RX_Gates.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## There are three sections here. See instructions below.\n",
    "Section 1 should be run using qiskit-terra master. This will cause standard compilation of RX(theta) into pulses.\n",
    "\n",
    "Section 2 should be run using Pranav's qiskit-terra fork, which will compile to a direct RX(theta) rotation. So after running Section 1, switch to the qiskit-terra fork, and restart the kernel.\n",
    "\n",
    "Section 3 is data analysis, which can be run with either qiskit-terra version. Easiest to keep running same fork, no need to restart kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "qubit_num = 0  # or change to a qubit that has bad coherence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 1: Standard Compilation (run with qiskit-terra master)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import time\n",
    "from collections import namedtuple\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit as q\n",
    "import qiskit.tools.jupyter\n",
    "from qiskit.pulse import pulse_lib as _  # only want to call pulse_lib as q.pulse.pulse_lib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pulse_compiler_helper_fns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AccountProvider for IBMQ(hub='ibm-q', group='open', project='main')>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.IBMQ.load_account() # Load account from disk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/alijavadi/Desktop/ajavadia-terra/qiskit/pulse/channels/pulse_channel_spec.py:87: DeprecationWarning: The PulseChannelSpec is deprecated. Use backend.configuration() instead. The supported methods require some migrations; check out the release notes for the complete details.\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "provider = q.IBMQ.get_provider(group='qiskit-terra', project='pulse-testing')\n",
    "backend = provider.get_backend('alt_almaden')\n",
    "config = backend.configuration()\n",
    "system = q.pulse.PulseChannelSpec.from_backend(backend)\n",
    "cmd_def = q.pulse.CmdDef.from_defaults(backend.defaults().cmd_def, backend.defaults().pulse_library)\n",
    "measure = cmd_def.get('measure', qubits=backend.configuration().meas_map[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.17453293  0.34906585  0.52359878  0.6981317   0.87266463  1.04719755\n",
      "  1.22173048  1.3962634   1.57079633  1.74532925  1.91986218  2.0943951\n",
      "  2.26892803  2.44346095  2.61799388  2.7925268   2.96705973]\n"
     ]
    }
   ],
   "source": [
    "num_angles = 17  # will exclude endpoints of 0 and 2pi\n",
    "angles = np.linspace(0, np.pi, num_angles+1, endpoint=False)[1:]  # get rid of endpoints\n",
    "print(angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "schedules = []\n",
    "for angle in angles:\n",
    "    schedule = cmd_def.get('u3', [qubit_num], P0=angle, P1=3*np.pi/2, P2=np.pi/2)  # RX(angle) = U3(angle, 3pi/2, pi/2)\n",
    "    schedule |= measure << schedule.duration\n",
    "    schedules.append(schedule)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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kSZO0ePHi/O133XWXJk6cqLq6Op133nl67733itFsAHAlx4WplpaWgoWpoUOH6vbbb9cFF1xwxH1f//rXtWDBAq1Zs0aPPfaYamtrJUm33HKLrrzySj333HOqqqrSf/3XfxWkLaVyxx13aObMmXrjjTc0c+ZM3XHHHaVu0nFZtmyZHnnkES1fvvyQ21OpVIla5GzDhw/XsmXL9PnPf77Tx+zdu1ff/OY39cQTT+jPf/6zdu/erWeffVaSdNppp+nFF1/Un/70J1144YWHBC0AwKEcF6ZuvfVWbdu2Teeee65uvvlmW8caPny4Tj75ZBnGoWUh3nnnHaXTaZ155pmSpLKyMoVCIVmWpfXr1+u8886TJF188cV65plnbLWhOx588EHV1dWpvr5eV155Zf72F198UWeddZbGjRvXaS/DrbfeqtNOO00NDQ1655138revWrVK8+fPlyTNnz9fjz/+eM++iB6wcOFCbd26VfPmzdPSpUu1ZMkSXXvttZo7d66uuuoqbdu2TbNmzdLUqVM1depUvfzyy5Kk559/XrNnz9Zll12mU089Vd/+9rf129/+VmeeeabOOOMMvfvuu5KkDz/8UJdeeqmmT5+u6dOn66WXXpIktbW1acGCBTrjjDNUV1enRx99NN+m7373u6qvr9eMGTO0a9cuSdITTzyhT3/605oyZYoaGhryty9ZskTXXHON5syZo3Hjxunuu+/OH+cHP/iBTj/9dDU2NuqKK67I9yi+++67Ov/88zVt2jTNmjVLb7/9drfes5EjR2r8+PEyzc7/iW/dulVjxozJ97SdddZZ+dc4Y8YMhcNhSVJdXZ3ef//9bp0fAPoSb6kbcLgbb7xRmzdv1urVqzu8f968eWprazvi9sWLF2v69OldOse7776ryspKXXPNNdq+fbumT5+uG2+8Uc3NzaqsrJTXm31bhgwZkv9C7GlvvvmmbrvtNq1Zs0a1tbXat29f/r6dO3dqzZo1evvttzVv3jxddNFFhzx348aNevjhh/XSSy8plUpp2rRpmjBhgiRp9+7dGjJkSP71fPjhh0V5PYW0dOlS/eEPf9Dq1atVW1urJUuWaNOmTVqzZo1CoZAikYhWrVqlYDCoLVu26IorrtAf//hHSdIbb7yhjRs3ql+/fho3bpy+9KUv6YUXXtDPfvYz/fznP9cPf/hDfeMb39DChQs1bdo0bd++Xeeff742bdqkW265RVVVVXrllVckKT9E2t7errq6Ot10001avHixli9frkWLFmnatGlat26dDMPQ8uXLdeedd+qWW26RJG3evFlPPfWUWltbdfrpp+vqq6/W66+/rkcffbTDz+26667TXXfdpdGjR+tPf/qTvvrVr2r16tVatWqVNm7cqO985zu239eTTjpJb7/9trZt26Zhw4bp8ccf73BY+1e/+pVmz55t+3wA0Fs5Lkwdy4oVK2wfI51O65VXXtETTzyhoUOH6rrrrtPDDz+sWbNmHfHYw3u1esq6det04YUX5ocb+/Xrl79v7ty5Mk1TJ598snbv3n3Ec9evX6+5c+fmexIaGhqK0uZSamhoUCgUkiQlk0l9/etf1+uvvy7TNLVly5b84yZNmpQPkyeeeGL+Mz7llFO0bt06SdKzzz6rt956K/+clpYWtba2au3atbr//vvzt9fU1EiS/H5/vvdywoQJWrNmjaTsPLzLL79cO3fuVCKR0MiRI/PP/cxnPqNAIKBAIKABAwZo165deumll9TY2Jh/HbljtrW16eWXX873KErKh5zGxkY1Njbafv9yr+cnP/mJvvjFL8o0TU2ZMkVbt2495DG/+c1vtHHjxqL20AKA27guTBWiZ2rw4MEaN26cRowYIUmaPXu2Nm3apEsuuUQtLS1KpVLyer3asWOHBg4cWND2d8ayrE6DWyAQOORxHensuQMHDtSOHTs0ZMgQ7dixwxWTp7uirKws//9Lly7VwIEDtWHDBmUymXzokbLBJ8c0zfyfTdPMz7fKZDJ67rnn8qEmp7PPxOfz5W/3eDxKp9OSpOuvv14LFy5UY2Ojnn/+eX3/+9/PP+fgzzD3nM4+y0wmo6qqKm3YsKFrb4ayw45PPfWUJHXreQ0NDfnwfe+998rj+WjbqbVr1+q2227T008/fUj7AQCHctycqfLycrW3t3d6/4oVK7R69eojfnU1SEnZybXNzc3au3evpGzPzpgxY2QYhqZOnZpf+ff73/++aMMbM2fO1MqVK/NtOniY71g+9alP6fHHH1c0GlVra+shKxcbGhr04IMPSsrOySpUr4aTtLS0aPDgwTJNUw899FA+3HTV2WefrV/84hf5P7/22muSpFmzZh1y+7FWQjY3N2vo0KGSpAceeOCY5839XYvFYmpra8uHocrKSo0aNUorV66UlA11r7/++lGPddNNN2nDhg3dClKS8j2d+/fv17Jly/SlL31JkvSXv/xFCxcu1IoVK4r2AwUAuJXjwlRNTY0mTZqk2bNn256A/tprr2nKlCl68skn9c1vflPnnHOOpGzPwOLFizV//nzNmTNHlmXpn/7pnyRJixYt0r333qsZM2aoqalJl1xyie3X1BXjxo3TDTfcoDlz5qi+vl6LFi3q8nMnTJigiy++WFOmTNEXvvAFTZs2LX/f9ddfr7Vr12r8+PFau3atrr/++p5ofkktWLBADz74oGbMmKEtW7Yc0mvVFbfffrs2btyouro6TZw4Uffcc4+k7Py9pqYmTZ48WfX19flhwc4sXrxYl112mWbNmpUfrj2ayZMnq6GhQfX19br00ks1ceJEVVZWSpKWL1+u++67T/X19Zo0aZJWrVolKbug4Hvf+94xj/3qq69q9OjRWrlypRYuXKhJkybl76uvr8///ze+8Q1NnDhRZ599tv793/9dY8aMyb+W9vZ2zZ8/X/X19frc5z53zHMCQF9ldDbU0OMnNgyLnd37DnZ271hbW5vKy8sViUR0zjnn6Kc//Wl+EjqOTzgcFteWvoNrC4olHA7LsqwO59S4bs4U0Jtcd911euuttxSPxzV//nyCFAC4EGEKKKH77ruv1E0AANjkuDlTAAAAbkKYAgAAsIEwBQAAYANhCgAAwIailkYwDGOBpAWSVFZWNmns2LFFOzcAAMDx2rRpk2VZVoedUCWrMzVx4kRr3fMvlOTcAAAA3VFZUf5ny7Imd3Qfw3wAAAA2EKYAAABsIEwBAADYQJgCAACwgTAFAABgA2EKAADABsIUAACADYQpAAAAGwhTAAAANhCmAAAAbCBMAQAA2ECYAgAAsIEwBQAAYANhCgAAwAbCFAAAgA2EKQAAABsIUwAAADYQpgAAAGwgTAEAANhAmAIAALCBMAUAAGADYQoAAMAGwhQAAIANhCkAAAAbCFMAAAA2EKYAAABsIEwBAADYQJgCAACwgTAFAABgA2EKAADABsIUAACADYQpAAAAGwhTAAAANhCmAAAAbCBMAQAA2ECYAgAAsIEwBQAAYANhCgAAwAbCFAAAgA2EKQAAABsIUwAAADYQpgAAAGwgTAEAANhAmAIAALCBMAUAAGADYQoAAMAGwhQAAIANhCkAAAAbCFMAAAA2EKYAAABsIEwBAADYQJgCAACwgTAFAABgA2EKAADABsIUAACADYQpAAAAGwhTAAAANhCmAAAAbCBMAQAA2ECYAgAAsIEwBQAAYANhCgAAwAbCFAAAgA2EKQAAABsIUwAAADYQpgAAAGwgTAEAANhAmAIAALCBMAUAAGADYQoAAMAGwhQAAIANhCkAAAAbCFMAAAA2EKYAAABsKGqYMgxjgWEYrxqG8eqePXuKeWoAAIAeUdQwZVnWMsuyJluWNbm2traYpwYAAOgRDPMBAADYQJgCAACwgTAFAABgA2EKAADABsIUAACADYQpAAAAGwhTAAAANhCmAAAAbCBMAQAA2ECYAgAAsIEwBQAAYANhCgAAwAbCFAAAgA2EKQAAABsIUwAAADYQpgAAAGwgTAEAANhAmAIAALCBMAUAAGADYQoAAMAGwhQAAIANhCkAAAAbCFMAAAA2EKYAAABsIEwBAADYQJgCAACwgTAFAABgA2EKAADABsIUAACADYQpAAAAGwhTAAAANhCmAAAAbCBMAQAA2ECYAgAAsIEwBQAAYANhCgAAwAbCFAAAgA2EKQAAABsIUwAAADYQpgAAAGwgTAEAANhAmAIAALCBMAUAAGADYQoAAMAGwhQAAIANhCkAAAAbCFMAAAA2EKYAAABsIEwBAADYQJgCAACwgTAFAABgA2EKAADABsIUAACADYQpAAAAGwhTAAAANhCmAAAAbCBMAQAA2ECYAgAAsIEwBQAAYANhCgAAwAbCFAAAgA2EKQAAABsIUwAAADYQpgAAAGwgTAEAANhAmAIAALCBMAUAAGADYQoAAMAGwhQAAIANhCkAAAAbCFMAAAA2EKYAAABsIEwBAADYQJgCAACwoahhyjCMBYZhvGoYxqt79uwp5qkBAAB6RFHDlGVZyyzLmmxZ1uTa2tpinhoAAKBHMMwHAABgA2EKAADABsIUAACADYQpAAAAGwhTAAAANhCmAAAAbCBMAQAA2OAtdQNQeMmUtHO/qT0thqrKLA3tl1HQX+pWAQDQOxGmehnLkt7bY2rbLlMeU9rXZiiakD5xQkYe+iEBACg4wlQvs7vZ0Ad7TZUFLZUHpXhS2t1kqiIkjRiQKXXzAADodeir6EUylrSryVQ6LZUHs7cFfJLfK+3abyqRKm37AADojQhTvcj+VkPN7YbKQ9Yht5cHLbXFpH2tRolaBgBA70WY6kV2NxlKpqXQYZPNvR7JY0of7DWVZqQPAICCIkz1EvGk1BIzFe5k1V5ZwFI0YSgSK267AADo7QhTvURzxFA0LgX9Vof3B3xSLCm1RPnIAQAoJL5Ze4kPmw1ZluTzdHy/YeQmohtKpYvbNgAAejPCVC+QSEltMfOIuVKHC/uzQ33RRHHaBQBAX0CY6gWicUOJpBTwdjzEl+P3SvGUFE2wqg8AgEIhTPUCrVFDiZTkO0YJVtOUZEmt7YQpAAAKhTDlchkrO1/K783OizqWkF/a02Yqnuz5tgEA0BcQplwunpRiSUNB39GH+HKCfkuJBEN9AAAUCmHK5WIJQ8kuDPHl+DxSMi3FmYQOAEBBEKZcLpbIhiNvFz/J3FAgPVMAABQGYcrFLEva32bIY3RtvlSOz5t9HlvLAABgH2HKxRIpqTVqKtRJ1fPOhP2W2mOG2mP0TgEAYBdhysXiyex8KX8X50vl+H1SIi1W9AEAUACEKReLJ7OhyNvJFjKdMQ1JVjaMAQAAewhTLhZPGpJ1oBhnNxkS28oAAFAAhCkXa44c6GU6Dn6v1BphEjoAAHYRplwqlpBaI6ZCge5NPs8J+i1F40xCBwDALsKUS8UOTD4PdHPyeU7Al9v0uLDtAgCgryFMuVQieaBYZzcnn+dk61IZSqTomQIAwA7ClEvlQlB3inUezjAsxeiZAgDAFsKUSxUiBHk9UiROzxQAAHYQplwonZGaI4YCPnvH8XssxRIGvVMAANhAmHKh9pihWNxQ0Hd8K/lygv7sBHRW9AEAcPwIUy6Uq3ze3W1kDuf1ZHu5ognCFAAAx4sw5ULJlJQ5zsrnhzOU3TAZAAAcH8KUCyXShgrVl+QxqTUFAIAdhCkXisazIagQvJ7sMF/G3vQrAAD6LMKUy6QzUiRmyHecxToP5/NYSqUMJZKFOR4AAH0NYcpl2mOGYglDAZsr+XICvuyE9nbqTQEAcFwIUy4TTUjxtGzXmMrxeqRUhuKdAAAcL8KUyyRThmTZ20bmcKZRmIrqAAD0RYQpl4mnpIIt5TvAa0pReqYAADguhCmXiSUkT6HDlCdbayqTKexxAQDoCwhTLpKxpHjCkLdAK/lyPKalVNqgeCcAAMeBMOUisYQUTxnyewtbFMrnkZJpKZZkqA8AgO4iTLlIJG4onizcSr4cnzc7zBeJF/a4AAD0BYQpF4klDKXThat+nmMY2b8I7TF6pgAA6C7ClIvEU5LRQ5+Y18OKPgAAjgdhykV6YiVfjsdkRR8AAMeDMOUSVg+t5MvxerIr+pLpnjk+AAC9FWHKJZJpKZkx5DELu5IvxzZ/vIwAACAASURBVOvJbqKcpDwCAADdQphyiVjCUDIp+b09c3yPmQ1sccojAADQLYQpl4jEs3OaeipMeT1SOi1FEoQpAAC6gzDlErmVdoXc4PhwXo/UEum54wMA0BsRplwilix8fanD+TxSNGEo0zPTsgAA6JUIUy4RSxg9HqY8pqV02lCKFX0AAHQZYcoFUmkple65sgg5Ho+UYkUfAADdQphygWQ6G3J6qixCjtfMTkJPppmEDgBAVxGmXCCezA69FatnKkHPFAAAXUaYcoHogbIIvh4OU6YhWRmDPfoAAOgGwpQLtMcMGUbPlkXI8XktNUcIUwAAdBVhygUicUO+In1Sfm925SAr+gAA6BrClMNlDsxh6umyCDke08ru0UeYAgCgSwhTDpdMS+mMIa+nOJU08yv6Ugz1AQDQFYQph0ums3WmitYzlas1Rc8UAABdQphyuGTKUDqTDTnFYBrZoUUKdwIA0DWEKYeLxrO9RN4ifVKGIVkyFEswzAcAQFcQphyuLWbIVHHKIuT4PJZaIoYsNjwGAOCYCFMOZllSW9SQ31vc8wa8lqIJg0roAAB0AWHKwVJpKZkxijZfKsfrOXBuJqEDAHBMhCkHS6azk8G9PbzB8eE8HmVrTVEeAQCAYypqmDIMY4FhGK8ahvHqnj17inlqV0qls5XIi94zZVIeAQCAripqmLIsa5llWZMty5pcW1tbzFO7UjKV7SEqVo2pHMPIztdKMWcKAIBjYpjPweLJ7DBfscNUToJhPgAAjokw5WBtMUOlijN+jyiPAABAFxCmHCqTyYYZv6805/f7LEXihuLJ0pwfAAC3IEw5VCKVnYDuK9IGx4fze7MT0BnqAwDg6AhTDpVKZyefe4u8ki/HY+bKI5Tm/AAAuAVhyqGSubIIJfqEPKaUpnAnAADHRJhyqFKVRTiYYRhKphnmAwDgaAhTDpVMG7JU3A2Oj2QpwQR0AACOijDlUG0xyVPiTiGfR2qNUR4BAICjIUw5UDojtbYb8ntL246Az1KM8ggAABwVYcqBYgkpkTbk95W2S8jvy1ZhjyaYNwUAQGcIUw6UTBtKl3AlX47XlNJWtuYVAADoGGHKgZIpKZXJhplSym94zIo+AAA6RZhyoGQ6G2JMB3w6hsSKPgAAjsIBX9c4nJN6gjymFCNMAQDQKcKUA7VFSz9fKsdrStG4oQzlEQAA6JBDvrKRk0xJbTGz5GURcvw+S7GkoWi81C0BAMCZCFMOE00YSiSzNZ6cIHCgPEIk7pyhRwAAnIQw5TD5lXyeUrcky2NKGSvbLgAAcCTClMMk06Xf4LgjbHgMAEDHHPaVjWTKkCFnBRePka3KDgAAjkSYcph4UjLkjPlSOV6PFE06K+ABAOAUhCkHsSypLW44Zr5UjseUEkmDeVMAAHSAMOUgsUS2ppNTVvLlBHyWEmx4DABAhwhTDhJNGIons+UInMTvleIpKUKtKQAAjkCYcpBESso4qCxCjnGgQyrOvCkAAI5AmHKQZMqQHLaSL4cVfQAAdIww5SBOXMmX4/UwZwoAgI4QphwkmnDeSr4cj5ntOUulS90SAACchTDlEMmUs8OUz2Mpmc72ngEAgI8QphyiPZ5dyRd0WFmEHD8bHgMA0CHClENE49nVfD5vqVvSMY+ZLSraHiNMAQBwMMKUQyRS2R35DAdnFY8pRVnRBwDAIQhTDhFPSqaDg5Qkec1shXbLmSORAACUBGHKISIOnnye4/FYSmYMJVnRBwBAHmHKAVJpKZk05HH4p+H1SOm02PAYAICDOPzru29oj+X25HP2+JnPk50kz4o+AAA+QphygPZYdiNhv0NX8uV4PVI6Y7CiDwCAgxCmHCCWdP5Kvhyfx1Jr1AUNBQCgSAhTDhBNyPGTz3N8HimekNKZUrcEAABnIEyVWMbKlhvwuuST8JgHVvQxCR0AAEmEqZJLpqRU2pDX4+zJ5zm+Ayv6EimG+gAAkAhTJReJG47eRuZwXo+UTFMJHQCAHMJUibXFskNmTl/Jl2Me2KOvNULPFAAAEmGq5Nqi7pl8nhPwSU0RQxl3jEwCANCjCFMllJ987rIw5fNYSqWYhA4AgESYKqlkSkq6aPJ5jteT3QInnmSoDwAAwlQJJVJSKpVdIecmPo+UymTbDwBAX0eYKqH2mKG4C8OUaWbLI0TZow8AAMJUKTVHDBlGNpy4jd8r7W1jEjoAAC78Gu8dMpbUFjVcUxLhcAGfpVjcUCJZ6pYAAFBahKkSSSSlZMqQz2WTz3N8B4p3UgkdANDXEaZKJJEylEq7b75UjtebDVNxeqYAAH0cYapEonEpkXZfwc4c05CsjBSjPAIAoI8jTJXI/vZsCHHj5PMcn1fa18okdABA3+bir3L3SqWl1oipkK/ULbEn5LfUHjMUjZe6JQAAlA5hqgTiyex8I5/X3V06fm+2ijuV0AEAfRlhqgTiyey+dm6dfJ7jPVAJnUnoAIC+jDBVAtGEoVTGvZPPD2ZIiiTomQIA9F2EqSLLWNLeFkPeXvLOB3zS/pZsTxsAAH1RL/lKd494QmqPGwoH3D1fKiccsBRJGGqL0TsFAOibCFNFFktmt2Bx6zYyh/N5sqsTmTcFAOirCFNFFktkJ217esk7bxiSDCkap2cKANA39ZKvdPdobjdkGAdCSC/hM6XmqKFMptQtAQCg+AhTRRSNS/vbTZX1kvlSOeGApbaIoZZoL0qIAAB0EWGqiCIJQ/GkFHR55fPDBXzZOVMRKqEDAPogW2HKMIy/G4bxXIHa0uvFEtmhsN5QX+pghiEZphRhRR8AoA/qkZ4pwzDqDcP4P4ZhtBqG0WIYxlOGYZzeE+dyC8uSmtsls5fmDb9HaokYSjNvCgDQxxQ8TBmGMUXSOkkfk/QdSd+VNEbSC4ZhjC/0+dyiLSY1tZsqC/au+VI54YCltpihpvZemhYBAOhET/RM3SUpIenTlmXdaVnWnZI+LcmSdMfBD/zaV/9NlRXlh/ya97nP9UCTSu/fv/5VfaYuqLMnhTT1k9lf1//rZ0vdrIIJ+KRk2lDbgUnofemzBQD0bV0qHWkYxnBlg9AcZbdjWyfpqx08brSkMyT90rKs93O3W5b1vmEYKyVdbhjGYMuydkrS22+/LUnyeDz6ylf+RRWVFRo9eozNl1R6sVhMwWDwkNs2b/7otc6b/68qK6vU8FGjS9G8govHYwoEgvJ5LLVEsmGqt362AAAc7phhyjCMaknPSxou6ReS3pQ0Q9KzkkKHPfyMA7+/dNgxTpQ0V9kgNknSE7n7+vfvr+bmZm3ZskUrHn74OF+Gc2zdulWNDefp1w88qIkTJ0qSkqlslfDK6lq1tzXpvb9v0R13ryxxSwvj/e1bdd0/z9HNd/5Gw0+apPaYoeiBVX297bMFAKAjXRnmu0HSKElXW5Z1nWVZd1uW9XlJKyXVHvbYoQd+f/+w238gKVcQYNjBd5x88sn6wS236Omnn9LTTz/drcY70U3/8V21tbVr2LCPXmZTe3Zi9omjT9a/3XCb1j+/Wuuff6qErSycn//424pE2jVw8DCFA1J7TNrbmv1r1ds+WwAAOtKVMHWhpF2S7j/s9ls7eGz4wO/5ikOGYfiU7ZVaffBjLEvKHPh12eVXq1///nrkkf9WazS7Kqyp3dD+NkP7Wg3tbTW0p8XQh82Gdjcb2t1kaNdhv3Y3Ze/f05J9/P627DFaIobaotkaSLGElEhJ6Uz2/IWWTCa1evVqXXbZZRo0aFD+9kjckGUZMiR99vMLVF1Tq+f+z2OFb0CRpZJJvbjuSTVc+EX1rx0s08yWfTh4EvpVV12t/v376/H//u8SthQAgJ5jWMdIFYZhxCS9YlnWmR3ct1/Sa5ZlzTzw5+sl3S7pPMuyVh+4bYikD5SdmP4/JW2TtEfZ4T4AAADH8wb7v5eM7hnZ4X1dPEZnievwdfAfHPj94KG8ZkkZSbkGXGtZ1hNDR5xiNfzzL1UW9smQ9MtbGjVkxHg1XnazJMk8qM/M0Ecb6h5t4b114D+W9VGDM7k/W8Yht3d6jIMfYx3Ug2Ud8tshcm1KJqNadtOnVXf2AtWdfbVkZJ/f1p5QZZlXiURC1ZUB3f29uRo2arwuuPzmY7TG2ZKJmH606NOa/pkF+tTsq5TJWGpuTeqEoTUK+D+qTPqD68/SiNGna/6/3FnC1gIAcPz+19WTOt3noyth6l1JYw3D8FiWlc7deKDHqeqwx75y4Pepku6RJMuyIoZh/FHSWcpmkT9LktcrTRgbVG1NUK9vWq+W/Tv0hSuuU90p5V1+Yc5TpnXjJuq9N1dr4cJ/lc/nV1NrQu0RQ0MHhvTOthY17dyYf60TPu7m1ypJ5fr4uIna8tpqXfOVf9X7HyZ04rByzZjcX8MGZUd8n332We3f+76+/5/f0mUXDz3G8QAAcKYbvtTa0tl9XZkz9ZikQZIuP+z2Gw9/oGVZWyS9KmmeYRgHf3P+RFKlpL2S0pLk9Rhqj6b07jt/1U9vv0FDh5+oM8+a24XmONslX1yonTu360ff/59qad6nfc1xDR0Y1ll1QxSy3tcv7lykoSf0jtcqffR6b/mP6xRpa9LEkz8KUps2bdLVV12psWPH6pLPf77ELQUAoGd0Zc5UjaS/KDt09wtJ/1fSTGV7n0KS/m9uztSBx09TtmzCPyQtPXDzwgPP90pqkrSyX/8BV9cOHqt33npJAwYO1eIl92rw0A6HIl3nmSd+o+U/X6Ky8gqNHT9Dnxh9gvbs/H/6wx+eUb/aIbr8uqWqnzyu1M0smCcee1AP/O+bVV5RqYsuukC1/Wv117/+VX/4wzMaMWKEHnn0MZ100kmlbiYAAMetsqL8z5ZlTe7ovmOGKUkyDGOEpB9Jmq3sFKHnlC3auUbS3w8OUwceP1XSEkn1yg7trZf0v5TtCbtR0kzDMGr7Dxyuuk/N0bxLFyhcVnF8r86h/t/mN/To7/63/vr6n5SMRzRixAhd9NmLdOElV2n9a62qLPeppjJQ6mYWxNtbm2Um39PLax7QS+tfVGtrq4YPz77ef/u3r6qq6vDRYAAA3MV2mOoJEyZMtK5bfL9a2pL5YaHeZueeqHxeUxf8jxGqKMuW2cpkLP1x0y69+te9Gj2yQl5Pj+w1XTS79kaVTls6Z9pQjRji9jlgAAB07GhhqmTf5IYhDeofUiSWKlUTelxzW1KjhpXng5Qkmaah0z/RX4NqQ/rHrkgJW2dfKp3R/paETvtEPw0fXFbq5gAAUBIl7RapqfIrnbZUqt6xnmRZlqyMpX5VRw7lVZT5NPHk/rIyltqj7g2T733QrqEDwhozslKGcbSiFQAA9F4lDVOD+oVUWe5Tc1uylM3oEfFERsGAR5Xlvg7vHz2iQsMGlen9XRFXhslYPC1L0sRx/VVV7i91cwAAKJmShqkB/YLqXx1QSy8MU81tCVWUdT7J3Os1NXFcf5WHvWpqTRS5dfZt29GmEwaVacQQhvcAAH1bScOUaRoaUBNUtBfOm2pqSWjk0DKVhTqvi3rCoLBOGFymXXtjymTc0zvVFkkqFPBq4rh+h1Q6BwCgLyr5UrKqCv8xt3hxm9yw3YCa0FEfZxiGTh1bo+pKv/Y1d1ql3lEsy9L7uyIaOjCsYQN75ypMAAC6wxFhKhTwKOLiidiHi8XTCgY8h6zi68yQAWGNHFKuD/fHXTF3qrU9qfKwTxNO7iePy8s6AABQCCX/NhzUP6h+VQHta3FHz0xXRONpBQPeLoUpSfr4qCpVV/i1t8nZ74FlWdq5J6pBtSENHUCvFAAAkgPClN/n0ZABIUVi6WM/2CWaWhOqrQmoPNyVfaSlYYPC+tgJ5drb7OyJ6C1tSYWDPp06tkamSSkEAAAkB4QpKTvUl0k7f4irqxKJjEYOKe9W4Bg1rFzhgEdNLc4NVHub4xpcG6RAJwAAB3FEmCoL+eTxGkqlM6Vuim2JZFp+v6mqiq4N8eWMGlquE0dUaPe+aA+1zJ62SLZ8xdhRVfRKAQBwEEeEqapyn8pCXrVF3D8JPTf5vCzUvTBlGIZGDC6Tx2M6slTE3qa4hg4Ia/SI3rUhNQAAdjkiTPWrCmhATdDRQ1xdFY2nFQp4VVHWtflSBxs1rFwjh5br/d3O2rMvkcwoGk/rYydUsIIPAIDDOOKb0TQNDR0YVjzp/knore1JDagJyO/rfjFLv8+jk4ZXKJ22lHbQHLLd+6L5PfgAAMChHBGmJKks6JVlyRW1ljqTyWRD0AmDjn+C9tCBYdXWBLVjjzN6pyzLUlt7Sh8bVn7Uau4AAPRVjglT5WU+BXymEkn3TkKPJbLzpaorj3/j3+oKv04ZXa229pQjguXeprgqK3wazh58AAB0yDFhqizkVTDgVTTu3qG+eCKtQMCjsM0enCEDwiov86nZARtA722Ka/TwSg2hSCcAAB1yTJiqrvCrutKvljb3TkKPxdMK+T0qC9oLUwP7BfWxE8q1c09pyyTE4ml5PKaGsgcfAACdckyYMk1DI4aUuboSejSeVnWFX16vvbfVNA2NGVGpgM9UrIQ9dR/sjmjk0DKNYIgPAIBOOSZMSVJlmU+G3DkJ3bIsJRIZDSlQL86g/iH1rw5o975YQY7XXZmMpUQyo5OGVyjg7/7KRAAA+gpHhalQ0Cu/352T0KPxtEJBj2qrgwU5XjDg0SmjaxSLp5VKFf/92LM/ppqqgAbXhop+bgAA3MRRYSoc9Crg9yiecN9QXzyRVjDgVUVZ9yqfH80Jg8tUXeFXU2vx55Hta07o5BMr1b9A4RAAgN7KUWGqPOxVyKUr+uKJjAI+U+Fg4YbEqsp9GjY4rA+b4spkijf0GYmmFAp6NMxGvSwAAPoKR4WpgN+jQf2DanFASYDuiiXSqijz2Z58fjDDMHTKSdWqDPuKum/hBx9GNLg2rIH96JUCAOBYHBWmJGlwbchRW6l0VTyRUb+qQMGPO7BfUP2qA9rXEi/4sTuSna9m6JTR1ce1JQ4AAH2N48JUedgnn8sqoafTlgxJ/asLH6Y8HlNjR1YqmcwUpUzC/pa4qit9TDwHAKCLHBemwkGvgn6PEi7a9Lg9mlR52NsjYUqSRo+oVG1NUPt7uHcqk7G0rymhMSMqCzqRHgCA3sxxYSoU9MjvNxVPuKdnKpbIKBjwqDzcMwEkGPBoxJAyNbUme3QiektbUlWVPo0eUdlj5wAAoLdxXJgKB70K+ExXlUdIHCiLEAz03Byjj4+qUr+qgPY191zv1If7YxrYL9Qjc78AAOitHBemTNPQ4Nqw2iLuWdEXT2ZUXdGzw2ID+gU1bGBI+1t6puZUWyQpv8/U+DE1Mk2jR84BAEBv5LgwJWVXsFmWilpbyY5kKqPKcn+Pn2fUsAp5PEaPBM19zQnV1gR1wiA2NQYAoDscGaaqKvwKBjyuWNGXTlsyDUOVRZiwfeIJ5Ro5tLzg+/XF4mnFE2mNGVlZ0DpZAAD0BY785gwGPPK5ZN5UT6/kO5jHY2rkkHIlk5mCBs19zXEN6h/Sx0dVFeyYAAD0FY4MU9lJ6O7omYrE0goHvaqq6PlhPkk6cXiFThhcpg8+jBTkeKl0Rs1tSY0cWtajE+gBAOitHBmmAn5TwYBHcRfUmkok0yoLe+Ur0vBYWcirMSMrFYunCzKn7MN9MQ2uDenkk6oL0DoAAPoeR4YpwzBUU+kvSsVvu+KJjKqKMPn8YCOGlGlQ/5D+scte71QmY6mpJaGPDSsv+msAAKC3cGSYkrKlAFIp56/mS2cslRe5WnhNZUCfHFOtSCxlax/DnXujGtg/pDEjKdIJAMDxcmyYqqkMKBjwOLp3yrIsyZJCJZhrNHxwtnfq/d3tx/X8TMZSc2tSHx+V3aoGAAAcH8eGqfJwtqJ4zMEr+qLxtEJBT0mGyGoqAzrt4zWKJ45vZd8/drVrSG1IJw6nVwoAADscG6ZCAa/8PtPRK/raIimVh32qqSrNfKOPnVChoQPD2vZBW7eeF0+kFY2l9ckxNUUp6QAAQG/m2DAV8JsK+D1KOHhFXyyeUmW5T+GgtyTnDwe9OuOTtQr6PWrqxjYzf3+/TSeNqNSJwyt6sHUAAPQNjg1TxoGq4k7umUoki7+S73DDB5dpzKhK7dwT7VLw3PFhRBVlPp3+iX4qC5UmBAIA0Js4NkxJUnWF39FhqhQr+Q5nmoamnDpAI4aW691/tCmV7vz9amlLqD2a0sRx/dmDDwCAAnF2mKr0yzQMR294XIqVfEe0IejV9AkDNXRAWO9ub1UqdWSgamlLaOeeqE4ZXaNPjqmRYRglaCkAAL2Po8NUTWVAZSGv2qOpUjflCOm0JdM0FPCXPkxJ0qDakKZNGKihA8u0eVuL9jbFlUxlFI2l9N6Odu3eF9cpY2o0feLAolVrBwCgL3D0pJlceYR4Iq2KEg+nHa49mlI44FWlg9o1fHCZwkGv3ti8T1vfb9N7H7TL4zHUryqgk0+q0iknVcvjIUgBAFBIjg5TAb9HPq+ptkiy1E05Qns0qfKwV9WVztqGpX91QDPOGKzxYxNqbU/K5zXVr8qvUIlWHAIA0Ns5+hvWNA1Vlvu0rzle6qYcIRJLa8SQckcOmRmGof7VAWpIAQBQBM5LAofJlkdwXq2pZCqjSjYHBgCgz3N8mAqHvHLiYj5DzljJBwAASsvxYao87JNpGketn1RsuVINQcIUAAB9nuPDVE2lX+UhryIOKo+QTGXk95mEKQAA4PwwVVXhVzjoVSTmnHlT8URaAb9H4SBhCgCAvs7xYcrnNRUKeh21rUxbNKXysJcJ6AAAwPlhSpIqy71KdrBFSqm0R1Ia2D/kyLIIAACguFyRBsrD/g73myuVdMZSFb1SAABALglTjitBYDmwTQAAoCRcEaaCAY8Mw1A6XfqCU6l0Rh6voQBhCgAAyCVhqrrCr7KQV5FY6csjJJMZ+b2mgn7CFAAAcEmYqqrwqSzkVbsDak0lUxn5qDEFAAAOcEWY8vs8qqrwK5Yofa2pSCytUMCrspCj94gGAABF4oowJUkVZc6oNdUeTam2OqAAw3wAAEAuClPhkC+/J14pJVMZDegXLHUzAACAQ7gmTAX9pgyjtG2wLEuGpHCQIT4AAJDlmjAV8GfLI5SydyqVtuT1mgzxAQCAPNeEqbKQV0G/R7F46Sah58oiULATAADkuCZMVR2oNVXK8giJZLYsAgU7AQBAjmvCVDjoVXWFX+0lLNyZSGXko2AnAAA4iGvClCT1qwooUcJaU5FYSpXlPgp2AgCAvKKGKcMwFhiG8aphGK/u2bOn288PBT0qZXWEWDytwf1DpWsAAABwnKKGKcuyllmWNdmyrMm1tbXdfn7Q75FKFKYymWxZhOpKf2kaAAAAHMlVw3yBgEcer6FUuviV0FNp9uQDAABHclWYCvo98ntNJUuwrUwimZHf52HyOQAAOISrwlQ45FUg4CnJhsfJ3Eq+ANXPAQDAR1wVpirLfKoI+0pSayqZzMjvMxUMuOotAwAAPcxVycA0DQ3qH1SkBGEqcSBM+byuessAAEAPc10yqCjzl6Q8QiSe1oCaoIxS77YMAAAcxXVhqlQTwDMZS/2rAyU5NwAAcC7XhalAwJTXYyqVKt6KvkQyrYDPVGW5r2jnBAAA7uC6MBX0e+T3mUoUNUxlyyKEg6zkAwAAh3JdmAr4PfIVudZUIpktixCgxhQAADiM68JUWcirYJFrTSVTVD8HAAAdc12YCvg96l8dKGqtqUQyk+8RAwAAOJgr08GAmqASRRzmSyYzqixj8jkAADiSK8NUWcgrQ5JlFafgVCKZUT/KIgAAgA64MkwFAx55vaZS6Z4PU6l0Rh6voSrKIgAAgA64M0z5PfIXaUVfNJZWOOBVdYW/x88FAADcx5VhKhDwyFekWlPJVG6DY1byAQCAI7kyTAUPrKwrxiT0XI2pUm1jAwAAnM2VYSrgN1Ue9ikW7/nyCIlkRqGgV17KIgAAgA64MiEYhqEhA4KKxnq+cGcylVFFGdvIAACAjrkyTElSdUVAhiFlMj27oi+VyqiijMnnAACgY64NU+GQVz6vqVS65+ZNZTKWDEMU7AQAAJ1ybZgK+j3y+Tw9Ogk9Gk8rFPCqupKeKQAA0DHXhqncXnnJHiyPEI2lFAp5VEHPFAAA6IRrw1Qo6JHf17PlERKpjPxeUyFqTAEAgE64Nkz5vNlCmj0appIZlYV9Mk2jx84BAADczbVhSpIG1AQUifZcralkMsPkcwAAcFSuDlP9q4OyLMmyeqY8QsayVBYmTAEAgM65OkxVlfsVDHgUTxR+qM+yLFkZMV8KAAAclavDVDDgkd9vKpEsfCX0aDytUNCjqnLKIgAAgM65Okz15Iq+9khK5WEfNaYAAMBRuTpMBf0e+b2mEj1QayqeSCsU9KosxL58AACgc64OU6ZpqLzM3yM9UwlW8gEAgC5wdZiSpOpyn+Lxws+ZSqYtVZbTKwUAAI7O9WGqpiogKbspcUFZUjBAmAIAAEfn/jBV6Vco6FWsgL1TmYwlw6AsAgAAODbXh6nysE9Bv0exROHCVDSeVijABscAAODYXB+mQoHCl0doiyRVXuZTTWWgYMcEAAC9k+vDlNdrKhzyFjRMRWNp1VRmq6sDAAAcjevDlCRVVfgLWgU9nkhT+RwAAHRJrwhT5WGvUunCreazJIUp1gkAALqgV4Sp6gq/TNNQKm1/qM+yLJms5AMAAF3UK8JUTWVAFWGf2iIp28dKpix5vSbzpQAAQJf0ijBVWe5TMOApSK2p9mhS4aCXsggAAKBLekWY8nlNlYW8BZmE3tqeUnWFX9UVTEAHAADH1ivClJSdN1WI8giRWEqDa0MyTaMArQIAAL1drwlT5WW+wqzos1jJBwAAuq73hKmQV6Zhb8Pj3J584SBhCgAAdE2vCVP9qgIqC9lb0ZdIZhTwexQKspIPAAB0Ta8JUzWVflWUedUWTR73MWLxtAJ+Dz1TM4kvxgAADMlJREFUAACgy3pNmPJ6TVVV+BW3UR6hpT2p6kpW8gEAgK7rNWFKyvZO2VnRF4mldMLAMCv5AABAl/WqMBUO+mQd5/xzy7JkSBTrBAAA3dK7wlTIK6/3/7d3bzFynncdx39/e3e99vqwPsU5uTkRIkUIqBWhcBCgFqUHqoSLXkSqRDgpEtxwEIJUkZC4LCBASIgoakGASlsIBaJKVYmgElcNpIWkgTSJaXpISZtYiQ+x48PaDxfzutm462TXTz3rHX8+0mpn3nmtefevxztfz7wzXpeFhZU/O3VqoWV6ep2PRQAAVmSiYmrn/IZsmZvO4aMrPwn9xMnTmZ1ZnzkxBQCswETF1LbN09k1v+GCYuq14wvZIKYAgBWaqJiqquzaviEnTq78Zb6Dr57KVbs3ZqOPRQAAVmCiYipJNm+aTlvhp6C31nLmTMtVuzddpKMCACbVxMXU3KaVn4Q++uTzdd7JBwCs2MTF1Na5mWzeNLWi86ZeO3E6szNTzpcCAFZs4mJqx7aZ7Nm5MQePnFz2nzl+4nQ2bljvmSkAYMUmLqaqKlfu2riiT0I/9OrJXH3FpkxPTdw4AICLbCLrYcvcdNZV5cwyTkRfWDiTdesq1+xx8jkAsHITGVNb56azccP6HDu+8Jb7Hju+kLnZqWzf6j83BgBWbiJjan7rTOa3zuTg4bc+b+rY8dPZODvlfCkA4IJMZExtmFmfm962Na8ee+tnpg4fPZXd2zdkZnr9GI4MAJg0ExlTyehdfVNT63LqTT5v6uSp01lXleuv2TLGIwMAJsnExtS2zTOZ2ziVo2/y7NSRowvZtnk6e3ZuHOORAQCTZGJjan7LTPbsms1Lrxw/7z6vHjuVbVtmsmXOh3UCABdmYmNq3brK9163LS1Z8r+WWTh9Jq8dP529V86lqsZ/gADARJjYmEqS3Ttms23zzJL/tcwrh05m5/YNueltzpcCAC7cRMfUts3TuXr3xnzr5eNp7Y0f4PnKkdGnnm/b7POlAIALN9ExVVX5/lt2ZNvcdA4def3ZqYOHT2Z2Zn2uv3rzKh4dADAJJjqmkmTPztlcs2cuLxx4LacWzmTh9Jm8cOBYbr5ua27a6yU+AKDPxL+Nrapy+w/sztHXTuWZrx5Oklx31eZ83/fMO/EcAOg21piqqnuT3Jske/fuHdv9zm+ZyU/cdmX27jmShdMtt9ywNTvnZ8d2/wDA5BprTLXWHkzyYJLs27evvcXu31W7ts9m13YBBQB8d038OVMAABeTmAIA6CCmAAA6iCkAgA5iCgCgg5gCAOggpgAAOogpAIAOYgoAoIOYAgDoIKYAADqIKQCADmIKAKCDmAIA6CCmAAA6iCkAgA5iCgCgg5gCAOggpgAAOogpAIAOYgoAoIOYAgDoIKYAADqIKQCADmIKAKCDmAIA6CCmAAA6iCkAgA5iCgCgg5gCAOggpgAAOogpAIAOYgoAoIOYAgDoIKYAADqIKQCADmIKAKCDmAIA6CCmAAA6iCkAgA5iCgCgg5gCAOggpgAAOogpAIAOYgoAoIOYAgDoIKYAADqIKQCADmIKAKCDmAIA6CCmAAA6iCkAgA5iCgCgg5gCAOggpgAAOogpAIAOYgoAoIOYAgDoIKYAADqIKQCADmIKAKCDmAIA6CCmAAA6iCkAgA5iCgCgg5gCAOggpgAAOogpAIAOYgoAoIOYAgDoIKYAADqIKQCADmIKAKCDmAIA6DDWmKqqe6vqsap67MCBA+O8awCAi2KsMdVae7C1dltr7bZdu3aN864BAC4KL/MBAHQQUwAAHcQUAEAHMQUA0EFMAQB0EFMAAB3EFABABzEFANBBTAEAdBBTAAAdxBQAQAcxBQDQQUwBAHQQUwAAHcQUAEAHMQUA0EFMAQB0EFMAAB3EFABABzEFANBBTAEAdBBTAAAdxBQAQAcxBQDQQUwBAHQQUwAAHcQUAEAHMQUA0EFMAQB0EFMAAB3EFABABzEFANBBTAEAdBBTAAAdxBQAQAcxBQDQQUwBAHQQUwAAHcQUAEAHMQUA0EFMAQB0EFMAAB3EFABABzEFANBBTAEAdBBTAAAdxBQAQAcxBQDQQUwBAHQQUwAAHcQUAEAHMQUA0EFMAQB0EFMAAB3EFABABzEFANBBTAEAdBBTAAAdxBQAQAcxBQDQQUwBAHQQUwAAHcQUAEAHMQUA0EFMAQB0EFMAAB3EFABABzEFANBBTAEAdBBTAAAdxBQAQAcxBQDQQUwBAHQQUwAAHabGeWdVdW+Se4erJ7Zu2fzkOO9/jdqV5MBqH8QaYVbLY07LY07LZ1bLY07LdynO6rrz3VCttXEeyOt3XPVYa+22VbnzNcScls+slseclsecls+slseclm+tzcrLfAAAHcQUAECH1YypB1fxvtcSc1o+s1oec1oec1o+s1oec1q+NTWrVTtnCgBgEniZDwCgg5gCAOgw9piqqndX1dNVtb+q7hv3/V9qqmpvVX22qp6qqv+uql8dtu+oqkeq6tnh+/Zhe1XVnwzze6Kq9q3uTzBeVbW+qv6zqj41XL+hqh4d5vSJqpoZtm8Yru8fbr9+NY97nKpqvqoeqqovDevqh62npVXVrw9/756sqo9V1aw1lVTVn1fVi1X15KJtK15DVXXPsP+zVXXPavwsF9t5ZvX7w9+/J6rqH6pqftFtHxxm9XRVvWvR9ol+bFxqTotu+82qalW1a7i+9tZUa21sX0nWJ/nfJDcmmUnyeJJbx3kMl9pXkquS7Bsub0nyTJJbk/xekvuG7fcl+dBw+b1JPp2kktye5NHV/hnGPK/fSPI3ST41XP/bJHcPlx9I8svD5V9J8sBw+e4kn1jtYx/jjP4yyS8Nl2eSzFtPS87pmiTPJdm4aC39nDXVkuTHk+xL8uSibStaQ0l2JPny8H37cHn7av9sY5rVHUmmhssfWjSrW4fHvQ1JbhgeD9dfDo+NS81p2L43yWeSfDXJrrW6psb9zNQPJdnfWvtya+1kko8nuWvMx3BJaa290Fr7wnD5SJKnMvolf1dGD4oZvv/McPmuJH/VRj6XZL6qrhrzYa+Kqro2yU8n+fBwvZK8I8lDwy7nzuns/B5K8s5h/4lWVVsz+qX1kSRprZ1srR2M9XQ+U0k2VtVUkk1JXog1ldbavyV5+ZzNK11D70rySGvt5dbaK0keSfLui3/047XUrFpr/9xaWxiufi7JtcPlu5J8vLV2orX2XJL9GT0uTvxj43nWVJL8UZLfSrL43XBrbk2NO6auSfL1RdefH7aRZHjZ4O1JHk2yp7X2QjIKriRXDLtdzjP844z+0p0Zru9McnDRL63Fs/j2nIbbDw37T7obk7yU5C+Gl0M/XFVzsZ6+Q2vtG0n+IMnXMoqoQ0k+H2vqfFa6hi7btXWOX8joWZbErN6gqu5M8o3W2uPn3LTm5jTumFrqX3E+myFJVW1O8vdJfq21dvjNdl1i28TPsKrel+TF1trnF29eYte2jNsm2VRGT6X/WWvt7UmOZvSSzPlcrnPKcM7PXRm93HJ1krkk71li18t9Tb2V883lsp9XVd2fZCHJR89uWmK3y3JWVbUpyf1Jfmepm5fYdknPadwx9XxGr4+edW2S/xvzMVxyqmo6o5D6aGvtk8Pmb519uWX4/uKw/XKd4Y8mubOqvpLRU+DvyOiZqvnhJZrkjbP49pyG27dl6aeYJ83zSZ5vrT06XH8oo7iynr7TTyV5rrX2UmvtVJJPJvmRWFPns9I1dDmvrQwnR78vyQfacMJPzGqxmzL6h8zjw+/1a5N8oaquzBqc07hj6j+S3Dy8W2Ymo5M4Hx7zMVxShnMuPpLkqdbaHy666eEkZ9+pcE+Sf1q0/WeHdzvcnuTQ2afeJ1lr7YOttWtba9dntG7+tbX2gSSfTfL+Ybdz53R2fu8f9r8k/gVzMbXWvpnk61V1y7DpnUn+J9bTUr6W5Paq2jT8PTw7K2tqaStdQ59JckdVbR+eBbxj2DbxqurdSX47yZ2ttWOLbno4yd3DO0NvSHJzkn/PZfjY2Fr7Ymvtitba9cPv9eczejPWN7MW19S4z3jP6Cz9ZzJ658L9477/S+0ryY9l9DTlE0n+a/h6b0bnYvxLkmeH7zuG/SvJnw7z+2KS21b7Z1iFmf1kXn83340Z/TLan+TvkmwYts8O1/cPt9+42sc9xvn8YJLHhjX1jxm968V6WnpWv5vkS0meTPLXGb3L6rJfU0k+ltF5ZKcyepD7xQtZQxmdL7R/+Pr51f65xjir/Rmd23P2d/oDi/a/f5jV00nes2j7RD82LjWnc27/Sl5/N9+aW1P+OxkAgA4+AR0AoIOYAgDoIKYAADqIKQCADmIKAKCDmAIA6CCmAAA6/D/fjk5+iRKD2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x864 with 2 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sanity check, show a schedule\n",
    "schedules[10].draw(plot_range=(0, 1500), channels=[config.drive(0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5dd45214407b8c0019f72135\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/ipywidgets/widgets/widget_layout.py:84: DeprecationWarning: Layout properties overflow_x and overflow_y have been deprecated and will be dropped in a future release. Please use the overflow shorthand property instead\n",
      "  warnings.warn(\"Layout properties overflow_x and overflow_y have been deprecated and will be dropped in a future release. Please use the overflow shorthand property instead\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "shots = 1000\n",
    "standard_job = q.execute(schedules, backend=backend, shots=shots)\n",
    "print(standard_job.job_id())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "## Section 2: Direct RX (Switch to Pranav's qiskit-terra fork, then restart kernel but don't clear output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import time\n",
    "from collections import namedtuple\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit as q\n",
    "import qiskit.tools.jupyter\n",
    "from qiskit.pulse import pulse_lib as _  # only want to call pulse_lib as q.pulse.pulse_lib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pulse_compiler_helper_fns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AccountProvider for IBMQ(hub='ibm-q', group='open', project='main')>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.IBMQ.load_account() # Load account from disk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/alijavadi/Desktop/ajavadia-terra/qiskit/pulse/channels/pulse_channel_spec.py:87: DeprecationWarning: The PulseChannelSpec is deprecated. Use backend.configuration() instead. The supported methods require some migrations; check out the release notes for the complete details.\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "provider = q.IBMQ.get_provider(group='qiskit-terra', project='pulse-testing')\n",
    "backend = provider.get_backend('alt_almaden')\n",
    "config = backend.configuration()\n",
    "system = q.pulse.PulseChannelSpec.from_backend(backend)\n",
    "cmd_def = q.pulse.CmdDef.from_defaults(backend.defaults().cmd_def, backend.defaults().pulse_library)\n",
    "measure = cmd_def.get('measure', qubits=backend.configuration().meas_map[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.17453293  0.34906585  0.52359878  0.6981317   0.87266463  1.04719755\n",
      "  1.22173048  1.3962634   1.57079633  1.74532925  1.91986218  2.0943951\n",
      "  2.26892803  2.44346095  2.61799388  2.7925268   2.96705973]\n"
     ]
    }
   ],
   "source": [
    "num_angles = 17  # will exclude endpoints of 0 and 2pi\n",
    "angles = np.linspace(0, np.pi, num_angles+1, endpoint=False)[1:]  # get rid of endpoints\n",
    "print(angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "schedules = []\n",
    "for angle in angles:\n",
    "    circuit = q.QuantumCircuit(20)\n",
    "    circuit.rx(angle, qubit_num)\n",
    "    decomposed_circuit = circuit.decompose()\n",
    "    pulse_compiler_helper_fns.update_basis_gates_and_cmd_def(decomposed_circuit, backend, system, cmd_def)\n",
    "    transpiled_circuit = q.transpile(circuit, backend, optimization_level=1)\n",
    "    schedule = q.schedule(transpiled_circuit, backend=backend, cmd_def=cmd_def)\n",
    "    schedule |= measure << schedule.duration\n",
    "    schedules.append(schedule)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x864 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sanity check, show a schedule\n",
    "schedules[10].draw(plot_range=(0, 1500), channels=[config.drive(0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5dd453edf501cd001811d73f\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/ipywidgets/widgets/widget_layout.py:84: DeprecationWarning: Layout properties overflow_x and overflow_y have been deprecated and will be dropped in a future release. Please use the overflow shorthand property instead\n",
      "  warnings.warn(\"Layout properties overflow_x and overflow_y have been deprecated and will be dropped in a future release. Please use the overflow shorthand property instead\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "shots = 1000\n",
    "direct_job = q.execute(schedules, backend=backend, shots=shots)\n",
    "print(direct_job.job_id())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 3: Data Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "standard_job = backend.retrieve_job('5dd45214407b8c0019f72135')\n",
    "direct_job = backend.retrieve_job('5dd453edf501cd001811d73f')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<JobStatus.DONE: 'job has successfully run'>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "direct_job.status()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "standard_result = standard_job.result()\n",
    "direct_result = direct_job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.ignis.verification.tomography.data import marginal_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.032, 0.075, 0.112, 0.127, 0.178, 0.241, 0.353, 0.442, 0.508, 0.57, 0.647, 0.74, 0.766, 0.832, 0.878, 0.924, 0.907]\n",
      "[0.034, 0.054, 0.094, 0.144, 0.183, 0.253, 0.355, 0.382, 0.514, 0.573, 0.659, 0.737, 0.781, 0.848, 0.888, 0.917, 0.921]\n"
     ]
    }
   ],
   "source": [
    "standard_fracs = []\n",
    "for i in range(num_angles):\n",
    "    counts = marginal_counts(standard_result.get_counts(i), meas_qubits=[qubit_num])\n",
    "    standard_fracs.append(counts.get('1', 0) / shots)\n",
    "print(standard_fracs)\n",
    "\n",
    "direct_fracs = []\n",
    "for i in range(num_angles):\n",
    "    counts = marginal_counts(direct_result.get_counts(i), meas_qubits=[qubit_num])\n",
    "    direct_fracs.append(counts.get('1', 0) / shots)\n",
    "print(direct_fracs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.17453293 0.34906585 0.52359878 0.6981317  0.87266463 1.04719755\n",
      " 1.22173048 1.3962634  1.57079633 1.74532925 1.91986218 2.0943951\n",
      " 2.26892803 2.44346095 2.61799388 2.7925268  2.96705973]\n"
     ]
    }
   ],
   "source": [
    "num_angles = 17  # will exclude endpoints of 0 and 2pi\n",
    "angles = np.linspace(0, np.pi, num_angles+1, endpoint=False)[1:]  # get rid of endpoints\n",
    "print(angles)\n",
    "standard_fracs = np.array([0.032, 0.075, 0.112, 0.127, 0.178, 0.241, 0.353, 0.442, 0.508, 0.57, 0.647, 0.74, 0.766, 0.832, 0.878, 0.924, 0.907])\n",
    "direct_fracs = np.array([0.034, 0.054, 0.094, 0.144, 0.183, 0.253, 0.355, 0.382, 0.514, 0.573, 0.659, 0.737, 0.781, 0.848, 0.888, 0.917, 0.921])\n",
    "expecteds = np.array([np.sin(angle / 2) ** 2 for angle in angles])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 10.  20.  30.  40.  50.  60.  70.  80.  90. 100. 110. 120. 130. 140.\n",
      " 150. 160. 170.]\n"
     ]
    }
   ],
   "source": [
    "num_angles = 17  # will exclude endpoints of 0 and 2pi\n",
    "angles = np.linspace(0, 180, num_angles+1, endpoint=False)[1:]  # get rid of endpoints\n",
    "print(angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x252 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 3.5))\n",
    "plt.ylabel('Probability of measuring |1>')\n",
    "plt.xlabel('Θ in degrees')\n",
    "plt.title('RX(Θ): Standard vs. Direct', fontsize=14)\n",
    "plt.scatter(angles, standard_fracs, marker='s', label='Standard')\n",
    "plt.scatter(angles, direct_fracs, marker='^', label='Direct')\n",
    "plt.plot(np.linspace(0, 180, 100), [np.sin(angle * np.pi /180 / 2) ** 2 for angle in np.linspace(0, 180, 100)],\n",
    "         label='Expected', color='black')\n",
    "ax.legend()\n",
    "_ = plt.axis([0, 180, 0, 1])\n",
    "plt.savefig('Figures/rx_standard_vs_direct.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x158.4 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 2.2))\n",
    "plt.xlabel('Θ in degrees')\n",
    "plt.ylabel('Residuals')\n",
    "plt.plot(angles, standard_fracs - expecteds, marker='s', label='Standard')\n",
    "plt.plot(angles, direct_fracs - expecteds, marker='^', label='Direct')\n",
    "plt.hlines(0, 0, 180, linestyles='dashed')\n",
    "ax.legend()\n",
    "_ = plt.axis([0, 180, -0.09, 0.05])\n",
    "plt.savefig('Figures/rx_standard_vs_direct_residuals.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.03860766915167121\n",
      "0.03242948611207921\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "print(np.sqrt(mean_squared_error(expecteds, standard_fracs)))\n",
    "print(np.sqrt(mean_squared_error(expecteds, direct_fracs)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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