demos/Challenge_circuit_extraction.ipynb

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   "cell_type": "markdown",
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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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       "// 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",
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\"9\", \"t\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1}, {\"source\": \"9\", \"target\": \"17\", \"t\": 2}, {\"source\": \"10\", \"target\": \"48\", \"t\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1}, {\"source\": \"11\", \"target\": \"14\", \"t\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1}, {\"source\": \"15\", \"target\": \"18\", \"t\": 2}, {\"source\": \"16\", \"target\": \"19\", \"t\": 2}, {\"source\": \"17\", \"target\": \"45\", \"t\": 1}, {\"source\": \"18\", \"target\": \"28\", \"t\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1}, {\"source\": \"20\", \"target\": \"21\", \"t\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 2}, {\"source\": \"21\", \"target\": \"23\", \"t\": 1}, {\"source\": \"22\", \"target\": \"24\", \"t\": 2}, {\"source\": \"23\", \"target\": \"25\", \"t\": 2}, {\"source\": \"24\", \"target\": \"27\", \"t\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 2}, {\"source\": \"26\", \"target\": \"33\", \"t\": 1}, {\"source\": \"27\", \"target\": \"29\", \"t\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 2}, {\"source\": \"28\", \"target\": \"31\", \"t\": 2}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1}, {\"source\": \"30\", \"target\": \"32\", \"t\": 2}, {\"source\": \"31\", \"target\": \"34\", \"t\": 1}, {\"source\": \"32\", \"target\": \"36\", \"t\": 1}, {\"source\": \"33\", \"target\": \"34\", \"t\": 2}, {\"source\": \"33\", \"target\": \"39\", \"t\": 2}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 2}, {\"source\": \"35\", \"target\": \"37\", \"t\": 1}, {\"source\": \"36\", \"target\": \"79\", \"t\": 1}, {\"source\": \"37\", \"target\": \"38\", \"t\": 2}, {\"source\": \"38\", \"target\": \"41\", \"t\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 2}, {\"source\": \"40\", \"target\": \"42\", \"t\": 1}, {\"source\": \"41\", \"target\": \"74\", \"t\": 1}, {\"source\": \"42\", \"target\": \"43\", \"t\": 2}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 2}, {\"source\": \"44\", \"target\": \"50\", \"t\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 2}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1}, {\"source\": \"47\", \"target\": \"48\", \"t\": 2}, {\"source\": \"47\", \"target\": \"52\", \"t\": 1}, {\"source\": \"48\", \"target\": \"49\", \"t\": 2}, {\"source\": \"49\", \"target\": \"51\", \"t\": 1}, {\"source\": \"50\", \"target\": \"51\", \"t\": 1}, {\"source\": \"50\", \"target\": \"54\", \"t\": 1}, {\"source\": \"51\", \"target\": \"59\", \"t\": 1}, {\"source\": \"52\", \"target\": \"53\", \"t\": 2}, {\"source\": 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\"target\": \"70\", \"t\": 1}, {\"source\": \"69\", \"target\": \"86\", \"t\": 2}, {\"source\": \"70\", \"target\": \"71\", \"t\": 2}, {\"source\": \"71\", \"target\": \"72\", \"t\": 1}, {\"source\": \"72\", \"target\": \"73\", \"t\": 2}, {\"source\": \"73\", \"target\": \"75\", \"t\": 1}, {\"source\": \"74\", \"target\": \"75\", \"t\": 1}, {\"source\": \"74\", \"target\": \"84\", \"t\": 1}, {\"source\": \"75\", \"target\": \"76\", \"t\": 2}, {\"source\": \"76\", \"target\": \"77\", \"t\": 1}, {\"source\": \"77\", \"target\": \"78\", \"t\": 2}, {\"source\": \"78\", \"target\": \"80\", \"t\": 1}, {\"source\": \"79\", \"target\": \"80\", \"t\": 1}, {\"source\": \"79\", \"target\": \"90\", \"t\": 2}, {\"source\": \"80\", \"target\": \"81\", \"t\": 2}, {\"source\": \"81\", \"target\": \"82\", \"t\": 1}, {\"source\": \"82\", \"target\": \"83\", \"t\": 2}, {\"source\": \"83\", \"target\": \"85\", \"t\": 1}, {\"source\": \"84\", \"target\": \"85\", \"t\": 1}, {\"source\": \"84\", \"target\": \"89\", \"t\": 2}, {\"source\": \"85\", \"target\": \"88\", \"t\": 2}, {\"source\": \"86\", \"target\": \"95\", \"t\": 1}, {\"source\": \"87\", \"target\": \"97\", \"t\": 1}, {\"source\": \"88\", \"target\": \"93\", \"t\": 1}, {\"source\": \"89\", \"target\": \"91\", \"t\": 1}, {\"source\": \"90\", \"target\": \"92\", \"t\": 1}, {\"source\": \"91\", \"target\": \"92\", \"t\": 2}, {\"source\": \"91\", \"target\": \"99\", \"t\": 1}, {\"source\": \"92\", \"target\": \"98\", \"t\": 1}, {\"source\": \"93\", \"target\": \"94\", \"t\": 2}, {\"source\": \"94\", \"target\": \"102\", \"t\": 1}, {\"source\": \"95\", \"target\": \"96\", \"t\": 2}, {\"source\": \"96\", \"target\": \"101\", \"t\": 1}, {\"source\": \"97\", \"target\": \"100\", \"t\": 1}]}'), 1020, 160, 20, 4.0, true, false);\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c1 = zx.extract_circuit(g1.copy())\n",
    "zx.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": [
    {
     "ename": "Exception",
     "evalue": "No extractable vertex found. Something went wrong",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mException\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-d825c137db1d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mc2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mzx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mextract_circuit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\Documents\\Projects\\pyzx\\pyzx\\extract.py\u001b[0m in \u001b[0;36mextract_circuit\u001b[1;34m(g, optimize_czs, optimize_cnots, quiet)\u001b[0m\n\u001b[0;32m    482\u001b[0m                 \u001b[0mw\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mneighbors\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrow\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mrow\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    483\u001b[0m                 \u001b[0mgood_verts\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mv\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mw\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 484\u001b[1;33m         \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mgood_verts\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mException\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"No extractable vertex found. Something went wrong\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    485\u001b[0m         \u001b[0mhads\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    486\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mw\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mgood_verts\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;31m# Update frontier vertices\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mException\u001b[0m: No extractable vertex found. Something went wrong"
     ]
    }
   ],
   "source": [
    "c2 = zx.extract_circuit(g2.copy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the ZX-diagram. **Can you extract it?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-2\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({baseUrl: \"../pyzx/js\",paths: {d3: \"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 \"green\";\n",
       "        else if (t == 2) return \"red\";\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",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels) {\n",
       "        var ntab = {};\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",
       "        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",
       "\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",
       "\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 - 5)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"8px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#ccc\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\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).select(\":first-child\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.select(\":first-child\").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.select(\":first-child\").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.select(\":first-child\").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-2',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 23.529411764705884, \"y\": 47.05882352941177, \"t\": 0, \"phase\": \"\"}, {\"name\": \"1\", \"x\": 23.529411764705884, \"y\": 70.58823529411765, \"t\": 0, \"phase\": \"\"}, {\"name\": \"2\", \"x\": 23.529411764705884, \"y\": 94.11764705882354, \"t\": 0, \"phase\": \"\"}, {\"name\": \"3\", \"x\": 23.529411764705884, \"y\": 117.64705882352942, \"t\": 0, \"phase\": \"\"}, {\"name\": \"4\", \"x\": 23.529411764705884, \"y\": 141.1764705882353, \"t\": 0, \"phase\": \"\"}, {\"name\": \"5\", \"x\": 70.58823529411765, \"y\": 141.1764705882353, \"t\": 1, \"phase\": \"\"}, {\"name\": \"6\", \"x\": 70.58823529411765, \"y\": 70.58823529411765, \"t\": 1, \"phase\": \"5\\u03c0/4\"}, {\"name\": \"7\", \"x\": 117.64705882352942, \"y\": 23.529411764705884, \"t\": 1, \"phase\": \"\"}, {\"name\": \"8\", \"x\": 117.64705882352942, \"y\": 47.05882352941177, \"t\": 1, \"phase\": \"5\\u03c0/4\"}, {\"name\": \"9\", \"x\": 141.1764705882353, \"y\": 141.1764705882353, \"t\": 1, \"phase\": \"3\\u03c0/2\"}, {\"name\": \"10\", \"x\": 164.7058823529412, \"y\": 23.529411764705884, \"t\": 1, \"phase\": \"\"}, {\"name\": \"11\", \"x\": 211.76470588235296, \"y\": 23.529411764705884, \"t\": 1, \"phase\": \"\"}, {\"name\": \"12\", \"x\": 235.29411764705884, \"y\": 23.529411764705884, \"t\": 1, \"phase\": \"\"}, {\"name\": \"13\", \"x\": 258.82352941176475, \"y\": 141.1764705882353, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"14\", \"x\": 329.4117647058824, \"y\": 23.529411764705884, \"t\": 1, \"phase\": \"\"}, {\"name\": \"15\", \"x\": 329.4117647058824, \"y\": 94.11764705882354, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"16\", \"x\": 376.47058823529414, \"y\": 23.529411764705884, \"t\": 1, \"phase\": \"\"}, {\"name\": \"17\", \"x\": 423.5294117647059, \"y\": 23.529411764705884, \"t\": 1, \"phase\": \"\"}, {\"name\": \"18\", \"x\": 447.0588235294118, \"y\": 117.64705882352942, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": 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       "</script>"
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   "source": [
    "zx.draw(g2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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