demos/Challenge_circuit_extraction.ipynb

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   "source": [
    "# Challenge: Circuit Extraction\n",
    "\n",
    "Our normal simplification procedure always yields ZX-diagrams that can be turned back into (ancilla-free) circuits.\n",
    "\n",
    "**Challenge**: find a means of deterministically realising the ZX-diagram g2 below, _without increasing T-count_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random, math, os, time\n",
    "import sys; sys.path.append('..')\n",
    "import pyzx as zx\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we load the circuit and do our \"normal\" simplification, which reduces T-count from 21 to 15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "old T-count: 21 --> new T-count: 15\n"
     ]
    }
   ],
   "source": [
    "c = zx.Circuit.load('../circuits/Fast/tof_3_before').to_basic_gates()\n",
    "g = c.to_graph()\n",
    "g1 = g.copy()\n",
    "zx.simplify.full_reduce(g1)\n",
    "print(\"old T-count: %s --> new T-count: %s\" % (zx.tcount(g), zx.tcount(g1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...and indeed the resulting ZX-diagram can be transformed back into a circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "    require.config({ baseUrl: \"../js\",\n",
       "                     paths: {d3: \"d3.v4.min\"} });\n",
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       "        pyzx.showGraph('#graph-output-1',\n",
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       "    });\n",
       "    </script>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c1 = zx.extract.streaming_extract(g1.copy())\n",
    "zx.d3.draw(c1.to_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point, we can use the simplification rule **gadget_phasepoly** to reduce the T-count by _one more_, down to 14."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "old T-count: 15 --> new T-count: 14\n"
     ]
    }
   ],
   "source": [
    "g2 = g1.copy()\n",
    "\n",
    "while True:\n",
    "    m = zx.rules.match_gadgets_phasepoly(g2)\n",
    "    if len(m) != 0: zx.rules.apply_gadget_phasepoly(g2, m)\n",
    "    else: break\n",
    "print(\"old T-count: %s --> new T-count: %s\" % (zx.tcount(g1), zx.tcount(g2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...but the circuit no longer extracts!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***Error in extraction***: Did not find any completely reducable row\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    c2 = zx.extract.streaming_extract(g2.copy())\n",
    "except ValueError as e:\n",
    "    print(\"***Error in extraction***: %s\" % e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the ZX-diagram. **Can you extract it?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "    require.config({ baseUrl: \"../js\",\n",
       "                     paths: {d3: \"d3.v4.min\"} });\n",
       "    require(['pyzx'], function(pyzx) {\n",
       "        pyzx.showGraph('#graph-output-2',\n",
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