demos/Demo_day_testing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6ec804df",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyzx as zx\n",
    "from pyzx import simplify\n",
    "from pyzx.utils import EdgeType, VertexType, FloatInt, FractionLike\n",
    "from pyzx.circuit.gates import TargetMapper\n",
    "from pyzx.graph import Graph\n",
    "from pyzx.graph.base import BaseGraph, VT, ET\n",
    "from fractions import Fraction\n",
    "import numpy as np\n",
    "from typing import Tuple, List, Dict, Set, FrozenSet\n",
    "from typing import Any, Callable, TypeVar, Optional, Union"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3efcc291",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "265774 346636\n"
     ]
    }
   ],
   "source": [
    "circ = zx.Circuit.load('../circuits/demo/max.qasm')\n",
    "g = circ.to_graph()\n",
    "print(g.num_vertices(), g.num_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5f8d2ef1",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spider_simp: 49216. 33864. 11554.  3 iterations\n",
      "id_simp: 4827.  1 iterations\n",
      "spider_simp: 8931.  1 iterations\n",
      "pivot_simp: 4525.  1 iterations\n",
      "pivot_gadget_simp: 30946. 14529. 8736. 5268. 3294. 2034. 1254. 680. 383. 173. 69. 35. 9. 4.  14 iterations\n",
      "id_simp: 11831.  1 iterations\n",
      "spider_simp: 2182. 1608. 1272. 925. 787. 617. 500. 444. 375. 345. 298. 245. 217. 192. 178. 171. 148. 124. 122. 119. 100. 90. 83. 77. 69. 61. 62. 51. 40. 37. 34. 32. 29. 24. 24. 21. 20. 15. 14. 12. 11. 8. 8. 6. 6. 5. 5. 5. 4. 2. 1. 1. 1.  53 iterations\n",
      "pivot_simp: 486. 186. 39. 6.  4 iterations\n",
      "lcomp_simp: 1800. 1737. 685. 682. 187. 156. 64. 55. 23. 13. 5. 1.  12 iterations\n",
      "id_simp: 2873.  1 iterations\n",
      "spider_simp: 953. 471. 341. 223. 162. 127. 103. 76. 56. 50. 40. 35. 30. 31. 28. 23. 18. 16. 13. 10. 9. 9. 7. 5. 5. 5. 5. 5. 4. 3. 3. 3. 1. 1. 1. 1.  36 iterations\n",
      "pivot_simp: 722. 318. 103. 15. 1.  5 iterations\n",
      "lcomp_simp: 193. 190. 33. 34. 2. 2.  6 iterations\n",
      "id_simp: 624.  1 iterations\n",
      "spider_simp: 268. 113. 80. 41. 27. 17. 16. 11. 7. 7. 7. 6. 4. 4. 4. 3. 2. 2. 2. 1. 1. 1.  22 iterations\n",
      "pivot_simp: 94. 7.  2 iterations\n",
      "lcomp_simp: 150. 151. 12. 11.  4 iterations\n",
      "id_simp: 221.  1 iterations\n",
      "spider_simp: 97. 31. 22. 11. 7. 7. 7. 5. 5. 5. 4. 4. 4. 2. 2. 1. 1. 1. 1. 1. 1. 1. 1.  23 iterations\n",
      "pivot_simp: 52. 1.  2 iterations\n",
      "lcomp_simp: 34. 34. 1. 1.  4 iterations\n",
      "id_simp: 68.  1 iterations\n",
      "spider_simp: 28. 13. 9. 2. 2. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  19 iterations\n",
      "pivot_simp: 7.  1 iterations\n",
      "lcomp_simp: 16. 16.  2 iterations\n",
      "id_simp: 11.  1 iterations\n",
      "spider_simp: 9. 1. 1.  3 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "lcomp_simp: 3. 3.  2 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 3.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "lcomp_simp: 2. 2.  2 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 2. 1. 1.  3 iterations\n",
      "id_simp: 9.  1 iterations\n",
      "spider_simp: 1. 1. 1. 1. 1. 1. 1. 1. 1.  9 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "gadget_simp: 7057.  1 iterations\n",
      "pivot_simp: 847.  1 iterations\n",
      "lcomp_simp: 4351. 4351.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 10. 3.  2 iterations\n",
      "id_simp: 7.  1 iterations\n",
      "spider_simp: 6. 1.  2 iterations\n",
      "pivot_simp: 3.  1 iterations\n",
      "lcomp_simp: 3. 3. 1. 1.  4 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "gadget_simp: 7.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 6. 6.  2 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "67367 218966\n",
      "CPU times: user 4min 3s, sys: 3.61 s, total: 4min 6s\n",
      "Wall time: 4min 9s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "zx.simplify.full_reduce(g, quiet=False)\n",
    "print(g.num_vertices(), g.num_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d91ef23e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12653 16495\n",
      "12653 16495\n",
      "25274 32974\n",
      "spider_simp: 4543. 3156. 1106. 6.  4 iterations\n",
      "id_simp: 507.  1 iterations\n",
      "spider_simp: 638. 3.  2 iterations\n",
      "pivot_simp: 587. 14. 6. 4. 2. 1. 2.  7 iterations\n",
      "pivot_gadget_simp: 2896. 1379. 823. 497. 296. 177. 123. 77. 54. 30. 16. 16. 9. 7. 7. 5. 5. 2.  18 iterations\n",
      "id_simp: 1410.  1 iterations\n",
      "spider_simp: 209. 119. 66. 46. 28. 35. 26. 34. 27. 21. 17. 26. 20. 15. 13. 11. 12. 10. 9. 14. 13. 10. 6. 8. 7. 9. 10. 5. 5. 7. 6. 5. 5. 6. 5. 4. 5. 6. 5. 5. 3. 3. 5. 3. 4. 4. 4. 5. 5. 3. 4. 3. 4. 4. 3. 3. 3. 3. 4. 3. 3. 3. 3. 3. 3. 4. 3. 3. 4. 3. 3. 3. 3. 3. 4. 3. 3. 3. 3. 3. 3. 4. 3. 3. 4. 3. 3. 3. 3. 3. 3. 3. 3. 3. 4. 3. 3. 3. 3. 4. 3. 3. 5. 4. 3. 3. 5. 4. 3. 3. 5. 4. 4. 4. 3. 3. 3. 3. 3. 3. 2. 3. 3. 3. 3. 3. 2. 3. 3. 3. 3. 3. 2. 3. 3. 3. 3. 3. 3. 4. 4. 4. 3. 3. 3. 2. 2. 2. 1. 2. 2. 2. 2. 1. 2. 2. 1. 1. 2. 1. 1. 2. 1. 1. 2. 1. 1. 2. 1. 1. 2. 2. 1. 2. 2. 2. 1. 1. 2. 2. 2. 1. 1. 1. 1. 1. 2. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  297 iterations\n",
      "pivot_simp: 16. 9.  2 iterations\n",
      "lcomp_simp: 239. 236. 66. 66. 15. 13. 6. 3. 1. 1.  10 iterations\n",
      "id_simp: 390.  1 iterations\n",
      "spider_simp: 158. 39. 19. 16. 12. 13. 9. 8. 5. 5. 7. 5. 7. 5. 5. 4. 5. 4. 3. 3. 4. 3. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  62 iterations\n",
      "pivot_simp: 98. 73. 26. 8. 1.  5 iterations\n",
      "lcomp_simp: 14. 14. 2. 2.  4 iterations\n",
      "id_simp: 122.  1 iterations\n",
      "spider_simp: 35. 7. 3. 3. 3. 11. 6. 2. 2. 2. 2. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  57 iterations\n",
      "pivot_simp: 4. 2.  2 iterations\n",
      "lcomp_simp: 41. 41. 5. 5.  4 iterations\n",
      "id_simp: 25.  1 iterations\n",
      "spider_simp: 18. 2. 1. 1. 1. 1. 1.  7 iterations\n",
      "pivot_simp: 14. 5. 1.  3 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 14.  1 iterations\n",
      "spider_simp: 5. 2. 1. 1. 1. 1. 1. 1. 1.  9 iterations\n",
      "lcomp_simp: 5. 5. 1. 1.  4 iterations\n",
      "gadget_simp: 550.  1 iterations\n",
      "pivot_simp: 35.  1 iterations\n",
      "lcomp_simp: 473. 473.  2 iterations\n",
      "pivot_simp: 2. 1.  2 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 2. 1.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
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      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
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      "pivot_simp: 1. 1.  2 iterations\n",
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      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1. 1.  2 iterations\n",
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      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_gadget_simp: 1. 1. 1.  3 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 3.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "gadget_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
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      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
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      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 2. 1.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "gadget_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 2. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1. 1.  2 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
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      "gadget_simp: 2.  1 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
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      "gadget_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
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      "id_simp: 1.  1 iterations\n",
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      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1. 1.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
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      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1. 1.  2 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 2. 1.  2 iterations\n",
      "id_simp: 4.  1 iterations\n",
      "spider_simp: 4.  1 iterations\n",
      "pivot_simp: 2. 2.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
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      "id_simp: 1.  1 iterations\n",
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      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
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      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 2. 1.  2 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "gadget_simp: 2.  1 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "pivot_gadget_simp: 1. 1.  2 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 3. 1. 1.  3 iterations\n",
      "pivot_simp: 1. 1. 2.  3 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "gadget_simp: 2.  1 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "pivot_gadget_simp: 2.  1 iterations\n",
      "id_simp: 4.  1 iterations\n",
      "spider_simp: 1. 1. 1. 1.  4 iterations\n",
      "pivot_simp: 1. 1. 1.  3 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "gadget_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1. 1.  2 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 2. 2. 1.  3 iterations\n",
      "pivot_simp: 2. 1.  2 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
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      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 1. 1. 1.  3 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
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      "id_simp: 1.  1 iterations\n",
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      "id_simp: 1.  1 iterations\n",
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      "spider_simp: 1.  1 iterations\n",
      "gadget_simp: 2.  1 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 1. 2.  2 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 3. 2.  2 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 4.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2. 1.  2 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 6.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2. 1.  2 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 4.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "lcomp_simp: 2. 2.  2 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2. 1.  2 iterations\n",
      "32 16\n",
      "CPU times: user 3min 28s, sys: 1.85 s, total: 3min 30s\n",
      "Wall time: 3min 31s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "circ = zx.Circuit.load('../circuits/demo/ex2_id_16.qasm')\n",
    "g = circ.to_graph()\n",
    "g1 = g.adjoint()\n",
    "print(g.num_vertices(), g.num_edges())\n",
    "print(g1.num_vertices(), g1.num_edges())\n",
    "g.compose(g1)\n",
    "print(g.num_vertices(), g.num_edges())\n",
    "zx.simplify.full_reduce(g, quiet=False)\n",
    "print(g.num_vertices(), g.num_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "33802712",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spider_simp: 4543. 3156. 1106. 6.  4 iterations\n",
      "id_simp: 507.  1 iterations\n",
      "spider_simp: 638. 3.  2 iterations\n",
      "pivot_simp: 587. 14. 6. 4. 2. 1. 2.  7 iterations\n",
      "pivot_gadget_simp: 2896. 1379. 823. 497. 296. 177. 123. 77. 54. 30. 16. 16. 9. 7. 7. 5. 5. 2.  18 iterations\n",
      "id_simp: 1410.  1 iterations\n",
      "spider_simp: 209. 119. 66. 46. 28. 35. 26. 34. 27. 21. 17. 26. 20. 15. 13. 11. 12. 10. 9. 14. 13. 10. 6. 8. 7. 9. 10. 5. 5. 7. 6. 5. 5. 6. 5. 4. 5. 6. 5. 5. 3. 3. 5. 3. 4. 4. 4. 5. 5. 3. 4. 3. 4. 4. 3. 3. 3. 3. 4. 3. 3. 3. 3. 3. 3. 4. 3. 3. 4. 3. 3. 3. 3. 3. 4. 3. 3. 3. 3. 3. 3. 4. 3. 3. 4. 3. 3. 3. 3. 3. 3. 3. 3. 3. 4. 3. 3. 3. 3. 4. 3. 3. 5. 4. 3. 3. 5. 4. 3. 3. 5. 4. 4. 4. 3. 3. 3. 3. 3. 3. 2. 3. 3. 3. 3. 3. 2. 3. 3. 3. 3. 3. 2. 3. 3. 3. 3. 3. 3. 4. 4. 4. 3. 3. 3. 2. 2. 2. 1. 2. 2. 2. 2. 1. 2. 2. 1. 1. 2. 1. 1. 2. 1. 1. 2. 1. 1. 2. 1. 1. 2. 2. 1. 2. 2. 2. 1. 1. 2. 2. 2. 1. 1. 1. 1. 1. 2. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  297 iterations\n",
      "pivot_simp: 16. 9.  2 iterations\n",
      "lcomp_simp: 239. 236. 66. 66. 15. 13. 6. 3. 1. 1.  10 iterations\n",
      "id_simp: 390.  1 iterations\n",
      "spider_simp: 158. 39. 19. 16. 12. 13. 9. 8. 5. 5. 7. 5. 7. 5. 5. 4. 5. 4. 3. 3. 4. 3. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  62 iterations\n",
      "pivot_simp: 98. 73. 26. 8. 1.  5 iterations\n",
      "lcomp_simp: 14. 14. 2. 2.  4 iterations\n",
      "id_simp: 122.  1 iterations\n",
      "spider_simp: 35. 7. 3. 3. 3. 11. 6. 2. 2. 2. 2. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.  57 iterations\n",
      "pivot_simp: 4. 2.  2 iterations\n",
      "lcomp_simp: 41. 41. 5. 5.  4 iterations\n",
      "id_simp: 25.  1 iterations\n",
      "spider_simp: 18. 2. 1. 1. 1. 1. 1.  7 iterations\n",
      "pivot_simp: 14. 5. 1.  3 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 14.  1 iterations\n",
      "spider_simp: 5. 2. 1. 1. 1. 1. 1. 1. 1.  9 iterations\n",
      "lcomp_simp: 5. 5. 1. 1.  4 iterations\n",
      "gadget_simp: 550.  1 iterations\n",
      "pivot_simp: 35.  1 iterations\n",
      "lcomp_simp: 473. 473.  2 iterations\n",
      "pivot_simp: 2. 1.  2 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 2. 1.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
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      "lcomp_simp: 1. 1.  2 iterations\n",
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      "id_simp: 2.  1 iterations\n",
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      "id_simp: 3.  1 iterations\n",
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      "pivot_gadget_simp: 1. 1. 1.  3 iterations\n",
      "id_simp: 3.  1 iterations\n",
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      "id_simp: 2.  1 iterations\n",
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      "gadget_simp: 1.  1 iterations\n",
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      "pivot_gadget_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
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      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
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      "id_simp: 3.  1 iterations\n",
      "spider_simp: 2. 1.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
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      "gadget_simp: 1.  1 iterations\n",
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      "pivot_gadget_simp: 1. 1.  2 iterations\n",
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    {
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     "text": [
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      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 1. 1. 1.  3 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "gadget_simp: 2.  1 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 1. 2.  2 iterations\n",
      "pivot_simp: 2.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_gadget_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1. 1.  2 iterations\n",
      "id_simp: 3. 2.  2 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 4.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2. 1.  2 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 6.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2. 1.  2 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 3.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 4.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "lcomp_simp: 2. 2.  2 iterations\n",
      "id_simp: 5.  1 iterations\n",
      "spider_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 2. 1.  2 iterations\n",
      "32 16\n",
      "CPU times: user 3min 28s, sys: 1.85 s, total: 3min 30s\n",
      "Wall time: 3min 31s\n"
     ]
    }
   ],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "7924a134",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spider_simp: 3. 2. 1. 1.  4 iterations\n",
      "id_simp: 2.  1 iterations\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-7XCTmCJ1\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-7XCTmCJ1',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 500, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 650, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 650, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"7\", \"t\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 2}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2}, {\"source\": \"4\", \"target\": \"25\", \"t\": 2}, {\"source\": \"4\", \"target\": \"9\", \"t\": 2}, {\"source\": \"4\", \"target\": \"16\", \"t\": 2}, {\"source\": \"5\", \"target\": \"6\", \"t\": 2}, {\"source\": \"6\", \"target\": \"7\", \"t\": 2}, {\"source\": \"6\", \"target\": \"8\", \"t\": 2}, {\"source\": \"7\", \"target\": \"12\", \"t\": 2}, {\"source\": \"7\", \"target\": \"16\", \"t\": 2}, {\"source\": \"7\", \"target\": \"21\", \"t\": 2}, {\"source\": \"7\", \"target\": \"23\", \"t\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2}, {\"source\": \"9\", \"target\": \"11\", \"t\": 2}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2}, {\"source\": \"12\", \"target\": \"15\", \"t\": 2}, {\"source\": \"15\", \"target\": \"24\", \"t\": 2}, {\"source\": \"16\", \"target\": \"20\", \"t\": 2}, {\"source\": \"20\", \"target\": \"21\", \"t\": 2}]}'), 700, 250, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g1 = g.copy()\n",
    "# zx.draw(g1, labels=True)\n",
    "zx.simplify.spider_simp(g1, quiet=False)\n",
    "# zx.draw(g1, labels=True)\n",
    "zx.simplify.id_simp(g1, quiet=False)\n",
    "# zx.draw(g1, labels=True)\n",
    "zx.simplify.to_gh(g1)\n",
    "zx.draw(g1, labels=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "25392e1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(6, 5, [], [26]), (9, 4, [], [27]), (21, 20, [], [28])]\n",
      "({(6, 26): [0, 1], (3, 8): [0, 2], (3, 7): [0, 1], (9, 27): [0, 1], (8, 16): [0, 1], (8, 25): [0, 1], (11, 16): [0, 1], (11, 25): [0, 1], (3, 11): [0, 1], (21, 28): [0, 1], (7, 16): [0, 1]}, [5, 4, 20], [(5, 26), (4, 27), (20, 28)], True)\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "Callable[args, result]: result must be a type. Got [(9, 8, [], [29])].",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/s7/yx9nfx_j7wz_n6b7jdj_9wr40000gn/T/ipykernel_41779/3218515417.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mrewrite\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpivot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmatches\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrewrite\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0msimp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\"pivot_gadget\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mCallable\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m...\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmatch_pivot_gadget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mCallable\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mg1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmatch_pivot_gadget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mpivot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmatches\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/miniconda3/lib/python3.7/typing.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, params)\u001b[0m\n\u001b[1;32m    761\u001b[0m                                 f\" Got {args}\")\n\u001b[1;32m    762\u001b[0m             \u001b[0mparams\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 763\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getitem_inner__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    764\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    765\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0m_tp_cache\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/lib/python3.7/typing.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(*args, **kwds)\u001b[0m\n\u001b[1;32m    252\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    253\u001b[0m             \u001b[0;32mpass\u001b[0m  \u001b[0;31m# All real errors (not unhashable args) are raised below.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 254\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    255\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0minner\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    256\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/lib/python3.7/typing.py\u001b[0m in \u001b[0;36m__getitem_inner__\u001b[0;34m(self, params)\u001b[0m\n\u001b[1;32m    780\u001b[0m             \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    781\u001b[0m             \u001b[0mmsg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"Callable[args, result]: result must be a type.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 782\u001b[0;31m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_type_check\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    783\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0margs\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mEllipsis\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    784\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy_with\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_TypingEllipsis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/lib/python3.7/typing.py\u001b[0m in \u001b[0;36m_type_check\u001b[0;34m(arg, msg, is_argument)\u001b[0m\n\u001b[1;32m    140\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0marg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    141\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 142\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"{msg} Got {arg!r:.100}.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    143\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0marg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    144\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: Callable[args, result]: result must be a type. Got [(9, 8, [], [29])]."
     ]
    }
   ],
   "source": [
    "matches = match_pivot_gadget(g1)\n",
    "print(matches)\n",
    "rewrite = pivot(g1, matches)\n",
    "print(rewrite)\n",
    "simp(g1,\"pivot_gadget\", Callable[..., match_pivot_gadget(g1)], Callable[[g1, match_pivot_gadget(g1)],pivot(g1, matches)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "00a1e819",
   "metadata": {},
   "outputs": [],
   "source": [
    "zx.simplify.pivot_gadget_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "zx.simplify.id_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "zx.simplify.gadget_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "zx.simplify.id_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "zx.simplify.spider_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "zx.simplify.lcomp_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "90e90734",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spider_simp: 15. 10. 6. 4. 3. 1. 1. 1.  8 iterations\n",
      "id_simp: 8. 3.  2 iterations\n",
      "pivot_simp: 1.  1 iterations\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circ1 = zx.Circuit.load('../circuits/qasm/tof3_5.qasm')\n",
    "g1 = circ1.to_graph()\n",
    "zx.simplify.spider_simp(g1, quiet=False)\n",
    "zx.simplify.id_simp(g1, quiet=False)\n",
    "zx.simplify.to_gh(g1)\n",
    "zx.simplify.pivot_simp(g1, quiet=False)\n",
    "# zx.simplify.pivot_gadget_simp(g1, quiet=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "496f9cad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-mUmLU1pg\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-mUmLU1pg',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 60, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 60, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 80, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 100, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 100, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 120, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 140, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 160, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 180, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 200, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 200, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 220, \"y\": 60, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 240, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 260, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 260, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 280, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 300, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 320, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 340, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 360, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 380, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 400, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 400, \"y\": 80, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 420, \"y\": 80, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 440, \"y\": 80, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 460, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 460, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 480, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 500, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 500, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 520, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 540, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 560, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 580, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"60\", \"x\": 600, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 600, \"y\": 80, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 620, \"y\": 80, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 640, \"y\": 80, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"69\", \"x\": 660, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"71\", \"x\": 680, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"72\", \"x\": 700, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"74\", \"x\": 720, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"75\", \"x\": 740, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"77\", \"x\": 760, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"78\", \"x\": 780, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"81\", \"x\": 800, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"82\", \"x\": 800, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"85\", \"x\": 820, \"y\": 60, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"86\", \"x\": 840, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"88\", \"x\": 820, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"90\", \"x\": 840, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"92\", \"x\": 860, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"93\", \"x\": 880, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"94\", \"x\": 880, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"95\", \"x\": 900, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"96\", \"x\": 920, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"98\", \"x\": 940, \"y\": 120, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"99\", \"x\": 960, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"102\", \"x\": 980, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"103\", \"x\": 980, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"106\", \"x\": 1000, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"112\", \"x\": 1060, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"113\", \"x\": 1080, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"114\", \"x\": 1100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"116\", \"x\": 1120, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"117\", \"x\": 1140, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"119\", \"x\": 1160, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"120\", \"x\": 1180, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"123\", \"x\": 1200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"124\", \"x\": 1200, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"127\", \"x\": 1220, \"y\": 60, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"128\", \"x\": 1240, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"131\", \"x\": 1260, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"132\", \"x\": 1260, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"133\", \"x\": 1260, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"134\", \"x\": 1260, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"135\", \"x\": 1260, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"10\", \"t\": 1}, {\"source\": \"1\", \"target\": \"7\", \"t\": 1}, {\"source\": \"2\", \"target\": \"28\", \"t\": 1}, {\"source\": \"3\", \"target\": \"69\", \"t\": 1}, {\"source\": \"4\", \"target\": \"6\", \"t\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 2}, {\"source\": \"6\", \"target\": \"8\", \"t\": 2}, {\"source\": \"7\", \"target\": \"12\", \"t\": 2}, {\"source\": \"7\", \"target\": \"19\", \"t\": 2}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2}, {\"source\": \"9\", \"target\": \"10\", \"t\": 2}, {\"source\": \"9\", \"target\": \"11\", \"t\": 2}, {\"source\": \"10\", \"target\": \"15\", \"t\": 2}, {\"source\": \"10\", \"target\": \"19\", \"t\": 2}, {\"source\": \"10\", \"target\": \"23\", \"t\": 2}, {\"source\": \"10\", \"target\": \"30\", \"t\": 2}, {\"source\": \"10\", \"target\": \"36\", \"t\": 2}, {\"source\": \"10\", \"target\": \"40\", \"t\": 2}, {\"source\": \"10\", \"target\": \"44\", \"t\": 2}, {\"source\": \"10\", \"target\": \"72\", \"t\": 2}, {\"source\": \"10\", \"target\": \"78\", \"t\": 2}, {\"source\": \"10\", \"target\": \"82\", \"t\": 2}, {\"source\": \"10\", \"target\": \"86\", \"t\": 2}, {\"source\": \"10\", \"target\": \"114\", \"t\": 2}, {\"source\": \"10\", \"target\": \"120\", \"t\": 2}, {\"source\": \"10\", \"target\": \"124\", \"t\": 2}, {\"source\": \"10\", \"target\": \"128\", \"t\": 2}, {\"source\": \"10\", \"target\": \"131\", \"t\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2}, {\"source\": \"15\", \"target\": \"18\", \"t\": 2}, {\"source\": \"18\", \"target\": \"27\", \"t\": 2}, {\"source\": \"19\", \"target\": \"22\", \"t\": 2}, {\"source\": \"22\", \"target\": \"23\", \"t\": 2}, {\"source\": \"23\", \"target\": \"52\", \"t\": 2}, {\"source\": \"27\", \"target\": \"28\", \"t\": 2}, {\"source\": \"27\", \"target\": \"29\", \"t\": 2}, {\"source\": \"28\", \"target\": \"33\", \"t\": 2}, {\"source\": \"28\", \"target\": \"40\", \"t\": 2}, {\"source\": \"29\", \"target\": \"30\", \"t\": 2}, {\"source\": \"30\", \"target\": \"32\", \"t\": 2}, {\"source\": \"32\", \"target\": \"33\", \"t\": 2}, {\"source\": \"33\", \"target\": \"35\", \"t\": 2}, {\"source\": \"35\", \"target\": \"36\", \"t\": 2}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2}, {\"source\": \"39\", \"target\": \"48\", \"t\": 2}, {\"source\": \"40\", \"target\": \"43\", \"t\": 2}, {\"source\": \"43\", \"target\": \"44\", \"t\": 2}, {\"source\": \"44\", \"target\": \"49\", \"t\": 2}, {\"source\": \"48\", \"target\": \"49\", \"t\": 2}, {\"source\": \"48\", \"target\": \"50\", \"t\": 2}, {\"source\": \"49\", \"target\": \"54\", \"t\": 2}, {\"source\": \"49\", \"target\": \"61\", \"t\": 2}, {\"source\": \"50\", \"target\": \"51\", \"t\": 2}, {\"source\": \"51\", \"target\": \"52\", \"t\": 2}, {\"source\": \"51\", \"target\": \"53\", \"t\": 2}, {\"source\": \"52\", \"target\": \"57\", \"t\": 2}, {\"source\": \"52\", \"target\": \"61\", \"t\": 2}, {\"source\": \"52\", \"target\": \"65\", \"t\": 2}, {\"source\": \"52\", \"target\": \"69\", \"t\": 2}, {\"source\": \"52\", \"target\": \"75\", \"t\": 2}, {\"source\": \"52\", \"target\": \"82\", \"t\": 2}, {\"source\": \"53\", \"target\": \"54\", \"t\": 2}, {\"source\": \"54\", \"target\": \"56\", \"t\": 2}, {\"source\": \"56\", \"target\": \"57\", \"t\": 2}, {\"source\": \"57\", \"target\": \"60\", \"t\": 2}, {\"source\": \"60\", \"target\": \"90\", \"t\": 2}, {\"source\": \"61\", \"target\": \"64\", \"t\": 2}, {\"source\": \"64\", \"target\": \"65\", \"t\": 2}, {\"source\": \"65\", \"target\": \"94\", \"t\": 2}, {\"source\": \"69\", \"target\": \"71\", \"t\": 2}, {\"source\": \"71\", \"target\": \"72\", \"t\": 2}, {\"source\": \"72\", \"target\": \"74\", \"t\": 2}, {\"source\": \"74\", \"target\": \"75\", \"t\": 2}, {\"source\": \"75\", \"target\": \"77\", \"t\": 2}, {\"source\": \"77\", \"target\": \"78\", \"t\": 2}, {\"source\": \"78\", \"target\": \"81\", \"t\": 2}, {\"source\": \"81\", \"target\": \"88\", \"t\": 2}, {\"source\": \"82\", \"target\": \"85\", \"t\": 2}, {\"source\": \"85\", \"target\": \"86\", \"t\": 2}, {\"source\": \"86\", \"target\": \"112\", \"t\": 2}, {\"source\": \"88\", \"target\": \"90\", \"t\": 2}, {\"source\": \"88\", \"target\": \"96\", \"t\": 2}, {\"source\": \"88\", \"target\": \"103\", \"t\": 2}, {\"source\": \"90\", \"target\": \"92\", \"t\": 2}, {\"source\": \"92\", \"target\": \"93\", \"t\": 2}, {\"source\": \"93\", \"target\": \"94\", \"t\": 2}, {\"source\": \"93\", \"target\": \"95\", \"t\": 2}, {\"source\": \"94\", \"target\": \"99\", \"t\": 2}, {\"source\": \"94\", \"target\": \"103\", \"t\": 2}, {\"source\": \"94\", \"target\": \"133\", \"t\": 1}, {\"source\": \"94\", \"target\": \"112\", \"t\": 2}, {\"source\": \"94\", \"target\": \"113\", \"t\": 2}, {\"source\": \"95\", \"target\": \"96\", \"t\": 2}, {\"source\": \"96\", \"target\": \"98\", \"t\": 2}, {\"source\": \"98\", \"target\": \"99\", \"t\": 2}, {\"source\": \"99\", \"target\": \"102\", \"t\": 2}, {\"source\": \"102\", \"target\": \"135\", \"t\": 2}, {\"source\": \"103\", \"target\": \"106\", \"t\": 2}, {\"source\": \"106\", \"target\": \"112\", \"t\": 2}, {\"source\": \"106\", \"target\": \"113\", \"t\": 2}, {\"source\": \"112\", \"target\": \"117\", \"t\": 2}, {\"source\": \"112\", \"target\": \"124\", \"t\": 2}, {\"source\": \"113\", \"target\": \"114\", \"t\": 2}, {\"source\": \"114\", \"target\": \"116\", \"t\": 2}, {\"source\": \"116\", \"target\": \"117\", \"t\": 2}, {\"source\": \"117\", \"target\": \"119\", \"t\": 2}, {\"source\": \"119\", \"target\": \"120\", \"t\": 2}, {\"source\": \"120\", \"target\": \"123\", \"t\": 2}, {\"source\": \"123\", \"target\": \"134\", \"t\": 2}, {\"source\": \"124\", \"target\": \"127\", \"t\": 2}, {\"source\": \"127\", \"target\": \"128\", \"t\": 2}, {\"source\": \"128\", \"target\": \"132\", \"t\": 2}]}'), 1280, 140, 20, 4.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "82\n"
     ]
    }
   ],
   "source": [
    "zx.draw(g1, labels=True)\n",
    "print(len(g1.vertices()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ba8326b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-B424sBM6\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
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       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-B424sBM6',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 350, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 450, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 650, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 650, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 650, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 2}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1}, {\"source\": \"4\", \"target\": \"6\", \"t\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1}, {\"source\": \"8\", \"target\": \"14\", \"t\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1}, {\"source\": \"10\", \"target\": \"12\", \"t\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 2}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1}, {\"source\": \"19\", \"target\": \"26\", \"t\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 1}]}'), 700, 250, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circ1 = zx.Circuit.load('../circuits/qasm/tof3.qasm')\n",
    "g1 = circ1.to_graph()\n",
    "zx.draw(g1, labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "911eb8ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spider_simp: 3. 2. 1.  3 iterations\n"
     ]
    },
    {
     "data": {
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       "<div style=\"overflow:auto\" id=\"graph-output-DVzXXstV\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
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       "    function edgeColor(t) {\n",
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       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
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       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
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       "\n",
       "        var shiftKey;\n",
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       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
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       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
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       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
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       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
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       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
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       "            .append(\"path\")\n",
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       "            .attr(\"fill\", \"none\")\n",
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       "            .attr(\"class\", \"selectable\");\n",
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       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
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       "            .append(\"circle\")\n",
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       "            .attr(\"stroke\", \"black\")\n",
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       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
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       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
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       "              .data(d => d.vdata)\n",
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       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
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       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
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       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
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       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
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       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
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       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
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       "                }\n",
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       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-DVzXXstV',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 650, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 650, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 650, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 2}, {\"source\": \"3\", \"target\": \"4\", \"t\": 2}, {\"source\": \"4\", \"target\": \"5\", \"t\": 2}, {\"source\": \"4\", \"target\": \"6\", \"t\": 2}, {\"source\": \"5\", \"target\": \"10\", \"t\": 2}, {\"source\": \"5\", \"target\": \"17\", \"t\": 2}, {\"source\": \"6\", \"target\": \"7\", \"t\": 2}, {\"source\": \"7\", \"target\": \"8\", \"t\": 2}, {\"source\": \"7\", \"target\": \"9\", \"t\": 2}, {\"source\": \"8\", \"target\": \"13\", \"t\": 2}, {\"source\": \"8\", \"target\": \"17\", \"t\": 2}, {\"source\": \"8\", \"target\": \"22\", \"t\": 2}, {\"source\": \"8\", \"target\": \"24\", \"t\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 2}, {\"source\": \"10\", \"target\": \"12\", \"t\": 2}, {\"source\": \"12\", \"target\": \"13\", \"t\": 2}, {\"source\": \"13\", \"target\": \"16\", \"t\": 2}, {\"source\": \"16\", \"target\": \"19\", \"t\": 2}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2}, {\"source\": \"19\", \"target\": \"26\", \"t\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 2}, {\"source\": \"22\", \"target\": \"25\", \"t\": 2}]}'), 700, 250, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zx.simplify.spider_simp(g1, quiet=False)\n",
    "zx.simplify.to_gh(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "672f6430",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "id_simp: 2.  1 iterations\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-Tne8MI1Y\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-Tne8MI1Y',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 650, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 650, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 650, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 2}, {\"source\": \"4\", \"target\": \"6\", \"t\": 2}, {\"source\": \"5\", \"target\": \"10\", \"t\": 2}, {\"source\": \"5\", \"target\": \"17\", \"t\": 2}, {\"source\": \"6\", \"target\": \"7\", \"t\": 2}, {\"source\": \"7\", \"target\": \"8\", \"t\": 2}, {\"source\": \"7\", \"target\": \"9\", \"t\": 2}, {\"source\": \"8\", \"target\": \"13\", \"t\": 2}, {\"source\": \"8\", \"target\": \"17\", \"t\": 2}, {\"source\": \"8\", \"target\": \"22\", \"t\": 2}, {\"source\": \"8\", \"target\": \"24\", \"t\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 2}, {\"source\": \"10\", \"target\": \"12\", \"t\": 2}, {\"source\": \"12\", \"target\": \"13\", \"t\": 2}, {\"source\": \"13\", \"target\": \"16\", \"t\": 2}, {\"source\": \"16\", \"target\": \"26\", \"t\": 2}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2}, {\"source\": \"21\", \"target\": \"22\", \"t\": 2}, {\"source\": \"22\", \"target\": \"25\", \"t\": 2}]}'), 700, 250, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
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     "text": [
      "pivot_gadget_simp: 3. 1.  2 iterations\n"
     ]
    },
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       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
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       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
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       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
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       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
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       "                update_hboxes();\n",
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       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
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       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
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       "            .on(\"start\", function() {\n",
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       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-UaD8WUBC',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 450, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 500, \"y\": 300, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 650, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 650, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 650, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 350, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1}, {\"source\": \"4\", \"target\": \"16\", \"t\": 2}, {\"source\": \"5\", \"target\": \"10\", \"t\": 2}, {\"source\": \"5\", \"target\": \"17\", \"t\": 2}, {\"source\": \"5\", \"target\": \"22\", \"t\": 2}, {\"source\": \"5\", \"target\": \"7\", \"t\": 2}, {\"source\": \"7\", \"target\": \"27\", \"t\": 2}, {\"source\": \"7\", \"target\": \"16\", \"t\": 2}, {\"source\": \"8\", \"target\": \"13\", \"t\": 2}, {\"source\": \"8\", \"target\": \"17\", \"t\": 2}, {\"source\": \"8\", \"target\": \"24\", \"t\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 2}, {\"source\": \"10\", \"target\": \"16\", \"t\": 2}, {\"source\": \"10\", \"target\": \"30\", \"t\": 2}, {\"source\": \"13\", \"target\": \"16\", \"t\": 2}, {\"source\": \"13\", \"target\": \"28\", \"t\": 2}, {\"source\": \"16\", \"target\": \"26\", \"t\": 2}, {\"source\": \"17\", \"target\": \"29\", \"t\": 2}, {\"source\": \"22\", \"target\": \"25\", \"t\": 2}]}'), 700, 350, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(8, 13), (17, 29), (7, 16), (8, 24), (10, 30), (8, 10), (13, 16), (1, 5), (5, 22), (5, 17), (7, 27), (4, 16), (13, 28), (16, 26), (8, 17), (0, 8), (22, 25), (5, 10), (10, 16), (5, 7), (2, 4)} 21\n",
      "dict_keys([0, 1, 2, 4, 5, 7, 8, 10, 13, 16, 17, 22, 24, 25, 26, 27, 28, 29, 30]) 19\n",
      "id_simp: 2.  1 iterations\n"
     ]
    },
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       "<div style=\"overflow:auto\" id=\"graph-output-UYv10Xji\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
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       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
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       "            s.nhd.push(t);\n",
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       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-UYv10Xji',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 450, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 500, \"y\": 300, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 650, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 650, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 650, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 350, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"2\", \"target\": \"16\", \"t\": 2}, {\"source\": \"5\", \"target\": \"10\", \"t\": 2}, {\"source\": \"5\", \"target\": \"17\", \"t\": 2}, {\"source\": \"5\", \"target\": \"7\", \"t\": 2}, {\"source\": \"5\", \"target\": \"25\", \"t\": 1}, {\"source\": \"7\", \"target\": \"27\", \"t\": 2}, {\"source\": \"7\", \"target\": \"16\", \"t\": 2}, {\"source\": \"8\", \"target\": \"13\", \"t\": 2}, {\"source\": \"8\", \"target\": \"17\", \"t\": 2}, {\"source\": \"8\", \"target\": \"24\", \"t\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 2}, {\"source\": \"10\", \"target\": \"16\", \"t\": 2}, {\"source\": \"10\", \"target\": \"30\", \"t\": 2}, {\"source\": \"13\", \"target\": \"16\", \"t\": 2}, {\"source\": \"13\", \"target\": \"28\", \"t\": 2}, {\"source\": \"16\", \"target\": \"26\", \"t\": 2}, {\"source\": \"17\", \"target\": \"29\", \"t\": 2}]}'), 700, 350, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(8, 13), (17, 29), (7, 16), (8, 24), (10, 30), (8, 10), (13, 16), (1, 5), (5, 25), (2, 16), (5, 17), (7, 27), (13, 28), (16, 26), (8, 17), (0, 8), (5, 10), (10, 16), (5, 7)} 19\n",
      "dict_keys([0, 1, 2, 5, 7, 8, 10, 13, 16, 17, 24, 25, 26, 27, 28, 29, 30]) 17\n"
     ]
    }
   ],
   "source": [
    "zx.simplify.id_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "zx.simplify.pivot_gadget_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "print(g1.edge_set(), len(g1.edge_set()))\n",
    "print(g1.vertices(), len(g1.vertices()))\n",
    "zx.simplify.id_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)\n",
    "print(g1.edge_set(), len(g1.edge_set()))\n",
    "print(g1.vertices(), len(g1.vertices()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2fc59810",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "d6ddb3bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-VpnK5u7Z\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-VpnK5u7Z',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 200, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 300, \"y\": 300, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 350, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 400, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 450, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 500, \"y\": 300, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 650, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 650, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 650, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 2}, {\"source\": \"4\", \"target\": \"6\", \"t\": 2}, {\"source\": \"5\", \"target\": \"10\", \"t\": 2}, {\"source\": \"5\", \"target\": \"17\", \"t\": 2}, {\"source\": \"6\", \"target\": \"7\", \"t\": 2}, {\"source\": \"6\", \"target\": \"27\", \"t\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 2}, {\"source\": \"7\", \"target\": \"9\", \"t\": 2}, {\"source\": \"8\", \"target\": \"13\", \"t\": 2}, {\"source\": \"8\", \"target\": \"17\", \"t\": 2}, {\"source\": \"8\", \"target\": \"22\", \"t\": 2}, {\"source\": \"8\", \"target\": \"24\", \"t\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 2}, {\"source\": \"10\", \"target\": \"12\", \"t\": 2}, {\"source\": \"12\", \"target\": \"13\", \"t\": 2}, {\"source\": \"12\", \"target\": \"28\", \"t\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 2}, {\"source\": \"16\", \"target\": \"26\", \"t\": 2}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2}, {\"source\": \"21\", \"target\": \"22\", \"t\": 2}, {\"source\": \"21\", \"target\": \"29\", \"t\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 2}]}'), 700, 350, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zx.simplify.id_simp(g1, quiet=False)\n",
    "zx.draw(g1, labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "9f7f9faf",
   "metadata": {},
   "outputs": [],
   "source": [
    "n0 = set([1,2,3])\n",
    "n1 = set([1,2,4])\n",
    "n2 = n0 & n1\n",
    "n0-=n2\n",
    "n1-=n2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "628ee777",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({3}, {4})"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n0, n1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "3b221b0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 2}"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "7bad9305",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-kUJQzEqi\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-kUJQzEqi',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 2}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1}]}'), 200, 200, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(1, 2), (2, 5), (2, 3), (0, 3), (3, 4)}\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-8jYPyGpy\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-8jYPyGpy',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1}]}'), 200, 200, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(1, 2), (0, 3), (2, 5), (3, 4)}\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-WrweFaTx\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-WrweFaTx',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1}]}'), 200, 200, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(1, 2), (0, 3), (2, 5), (3, 4)}\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-81wbakjU\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-81wbakjU',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 2}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1}]}'), 200, 200, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "c2 = zx.Circuit.load('../circuits/qasm/cz.qasm')\n",
    "g2 = c2.to_graph()\n",
    "zx.draw(g2, labels=True)\n",
    "print(g2.edge_set())\n",
    "\n",
    "g2.remove_edge((2,3))\n",
    "zx.draw(g2, labels=True)\n",
    "print(g2.edge_set())\n",
    "\n",
    "g2.add_edge((3,3), EdgeType.HADAMARD)\n",
    "zx.draw(g2, labels=True)\n",
    "print(g2.edge_set())\n",
    "\n",
    "g2.add_edge((3,2), EdgeType.HADAMARD)\n",
    "zx.draw(g2, labels=True)\n",
    "print(g2.num_edges())\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "10e29840",
   "metadata": {},
   "outputs": [],
   "source": [
    "zx.simplify.full_reduce(g2, quiet = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "0d6fad55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-Ugj5eNGR\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-Ugj5eNGR',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 150, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 175.0, \"y\": 125.0, \"t\": 3, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 250, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 250, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 275.0, \"y\": 225.0, \"t\": 3, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 300, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 350, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 400, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 400, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 425.0, \"y\": 225.0, \"t\": 3, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 450, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 500, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 525.0, \"y\": 125.0, \"t\": 3, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 550, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 600, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"7\", \"t\": 1}, {\"source\": \"1\", \"target\": \"8\", \"t\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 2}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1}, {\"source\": \"7\", \"target\": \"25\", \"t\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1}, {\"source\": \"8\", \"target\": \"26\", \"t\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1}, {\"source\": \"12\", \"target\": \"16\", \"t\": 2}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 1}, {\"source\": \"14\", \"target\": \"20\", \"t\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 2}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1}, {\"source\": \"18\", \"target\": \"21\", \"t\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 2}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1}, {\"source\": \"19\", \"target\": \"23\", \"t\": 2}, {\"source\": \"20\", \"target\": \"21\", \"t\": 1}, {\"source\": \"20\", \"target\": \"32\", \"t\": 1}, {\"source\": \"22\", \"target\": \"33\", \"t\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 1}, {\"source\": \"24\", \"target\": \"27\", \"t\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 2}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1}, {\"source\": \"25\", \"target\": \"29\", \"t\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1}, {\"source\": \"26\", \"target\": \"30\", \"t\": 1}, {\"source\": \"28\", \"target\": \"31\", \"t\": 1}]}'), 650, 350, 50, 10.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-kvZNhsdX\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-kvZNhsdX',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 40, \"y\": 80, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 60, \"y\": 80, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 60, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 80, \"y\": 80, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 100, 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       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spider_simp: 11. 8. 3. 2. 2. 1.  6 iterations\n",
      "id_simp: 6. 1.  2 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "pivot_gadget_simp: 8. 6. 2. 2.  4 iterations\n",
      "id_simp: 7.  1 iterations\n",
      "spider_simp: 2. 1. 1.  3 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_boundary_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 3.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "gadget_simp: 2.  1 iterations\n",
      "pivot_simp: 1.  1 iterations\n",
      "lcomp_simp: 1. 1.  2 iterations\n",
      "id_simp: 4.  1 iterations\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-3Bgr8glb\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-3Bgr8glb',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"89\", \"x\": 820, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"90\", \"x\": 820, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"91\", \"x\": 820, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"92\", \"x\": 820, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"93\", \"x\": 820, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"89\", \"t\": 1}, {\"source\": \"1\", \"target\": \"90\", \"t\": 1}, {\"source\": \"2\", \"target\": \"91\", \"t\": 1}, {\"source\": \"3\", \"target\": \"92\", \"t\": 1}, {\"source\": \"4\", \"target\": \"93\", \"t\": 1}]}'), 840, 140, 20, 4.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "5\n",
      "[]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-ybn1Zovf\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-ybn1Zovf',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"89\", \"x\": 820, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"90\", \"x\": 820, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"91\", \"x\": 820, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"92\", \"x\": 820, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"93\", \"x\": 820, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"89\", \"t\": 1}, {\"source\": \"1\", \"target\": \"90\", \"t\": 1}, {\"source\": \"2\", \"target\": \"91\", \"t\": 1}, {\"source\": \"3\", \"target\": \"92\", \"t\": 1}, {\"source\": \"4\", \"target\": \"93\", \"t\": 1}]}'), 840, 140, 20, 4.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 27.5 ms, sys: 8.58 ms, total: 36.1 ms\n",
      "Wall time: 56 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "circ = zx.Circuit.load('../circuits/demo/ex2_id_5.qasm')\n",
    "zx.draw(circ, labels = True)\n",
    "g = circ.to_graph()\n",
    "zx.draw(g, labels = True)\n",
    "zx.simplify.full_reduce(g, quiet=False)\n",
    "zx.draw(g, labels = True)\n",
    "print(g.num_vertices())\n",
    "print(g.num_edges())\n",
    "print([e for e in g.edges() if g.edge_type(e) == EdgeType.HADAMARD])\n",
    "zx.simplify.copy_simp(g, quiet=False)\n",
    "zx.draw(g, labels = True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b88fef76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-27IG2Qqz\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-27IG2Qqz',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"89\", \"x\": 860, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"90\", \"x\": 860, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"91\", \"x\": 860, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"92\", \"x\": 860, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"93\", \"x\": 860, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"89\", \"t\": 1}, {\"source\": \"1\", \"target\": \"90\", \"t\": 1}, {\"source\": \"2\", \"target\": \"91\", \"t\": 1}, {\"source\": \"3\", \"target\": \"92\", \"t\": 1}, {\"source\": \"4\", \"target\": \"93\", \"t\": 1}]}'), 880, 140, 20, 4.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-D6rUXk8b\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-D6rUXk8b',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"89\", \"x\": 860, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"90\", \"x\": 860, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"91\", \"x\": 860, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"92\", \"x\": 860, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"93\", \"x\": 860, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"89\", \"t\": 1}, {\"source\": \"1\", \"target\": \"90\", \"t\": 1}, {\"source\": \"2\", \"target\": \"91\", \"t\": 1}, {\"source\": \"3\", \"target\": \"92\", \"t\": 1}, {\"source\": \"4\", \"target\": \"93\", \"t\": 1}]}'), 880, 140, 20, 4.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-7q6vhYWB\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({paths: {d3: \"https://d3js.org/d3.v5.min\"} });\n",
       "// PyZX - Python library for quantum circuit rewriting \n",
       "//        and optimisation using the ZX-calculus\n",
       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
       "\n",
       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
       "// you may not use this file except in compliance with the License.\n",
       "// You may obtain a copy of the License at\n",
       "\n",
       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
       "\n",
       "// Unless required by applicable law or agreed to in writing, software\n",
       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
       "// See the License for the specific language governing permissions and\n",
       "// limitations under the License.\n",
       "\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"#ccffcc\";\n",
       "        else if (t == 2) return \"#ff8888\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    var symbolGround = {\n",
       "        draw: function(context, size){\n",
       "            let s = size/2;\n",
       "\n",
       "            context.moveTo(0,-s);\n",
       "            context.lineTo(0,0);\n",
       "\n",
       "            context.moveTo(-s,0);\n",
       "            context.lineTo(s,0);\n",
       "\n",
       "            context.moveTo(-2*s/3,s/3);\n",
       "            context.lineTo(2*s/3,s/3);\n",
       "\n",
       "            context.moveTo(-s/3,2*s/3);\n",
       "            context.lineTo(s/3,2*s/3);\n",
       "        }\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
       "        var ntab = {};\n",
       "\n",
       "        var groundOffset = 2.5 * node_size;\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        // Draw a ground symbol connected to the node.\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
       "            .attr(\"class\", \"selectable\");\n",
       "        node.filter(function(d) { return d.ground; })\n",
       "            .append(\"path\")\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\")\n",
       "            .attr(\"fill\", \"none\")\n",
       "            .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
       "            .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\")\n",
       "            .attr(\"class\", \"selectable\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 8)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"10px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#999\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        // Display the chosen data fields over the node.\n",
       "        node.filter(d => d.vdata.length > 0)\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"8px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#c66\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;')\n",
       "            .selectAll(\"tspan\")\n",
       "              .data(d => d.vdata)\n",
       "              .enter()\n",
       "              .append(\"tspan\")\n",
       "              .attr(\"x\", \"0\")\n",
       "              .attr(\"dy\", \"1.2em\")\n",
       "              .text(x => x.join(\": \"));\n",
       "\n",
       "        if (scalar_str != \"\") {\n",
       "            svg.append(\"text\")\n",
       "                .text(scalar_str)\n",
       "                .attr(\"x\", 60).attr(\"y\", 40)\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-7q6vhYWB',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"89\", \"x\": 860, \"y\": 40, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"90\", \"x\": 860, \"y\": 60, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"91\", \"x\": 860, \"y\": 80, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"92\", \"x\": 860, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"93\", \"x\": 860, \"y\": 120, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"89\", \"t\": 1}, {\"source\": \"1\", \"target\": \"90\", \"t\": 1}, {\"source\": \"2\", \"target\": \"91\", \"t\": 1}, {\"source\": \"3\", \"target\": \"92\", \"t\": 1}, {\"source\": \"4\", \"target\": \"93\", \"t\": 1}]}'), 880, 140, 20, 4.0, false, true, '');\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zx.draw(g, labels = True)\n",
    "zx.simplify.full_reduce(g, quiet = False)\n",
    "zx.draw(g, labels = True)\n",
    "zx.simplify.gadget_simp(g, quiet = False)\n",
    "zx.draw(g, labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf9d5f8a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.10"
  }
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 "nbformat": 4,
 "nbformat_minor": 5
}