWTB6pGxfE9JCIiOelSr7y1PbYA8GGtD/HeO+9hwD8DDO4hzMjOQM+N\nPTG7zWy4lXOTOULdzX1vLk7cOoEVMSsMLiP2biwm7J2A9T3Wwy6/nYzR6a5g/oJY/eFqjN41Gufv\nnTe4nJUnV+Li/YsIfC9Qxuj0U7NsTfh7+8P3L1+DewjF/8/s2rlGZ5POUpubfp79ULVUVUzaZ/jw\n/UeZj/Dp35/ix04/wqGog4zR6U6lUmHZB8uw+cJmbL+03eByIhMi8d2R77Cy60qTT0j2JqUKlcKa\nj9ag35Z+uPn4psHlBBwIwBPNE5MtT6aLFlVaYFD9QeizqQ80Wo1BZai1avj+5YuvG3yNJk5NZI6Q\niIiILN1bndgCwIIOC3Dh3gUsObZE732FEBgeOhy17Wujv1d/E0SnuyIFimDjxxvht8cPJ2+f1Hv/\nx08eP0vQXcu5miBC3bk7uCOwbSC6re+Gx08e673/iVsn4LfHD390+0OxBP2pp8vyDN422KDGk4VR\nCxF7Nxbz2pl2nd/cqFQq/Nz5Z/x17i+sP7Ne7/01Wg16b+qNTtU7oZtrNxNEqLtShUrht49+Q9+Q\nvrj68Kre+99OvY3/bfgfVnZdicolKpsgQt21qNIC3zT8Br5/+SJLk6X3/nuu7sGSY0uwvsd65LfJ\nb4IIdTe55WQICMw8YNgQ4unh02GbzxaTWsg3dwIRERFZj7c+sbXLb4cNH2+A/35/7Lm6R699FxxZ\ngMiESCz9YKnZJo7JiWs5VyzqsAjd1nfD7dTbOu+n1qrRc2NPNHVsqniC/lQ/r35o5tQMX4Z8qVcP\nzq3Ht9B1XVcs/WApatvXNmGEulGpVFjZdSWiEqP0ft52z9U9mBsxFyG9QlDYtrCJItRdmcJlsLnn\nZgzZMQQxt2L02nda+DSkZaVhfvv5JopOPy2rtMSUllPQeW1npDxJ0Xm/J+on6LmxJ/p59kOnGp1M\nGKHuJrWYhBJ2JTBo6yC9Gk8u3b+EPpv6YE23NSZf0ksX+Wzy4fduv2NFzAqsPa3fEkBrT6/F6lOr\nseajNSZdE5mIiIgs11uf2AJA9TLVseHjDfD9y1fnL+wbYzci+HAwtvfejuIFi5s4Qt19UvcTfOnx\nJXzW+OBR5qNctxdCYPiO4VBr1VjccbFFJOhPfd/xe9zPuI+vt32t0xf2R5mP0GVdF3xV/yvFewWf\nV7RAUWzutRkzDszQubfzaOJR+P7li3Xd16FKySomjlB37g7uWNJpCbqs64JL9y/ptM+iqEX44/Qf\n+PPjP80+MVFOBr87GK2qtMLHGz5GRnZGrttna7LRc6O0TvHUVlPNEKFuniaEJ2+fRMDBAJ32SUxJ\nRPs17TGrzSy0qdrGxBHqrmKxitjmuw3DQ4djf/x+nfbZc3UPRuwcge29t6N80fImjpCIiIgslikf\n8jUHOU/hr9i/dJp45NeTvwr7IHtx4uYJ2Y4tJ61WK4ZtHyaa/NxEJKUmvXG7bE226BfSTzRY1kA8\nzHhoxgh1l5KZIhotbySGbR8m1Br1G7e7k3pHuC9xF8N3DDfbeqL6OnX7lCgfVF5sOLshx+0OJxwW\n5eaVEyHnQ8wUmf6WH18uKgVXEufunstxu8VRi4XzAmcR/zDeTJHpJ0udJT7Z+InwXuUtUjJT3rhd\nZnam6LWxl+j0eyfxRP3EjBHq7kbyDVHj+xpi4p6JOd4DcQ/jhNsPbiLwYM5rkyppz5U9ouy8srlO\njLXt4jZRdl5ZsT9+v6zHzwNVo+L4HhIRkZx0qVesvuaRu/LcdnGbKDevnPjlxC+vfDlMz0oXk/ZO\nEs4LnBWdAVkXGq1GTNgzQTh96ySibkS98vq1R9dEx987iva/tRePnzxWIELdPUh/ILxXeYs2v7YR\nN1NuvvJ6WFyYcFnkIqbum2qxSe1TMbdiRMXgimL0ztGvzDyt0WrEoiOLRJm5ZRSdAVlXq2JWCfsg\ne/Hbqd9eed+TM5PFF5u/ENUWVhNXH1xVKELdqDVqMWDLAOH5k6c4fvP4K69fun9JeC31Eh+t+0ik\nZ6UrEKHuklKTRMNlDUWfTX1e26i18/JOUT6ovAiODFYgOv1EXo8UDvMdRHBksMhSZ73wmlqjFkER\nQaLC/ApGz4D8OkzKjMf3kIiI5KRLvaL6/w2tlkqlkmXN0+fF3o1F7029kaXJwkCvgShesDgSHyfi\nx6M/omGlhlj6wVLFZnXV1+bzmzHgnwGoX6E+etbuCbVWjdNJp/H76d/xTYNvMKXVFBTIV0DpMHOl\n0Wow68AsLIpehA9rfoj21drjTtod7L+2H8duHsO37b9Fd7fuSoepk3vp9zBo6yCcunMK3V27o0HF\nBjh/7zy2XNiCgvkLYnnn5ahVtpbSYerk2M1j6LelH0oXKo33Xd5H1ZJVEZkQiY3nNuJ9l/fxrc+3\nKFqgqNJh5koIgRUxKzBp3yS0r9YejR0bo6RdSWy7tA2hl0Ph7+2PwQ0HW9RQ/TdJzUrFxL0T8cfp\nP9DPsx9qlq0JtVaNNf+uwdWHV/F7t9/RyrmV0mHq5MqDKxjwzwDEP4rH1w2+Rrki5ZCUloQlx5bA\nqbgT1nRbY5IJvExRr7xt+B4SEZGcdKlXmNi+gRAC4fHhWPPvGmiEBsULFseXHl/Cs4Kn7McytfTs\ndPx97m9subgFRW2LwqmEEwbWH2gRE8bo63rydWw6twnh8eGoVKwSatvXxufun6NIgSJKh6YXIQQi\nEyKx88pOnLh1Am7l3NDMqRk61+ys2PIxhsrWZGPTuU04cuMILj+8jMaVGuP96u/Dq4KX0qHp7WHG\nQ/x66lecu3sOd9Pvon219vio1kdW+ezm5QeXsTJmJW6m3kSWJgs9XHugU41OVtGQ9bJD1w/hj9N/\nIC07DXb57NDXsy8aOTYy2fGYlBmP7yEREcmJiS0REZGeWK8Yj+8hERHJSZd6xbq6hoiIiIiIiIhe\nwsSWiIiIiIiIrBoTWyIiIiIiIrJqTGyJiIiIiIjIqjGxJSIiIiIiIqvGxJaIiIiIiIisGhNbIiIi\nIiIismpMbImIiIiIiMiqMbElIiIiIiIiq8bEloiIiIiIiKwaE1siIiIiIiKyakxsiYiIiIiIyKox\nsc1FdjagVgNCKB2J8TIyAI1G6SjkkZICaLVKR2E8IYBHj/LG9aXVAsnJeeNcNBogNVXpKOShVgOZ\nmUpHYTwh/vt7TERERPQyJravERcHTJwIvPsuUKQIYGcHFCwItG4NzJ8P3LundIS6EQKIjAT69QNq\n1ABKlQIKFABKlgR69ADWrgWyspSOUjdZWcCffwJdugAVKgAODtJnUrky8M03wMGD1pNQ3b8PLFgA\nNG0qfRZOTtJ1Vq8e4O8PXL2qdIS6i40F/PwAV1egcGGgUiWgTBnA2xtYtgx4/FjpCHWj1QK7dgFf\nfildXwULAuXKAVWqAB9/DGzdaj2NQmlpwIoVwAcfAMWKSedSsiRQp450r5w8qXSEuktMBGbNku6V\n/PmBQoWAokWBFi2AmTOBW7eUjpCIiIgsBRPb51y8CPTqBTRoICVSQUHSF3O1Gnj4EBg9Gjh7VkoS\nR4wAbt9WOuI327ULaNQI+OwzoHZt4K+/pC+82dnAhQtAx47AL78ALi7ADz8AT54oHfHrqdXATz8B\nVasCS5ZIn09UlHQuaWnAnj1SYjhgANCkCbBzp+UmuA8fAmPHSu/58eNSEhsXJ11jSUlSInj/vvS5\nffEFcP260hG/2cWLQLduwHvvST///jvw4IF0LufPA2PGSJ9FlSrAjBnSZ2WJtFpg40bA3R0YP176\nf2Sk1MOZlgbs2wd06CCdQ/Xq0nla6kiB1FQgMBB45x0gJATw9QXi46V76PFj4NdfpYaHDz4A2rSR\nztNSXbsG9O8P1K0rJa/+/tLnoVZL19nUqdLv3dyk7Sz5XiEiIiIzEVZOjlO4d0+IYcOEKFNGiDlz\nhEhJyXn7GzeEGD5ciNKlhZg+XYjHj40OQTZnzgjx/vtCuLgIsWGDEGp1zttHRQnRsaMQ77wjxMaN\nQmi15okzN1qtEFu3CuHqKkSbNkIcP57z9mq1EOvWCVGzprR9TIx54tTFkydCLFggRLlyQgwYIMTN\nmzlvn5wsxOTJ0vU1ZowQDx6YJ05dJCUJMWTIf/dKenrO21+9KsQnnwhRsaIQy5YJkZ1tnjh1ERkp\nxLvvCuHlJV1ruV37+/cL0bChEPXrCxEebp4YdaHRCLFqlRCVKgnxv/9JfwNykpUlxMqVQjg5CdGt\nmxAXLpglTJ2kpAgxcaJ07U+eLP1tzsm9e0JMmiRtP26cEA8fyhNHHqgaFcf3kIiI5KRLvWL1NY8x\nlWdmphDffSdE2bJCfP21EHfu6Lf/1atC+PoK4eAgxJIl0hdGpdy6JcRXX0nJ03ffScmUPvbsEcLd\nXYjmzaVkV0kxMUK0bStErVpC/POPfsl2VpYQP/wgRPnyQnzxhdQIoRStVmosqFZNamw4fVq//W/e\nFGLgQOn6DAoSIiPDNHHqIj1diNmzpYR26FApwdVHdLQQrVoJ4eam/2cqt/h4IXr1khLBX3+VEkNd\naTRCrF0rhLOzEF26CBEba7o4dXHwoBANGgjRqJGUqOsjPV2IwEDp+ho8WP+/f3JSq4X4+WchKlQQ\n4rPP9L9vExOF6N9f+vsXHCz9bTcGkzLj8T0kIiI55YnEdseOHaJmzZrCxcVFBAYGvvK6IZWnWi3E\n6tXSl9P338+9hyM3x45JvYQ1awqxaZN5v7Q/37s3apQQ9+8bXpZaLcQvv0i9a76+UgJgTvHxUjJa\nvrwQP/5oXO/eo0dC+PlJ78u0aUKkpsoWpk7CwoRo2lRqLNi1y7iyYmOlJMrZWYjff9cvETNWVpbU\n0/q0d+/iRcPL0mqlpNbNTUpyzd2AkpQk9YCXLi3E1KnGXRMZGVJjQ9myUi98YqJ8ceri1CkhunaV\nPhdjr4m7d4UYMUJqtJg507z3ilYr/c10c5Ma1aKjjSvvzBkhPvjA+HuFSZnx+B4SEZGcrD6xVavV\nolq1aiIuLk5kZWUJd3d3EftSF4k+ladWK0RIiBB16khJx/798sWq1QqxY4cQ9epJZUdEyFf266Sn\nSz2z9vZCfP65vEno48fSF//SpaUh16b+0n75shB9+0rHmzhRStblEhf331DYRYtyHzprrLAwKWmr\nVk0aHprbUHB9hIf/NxRWl6GzxsjKkho5nJ2FeO89ea/n7Gypd07XobPGun//v+GtX38tREKCfGU/\neCANgS1dWogJE3IfOmus8+eF6NlTavz57jt5e/EvX5bKrlhRiOXLTTsCRauVGnwaNhTCw0OIbdvk\nvZ6f3iteXtJoFH0xKTMe30MiIpKT1Se2kZGRwsfH59nPc+bMEXPmzHlhG11OMj1diBUrhKhbV0o8\nt2wxXVKgVksJjZOTNJx2yxZ5k5ubN4Xw95e+2Hbtqv/wVn2PNXKkEKVKSYmn3M+tnjghDTssU0ZK\npI3pbc7N0aPS++XgID0XndtzrvrIzpYaTFq2lJ5tXrXKdM+SajRC/Pmn1BPs7i5d12lp8pWfnCzE\n4sXSM9dt2ghx4IB8Zb8sLU16Tvfptbxnj7y90VevSklnmTLSMFVTjkC4fl06RqlS0lDtc+fkK1ur\nlRoWevaUeohnzzbtc/1RUdJn7+QkxPz58t6XWVnSUO7GjYWoUUOI9etNNwJBq5XKr1ZNOt769bo/\nosGkzHh8D4mISE5Wn9hu2LBB9O/f/9nPv/32mxgyZMgL27zpJDMzhdi5UxomWKqUNOR4507zDRN+\n8kSI336Teg0qVRJi7FghjhwxLMm9d08qq1MnIUqWlM5Jzi/OuUlKEiIgQAhHR6m3MDhYShoMcfmy\n9GXZy0uIypWlch89kjfenJw+LT2LXLKkNGRxzRrDJmfSaIQ4fFj6XCtVkr44//ab+SZH0mqlXq6O\nHaXEbcAAqQdM32erhZAafrZsEeLTT6X35eOP5R3NoMvxlyyRGp2qVRNiyhSpEcWQezUpSeoNfu89\n6X0ZNUqIK1fkj/lNEhOFGD9eStabN5caCQzpIdZqpSHoAQHSMF0XF2kCMnPeK8eOCdG7txAlSkjX\nxJ9/GjaaIitLup6GDJGegW3VSoi//5a3wS8narU03LlVK+n4w4ZJ8eR0rzIpMx7fQyIikpMu9Yrq\n/ze0SH/99RdCQ0OxfPlyAMCaNWsQFRWF77///tk2KpUKQ4dOQ1oa8OgRUKiQN5KSvBEVJa3b2LUr\n0Lu3tMyFUs6elZYJ2bIFuHMHaN4cqF9fWqqicmVp3U87O2kZkZQUaRmhK1eAU6eAw4elpVXatAE+\n+gjo3l1ax1EJGg0QHg788QewbZu0RmazZoCnp7QEUqVK0nqZBQpIyyU9eiStQ3nhAhATA0RESEuS\ndOkiraPbti2QL58y55KSIn0e69YB+/dL67A2biytJVutmrSWabFiUnwZGdLaxdevA+fOAceOSevm\nli8vLXnTs6e0LIlSrl2T1vjduFFaV7ZJE6BhQ+n6d3aW1mMtUkRaBik1Fbh7V1or98wZ4MgRaekh\nLy/gf/+TPhcHB2XOQwjg6FHpXDZtAtLTgZYtpdhcXQFHR6BsWen60miA5GRpyZfLl4F//5Wur2vX\npCWIevUCOnWS1j1VQnY2sH27tMzWtm2Avb1037u7S/dKxYrSvZIvn3SvPHgg3Svnz0v3yoEDgEoF\ndO4s/f1q0kT6WQkPHwLr1wObN0tLBNWpI8VTp450r5QvL90rKpV0r9y9K90rZ85I11ZEhLQEUdeu\nQJ8+0r+VcuUKsGaNdO/Hxf13r2i14bh1KxyFCknXV3CwPyy4arQKKpWK7yEREclGl3rFohPbI0eO\nYPr06QgNDQUAzJkzBzY2NvDz83u2jUqlwjvvCJQpI611WrOmtA5o48ZSwmhpEhKkZPXYMeDSJemL\n+IMH0rqZKhVQooT0JdjFRUp8GzeW1tW1s1M68hcJAZw+La0pGxMjJUo3bkjJRnY2YGsLlColJUk1\na0pfgps3lxIUGwtbPfnJEynBO3ZMSpDi46WEKTVVamwoWFBKqBwdpfg9PIAWLZRtLHmThw+lpDsm\nRkosEhKkNXIzMqTXixSRrq/KlaVk3MtL+lyKFVM27pcJId0bBw5In8m5c8DNm9I6v1lZUkJYvLjU\nAFG1qpQwNmwo/Zc/v9LRv0itlu6ViAipkeviRamB6+FDKUG3tQVKl5aup+rVpYaixo2l+0apZPZN\nUlOlxocjR6TP5MoVqdEnOVmK1c5OakhxcgJq1ZL+djVpolxjSU5u35bOIzpa+kzi4qTPJC0NSEpi\nUmYsJrZERCQnq09s1Wo1atasib1796JixYp49913sXbtWri6uj7bhpUnERHJifWK8fgeEhGRnHSp\nVyysb+NF+fPnx+LFi+Hj4wONRoN+/fq9kNQSERERERERWXSPrS7YKkxERHJivWI8vodERCQnXeoV\nC3vakYiIiIiIiEg/TGyJiIiIiIjIqjGxJSIiIiIiIqvGxJaIiIiIiIisGhNbIiIiIiIismpMbImI\niIiIiMiqMbElIiIiIiIiq8bEloiIiIiIiKwaE1siIiIiIiKyakxsiYiIiIiIyKoxsSUiIiIAQGho\nKGrVqoXq1atj7ty5r91m2LBhqF69Otzd3RETE2PmCImIiF6PiS0RERFBo9FgyJAhCA0NRWxsLNau\nXYtz5869sM327dtx+fJlXLp0CcuWLcPXX3+tULREREQvYmJLRESAAMgkAAAKuUlEQVREiI6OhouL\nC5ydnWFra4tevXohJCTkhW22bNmCzz//HADQqFEjPHr0CHfu3FEiXCIiohcwsSUiIiIkJibCycnp\n2c+Ojo5ITEzMdZsbN26YLUYiIqI3ya90AERERKQ8lUql03ZCCJ32U6mmP/eT9///R0REpIvw//9P\nd0xsiYiICJUqVUJCQsKznxMSEuDo6JjjNjdu3EClSpVeW54Q000SJxERvQ288XyDqErln+seHIpM\nREREaNCgAS5duoT4+HhkZWVh/fr16NKlywvbdOnSBatXrwYAHDlyBCVLlkT58uWVCJeIiOgF7LEl\nIiIi5M+fH4sXL4aPjw80Gg369esHV1dXLF26FADw1VdfoWPHjti+fTtcXFxQpEgRrFy5UuGoiYiI\nJCrx8sMyVkalUr3yvA8REZGhWK8Yj+8hERHJSZd6hUORiYiIiIiIyKoxsSUiIiIiIiKrxsTWgoSH\nhysdgizyynkAPBdLlVfOJa+cB5C3zoXoeXnl2s4r5wHwXCxVXjmXvHIeQN46F10wsbUgeeXiyyvn\nAfBcLFVeOZe8ch5A3joXoufllWs7r5wHwHOxVHnlXPLKeQB561x0wcSWiIiIiIiIrBoTWyIiIiIi\nIrJqVr/cj4eHB06dOqV0GERElEe4u7vj5MmTSodh1Vg3ExGRnHSpm60+sSUiIiIiIqK3G4ciExER\nERERkVVjYktERERERERWjYktERERERERWbU8ldgGBwfDxsYGDx48UDoUg0yZMgXu7u7w8PBA27Zt\nkZCQoHRIBhs7dixcXV3h7u6Obt26ITk5WemQDLZhwwbUrl0b+fLlw4kTJ5QOR2+hoaGoVasWqlev\njrlz5yodjlH69u2L8uXLo27dukqHYpSEhAS0bt0atWvXRp06dbBo0SKlQzJYZmYmGjVqBA8PD7i5\nuWHChAlKh2QUjUYDT09PdO7cWelQ8gzWzZaDdbPlYN1seVg3Wy6d62aRR1y/fl34+PgIZ2dncf/+\nfaXDMUhKSsqzfy9atEj069dPwWiMs2vXLqHRaIQQQvj5+Qk/Pz+FIzLcuXPnxIULF4S3t7c4fvy4\n0uHoRa1Wi2rVqom4uDiRlZUl3N3dRWxsrNJhGezAgQPixIkTok6dOkqHYpRbt26JmJgYIYQQjx8/\nFjVq1LDqzyUtLU0IIUR2drZo1KiROHjwoMIRGS44OFj4+vqKzp07Kx1KnsC62bKwbrYMrJstE+tm\ny6Vr3ZxnemxHjRqFefPmKR2GUYoVK/bs36mpqShbtqyC0RinX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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "ng_vec = np.linspace(-1, 1, 200)\n", "\n", "energies = array([hamiltonian(Ec, Ej, N, ng).eigenenergies() for ng in ng_vec])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_energies(ng_vec, energies, ymax=(7.5, 3.0));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+zDJlZKchtenSRT/tmklt/8OHA05OstOQ2gwYAERGAoGBspOQVj14ADx8CDg7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\nrkJggg==\n", "text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intermediate regime" ] }, { "cell_type": "code", "collapsed": false, "input": [ "ng_vec = np.linspace(-4, 4, 200)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ "Ec = 1.0\n", "Ej = 5.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "energies = array([hamiltonian(Ec, Ej, N, ng).eigenenergies() for ng in ng_vec])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_energies(ng_vec, energies, ymax=(50, 3));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Xl4BpfHkp79YUL86/lhaGEg4scgFt4Z9/myjUT4yN4ShHFrk+NjaIdHQ0yYuj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WY/Xx1Vh6cClSSlMwtutYTOkxBV09u5oo+ssVVxXj28PfYvGBxahtrMXEmIkY130cQtxDrvvc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\n", "text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "Ec = 1.0\n", "Ej = 10.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 }, { "cell_type": "code", "collapsed": false, "input": [ "energies = array([hamiltonian(Ec, Ej, N, ng).eigenenergies() for ng in ng_vec])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 30 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_energies(ng_vec, energies, ymax=(50, 3));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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6e3sZtIw6Z8+exYIFC7Bw4UK37xHFLX9R+fpiY1AQGnhaC8EVgiBm9BACQHZo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WSwoBVzbDYTOXw4hpXzGwx/kNOnm7CglWfo9XvJ6dPNWJF1+/Zocvv2p6zI8uz8n5A7d8Z6Lcfp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\n45J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"text": [ "" ] } ], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Transmon regime" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Ec = 1.0\n", "Ej = 50.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "energies = array([hamiltonian(Ec, Ej, N, ng).eigenenergies() for ng in ng_vec])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_energies(ng_vec, energies, ymax=(50, 3));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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JeVLR26iYTHoUFm5CSclr8PNLRVjYSvj7z+i2V99kakBV1ScoLt6K1tZixMQ8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\nEZBiBhfLCxcu6Mknn2TaEwAAhlCbgeSguQVSyFtvvaWOjg5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"text": [ "" ] } ], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the energy-level splitting is essentially independent of the gate bias $n_g$, at least for the lowest few states. This device insensitive to charge noise. But at the same time the two lowest energy states are no longer well separated from higher states (it has become more like an harmonic oscillator). But some anharmonicity still remains, and it can still be used as a qubit if the leakage of occupation probability of the higher states can be kept under control." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Focus on the two lowest energy states\n", "\n", "Let's go back to the charge regime, and look at the lowest few energy levels again:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 10\n", "Ec = 1.0\n", "Ej = 1.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 35 }, { "cell_type": "code", "collapsed": false, "input": [ "ng_vec = np.linspace(-1, 1, 200)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 37 }, { "cell_type": "code", "collapsed": false, "input": [ "energies = array([hamiltonian(Ec, Ej, N, ng).eigenenergies() for ng in ng_vec])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 38 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_energies(ng_vec, energies, ymax=(10, 3));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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JkiXS8fD226l/3dkZ+OYbuXH0779qshFRamxn1q4yZYCbN2UVntQ7exaoVEl1CkpLytFE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\n", "text": [ "" ] } ], "prompt_number": 39 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that around $n_g = 0.5$ we have two lowest energy levels that are well separated for the higher energy levels:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "ng_vec = np.linspace(0.25, 0.75, 200)\n", "energies = array([hamiltonian(Ec, Ej, N, ng).eigenenergies() for ng in ng_vec])\n", "plot_energies(ng_vec, energies, ymax=(10, 1.1));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Hdl5sk1csjDYEAHgTBa+Vb+PbeW4vvSSdPGnMzZ08WQoONjsyALj4Nm40fv/9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\nZISnIACA6+Tm5io3N9fpMgAAQDeL+MCbmJio4uL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"text": [ "" ] } ], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's tune the system to $n_g = 0.5$ and look at the Hamiltonian and its eigenstates in detail" ] }, { "cell_type": "code", "collapsed": false, "input": [ "H = hamiltonian(Ec, Ej, N, 0.5)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [ "H" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "Quantum object: dims = [[21], [21]], shape = [21, 21], type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}441.0 & -0.500 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-0.500 & 361.0 & -0.500 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & -0.500 & 289.0 & -0.500 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & -0.500 & 225.0 & -0.500 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & -0.500 & 169.0 & \\cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 121.0 & -0.500 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & -0.500 & 169.0 & -0.500 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & -0.500 & 225.0 & -0.500 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & -0.500 & 289.0 & -0.500\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \\cdots & 0.0 & 0.0 & 0.0 & -0.500 & 361.0\\\\\\end{array}\\right)\\end{equation*}" ], "metadata": {}, "output_type": "pyout", "prompt_number": 43, "text": [ "Quantum object: dims = [[21], [21]], shape = [21, 21], type = oper, isherm = True\n", "Qobj data =\n", "[[ 441. -0.5 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ -0.5 361. -0.5 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. -0.5 289. -0.5 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. -0.5 225. -0.5 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. -0.5 169. -0.5 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. -0.5 121. -0.5 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. -0.5 81. -0.5 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. -0.5 49. -0.5 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. -0.5 25. -0.5\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. -0.5 9.\n", " -0.5 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. -0.5\n", " 1. -0.5 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " -0.5 1. -0.5 0. 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. -0.5 9. -0.5 0. 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. -0.5 25. -0.5 0. 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. -0.5 49. -0.5 0. 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. -0.5 81. -0.5 0. 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. -0.5 121. -0.5 0. 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. -0.5 169. -0.5 0.\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. -0.5 225. -0.5\n", " 0. ]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. -0.5 289.\n", " -0.5]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", " 0. 0. 0. 0. 0. 0. 0. 0. 0. -0.5\n", " 361. ]]" ] } ], "prompt_number": 43 }, { "cell_type": "code", "collapsed": false, "input": [ "evals, ekets = H.eigenstates()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 44 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The eigenenergies are sorted:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "evals" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 45, "text": [ "array([ 0.47065435, 1.46676684, 9.01371984, 9.01760693,\n", " 25.00520901, 25.00520943, 49.00260427, 49.00260427,\n", " 81.00156252, 81.00156252, 121.00104167, 121.00104167,\n", " 169.00074405, 169.00074405, 225.00055804, 225.00055804,\n", " 289.00043403, 289.00043411, 361.00034728, 361.00347214,\n", " 441.00312494])" ] } ], "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Only two states have a significant weight in the two lowest eigenstates:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "ekets[0].full() > 0.1" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 46, "text": [ "array([[False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [ True],\n", " [ True],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False]], dtype=bool)" ] } ], "prompt_number": 46 }, { "cell_type": "code", "collapsed": false, "input": [ "abs(ekets[1].full()) > 0.1" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 47, "text": [ "array([[False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [ True],\n", " [ True],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False],\n", " [False]], dtype=bool)" ] } ], "prompt_number": 47 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use these two isolated eigenstates to define a qubit basis:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "psi_g = ekets[0] # basis(2, 0)\n", "psi_e = ekets[1] # basis(2, 1)\n", "\n", "#psi_g = basis(2, 0)\n", "#psi_e = basis(2, 1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 48 }, { "cell_type": "markdown", "metadata": {}, "source": [ "and corresponding Pauli matrices:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sx = psi_g * psi_e.dag() + psi_e * psi_g.dag()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 49 }, { "cell_type": "code", "collapsed": false, "input": [ "sz = psi_g * psi_g.dag() - psi_e * psi_e.dag()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 50 }, { "cell_type": "markdown", "metadata": {}, "source": [ "and an effective qubit Hamiltonian" ] }, { "cell_type": "code", "collapsed": false, "input": [ "evals[1]-evals[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 51, "text": [ "0.99611248758221715" ] } ], "prompt_number": 51 }, { "cell_type": "code", "collapsed": false, "input": [ "H0 = 0.5 * (evals[1]-evals[0]) * sz\n", "\n", "A = 0.25 # some driving amplitude\n", "Hd = 0.5 * A * sx # obtained by driving ng(t), \n", " #but now H0 is in the eigenbasis so the drive becomes a sigma_x" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 52 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Doing this we have a bunch of extra energy levels in the system that aren't involved in the dynamics, but so far they are still in the Hamiltonian." ] }, { "cell_type": "code", "collapsed": false, "input": [ "qubit_evals = H0.eigenenergies()\n", "\n", "qubit_evals - qubit_evals[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 53, "text": [ "array([ 0. , 0.49805624, 0.49805624, 0.49805624, 0.49805624,\n", " 0.49805624, 0.49805624, 0.49805624, 0.49805624, 0.49805624,\n", " 0.49805624, 0.49805624, 0.49805624, 0.49805624, 0.49805624,\n", " 0.49805624, 0.49805624, 0.49805624, 0.49805624, 0.49805624,\n", " 0.99611249])" ] } ], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "energy_level_diagram([H0, Hd], figsize=(4,2));" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python3.4/dist-packages/qutip/visualization.py:571: UserWarning: Deprecated: Use plot_energy_levels\n", " warnings.warn(\"Deprecated: Use plot_energy_levels\")\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAAB+CAYAAADIv5ZiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8x97Ur3xTWtNTgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Imagine that we also can drive a $\\sigma_x$ type of interaction (e.g., external field):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Heff = [H0, [Hd, 'sin(wd*t)']]\n", "\n", "args = {'wd': (evals[1]-evals[0])}" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 55 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the Rabi oscillation dynamics of the qubit when initially placed in the ground state:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "psi0 = psi_g" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 56 }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = np.linspace(0.0, 100.0, 500)\n", "result = mesolve(Heff, psi0, tlist, [], [ket2dm(psi_e)], args=args)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 58 }, { "cell_type": "code", "collapsed": false, "input": [ "visualize_dynamics(result, r'$\\rho_{ee}$');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ataBiRUhJsZ1EpHC8Xrj/fujbVyVcAqdYMWjdGmbMsJ1E/kxFXArkhRfgmWc0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\nHjRrZjuNiPts2mSmqOzaZbb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"text": [ "" ] } ], "prompt_number": 59 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that only the two selected states are included in the dynamics, and very little leakage to other levels occur.\n", "\n", "Instead of keeping all the inactive quantum states in the calculation we can eliminate them using Qobj.extract_state, so that we obtain a true two-level system." ] }, { "cell_type": "code", "collapsed": false, "input": [ "where(abs(ekets[0].full().flatten()) > 0.1)[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 60, "text": [ "array([10, 11])" ] } ], "prompt_number": 60 }, { "cell_type": "code", "collapsed": false, "input": [ "where(abs(ekets[1].full().flatten()) > 0.1)[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 61, "text": [ "array([10, 11])" ] } ], "prompt_number": 61 }, { "cell_type": "code", "collapsed": false, "input": [ "keep_states = where(abs(ekets[1].full().flatten()) > 0.1)[0]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 62 }, { "cell_type": "code", "collapsed": false, "input": [ "H0 = H0.extract_states(keep_states)\n", "\n", "H0" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}2.406\\times10^{-04} & 0.496\\\\0.496 & 2.406\\times10^{-04}\\\\\\end{array}\\right)\\end{equation*}" ], "metadata": {}, "output_type": "pyout", "prompt_number": 63, "text": [ "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n", "Qobj data =\n", "[[ 2.40574436e-04 4.96105212e-01]\n", " [ 4.96105212e-01 2.40574436e-04]]" ] } ], "prompt_number": 63 }, { "cell_type": "code", "collapsed": false, "input": [ "Hd = Hd.extract_states(keep_states)\n", "\n", "Hd" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.125 & 0.0\\\\0.0 & -0.125\\\\\\end{array}\\right)\\end{equation*}" ], "metadata": {}, "output_type": "pyout", "prompt_number": 64, "text": [ "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n", "Qobj data =\n", "[[ 0.12451032 0. ]\n", " [ 0. -0.12451032]]" ] } ], "prompt_number": 64 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And if we look at the energy level diagram now we see that we only have two states in the system, as desired." ] }, { "cell_type": "code", "collapsed": false, "input": [ "energy_level_diagram([H0, Hd], figsize=(4,2));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 65 }, { "cell_type": "code", "collapsed": false, "input": [ "Heff = [H0, [Hd, 'sin(wd*t)']]\n", "\n", "args = {'wd': (evals[1]-evals[0])}" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 66 }, { "cell_type": "code", "collapsed": false, "input": [ "psi0 = psi0.extract_states(keep_states)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 67 }, { "cell_type": "code", "collapsed": false, "input": [ "psi_e = psi_e.extract_states(keep_states)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 68 }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = np.linspace(0.0, 100.0, 500)\n", "result = mesolve(Heff, psi0, tlist, [], [ket2dm(psi_e)], args=args)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 69 }, { "cell_type": "code", "collapsed": false, "input": [ "visualize_dynamics(result, r'$\\rho_{ee}$');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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cjB8v9erlOgUiSUqKHZSWnu46CSQKcRTS3LnSb79xHDOCq2xZ6brrpGefdZ0E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\nHoJeecV6q8JlkwMQam67TXr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"text": [ "" ] } ], "prompt_number": 70 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software versions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip.ipynbtools import version_table; version_table()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
IPython2.0.0
Cython0.20.1post0
OSposix [linux]
Python3.4.1 (default, Jun 9 2014, 17:34:49) \n", "[GCC 4.8.3]
SciPy0.13.3
Numpy1.8.1
matplotlib1.3.1
QuTiP3.0.0.dev-5a88aa8
Thu Jun 26 14:05:41 2014 JST
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 71, "text": [ "" ] } ], "prompt_number": 71 } ], "metadata": {} } ] }