scratchpads/FSim gate.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys; sys.path.append('..')\n",
    "import random, math, os\n",
    "import pyzx as zx\n",
    "from fractions import Fraction\n",
    "import numpy as np\n",
    "np.set_printoptions(linewidth=500)\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"167.060615pt\" version=\"1.1\" viewBox=\"0 0 590.4 167.060615\" width=\"590.4pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 167.060615 \n",
       "L 590.4 167.060615 \n",
       "L 590.4 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 227.488401 90.485266 \n",
       "L 272.629467 135.626332 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 227.488401 135.626332 \n",
       "L 272.629467 90.485266 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 272.629467 90.485266 \n",
       "L 317.770533 67.914734 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 272.629467 90.485266 \n",
       "L 362.911599 90.485266 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_5\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 272.629467 135.626332 \n",
       "L 317.770533 67.914734 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_6\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 272.629467 135.626332 \n",
       "L 362.911599 135.626332 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_7\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 317.770533 67.914734 \n",
       "L 317.770533 22.773668 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_2\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 227.488401 94.999373 \n",
       "C 228.685556 94.999373 229.83384 94.523738 230.680357 93.677222 \n",
       "C 231.526873 92.830705 232.002508 91.682422 232.002508 90.485266 \n",
       "C 232.002508 89.288111 231.526873 88.139828 230.680357 87.293311 \n",
       "C 229.83384 86.446795 228.685556 85.97116 227.488401 85.97116 \n",
       "C 226.291246 85.97116 225.142962 86.446795 224.296446 87.293311 \n",
       "C 223.449929 88.139828 222.974295 89.288111 222.974295 90.485266 \n",
       "C 222.974295 91.682422 223.449929 92.830705 224.296446 93.677222 \n",
       "C 225.142962 94.523738 226.291246 94.999373 227.488401 94.999373 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 227.488401 140.140439 \n",
       "C 228.685556 140.140439 229.83384 139.664804 230.680357 138.818288 \n",
       "C 231.526873 137.971771 232.002508 136.823487 232.002508 135.626332 \n",
       "C 232.002508 134.429177 231.526873 133.280893 230.680357 132.434377 \n",
       "C 229.83384 131.58786 228.685556 131.112226 227.488401 131.112226 \n",
       "C 226.291246 131.112226 225.142962 131.58786 224.296446 132.434377 \n",
       "C 223.449929 133.280893 222.974295 134.429177 222.974295 135.626332 \n",
       "C 222.974295 136.823487 223.449929 137.971771 224.296446 138.818288 \n",
       "C 225.142962 139.664804 226.291246 140.140439 227.488401 140.140439 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 272.629467 99.51348 \n",
       "C 275.023777 99.51348 277.320345 98.56221 279.013378 96.869177 \n",
       "C 280.706411 95.176144 281.65768 92.879577 281.65768 90.485266 \n",
       "C 281.65768 88.090956 280.706411 85.794389 279.013378 84.101356 \n",
       "C 277.320345 82.408323 275.023777 81.457053 272.629467 81.457053 \n",
       "C 270.235157 81.457053 267.938589 82.408323 266.245556 84.101356 \n",
       "C 264.552523 85.794389 263.601254 88.090956 263.601254 90.485266 \n",
       "C 263.601254 92.879577 264.552523 95.176144 266.245556 96.869177 \n",
       "C 267.938589 98.56221 270.235157 99.51348 272.629467 99.51348 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 272.629467 144.654545 \n",
       "C 275.023777 144.654545 277.320345 143.703276 279.013378 142.010243 \n",
       "C 280.706411 140.31721 281.65768 138.020642 281.65768 135.626332 \n",
       "C 281.65768 133.232022 280.706411 130.935454 279.013378 129.242422 \n",
       "C 277.320345 127.549389 275.023777 126.598119 272.629467 126.598119 \n",
       "C 270.235157 126.598119 267.938589 127.549389 266.245556 129.242422 \n",
       "C 264.552523 130.935454 263.601254 133.232022 263.601254 135.626332 \n",
       "C 263.601254 138.020642 264.552523 140.31721 266.245556 142.010243 \n",
       "C 267.938589 143.703276 270.235157 144.654545 272.629467 144.654545 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 317.770533 76.942947 \n",
       "C 320.164843 76.942947 322.461411 75.991677 324.154444 74.298644 \n",
       "C 325.847477 72.605611 326.798746 70.309044 326.798746 67.914734 \n",
       "C 326.798746 65.520423 325.847477 63.223856 324.154444 61.530823 \n",
       "C 322.461411 59.83779 320.164843 58.88652 317.770533 58.88652 \n",
       "C 315.376223 58.88652 313.079655 59.83779 311.386622 61.530823 \n",
       "C 309.693589 63.223856 308.74232 65.520423 308.74232 67.914734 \n",
       "C 308.74232 70.309044 309.693589 72.605611 311.386622 74.298644 \n",
       "C 313.079655 75.991677 315.376223 76.942947 317.770533 76.942947 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 317.770533 31.801881 \n",
       "C 320.164843 31.801881 322.461411 30.850611 324.154444 29.157578 \n",
       "C 325.847477 27.464546 326.798746 25.167978 326.798746 22.773668 \n",
       "C 326.798746 20.379358 325.847477 18.08279 324.154444 16.389757 \n",
       "C 322.461411 14.696724 320.164843 13.745455 317.770533 13.745455 \n",
       "C 315.376223 13.745455 313.079655 14.696724 311.386622 16.389757 \n",
       "C 309.693589 18.08279 308.74232 20.379358 308.74232 22.773668 \n",
       "C 308.74232 25.167978 309.693589 27.464546 311.386622 29.157578 \n",
       "C 313.079655 30.850611 315.376223 31.801881 317.770533 31.801881 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 362.911599 94.999373 \n",
       "C 364.108754 94.999373 365.257038 94.523738 366.103554 93.677222 \n",
       "C 366.950071 92.830705 367.425705 91.682422 367.425705 90.485266 \n",
       "C 367.425705 89.288111 366.950071 88.139828 366.103554 87.293311 \n",
       "C 365.257038 86.446795 364.108754 85.97116 362.911599 85.97116 \n",
       "C 361.714444 85.97116 360.56616 86.446795 359.719643 87.293311 \n",
       "C 358.873127 88.139828 358.397492 89.288111 358.397492 90.485266 \n",
       "C 358.397492 91.682422 358.873127 92.830705 359.719643 93.677222 \n",
       "C 360.56616 94.523738 361.714444 94.999373 362.911599 94.999373 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path clip-path=\"url(#p63e9ac6467)\" d=\"M 362.911599 140.140439 \n",
       "C 364.108754 140.140439 365.257038 139.664804 366.103554 138.818288 \n",
       "C 366.950071 137.971771 367.425705 136.823487 367.425705 135.626332 \n",
       "C 367.425705 134.429177 366.950071 133.280893 366.103554 132.434377 \n",
       "C 365.257038 131.58786 364.108754 131.112226 362.911599 131.112226 \n",
       "C 361.714444 131.112226 360.56616 131.58786 359.719643 132.434377 \n",
       "C 358.873127 133.280893 358.397492 134.429177 358.397492 135.626332 \n",
       "C 358.397492 136.823487 358.873127 137.971771 359.719643 138.818288 \n",
       "C 360.56616 139.664804 361.714444 140.140439 362.911599 140.140439 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_1\">\n",
       "    <!-- 23π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "     <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "     <path d=\"M 3.609375 54.6875 \n",
       "L 56 54.6875 \n",
       "L 56 45.703125 \n",
       "L 49.125 45.703125 \n",
       "L 49.125 12.109375 \n",
       "Q 49.125 8.59375 50.3125 7.046875 \n",
       "Q 51.515625 5.515625 54.203125 5.515625 \n",
       "Q 54.9375 5.515625 56 5.640625 \n",
       "Q 57.078125 5.765625 57.421875 5.8125 \n",
       "L 57.421875 -0.6875 \n",
       "Q 55.71875 -1.3125 53.90625 -1.609375 \n",
       "Q 52.09375 -1.90625 50.296875 -1.90625 \n",
       "Q 44.4375 -1.90625 42.1875 1.296875 \n",
       "Q 39.9375 4.5 39.9375 13.09375 \n",
       "L 39.9375 45.703125 \n",
       "L 19.78125 45.703125 \n",
       "L 19.78125 0 \n",
       "L 10.59375 0 \n",
       "L 10.59375 45.703125 \n",
       "L 3.609375 45.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-960\"/>\n",
       "     <path d=\"M 25.390625 72.90625 \n",
       "L 33.6875 72.90625 \n",
       "L 8.296875 -9.28125 \n",
       "L 0 -9.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-47\"/>\n",
       "     <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(258.693842 113.055799)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_2\">\n",
       "    <!-- 23π/12 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(258.693842 158.196865)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_3\">\n",
       "    <!-- 19π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 10.984375 1.515625 \n",
       "L 10.984375 10.5 \n",
       "Q 14.703125 8.734375 18.5 7.8125 \n",
       "Q 22.3125 6.890625 25.984375 6.890625 \n",
       "Q 35.75 6.890625 40.890625 13.453125 \n",
       "Q 46.046875 20.015625 46.78125 33.40625 \n",
       "Q 43.953125 29.203125 39.59375 26.953125 \n",
       "Q 35.25 24.703125 29.984375 24.703125 \n",
       "Q 19.046875 24.703125 12.671875 31.3125 \n",
       "Q 6.296875 37.9375 6.296875 49.421875 \n",
       "Q 6.296875 60.640625 12.9375 67.421875 \n",
       "Q 19.578125 74.21875 30.609375 74.21875 \n",
       "Q 43.265625 74.21875 49.921875 64.515625 \n",
       "Q 56.59375 54.828125 56.59375 36.375 \n",
       "Q 56.59375 19.140625 48.40625 8.859375 \n",
       "Q 40.234375 -1.421875 26.421875 -1.421875 \n",
       "Q 22.703125 -1.421875 18.890625 -0.6875 \n",
       "Q 15.09375 0.046875 10.984375 1.515625 \n",
       "z\n",
       "M 30.609375 32.421875 \n",
       "Q 37.25 32.421875 41.125 36.953125 \n",
       "Q 45.015625 41.5 45.015625 49.421875 \n",
       "Q 45.015625 57.28125 41.125 61.84375 \n",
       "Q 37.25 66.40625 30.609375 66.40625 \n",
       "Q 23.96875 66.40625 20.09375 61.84375 \n",
       "Q 16.21875 57.28125 16.21875 49.421875 \n",
       "Q 16.21875 41.5 20.09375 36.953125 \n",
       "Q 23.96875 32.421875 30.609375 32.421875 \n",
       "z\n",
       "\" id=\"DejaVuSans-57\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(303.834908 45.344201)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p63e9ac6467\">\n",
       "   <rect height=\"144\" width=\"576\" x=\"7.2\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = zx.Circuit(2)\n",
    "c.gates = [zx.gates.FSim(Fraction(1,2), Fraction(1,6), 0, 1)]\n",
    "g = c.to_graph(zh=True)\n",
    "zx.draw(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.       +0.j ,  0.       +0.j ,  0.       +0.j ,  0.       +0.j ],\n",
       "       [ 0.       +0.j ,  0.       +0.j , -0.       -1.j ,  0.       +0.j ],\n",
       "       [ 0.       +0.j , -0.       -1.j ,  0.       +0.j ,  0.       +0.j ],\n",
       "       [ 0.       +0.j ,  0.       +0.j ,  0.       +0.j ,  0.8660254-0.5j]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8660254037844387-0.49999999999999994j)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp((-1.0j/6.0) * math.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"158.4pt\" version=\"1.1\" viewBox=\"0 0 590.4 158.4\" width=\"590.4pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 158.4 \n",
       "L 590.4 158.4 \n",
       "L 590.4 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 38.515508 53.531551 \n",
       "L 89.852406 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 38.515508 104.868449 \n",
       "L 89.852406 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 89.852406 53.531551 \n",
       "L 89.852406 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 89.852406 53.531551 \n",
       "L 141.189305 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_5\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 89.852406 104.868449 \n",
       "L 141.189305 104.868449 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_6\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 141.189305 104.868449 \n",
       "L 192.526203 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_7\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 141.189305 53.531551 \n",
       "L 243.863102 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_8\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 192.526203 104.868449 \n",
       "L 243.863102 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_9\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 243.863102 104.868449 \n",
       "L 243.863102 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_10\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 243.863102 104.868449 \n",
       "L 295.2 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_11\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 243.863102 53.531551 \n",
       "L 346.536898 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_12\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 295.2 104.868449 \n",
       "L 346.536898 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 346.536898 104.868449 \n",
       "L 346.536898 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 346.536898 104.868449 \n",
       "L 397.873797 104.868449 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 346.536898 53.531551 \n",
       "L 449.210695 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_16\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 397.873797 104.868449 \n",
       "L 449.210695 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_17\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 449.210695 53.531551 \n",
       "L 449.210695 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_18\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 449.210695 53.531551 \n",
       "L 500.547594 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_19\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 449.210695 104.868449 \n",
       "L 500.547594 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_20\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 500.547594 53.531551 \n",
       "L 551.884492 53.531551 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_21\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 500.547594 104.868449 \n",
       "L 551.884492 104.868449 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_2\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 38.515508 58.665241 \n",
       "C 39.876978 58.665241 41.18287 58.124323 42.145575 57.161618 \n",
       "C 43.10828 56.198913 43.649198 54.893021 43.649198 53.531551 \n",
       "C 43.649198 52.17008 43.10828 50.864189 42.145575 49.901484 \n",
       "C 41.18287 48.938779 39.876978 48.397861 38.515508 48.397861 \n",
       "C 37.154038 48.397861 35.848146 48.938779 34.885441 49.901484 \n",
       "C 33.922736 50.864189 33.381818 52.17008 33.381818 53.531551 \n",
       "C 33.381818 54.893021 33.922736 56.198913 34.885441 57.161618 \n",
       "C 35.848146 58.124323 37.154038 58.665241 38.515508 58.665241 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 38.515508 110.002139 \n",
       "C 39.876978 110.002139 41.18287 109.461221 42.145575 108.498516 \n",
       "C 43.10828 107.535811 43.649198 106.22992 43.649198 104.868449 \n",
       "C 43.649198 103.506979 43.10828 102.201087 42.145575 101.238382 \n",
       "C 41.18287 100.275677 39.876978 99.734759 38.515508 99.734759 \n",
       "C 37.154038 99.734759 35.848146 100.275677 34.885441 101.238382 \n",
       "C 33.922736 102.201087 33.381818 103.506979 33.381818 104.868449 \n",
       "C 33.381818 106.22992 33.922736 107.535811 34.885441 108.498516 \n",
       "C 35.848146 109.461221 37.154038 110.002139 38.515508 110.002139 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 89.852406 63.79893 \n",
       "C 92.575347 63.79893 95.18713 62.717095 97.11254 60.791685 \n",
       "C 99.03795 58.866275 100.119786 56.254492 100.119786 53.531551 \n",
       "C 100.119786 50.80861 99.03795 48.196827 97.11254 46.271417 \n",
       "C 95.18713 44.346007 92.575347 43.264171 89.852406 43.264171 \n",
       "C 87.129465 43.264171 84.517683 44.346007 82.592273 46.271417 \n",
       "C 80.666863 48.196827 79.585027 50.80861 79.585027 53.531551 \n",
       "C 79.585027 56.254492 80.666863 58.866275 82.592273 60.791685 \n",
       "C 84.517683 62.717095 87.129465 63.79893 89.852406 63.79893 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 89.852406 115.135829 \n",
       "C 92.575347 115.135829 95.18713 114.053993 97.11254 112.128583 \n",
       "C 99.03795 110.203173 100.119786 107.59139 100.119786 104.868449 \n",
       "C 100.119786 102.145508 99.03795 99.533725 97.11254 97.608315 \n",
       "C 95.18713 95.682905 92.575347 94.60107 89.852406 94.60107 \n",
       "C 87.129465 94.60107 84.517683 95.682905 82.592273 97.608315 \n",
       "C 80.666863 99.533725 79.585027 102.145508 79.585027 104.868449 \n",
       "C 79.585027 107.59139 80.666863 110.203173 82.592273 112.128583 \n",
       "C 84.517683 114.053993 87.129465 115.135829 89.852406 115.135829 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 141.189305 115.135829 \n",
       "C 143.912246 115.135829 146.524029 114.053993 148.449439 112.128583 \n",
       "C 150.374849 110.203173 151.456684 107.59139 151.456684 104.868449 \n",
       "C 151.456684 102.145508 150.374849 99.533725 148.449439 97.608315 \n",
       "C 146.524029 95.682905 143.912246 94.60107 141.189305 94.60107 \n",
       "C 138.466364 94.60107 135.854581 95.682905 133.929171 97.608315 \n",
       "C 132.003761 99.533725 130.921925 102.145508 130.921925 104.868449 \n",
       "C 130.921925 107.59139 132.003761 110.203173 133.929171 112.128583 \n",
       "C 135.854581 114.053993 138.466364 115.135829 141.189305 115.135829 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 141.189305 63.79893 \n",
       "C 143.912246 63.79893 146.524029 62.717095 148.449439 60.791685 \n",
       "C 150.374849 58.866275 151.456684 56.254492 151.456684 53.531551 \n",
       "C 151.456684 50.80861 150.374849 48.196827 148.449439 46.271417 \n",
       "C 146.524029 44.346007 143.912246 43.264171 141.189305 43.264171 \n",
       "C 138.466364 43.264171 135.854581 44.346007 133.929171 46.271417 \n",
       "C 132.003761 48.196827 130.921925 50.80861 130.921925 53.531551 \n",
       "C 130.921925 56.254492 132.003761 58.866275 133.929171 60.791685 \n",
       "C 135.854581 62.717095 138.466364 63.79893 141.189305 63.79893 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 192.526203 115.135829 \n",
       "C 195.249144 115.135829 197.860927 114.053993 199.786337 112.128583 \n",
       "C 201.711747 110.203173 202.793583 107.59139 202.793583 104.868449 \n",
       "C 202.793583 102.145508 201.711747 99.533725 199.786337 97.608315 \n",
       "C 197.860927 95.682905 195.249144 94.60107 192.526203 94.60107 \n",
       "C 189.803262 94.60107 187.191479 95.682905 185.266069 97.608315 \n",
       "C 183.340659 99.533725 182.258824 102.145508 182.258824 104.868449 \n",
       "C 182.258824 107.59139 183.340659 110.203173 185.266069 112.128583 \n",
       "C 187.191479 114.053993 189.803262 115.135829 192.526203 115.135829 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 243.863102 115.135829 \n",
       "C 246.586043 115.135829 249.197825 114.053993 251.123235 112.128583 \n",
       "C 253.048645 110.203173 254.130481 107.59139 254.130481 104.868449 \n",
       "C 254.130481 102.145508 253.048645 99.533725 251.123235 97.608315 \n",
       "C 249.197825 95.682905 246.586043 94.60107 243.863102 94.60107 \n",
       "C 241.140161 94.60107 238.528378 95.682905 236.602968 97.608315 \n",
       "C 234.677558 99.533725 233.595722 102.145508 233.595722 104.868449 \n",
       "C 233.595722 107.59139 234.677558 110.203173 236.602968 112.128583 \n",
       "C 238.528378 114.053993 241.140161 115.135829 243.863102 115.135829 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 243.863102 63.79893 \n",
       "C 246.586043 63.79893 249.197825 62.717095 251.123235 60.791685 \n",
       "C 253.048645 58.866275 254.130481 56.254492 254.130481 53.531551 \n",
       "C 254.130481 50.80861 253.048645 48.196827 251.123235 46.271417 \n",
       "C 249.197825 44.346007 246.586043 43.264171 243.863102 43.264171 \n",
       "C 241.140161 43.264171 238.528378 44.346007 236.602968 46.271417 \n",
       "C 234.677558 48.196827 233.595722 50.80861 233.595722 53.531551 \n",
       "C 233.595722 56.254492 234.677558 58.866275 236.602968 60.791685 \n",
       "C 238.528378 62.717095 241.140161 63.79893 243.863102 63.79893 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 295.2 115.135829 \n",
       "C 297.922941 115.135829 300.534724 114.053993 302.460134 112.128583 \n",
       "C 304.385544 110.203173 305.46738 107.59139 305.46738 104.868449 \n",
       "C 305.46738 102.145508 304.385544 99.533725 302.460134 97.608315 \n",
       "C 300.534724 95.682905 297.922941 94.60107 295.2 94.60107 \n",
       "C 292.477059 94.60107 289.865276 95.682905 287.939866 97.608315 \n",
       "C 286.014456 99.533725 284.93262 102.145508 284.93262 104.868449 \n",
       "C 284.93262 107.59139 286.014456 110.203173 287.939866 112.128583 \n",
       "C 289.865276 114.053993 292.477059 115.135829 295.2 115.135829 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_12\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 346.536898 115.135829 \n",
       "C 349.259839 115.135829 351.871622 114.053993 353.797032 112.128583 \n",
       "C 355.722442 110.203173 356.804278 107.59139 356.804278 104.868449 \n",
       "C 356.804278 102.145508 355.722442 99.533725 353.797032 97.608315 \n",
       "C 351.871622 95.682905 349.259839 94.60107 346.536898 94.60107 \n",
       "C 343.813957 94.60107 341.202175 95.682905 339.276765 97.608315 \n",
       "C 337.351355 99.533725 336.269519 102.145508 336.269519 104.868449 \n",
       "C 336.269519 107.59139 337.351355 110.203173 339.276765 112.128583 \n",
       "C 341.202175 114.053993 343.813957 115.135829 346.536898 115.135829 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_13\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 346.536898 63.79893 \n",
       "C 349.259839 63.79893 351.871622 62.717095 353.797032 60.791685 \n",
       "C 355.722442 58.866275 356.804278 56.254492 356.804278 53.531551 \n",
       "C 356.804278 50.80861 355.722442 48.196827 353.797032 46.271417 \n",
       "C 351.871622 44.346007 349.259839 43.264171 346.536898 43.264171 \n",
       "C 343.813957 43.264171 341.202175 44.346007 339.276765 46.271417 \n",
       "C 337.351355 48.196827 336.269519 50.80861 336.269519 53.531551 \n",
       "C 336.269519 56.254492 337.351355 58.866275 339.276765 60.791685 \n",
       "C 341.202175 62.717095 343.813957 63.79893 346.536898 63.79893 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_14\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 397.873797 115.135829 \n",
       "C 400.596738 115.135829 403.208521 114.053993 405.133931 112.128583 \n",
       "C 407.059341 110.203173 408.141176 107.59139 408.141176 104.868449 \n",
       "C 408.141176 102.145508 407.059341 99.533725 405.133931 97.608315 \n",
       "C 403.208521 95.682905 400.596738 94.60107 397.873797 94.60107 \n",
       "C 395.150856 94.60107 392.539073 95.682905 390.613663 97.608315 \n",
       "C 388.688253 99.533725 387.606417 102.145508 387.606417 104.868449 \n",
       "C 387.606417 107.59139 388.688253 110.203173 390.613663 112.128583 \n",
       "C 392.539073 114.053993 395.150856 115.135829 397.873797 115.135829 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_15\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 449.210695 63.79893 \n",
       "C 451.933636 63.79893 454.545419 62.717095 456.470829 60.791685 \n",
       "C 458.396239 58.866275 459.478075 56.254492 459.478075 53.531551 \n",
       "C 459.478075 50.80861 458.396239 48.196827 456.470829 46.271417 \n",
       "C 454.545419 44.346007 451.933636 43.264171 449.210695 43.264171 \n",
       "C 446.487754 43.264171 443.875971 44.346007 441.950561 46.271417 \n",
       "C 440.025151 48.196827 438.943316 50.80861 438.943316 53.531551 \n",
       "C 438.943316 56.254492 440.025151 58.866275 441.950561 60.791685 \n",
       "C 443.875971 62.717095 446.487754 63.79893 449.210695 63.79893 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_16\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 449.210695 115.135829 \n",
       "C 451.933636 115.135829 454.545419 114.053993 456.470829 112.128583 \n",
       "C 458.396239 110.203173 459.478075 107.59139 459.478075 104.868449 \n",
       "C 459.478075 102.145508 458.396239 99.533725 456.470829 97.608315 \n",
       "C 454.545419 95.682905 451.933636 94.60107 449.210695 94.60107 \n",
       "C 446.487754 94.60107 443.875971 95.682905 441.950561 97.608315 \n",
       "C 440.025151 99.533725 438.943316 102.145508 438.943316 104.868449 \n",
       "C 438.943316 107.59139 440.025151 110.203173 441.950561 112.128583 \n",
       "C 443.875971 114.053993 446.487754 115.135829 449.210695 115.135829 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_17\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 500.547594 63.79893 \n",
       "C 503.270535 63.79893 505.882317 62.717095 507.807727 60.791685 \n",
       "C 509.733137 58.866275 510.814973 56.254492 510.814973 53.531551 \n",
       "C 510.814973 50.80861 509.733137 48.196827 507.807727 46.271417 \n",
       "C 505.882317 44.346007 503.270535 43.264171 500.547594 43.264171 \n",
       "C 497.824653 43.264171 495.21287 44.346007 493.28746 46.271417 \n",
       "C 491.36205 48.196827 490.280214 50.80861 490.280214 53.531551 \n",
       "C 490.280214 56.254492 491.36205 58.866275 493.28746 60.791685 \n",
       "C 495.21287 62.717095 497.824653 63.79893 500.547594 63.79893 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_18\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 500.547594 115.135829 \n",
       "C 503.270535 115.135829 505.882317 114.053993 507.807727 112.128583 \n",
       "C 509.733137 110.203173 510.814973 107.59139 510.814973 104.868449 \n",
       "C 510.814973 102.145508 509.733137 99.533725 507.807727 97.608315 \n",
       "C 505.882317 95.682905 503.270535 94.60107 500.547594 94.60107 \n",
       "C 497.824653 94.60107 495.21287 95.682905 493.28746 97.608315 \n",
       "C 491.36205 99.533725 490.280214 102.145508 490.280214 104.868449 \n",
       "C 490.280214 107.59139 491.36205 110.203173 493.28746 112.128583 \n",
       "C 495.21287 114.053993 497.824653 115.135829 500.547594 115.135829 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_19\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 551.884492 58.665241 \n",
       "C 553.245962 58.665241 554.551854 58.124323 555.514559 57.161618 \n",
       "C 556.477264 56.198913 557.018182 54.893021 557.018182 53.531551 \n",
       "C 557.018182 52.17008 556.477264 50.864189 555.514559 49.901484 \n",
       "C 554.551854 48.938779 553.245962 48.397861 551.884492 48.397861 \n",
       "C 550.523022 48.397861 549.21713 48.938779 548.254425 49.901484 \n",
       "C 547.29172 50.864189 546.750802 52.17008 546.750802 53.531551 \n",
       "C 546.750802 54.893021 547.29172 56.198913 548.254425 57.161618 \n",
       "C 549.21713 58.124323 550.523022 58.665241 551.884492 58.665241 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_20\">\n",
       "    <path clip-path=\"url(#p02ffb9e8ff)\" d=\"M 551.884492 110.002139 \n",
       "C 553.245962 110.002139 554.551854 109.461221 555.514559 108.498516 \n",
       "C 556.477264 107.535811 557.018182 106.22992 557.018182 104.868449 \n",
       "C 557.018182 103.506979 556.477264 102.201087 555.514559 101.238382 \n",
       "C 554.551854 100.275677 553.245962 99.734759 551.884492 99.734759 \n",
       "C 550.523022 99.734759 549.21713 100.275677 548.254425 101.238382 \n",
       "C 547.29172 102.201087 546.750802 103.506979 546.750802 104.868449 \n",
       "C 546.750802 106.22992 547.29172 107.535811 548.254425 108.498516 \n",
       "C 549.21713 109.461221 550.523022 110.002139 551.884492 110.002139 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_1\">\n",
       "    <!-- π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 3.609375 54.6875 \n",
       "L 56 54.6875 \n",
       "L 56 45.703125 \n",
       "L 49.125 45.703125 \n",
       "L 49.125 12.109375 \n",
       "Q 49.125 8.59375 50.3125 7.046875 \n",
       "Q 51.515625 5.515625 54.203125 5.515625 \n",
       "Q 54.9375 5.515625 56 5.640625 \n",
       "Q 57.078125 5.765625 57.421875 5.8125 \n",
       "L 57.421875 -0.6875 \n",
       "Q 55.71875 -1.3125 53.90625 -1.609375 \n",
       "Q 52.09375 -1.90625 50.296875 -1.90625 \n",
       "Q 44.4375 -1.90625 42.1875 1.296875 \n",
       "Q 39.9375 4.5 39.9375 13.09375 \n",
       "L 39.9375 45.703125 \n",
       "L 19.78125 45.703125 \n",
       "L 19.78125 0 \n",
       "L 10.59375 0 \n",
       "L 10.59375 45.703125 \n",
       "L 3.609375 45.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-960\"/>\n",
       "     <path d=\"M 25.390625 72.90625 \n",
       "L 33.6875 72.90625 \n",
       "L 8.296875 -9.28125 \n",
       "L 0 -9.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-47\"/>\n",
       "     <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(132.34368 79.2)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"60.205078\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"93.896484\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"157.519531\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_2\">\n",
       "    <!-- π/2 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(186.225578 130.536898)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"60.205078\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"93.896484\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_3\">\n",
       "    <!-- 3π/2 -->\n",
       "    <defs>\n",
       "     <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(286.354375 130.536898)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"123.828125\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"157.519531\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_4\">\n",
       "    <!-- 23π/12 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(486.611969 79.2)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_5\">\n",
       "    <!-- 23π/12 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(486.611969 130.536898)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p02ffb9e8ff\">\n",
       "   <rect height=\"144\" width=\"576\" x=\"7.2\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g0 = zx.qasm(\"\"\"\n",
    "qreg q[1];\n",
    "qreg r[1];\n",
    "cx r[0], q[0];\n",
    "h r[0];\n",
    "rz(0.0833333333333*pi) q[0];\n",
    "rz(0.5*pi) r[0];\n",
    "cx q[0], r[0];\n",
    "rz(-0.5*pi) r[0];\n",
    "cx q[0], r[0];\n",
    "h r[0];\n",
    "cx r[0], q[0];\n",
    "rz(-0.0833333333333*pi) q[0];\n",
    "rz(-0.0833333333333*pi) r[0];\n",
    "\"\"\").to_graph()\n",
    "\n",
    "zx.draw(g0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"165.069098pt\" version=\"1.1\" viewBox=\"0 0 590.4 165.069098\" width=\"590.4pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 165.069098 \n",
       "L 590.4 165.069098 \n",
       "L 590.4 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 102.686631 98.451337 \n",
       "L 333.702674 136.954011 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 102.686631 136.954011 \n",
       "L 141.189305 136.954011 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 141.189305 136.954011 \n",
       "L 256.697326 59.948663 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 141.189305 136.954011 \n",
       "L 333.702674 136.954011 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_5\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 141.189305 136.954011 \n",
       "L 487.713369 98.451337 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_6\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 256.697326 59.948663 \n",
       "L 333.702674 136.954011 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_7\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 256.697326 59.948663 \n",
       "L 256.697326 21.445989 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_8\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 333.702674 136.954011 \n",
       "L 487.713369 136.954011 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_2\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 102.686631 102.301604 \n",
       "C 103.707734 102.301604 104.687152 101.895916 105.409181 101.173887 \n",
       "C 106.13121 100.451858 106.536898 99.47244 106.536898 98.451337 \n",
       "C 106.536898 97.430234 106.13121 96.450815 105.409181 95.728787 \n",
       "C 104.687152 95.006758 103.707734 94.60107 102.686631 94.60107 \n",
       "C 101.665528 94.60107 100.68611 95.006758 99.964081 95.728787 \n",
       "C 99.242052 96.450815 98.836364 97.430234 98.836364 98.451337 \n",
       "C 98.836364 99.47244 99.242052 100.451858 99.964081 101.173887 \n",
       "C 100.68611 101.895916 101.665528 102.301604 102.686631 102.301604 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 102.686631 140.804278 \n",
       "C 103.707734 140.804278 104.687152 140.39859 105.409181 139.676561 \n",
       "C 106.13121 138.954532 106.536898 137.975114 106.536898 136.954011 \n",
       "C 106.536898 135.932908 106.13121 134.953489 105.409181 134.231461 \n",
       "C 104.687152 133.509432 103.707734 133.103743 102.686631 133.103743 \n",
       "C 101.665528 133.103743 100.68611 133.509432 99.964081 134.231461 \n",
       "C 99.242052 134.953489 98.836364 135.932908 98.836364 136.954011 \n",
       "C 98.836364 137.975114 99.242052 138.954532 99.964081 139.676561 \n",
       "C 100.68611 140.39859 101.665528 140.804278 102.686631 140.804278 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 141.189305 144.654545 \n",
       "C 143.231511 144.654545 145.190348 143.843169 146.634405 142.399111 \n",
       "C 148.078463 140.955054 148.88984 138.996216 148.88984 136.954011 \n",
       "C 148.88984 134.911805 148.078463 132.952968 146.634405 131.50891 \n",
       "C 145.190348 130.064853 143.231511 129.253476 141.189305 129.253476 \n",
       "C 139.147099 129.253476 137.188262 130.064853 135.744204 131.50891 \n",
       "C 134.300147 132.952968 133.48877 134.911805 133.48877 136.954011 \n",
       "C 133.48877 138.996216 134.300147 140.955054 135.744204 142.399111 \n",
       "C 137.188262 143.843169 139.147099 144.654545 141.189305 144.654545 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 256.697326 67.649198 \n",
       "C 258.739532 67.649198 260.698369 66.837821 262.142427 65.393763 \n",
       "C 263.586484 63.949706 264.397861 61.990869 264.397861 59.948663 \n",
       "C 264.397861 57.906457 263.586484 55.94762 262.142427 54.503563 \n",
       "C 260.698369 53.059505 258.739532 52.248128 256.697326 52.248128 \n",
       "C 254.655121 52.248128 252.696283 53.059505 251.252226 54.503563 \n",
       "C 249.808168 55.94762 248.996791 57.906457 248.996791 59.948663 \n",
       "C 248.996791 61.990869 249.808168 63.949706 251.252226 65.393763 \n",
       "C 252.696283 66.837821 254.655121 67.649198 256.697326 67.649198 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 333.702674 144.654545 \n",
       "C 335.744879 144.654545 337.703717 143.843169 339.147774 142.399111 \n",
       "C 340.591832 140.955054 341.403209 138.996216 341.403209 136.954011 \n",
       "C 341.403209 134.911805 340.591832 132.952968 339.147774 131.50891 \n",
       "C 337.703717 130.064853 335.744879 129.253476 333.702674 129.253476 \n",
       "C 331.660468 129.253476 329.701631 130.064853 328.257573 131.50891 \n",
       "C 326.813516 132.952968 326.002139 134.911805 326.002139 136.954011 \n",
       "C 326.002139 138.996216 326.813516 140.955054 328.257573 142.399111 \n",
       "C 329.701631 143.843169 331.660468 144.654545 333.702674 144.654545 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 487.713369 102.301604 \n",
       "C 488.734472 102.301604 489.71389 101.895916 490.435919 101.173887 \n",
       "C 491.157948 100.451858 491.563636 99.47244 491.563636 98.451337 \n",
       "C 491.563636 97.430234 491.157948 96.450815 490.435919 95.728787 \n",
       "C 489.71389 95.006758 488.734472 94.60107 487.713369 94.60107 \n",
       "C 486.692266 94.60107 485.712848 95.006758 484.990819 95.728787 \n",
       "C 484.26879 96.450815 483.863102 97.430234 483.863102 98.451337 \n",
       "C 483.863102 99.47244 484.26879 100.451858 484.990819 101.173887 \n",
       "C 485.712848 101.895916 486.692266 102.301604 487.713369 102.301604 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 487.713369 140.804278 \n",
       "C 488.734472 140.804278 489.71389 140.39859 490.435919 139.676561 \n",
       "C 491.157948 138.954532 491.563636 137.975114 491.563636 136.954011 \n",
       "C 491.563636 135.932908 491.157948 134.953489 490.435919 134.231461 \n",
       "C 489.71389 133.509432 488.734472 133.103743 487.713369 133.103743 \n",
       "C 486.692266 133.103743 485.712848 133.509432 484.990819 134.231461 \n",
       "C 484.26879 134.953489 483.863102 135.932908 483.863102 136.954011 \n",
       "C 483.863102 137.975114 484.26879 138.954532 484.990819 139.676561 \n",
       "C 485.712848 140.39859 486.692266 140.804278 487.713369 140.804278 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path clip-path=\"url(#pc81c2a733b)\" d=\"M 256.697326 29.146524 \n",
       "C 258.739532 29.146524 260.698369 28.335147 262.142427 26.89109 \n",
       "C 263.586484 25.447032 264.397861 23.488195 264.397861 21.445989 \n",
       "C 264.397861 19.403784 263.586484 17.444946 262.142427 16.000889 \n",
       "C 260.698369 14.556831 258.739532 13.745455 256.697326 13.745455 \n",
       "C 254.655121 13.745455 252.696283 14.556831 251.252226 16.000889 \n",
       "C 249.808168 17.444946 248.996791 19.403784 248.996791 21.445989 \n",
       "C 248.996791 23.488195 249.808168 25.447032 251.252226 26.89109 \n",
       "C 252.696283 28.335147 254.655121 29.146524 256.697326 29.146524 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_1\">\n",
       "    <!-- 17π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     <path d=\"M 8.203125 72.90625 \n",
       "L 55.078125 72.90625 \n",
       "L 55.078125 68.703125 \n",
       "L 28.609375 0 \n",
       "L 18.3125 0 \n",
       "L 43.21875 64.59375 \n",
       "L 8.203125 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-55\"/>\n",
       "     <path d=\"M 3.609375 54.6875 \n",
       "L 56 54.6875 \n",
       "L 56 45.703125 \n",
       "L 49.125 45.703125 \n",
       "L 49.125 12.109375 \n",
       "Q 49.125 8.59375 50.3125 7.046875 \n",
       "Q 51.515625 5.515625 54.203125 5.515625 \n",
       "Q 54.9375 5.515625 56 5.640625 \n",
       "Q 57.078125 5.765625 57.421875 5.8125 \n",
       "L 57.421875 -0.6875 \n",
       "Q 55.71875 -1.3125 53.90625 -1.609375 \n",
       "Q 52.09375 -1.90625 50.296875 -1.90625 \n",
       "Q 44.4375 -1.90625 42.1875 1.296875 \n",
       "Q 39.9375 4.5 39.9375 13.09375 \n",
       "L 39.9375 45.703125 \n",
       "L 19.78125 45.703125 \n",
       "L 19.78125 0 \n",
       "L 10.59375 0 \n",
       "L 10.59375 45.703125 \n",
       "L 3.609375 45.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-960\"/>\n",
       "     <path d=\"M 25.390625 72.90625 \n",
       "L 33.6875 72.90625 \n",
       "L 8.296875 -9.28125 \n",
       "L 0 -9.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-47\"/>\n",
       "     <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(127.25368 156.205348)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-55\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_2\">\n",
       "    <!-- 17π/12 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(319.767049 156.205348)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-55\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_3\">\n",
       "    <!-- π/12 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(247.851701 40.697326)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"60.205078\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"93.896484\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"157.519531\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pc81c2a733b\">\n",
       "   <rect height=\"144\" width=\"576\" x=\"7.2\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zx.full_reduce(g0)\n",
    "zx.draw(g0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"158.4pt\" version=\"1.1\" viewBox=\"0 0 590.4 158.4\" width=\"590.4pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 158.4 \n",
       "L 590.4 158.4 \n",
       "L 590.4 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 39.767627 47.270953 \n",
       "L 103.625721 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 39.767627 111.129047 \n",
       "L 103.625721 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 103.625721 111.129047 \n",
       "L 103.625721 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 103.625721 111.129047 \n",
       "L 167.483814 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_5\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 103.625721 47.270953 \n",
       "L 167.483814 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_6\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 167.483814 47.270953 \n",
       "L 167.483814 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_7\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 167.483814 47.270953 \n",
       "L 231.341907 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_8\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 167.483814 111.129047 \n",
       "L 231.341907 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_9\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 231.341907 111.129047 \n",
       "L 231.341907 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_10\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 231.341907 111.129047 \n",
       "L 295.2 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_11\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 231.341907 47.270953 \n",
       "L 295.2 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_12\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 295.2 111.129047 \n",
       "L 295.2 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 295.2 111.129047 \n",
       "L 359.058093 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 295.2 47.270953 \n",
       "L 422.916186 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 359.058093 111.129047 \n",
       "L 422.916186 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_16\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 422.916186 111.129047 \n",
       "L 422.916186 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_17\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 422.916186 111.129047 \n",
       "L 486.774279 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_18\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 422.916186 47.270953 \n",
       "L 486.774279 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_19\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 486.774279 47.270953 \n",
       "L 550.632373 47.270953 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_20\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 486.774279 111.129047 \n",
       "L 550.632373 111.129047 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_2\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 39.767627 53.656763 \n",
       "C 41.461164 53.656763 43.085565 52.983914 44.283077 51.786403 \n",
       "C 45.480588 50.588891 46.153437 48.96449 46.153437 47.270953 \n",
       "C 46.153437 45.577417 45.480588 43.953015 44.283077 42.755504 \n",
       "C 43.085565 41.557993 41.461164 40.885144 39.767627 40.885144 \n",
       "C 38.074091 40.885144 36.44969 41.557993 35.252178 42.755504 \n",
       "C 34.054667 43.953015 33.381818 45.577417 33.381818 47.270953 \n",
       "C 33.381818 48.96449 34.054667 50.588891 35.252178 51.786403 \n",
       "C 36.44969 52.983914 38.074091 53.656763 39.767627 53.656763 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 39.767627 117.514856 \n",
       "C 41.461164 117.514856 43.085565 116.842007 44.283077 115.644496 \n",
       "C 45.480588 114.446985 46.153437 112.822583 46.153437 111.129047 \n",
       "C 46.153437 109.43551 45.480588 107.811109 44.283077 106.613597 \n",
       "C 43.085565 105.416086 41.461164 104.743237 39.767627 104.743237 \n",
       "C 38.074091 104.743237 36.44969 105.416086 35.252178 106.613597 \n",
       "C 34.054667 107.811109 33.381818 109.43551 33.381818 111.129047 \n",
       "C 33.381818 112.822583 34.054667 114.446985 35.252178 115.644496 \n",
       "C 36.44969 116.842007 38.074091 117.514856 39.767627 117.514856 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 103.625721 123.900665 \n",
       "C 107.012793 123.900665 110.261597 122.554967 112.656619 120.159945 \n",
       "C 115.051641 117.764923 116.397339 114.516119 116.397339 111.129047 \n",
       "C 116.397339 107.741974 115.051641 104.493171 112.656619 102.098148 \n",
       "C 110.261597 99.703126 107.012793 98.357428 103.625721 98.357428 \n",
       "C 100.238648 98.357428 96.989845 99.703126 94.594822 102.098148 \n",
       "C 92.1998 104.493171 90.854102 107.741974 90.854102 111.129047 \n",
       "C 90.854102 114.516119 92.1998 117.764923 94.594822 120.159945 \n",
       "C 96.989845 122.554967 100.238648 123.900665 103.625721 123.900665 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 103.625721 60.042572 \n",
       "C 107.012793 60.042572 110.261597 58.696874 112.656619 56.301852 \n",
       "C 115.051641 53.906829 116.397339 50.658026 116.397339 47.270953 \n",
       "C 116.397339 43.883881 115.051641 40.635077 112.656619 38.240055 \n",
       "C 110.261597 35.845033 107.012793 34.499335 103.625721 34.499335 \n",
       "C 100.238648 34.499335 96.989845 35.845033 94.594822 38.240055 \n",
       "C 92.1998 40.635077 90.854102 43.883881 90.854102 47.270953 \n",
       "C 90.854102 50.658026 92.1998 53.906829 94.594822 56.301852 \n",
       "C 96.989845 58.696874 100.238648 60.042572 103.625721 60.042572 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 167.483814 60.042572 \n",
       "C 170.870887 60.042572 174.11969 58.696874 176.514712 56.301852 \n",
       "C 178.909734 53.906829 180.255432 50.658026 180.255432 47.270953 \n",
       "C 180.255432 43.883881 178.909734 40.635077 176.514712 38.240055 \n",
       "C 174.11969 35.845033 170.870887 34.499335 167.483814 34.499335 \n",
       "C 164.096741 34.499335 160.847938 35.845033 158.452916 38.240055 \n",
       "C 156.057893 40.635077 154.712195 43.883881 154.712195 47.270953 \n",
       "C 154.712195 50.658026 156.057893 53.906829 158.452916 56.301852 \n",
       "C 160.847938 58.696874 164.096741 60.042572 167.483814 60.042572 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 167.483814 123.900665 \n",
       "C 170.870887 123.900665 174.11969 122.554967 176.514712 120.159945 \n",
       "C 178.909734 117.764923 180.255432 114.516119 180.255432 111.129047 \n",
       "C 180.255432 107.741974 178.909734 104.493171 176.514712 102.098148 \n",
       "C 174.11969 99.703126 170.870887 98.357428 167.483814 98.357428 \n",
       "C 164.096741 98.357428 160.847938 99.703126 158.452916 102.098148 \n",
       "C 156.057893 104.493171 154.712195 107.741974 154.712195 111.129047 \n",
       "C 154.712195 114.516119 156.057893 117.764923 158.452916 120.159945 \n",
       "C 160.847938 122.554967 164.096741 123.900665 167.483814 123.900665 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 231.341907 123.900665 \n",
       "C 234.72898 123.900665 237.977783 122.554967 240.372805 120.159945 \n",
       "C 242.767827 117.764923 244.113525 114.516119 244.113525 111.129047 \n",
       "C 244.113525 107.741974 242.767827 104.493171 240.372805 102.098148 \n",
       "C 237.977783 99.703126 234.72898 98.357428 231.341907 98.357428 \n",
       "C 227.954834 98.357428 224.706031 99.703126 222.311009 102.098148 \n",
       "C 219.915987 104.493171 218.570288 107.741974 218.570288 111.129047 \n",
       "C 218.570288 114.516119 219.915987 117.764923 222.311009 120.159945 \n",
       "C 224.706031 122.554967 227.954834 123.900665 231.341907 123.900665 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 231.341907 60.042572 \n",
       "C 234.72898 60.042572 237.977783 58.696874 240.372805 56.301852 \n",
       "C 242.767827 53.906829 244.113525 50.658026 244.113525 47.270953 \n",
       "C 244.113525 43.883881 242.767827 40.635077 240.372805 38.240055 \n",
       "C 237.977783 35.845033 234.72898 34.499335 231.341907 34.499335 \n",
       "C 227.954834 34.499335 224.706031 35.845033 222.311009 38.240055 \n",
       "C 219.915987 40.635077 218.570288 43.883881 218.570288 47.270953 \n",
       "C 218.570288 50.658026 219.915987 53.906829 222.311009 56.301852 \n",
       "C 224.706031 58.696874 227.954834 60.042572 231.341907 60.042572 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 295.2 123.900665 \n",
       "C 298.587073 123.900665 301.835876 122.554967 304.230898 120.159945 \n",
       "C 306.62592 117.764923 307.971619 114.516119 307.971619 111.129047 \n",
       "C 307.971619 107.741974 306.62592 104.493171 304.230898 102.098148 \n",
       "C 301.835876 99.703126 298.587073 98.357428 295.2 98.357428 \n",
       "C 291.812927 98.357428 288.564124 99.703126 286.169102 102.098148 \n",
       "C 283.77408 104.493171 282.428381 107.741974 282.428381 111.129047 \n",
       "C 282.428381 114.516119 283.77408 117.764923 286.169102 120.159945 \n",
       "C 288.564124 122.554967 291.812927 123.900665 295.2 123.900665 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 295.2 60.042572 \n",
       "C 298.587073 60.042572 301.835876 58.696874 304.230898 56.301852 \n",
       "C 306.62592 53.906829 307.971619 50.658026 307.971619 47.270953 \n",
       "C 307.971619 43.883881 306.62592 40.635077 304.230898 38.240055 \n",
       "C 301.835876 35.845033 298.587073 34.499335 295.2 34.499335 \n",
       "C 291.812927 34.499335 288.564124 35.845033 286.169102 38.240055 \n",
       "C 283.77408 40.635077 282.428381 43.883881 282.428381 47.270953 \n",
       "C 282.428381 50.658026 283.77408 53.906829 286.169102 56.301852 \n",
       "C 288.564124 58.696874 291.812927 60.042572 295.2 60.042572 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_12\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 359.058093 123.900665 \n",
       "C 362.445166 123.900665 365.693969 122.554967 368.088991 120.159945 \n",
       "C 370.484013 117.764923 371.829712 114.516119 371.829712 111.129047 \n",
       "C 371.829712 107.741974 370.484013 104.493171 368.088991 102.098148 \n",
       "C 365.693969 99.703126 362.445166 98.357428 359.058093 98.357428 \n",
       "C 355.67102 98.357428 352.422217 99.703126 350.027195 102.098148 \n",
       "C 347.632173 104.493171 346.286475 107.741974 346.286475 111.129047 \n",
       "C 346.286475 114.516119 347.632173 117.764923 350.027195 120.159945 \n",
       "C 352.422217 122.554967 355.67102 123.900665 359.058093 123.900665 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_13\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 422.916186 123.900665 \n",
       "C 426.303259 123.900665 429.552062 122.554967 431.947084 120.159945 \n",
       "C 434.342107 117.764923 435.687805 114.516119 435.687805 111.129047 \n",
       "C 435.687805 107.741974 434.342107 104.493171 431.947084 102.098148 \n",
       "C 429.552062 99.703126 426.303259 98.357428 422.916186 98.357428 \n",
       "C 419.529113 98.357428 416.28031 99.703126 413.885288 102.098148 \n",
       "C 411.490266 104.493171 410.144568 107.741974 410.144568 111.129047 \n",
       "C 410.144568 114.516119 411.490266 117.764923 413.885288 120.159945 \n",
       "C 416.28031 122.554967 419.529113 123.900665 422.916186 123.900665 \n",
       "z\n",
       "\" style=\"fill:#ff0000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_14\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 422.916186 60.042572 \n",
       "C 426.303259 60.042572 429.552062 58.696874 431.947084 56.301852 \n",
       "C 434.342107 53.906829 435.687805 50.658026 435.687805 47.270953 \n",
       "C 435.687805 43.883881 434.342107 40.635077 431.947084 38.240055 \n",
       "C 429.552062 35.845033 426.303259 34.499335 422.916186 34.499335 \n",
       "C 419.529113 34.499335 416.28031 35.845033 413.885288 38.240055 \n",
       "C 411.490266 40.635077 410.144568 43.883881 410.144568 47.270953 \n",
       "C 410.144568 50.658026 411.490266 53.906829 413.885288 56.301852 \n",
       "C 416.28031 58.696874 419.529113 60.042572 422.916186 60.042572 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_15\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 486.774279 60.042572 \n",
       "C 490.161352 60.042572 493.410155 58.696874 495.805178 56.301852 \n",
       "C 498.2002 53.906829 499.545898 50.658026 499.545898 47.270953 \n",
       "C 499.545898 43.883881 498.2002 40.635077 495.805178 38.240055 \n",
       "C 493.410155 35.845033 490.161352 34.499335 486.774279 34.499335 \n",
       "C 483.387207 34.499335 480.138403 35.845033 477.743381 38.240055 \n",
       "C 475.348359 40.635077 474.002661 43.883881 474.002661 47.270953 \n",
       "C 474.002661 50.658026 475.348359 53.906829 477.743381 56.301852 \n",
       "C 480.138403 58.696874 483.387207 60.042572 486.774279 60.042572 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_16\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 486.774279 123.900665 \n",
       "C 490.161352 123.900665 493.410155 122.554967 495.805178 120.159945 \n",
       "C 498.2002 117.764923 499.545898 114.516119 499.545898 111.129047 \n",
       "C 499.545898 107.741974 498.2002 104.493171 495.805178 102.098148 \n",
       "C 493.410155 99.703126 490.161352 98.357428 486.774279 98.357428 \n",
       "C 483.387207 98.357428 480.138403 99.703126 477.743381 102.098148 \n",
       "C 475.348359 104.493171 474.002661 107.741974 474.002661 111.129047 \n",
       "C 474.002661 114.516119 475.348359 117.764923 477.743381 120.159945 \n",
       "C 480.138403 122.554967 483.387207 123.900665 486.774279 123.900665 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_17\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 550.632373 53.656763 \n",
       "C 552.325909 53.656763 553.95031 52.983914 555.147822 51.786403 \n",
       "C 556.345333 50.588891 557.018182 48.96449 557.018182 47.270953 \n",
       "C 557.018182 45.577417 556.345333 43.953015 555.147822 42.755504 \n",
       "C 553.95031 41.557993 552.325909 40.885144 550.632373 40.885144 \n",
       "C 548.938836 40.885144 547.314435 41.557993 546.116923 42.755504 \n",
       "C 544.919412 43.953015 544.246563 45.577417 544.246563 47.270953 \n",
       "C 544.246563 48.96449 544.919412 50.588891 546.116923 51.786403 \n",
       "C 547.314435 52.983914 548.938836 53.656763 550.632373 53.656763 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_18\">\n",
       "    <path clip-path=\"url(#p562c5b2643)\" d=\"M 550.632373 117.514856 \n",
       "C 552.325909 117.514856 553.95031 116.842007 555.147822 115.644496 \n",
       "C 556.345333 114.446985 557.018182 112.822583 557.018182 111.129047 \n",
       "C 557.018182 109.43551 556.345333 107.811109 555.147822 106.613597 \n",
       "C 553.95031 105.416086 552.325909 104.743237 550.632373 104.743237 \n",
       "C 548.938836 104.743237 547.314435 105.416086 546.116923 106.613597 \n",
       "C 544.919412 107.811109 544.246563 109.43551 544.246563 111.129047 \n",
       "C 544.246563 112.822583 544.919412 114.446985 546.116923 115.644496 \n",
       "C 547.314435 116.842007 548.938836 117.514856 550.632373 117.514856 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_1\">\n",
       "    <!-- 19π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     <path d=\"M 10.984375 1.515625 \n",
       "L 10.984375 10.5 \n",
       "Q 14.703125 8.734375 18.5 7.8125 \n",
       "Q 22.3125 6.890625 25.984375 6.890625 \n",
       "Q 35.75 6.890625 40.890625 13.453125 \n",
       "Q 46.046875 20.015625 46.78125 33.40625 \n",
       "Q 43.953125 29.203125 39.59375 26.953125 \n",
       "Q 35.25 24.703125 29.984375 24.703125 \n",
       "Q 19.046875 24.703125 12.671875 31.3125 \n",
       "Q 6.296875 37.9375 6.296875 49.421875 \n",
       "Q 6.296875 60.640625 12.9375 67.421875 \n",
       "Q 19.578125 74.21875 30.609375 74.21875 \n",
       "Q 43.265625 74.21875 49.921875 64.515625 \n",
       "Q 56.59375 54.828125 56.59375 36.375 \n",
       "Q 56.59375 19.140625 48.40625 8.859375 \n",
       "Q 40.234375 -1.421875 26.421875 -1.421875 \n",
       "Q 22.703125 -1.421875 18.890625 -0.6875 \n",
       "Q 15.09375 0.046875 10.984375 1.515625 \n",
       "z\n",
       "M 30.609375 32.421875 \n",
       "Q 37.25 32.421875 41.125 36.953125 \n",
       "Q 45.015625 41.5 45.015625 49.421875 \n",
       "Q 45.015625 57.28125 41.125 61.84375 \n",
       "Q 37.25 66.40625 30.609375 66.40625 \n",
       "Q 23.96875 66.40625 20.09375 61.84375 \n",
       "Q 16.21875 57.28125 16.21875 49.421875 \n",
       "Q 16.21875 41.5 20.09375 36.953125 \n",
       "Q 23.96875 32.421875 30.609375 32.421875 \n",
       "z\n",
       "\" id=\"DejaVuSans-57\"/>\n",
       "     <path d=\"M 3.609375 54.6875 \n",
       "L 56 54.6875 \n",
       "L 56 45.703125 \n",
       "L 49.125 45.703125 \n",
       "L 49.125 12.109375 \n",
       "Q 49.125 8.59375 50.3125 7.046875 \n",
       "Q 51.515625 5.515625 54.203125 5.515625 \n",
       "Q 54.9375 5.515625 56 5.640625 \n",
       "Q 57.078125 5.765625 57.421875 5.8125 \n",
       "L 57.421875 -0.6875 \n",
       "Q 55.71875 -1.3125 53.90625 -1.609375 \n",
       "Q 52.09375 -1.90625 50.296875 -1.90625 \n",
       "Q 44.4375 -1.90625 42.1875 1.296875 \n",
       "Q 39.9375 4.5 39.9375 13.09375 \n",
       "L 39.9375 45.703125 \n",
       "L 19.78125 45.703125 \n",
       "L 19.78125 0 \n",
       "L 10.59375 0 \n",
       "L 10.59375 45.703125 \n",
       "L 3.609375 45.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-960\"/>\n",
       "     <path d=\"M 25.390625 72.90625 \n",
       "L 33.6875 72.90625 \n",
       "L 8.296875 -9.28125 \n",
       "L 0 -9.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-47\"/>\n",
       "     <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(345.122468 143.058093)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_2\">\n",
       "    <!-- 23π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(472.838654 79.2)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_3\">\n",
       "    <!-- 23π/12 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(472.838654 143.058093)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p562c5b2643\">\n",
       "   <rect height=\"144\" width=\"576\" x=\"7.2\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = zx.Circuit(2)\n",
    "c.gates = [\n",
    "    zx.gates.SWAP(0,1),\n",
    "    zx.gates.ParityPhase(Fraction(19,12), 0, 1),\n",
    "    zx.gates.ZPhase(0, Fraction(-1,12)),\n",
    "    zx.gates.ZPhase(1, Fraction(-1,12))\n",
    "]\n",
    "g1 = c.to_graph()\n",
    "zx.draw(g1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.       +0.j , 0.       +0.j , 0.       +0.j , 0.       +0.j ],\n",
       "       [0.       +0.j , 0.       +0.j , 0.       -1.j , 0.       +0.j ],\n",
       "       [0.       +0.j , 0.       -1.j , 0.       +0.j , 0.       +0.j ],\n",
       "       [0.       +0.j , 0.       +0.j , 0.       +0.j , 0.8660254-0.5j]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g0.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.       +0.j ,  0.       +0.j ,  0.       +0.j ,  0.       +0.j ],\n",
       "       [ 0.       +0.j ,  0.       +0.j , -0.       -1.j ,  0.       +0.j ],\n",
       "       [ 0.       +0.j , -0.       -1.j ,  0.       +0.j ,  0.       +0.j ],\n",
       "       [ 0.       +0.j ,  0.       +0.j ,  0.       +0.j ,  0.8660254-0.5j]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g1.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zx.compare_tensors(g0,g1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"165.069098pt\" version=\"1.1\" viewBox=\"0 0 590.4 165.069098\" width=\"590.4pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 165.069098 \n",
       "L 590.4 165.069098 \n",
       "L 590.4 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 83.435294 98.451337 \n",
       "L 468.462032 136.954011 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 83.435294 136.954011 \n",
       "L 198.943316 98.451337 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 198.943316 98.451337 \n",
       "L 429.959358 59.948663 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 198.943316 98.451337 \n",
       "L 506.964706 98.451337 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_5\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 429.959358 59.948663 \n",
       "L 468.462032 136.954011 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_6\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 429.959358 59.948663 \n",
       "L 429.959358 21.445989 \n",
       "\" style=\"fill:none;stroke:#0099ff;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_7\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 468.462032 136.954011 \n",
       "L 506.964706 136.954011 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_2\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 83.435294 102.301604 \n",
       "C 84.456397 102.301604 85.435816 101.895916 86.157844 101.173887 \n",
       "C 86.879873 100.451858 87.285561 99.47244 87.285561 98.451337 \n",
       "C 87.285561 97.430234 86.879873 96.450815 86.157844 95.728787 \n",
       "C 85.435816 95.006758 84.456397 94.60107 83.435294 94.60107 \n",
       "C 82.414191 94.60107 81.434773 95.006758 80.712744 95.728787 \n",
       "C 79.990715 96.450815 79.585027 97.430234 79.585027 98.451337 \n",
       "C 79.585027 99.47244 79.990715 100.451858 80.712744 101.173887 \n",
       "C 81.434773 101.895916 82.414191 102.301604 83.435294 102.301604 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 83.435294 140.804278 \n",
       "C 84.456397 140.804278 85.435816 140.39859 86.157844 139.676561 \n",
       "C 86.879873 138.954532 87.285561 137.975114 87.285561 136.954011 \n",
       "C 87.285561 135.932908 86.879873 134.953489 86.157844 134.231461 \n",
       "C 85.435816 133.509432 84.456397 133.103743 83.435294 133.103743 \n",
       "C 82.414191 133.103743 81.434773 133.509432 80.712744 134.231461 \n",
       "C 79.990715 134.953489 79.585027 135.932908 79.585027 136.954011 \n",
       "C 79.585027 137.975114 79.990715 138.954532 80.712744 139.676561 \n",
       "C 81.434773 140.39859 82.414191 140.804278 83.435294 140.804278 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 198.943316 106.151872 \n",
       "C 200.985521 106.151872 202.944358 105.340495 204.388416 103.896437 \n",
       "C 205.832473 102.45238 206.64385 100.493543 206.64385 98.451337 \n",
       "C 206.64385 96.409131 205.832473 94.450294 204.388416 93.006237 \n",
       "C 202.944358 91.562179 200.985521 90.750802 198.943316 90.750802 \n",
       "C 196.90111 90.750802 194.942273 91.562179 193.498215 93.006237 \n",
       "C 192.054158 94.450294 191.242781 96.409131 191.242781 98.451337 \n",
       "C 191.242781 100.493543 192.054158 102.45238 193.498215 103.896437 \n",
       "C 194.942273 105.340495 196.90111 106.151872 198.943316 106.151872 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 429.959358 67.649198 \n",
       "C 432.001564 67.649198 433.960401 66.837821 435.404459 65.393763 \n",
       "C 436.848516 63.949706 437.659893 61.990869 437.659893 59.948663 \n",
       "C 437.659893 57.906457 436.848516 55.94762 435.404459 54.503563 \n",
       "C 433.960401 53.059505 432.001564 52.248128 429.959358 52.248128 \n",
       "C 427.917153 52.248128 425.958315 53.059505 424.514258 54.503563 \n",
       "C 423.0702 55.94762 422.258824 57.906457 422.258824 59.948663 \n",
       "C 422.258824 61.990869 423.0702 63.949706 424.514258 65.393763 \n",
       "C 425.958315 66.837821 427.917153 67.649198 429.959358 67.649198 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 468.462032 144.654545 \n",
       "C 470.504238 144.654545 472.463075 143.843169 473.907132 142.399111 \n",
       "C 475.35119 140.955054 476.162567 138.996216 476.162567 136.954011 \n",
       "C 476.162567 134.911805 475.35119 132.952968 473.907132 131.50891 \n",
       "C 472.463075 130.064853 470.504238 129.253476 468.462032 129.253476 \n",
       "C 466.419826 129.253476 464.460989 130.064853 463.016932 131.50891 \n",
       "C 461.572874 132.952968 460.761497 134.911805 460.761497 136.954011 \n",
       "C 460.761497 138.996216 461.572874 140.955054 463.016932 142.399111 \n",
       "C 464.460989 143.843169 466.419826 144.654545 468.462032 144.654545 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 506.964706 102.301604 \n",
       "C 507.985809 102.301604 508.965227 101.895916 509.687256 101.173887 \n",
       "C 510.409285 100.451858 510.814973 99.47244 510.814973 98.451337 \n",
       "C 510.814973 97.430234 510.409285 96.450815 509.687256 95.728787 \n",
       "C 508.965227 95.006758 507.985809 94.60107 506.964706 94.60107 \n",
       "C 505.943603 94.60107 504.964184 95.006758 504.242156 95.728787 \n",
       "C 503.520127 96.450815 503.114439 97.430234 503.114439 98.451337 \n",
       "C 503.114439 99.47244 503.520127 100.451858 504.242156 101.173887 \n",
       "C 504.964184 101.895916 505.943603 102.301604 506.964706 102.301604 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 506.964706 140.804278 \n",
       "C 507.985809 140.804278 508.965227 140.39859 509.687256 139.676561 \n",
       "C 510.409285 138.954532 510.814973 137.975114 510.814973 136.954011 \n",
       "C 510.814973 135.932908 510.409285 134.953489 509.687256 134.231461 \n",
       "C 508.965227 133.509432 507.985809 133.103743 506.964706 133.103743 \n",
       "C 505.943603 133.103743 504.964184 133.509432 504.242156 134.231461 \n",
       "C 503.520127 134.953489 503.114439 135.932908 503.114439 136.954011 \n",
       "C 503.114439 137.975114 503.520127 138.954532 504.242156 139.676561 \n",
       "C 504.964184 140.39859 505.943603 140.804278 506.964706 140.804278 \n",
       "z\n",
       "\" style=\"stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path clip-path=\"url(#p260f90f972)\" d=\"M 429.959358 29.146524 \n",
       "C 432.001564 29.146524 433.960401 28.335147 435.404459 26.89109 \n",
       "C 436.848516 25.447032 437.659893 23.488195 437.659893 21.445989 \n",
       "C 437.659893 19.403784 436.848516 17.444946 435.404459 16.000889 \n",
       "C 433.960401 14.556831 432.001564 13.745455 429.959358 13.745455 \n",
       "C 427.917153 13.745455 425.958315 14.556831 424.514258 16.000889 \n",
       "C 423.0702 17.444946 422.258824 19.403784 422.258824 21.445989 \n",
       "C 422.258824 23.488195 423.0702 25.447032 424.514258 26.89109 \n",
       "C 425.958315 28.335147 427.917153 29.146524 429.959358 29.146524 \n",
       "z\n",
       "\" style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_1\">\n",
       "    <!-- 23π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "     <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "     <path d=\"M 3.609375 54.6875 \n",
       "L 56 54.6875 \n",
       "L 56 45.703125 \n",
       "L 49.125 45.703125 \n",
       "L 49.125 12.109375 \n",
       "Q 49.125 8.59375 50.3125 7.046875 \n",
       "Q 51.515625 5.515625 54.203125 5.515625 \n",
       "Q 54.9375 5.515625 56 5.640625 \n",
       "Q 57.078125 5.765625 57.421875 5.8125 \n",
       "L 57.421875 -0.6875 \n",
       "Q 55.71875 -1.3125 53.90625 -1.609375 \n",
       "Q 52.09375 -1.90625 50.296875 -1.90625 \n",
       "Q 44.4375 -1.90625 42.1875 1.296875 \n",
       "Q 39.9375 4.5 39.9375 13.09375 \n",
       "L 39.9375 45.703125 \n",
       "L 19.78125 45.703125 \n",
       "L 19.78125 0 \n",
       "L 10.59375 0 \n",
       "L 10.59375 45.703125 \n",
       "L 3.609375 45.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-960\"/>\n",
       "     <path d=\"M 25.390625 72.90625 \n",
       "L 33.6875 72.90625 \n",
       "L 8.296875 -9.28125 \n",
       "L 0 -9.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-47\"/>\n",
       "     <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(185.007691 117.702674)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_2\">\n",
       "    <!-- 23π/12 -->\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(454.526407 156.205348)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"text_3\">\n",
       "    <!-- 19π/12 -->\n",
       "    <defs>\n",
       "     <path d=\"M 10.984375 1.515625 \n",
       "L 10.984375 10.5 \n",
       "Q 14.703125 8.734375 18.5 7.8125 \n",
       "Q 22.3125 6.890625 25.984375 6.890625 \n",
       "Q 35.75 6.890625 40.890625 13.453125 \n",
       "Q 46.046875 20.015625 46.78125 33.40625 \n",
       "Q 43.953125 29.203125 39.59375 26.953125 \n",
       "Q 35.25 24.703125 29.984375 24.703125 \n",
       "Q 19.046875 24.703125 12.671875 31.3125 \n",
       "Q 6.296875 37.9375 6.296875 49.421875 \n",
       "Q 6.296875 60.640625 12.9375 67.421875 \n",
       "Q 19.578125 74.21875 30.609375 74.21875 \n",
       "Q 43.265625 74.21875 49.921875 64.515625 \n",
       "Q 56.59375 54.828125 56.59375 36.375 \n",
       "Q 56.59375 19.140625 48.40625 8.859375 \n",
       "Q 40.234375 -1.421875 26.421875 -1.421875 \n",
       "Q 22.703125 -1.421875 18.890625 -0.6875 \n",
       "Q 15.09375 0.046875 10.984375 1.515625 \n",
       "z\n",
       "M 30.609375 32.421875 \n",
       "Q 37.25 32.421875 41.125 36.953125 \n",
       "Q 45.015625 41.5 45.015625 49.421875 \n",
       "Q 45.015625 57.28125 41.125 61.84375 \n",
       "Q 37.25 66.40625 30.609375 66.40625 \n",
       "Q 23.96875 66.40625 20.09375 61.84375 \n",
       "Q 16.21875 57.28125 16.21875 49.421875 \n",
       "Q 16.21875 41.5 20.09375 36.953125 \n",
       "Q 23.96875 32.421875 30.609375 32.421875 \n",
       "z\n",
       "\" id=\"DejaVuSans-57\"/>\n",
       "    </defs>\n",
       "    <g style=\"fill:#0000ff;\" transform=\"translate(416.023733 40.697326)scale(0.08 -0.08)\">\n",
       "     <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"63.623047\" xlink:href=\"#DejaVuSans-57\"/>\n",
       "     <use x=\"127.246094\" xlink:href=\"#DejaVuSans-960\"/>\n",
       "     <use x=\"187.451172\" xlink:href=\"#DejaVuSans-47\"/>\n",
       "     <use x=\"221.142578\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     <use x=\"284.765625\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p260f90f972\">\n",
       "   <rect height=\"144\" width=\"576\" x=\"7.2\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zx.full_reduce(g1)\n",
    "zx.draw(g1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = c.to_graph(zh=True)\n",
    "zx.d3.draw(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "g.apply_state(g.qubit_count() * \"+\")\n",
    "g.apply_effect(g.qubit_count() * \"+\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "zx.d3.draw(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "g1 = g.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "zx.hsimplify.hpivot_simp(g1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "g1.normalise()\n",
    "zx.d3.draw(g1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = open('sim.graphml', 'w')\n",
    "f.write(zx.to_graphml(g1))\n",
    "f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hd = [v for v in g.vertices() if g.vertex_degree(v) > 2]\n",
    "(sum(g.vertex_degree(v) for v in hd)/float(len(hd)), len(hd))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hd = [v for v in g1.vertices() if g1.vertex_degree(v) > 2]\n",
    "(sum(g1.vertex_degree(v) for v in hd)/float(len(hd)), len(hd))"
   ]
  },
  {
   "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",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}