demos/gettingstarted-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting Started\n",
    "\n",
    "We start by importing the library and configuring matplotlib to display the figures in a nice way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (1582183910.py, line 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"/var/folders/s7/yx9nfx_j7wz_n6b7jdj_9wr40000gn/T/ipykernel_59015/1582183910.py\"\u001b[0;36m, line \u001b[0;32m3\u001b[0m\n\u001b[0;31m    import ..pyzx as zx\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "import sys; sys.path.insert(0, '..') # So that we import the local copy of pyzx if you have installed from Github\n",
    "import random\n",
    "import pyzx as zx\n",
    "from pyzx import utils, simplify\n",
    "from fractions import Fraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "zx."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['I0 0 S10', 'I1 1 S7', 'I2 2 S6', 'O3 0 S25', 'O4 1 S26', 'O5 2 S22', 'H6 S8', 'Z7 S8 S13', 'X8 S9', 'Z9 S11 7*pi/4', 'Z10 S11 S16', 'X11 S12', 'Z12 S14 1*pi/4', 'Z13 S14 S18', 'X14 S15', 'Z15 S17 7*pi/4', 'Z16 S17 S20', 'X17 S19', 'Z18 S21 1*pi/4', 'Z19 S22 1*pi/4', 'Z20 S21 S23', 'X21 S24', 'H22', 'Z23 S25 1*pi/4', 'Z24 S26 7*pi/4', 'Z25 S26', 'X26']\n"
     ]
    }
   ],
   "source": [
    "my_file = open(\"../circuits/zx/tof3.zx\")\n",
    "data = my_file.read()\n",
    "line_list = [ line.split(' //')[0] for line in data.split('\\n') if line[0:2] != '//' and line != '']\n",
    "print(line_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[((0, 10), 'S'), ((1, 7), 'S'), ((2, 6), 'S')], [((6, 8), 'S'), ((7, 8), 'S'), ((7, 13), 'S'), ((8, 9), 'S'), ((9, 11), 'S'), ((10, 11), 'S'), ((10, 16), 'S'), ((11, 12), 'S'), ((12, 14), 'S'), ((13, 14), 'S'), ((13, 18), 'S'), ((14, 15), 'S'), ((15, 17), 'S'), ((16, 17), 'S'), ((16, 20), 'S'), ((17, 19), 'S'), ((18, 21), 'S'), ((19, 22), 'S'), ((20, 21), 'S'), ((20, 23), 'S'), ((21, 24), 'S'), ((23, 25), 'S'), ((24, 26), 'S'), ((25, 26), 'S')], [((3, 25), 'S'), ((4, 26), 'S'), ((5, 22), 'S')]]\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",
       "// 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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   "source": [
    "newGraph = zx.Graph()\n",
    "inputs = []    # each item: (id, qubit)\n",
    "outputs = []   # each item: (id, qubit)\n",
    "vertices = []  # each item: (id, vertexType)\n",
    "edges = []     # each item: ((id_s, id_t), edgeType)\n",
    "id2label = {}\n",
    "for line in line_list:\n",
    "    if line[0] == 'I' or line[0] == 'O' or line[0] == 'Z' or line[0] == 'X' or line[0] == 'H':\n",
    "        items = line[1:].split(' ')\n",
    "        if line[0] == 'I' or line[0] == 'O':\n",
    "            newVIdx = len(id2label)\n",
    "            id2label[int(items[0])] = newVIdx\n",
    "            if line[0] == 'I':\n",
    "                inputs.append(newVIdx)\n",
    "                newGraph.add_vertex(ty=utils.VertexType.BOUNDARY, qubit = int(items[1]), row=0)\n",
    "            else:\n",
    "                outputs.append(newVIdx)\n",
    "                newGraph.add_vertex(ty=utils.VertexType.BOUNDARY, qubit = int(items[1]))\n",
    "            \n",
    "            \n",
    "            for it in items[2:]:\n",
    "                et = it[0]\n",
    "                id_t = int(it[1:])\n",
    "                edges.append(((int(items[0]),id_t), et))\n",
    "            \n",
    "        elif line[0] == 'Z' or line[0] == 'X' or line[0] == 'H' :\n",
    "            newVIdx = len(id2label)\n",
    "            id2label[int(items[0])] = newVIdx\n",
    "            vertices.append(newVIdx)\n",
    "            \n",
    "            # check if phase\n",
    "            last_item = items[len(items)-1]\n",
    "            phase = 0\n",
    "            if last_item != items[0] and last_item[0] != 'S' and last_item[0] != 'H':\n",
    "                items = items[:-1]\n",
    "                numerator, denominator = int(last_item.split('*pi/')[0]), int(last_item.split('*pi/')[1])\n",
    "                phase = Fraction(numerator, denominator)\n",
    "            \n",
    "            if line[0] == 'Z':\n",
    "                newGraph.add_vertex(ty=utils.VertexType.Z, phase=phase)\n",
    "            elif line[0] == 'X':\n",
    "                newGraph.add_vertex(ty=utils.VertexType.X, phase=phase)\n",
    "            else:\n",
    "                newGraph.add_vertex(ty=utils.VertexType.H_BOX, phase=phase)\n",
    "            \n",
    "            for it in items[1:]:\n",
    "                et = it[0]\n",
    "                id_t = int(it[1:])\n",
    "                edges.append(((int(items[0]),id_t), et))\n",
    "        else:\n",
    "            continue\n",
    "    else:\n",
    "        break;\n",
    "        \n",
    "edgeStartList = [[],[],[]]\n",
    "\n",
    "for e in edges:\n",
    "    if id2label[e[0][0]] in inputs:\n",
    "        edgeStartList[0].append(e)\n",
    "    elif id2label[e[0][0]] in vertices:\n",
    "        edgeStartList[1].append(e)\n",
    "    else:\n",
    "        edgeStartList[2].append(e)\n",
    "print(edgeStartList)\n",
    "        \n",
    "max_row = 0\n",
    "for vi in edgeStartList[0]:\n",
    "    s_row, s_qubit = newGraph.row(id2label[vi[0][0]]), newGraph.qubit(id2label[vi[0][0]])\n",
    "    newGraph.set_row(id2label[vi[0][1]], s_row+1)\n",
    "    newGraph.set_qubit(id2label[vi[0][1]],s_qubit)\n",
    "    max_row = max(max_row, s_row+1)\n",
    "    if e[1] == 'S':\n",
    "        newGraph.add_edge((id2label[vi[0][0]],id2label[vi[0][1]]))\n",
    "    else:\n",
    "        newGraph.add_edge((id2label[vi[0][0]],id2label[vi[0][1]]), edgetype=utils.EdgeType.HADAMARD)\n",
    "\n",
    "\n",
    "\n",
    "# for e in edges:\n",
    "#     s_row = newGraph.row(id2label[e[0][0]])\n",
    "# #     newGraph.set_row(id2label[e[0][1]], s_row+1)\n",
    "#     max_row = max(max_row, s_row+1)\n",
    "#     if e[1] == 'S':\n",
    "#         newGraph.add_edge((id2label[e[0][0]],id2label[e[0][1]]))\n",
    "#     else:\n",
    "#         newGraph.add_edge((id2label[e[0][0]],id2label[e[0][1]]), edgetype=utils.EdgeType.HADAMARD)\n",
    "\n",
    "# # for o in outputs:\n",
    "# #     newGraph.set_row(o, max_row+1)\n",
    "    \n",
    "zx.draw(newGraph, labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2]\n",
      "[3, 4, 5]\n",
      "[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]\n",
      "[((0, 10), 'S'), ((1, 7), 'S'), ((2, 6), 'S'), ((3, 25), 'S'), ((4, 26), 'S'), ((5, 22), 'S'), ((6, 8), 'S'), ((7, 8), 'S'), ((7, 13), 'S'), ((8, 9), 'S'), ((9, 11), 'S'), ((10, 11), 'S'), ((10, 16), 'S'), ((11, 12), 'S'), ((12, 14), 'S'), ((13, 14), 'S'), ((13, 18), 'S'), ((14, 15), 'S'), ((15, 17), 'S'), ((16, 17), 'S'), ((16, 20), 'S'), ((17, 19), 'S'), ((18, 21), 'S'), ((19, 22), 'S'), ((20, 21), 'S'), ((20, 23), 'S'), ((21, 24), 'S'), ((23, 25), 'S'), ((24, 26), 'S'), ((25, 26), 'S')]\n"
     ]
    }
   ],
   "source": [
    "print(inputs)\n",
    "print(outputs)\n",
    "print(vertices)\n",
    "print(edges)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-w5ossV8S\"></div>\n",
       "<script type=\"module\">\n",
       "var d3;\n",
       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\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",
       "// 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",
       "function showGraph(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",
       "showGraph('#graph-output-w5ossV8S',\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,\n",
       "  10.0, false, true, '');\n",
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circ = zx.Circuit.load(\"../circuits/qasm/tof3.qasm\")\n",
    "g = circ.to_graph()\n",
    "zx.draw(g, labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "g1 = zx.Graph()\n",
    "g1.add_vertex(ty=utils.VertexType.BOUNDARY)\n",
    "g1.add_vertex(ty=utils.VertexType.BOUNDARY)\n",
    "g1.add_vertex(ty=utils.VertexType.Z)\n",
    "g1.add_vertex(ty=utils.VertexType.X)\n",
    "g1.add_vertex(ty=utils.VertexType.BOUNDARY)\n",
    "g1.add_vertex(ty=utils.VertexType.BOUNDARY)\n",
    "g1.set_qubit(0,0)\n",
    "g1.set_qubit(2,0)\n",
    "g1.set_qubit(4,0)\n",
    "g1.set_qubit(1,1)\n",
    "g1.set_qubit(3,1)\n",
    "g1.set_qubit(5,1)\n",
    "g1.add_edge((0,2))\n",
    "g1.add_edge((2,3))\n",
    "g1.add_edge((2,4))\n",
    "g1.add_edge((1,3))\n",
    "g1.add_edge((3,5))\n",
    "g1.set_row(0,0)\n",
    "g1.set_row(2,1)\n",
    "g1.set_row(4,2)\n",
    "g1.set_row(1,0)\n",
    "g1.set_row(3,1)\n",
    "g1.set_row(5,2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inputs:  0\n",
      "Outputs:  0\n",
      "Vertices:  6\n",
      "Edges:  5\n"
     ]
    }
   ],
   "source": [
    "print(\"Inputs: \", g1.num_inputs())\n",
    "print(\"Outputs: \", g1.num_outputs())\n",
    "print(\"Vertices: \", g1.num_vertices())\n",
    "print(\"Edges: \", g1.num_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
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    "zx.draw_matplotlib(g1, labels=True)"
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   "metadata": {},
   "source": [
    "Then we can create a new random Clifford circuit and visualise it."
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  },
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   "cell_type": "code",
   "execution_count": 3,
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       "    <!-- 3π/2 -->\r\n",
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       "    <!-- π -->\r\n",
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       "  </g>\r\n",
       " </g>\r\n",
       " <defs>\r\n",
       "  <clipPath id=\"p4c63f13965\">\r\n",
       "   <rect height=\"144\" width=\"576\" x=\"7.2\" y=\"7.2\"/>\r\n",
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       " </defs>\r\n",
       "</svg>\r\n"
      ],
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qubit_amount = 4\n",
    "depth = 15\n",
    "random.seed(1337)\n",
    "circ = zx.generate.cliffords(qubit_amount, depth)\n",
    "zx.draw_matplotlib(circ,labels=True,h_edge_draw='box')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The green and red nodes represent Z- and X-phase gates respectively, the yellow boxes are Hadamard gates, and the vertical lines going between two different colored nodes are CNOT gates.\n",
    "\n",
    "Internally this circuit is represented as a graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph(46 vertices, 49 edges)\n",
      "All edges:  [(0, 4), (1, 5), (2, 6), (3, 7), (4, 13), (5, 11), (6, 8), (7, 9), (8, 10), (9, 12), (10, 14), (11, 18), (12, 15), (13, 19), (14, 15), (14, 17), (15, 16), (16, 17), (16, 24), (17, 20), (18, 19), (18, 21), (19, 23), (20, 22), (21, 29), (22, 25), (23, 28), (24, 27), (25, 26), (26, 31), (27, 33), (28, 29), (28, 30), (29, 35), (30, 31), (30, 37), (31, 32), (32, 33), (32, 34), (33, 41), (34, 36), (35, 39), (36, 37), (36, 40), (37, 38), (38, 42), (39, 43), (40, 44), (41, 45)]\n",
      "\n",
      "The neighbors of a particular vertex:  [15, 10, 17]\n"
     ]
    }
   ],
   "source": [
    "print(circ)\n",
    "print(\"All edges: \", list(circ.edges()))\n",
    "print(\"\\nThe neighbors of a particular vertex: \", list(circ.neighbors(14)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using this graph representation we can use the rules of the ZX-calculus to simplify it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = circ.copy()\n",
    "zx.clifford_simp(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "<script type=\"module\">\n",
       "var d3;\n",
       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\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",
       "// 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",
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       "    if (t == 1) return \"black\";\n",
       "    else if (t == 2) return \"#08f\";\n",
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       "function nodeStyle(selected) {\n",
       "    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",
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       "\n",
       "        context.moveTo(-s/3,2*s/3);\n",
       "        context.lineTo(s/3,2*s/3);\n",
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       "\n",
       "function showGraph(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",
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       "\n",
       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
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       "\n",
       "    graph.links.forEach(function(d) {\n",
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       "        var t = ntab[d.target];\n",
       "        d.source = s;\n",
       "        d.target = t;\n",
       "        s.nhd.push(t);\n",
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       "\n",
       "    var shiftKey;\n",
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       "\n",
       "    var svg = d3.select(tag)\n",
       "    //.attr(\"tabindex\", 1)\n",
       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
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       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "        .attr(\"width\", width)\n",
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       "    var link = svg.append(\"g\")\n",
       "        .attr(\"class\", \"link\")\n",
       "        .selectAll(\"line\")\n",
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       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
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       "    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",
       "showGraph('#graph-output-FReXQH1a',\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\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 100, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 150, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 200, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 200, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 200, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"23\", \"t\": 1}, {\"source\": \"1\", \"target\": \"11\", \"t\": 2}, {\"source\": \"2\", \"target\": \"6\", \"t\": 1}, {\"source\": \"3\", \"target\": \"9\", \"t\": 2}, {\"source\": \"6\", \"target\": \"16\", \"t\": 2}, {\"source\": \"6\", \"target\": \"32\", \"t\": 2}, {\"source\": \"6\", \"target\": \"21\", \"t\": 2}, {\"source\": \"6\", \"target\": \"11\", \"t\": 2}, {\"source\": \"9\", \"target\": \"32\", \"t\": 2}, {\"source\": \"9\", \"target\": \"21\", \"t\": 2}, {\"source\": \"9\", \"target\": \"11\", \"t\": 2}, {\"source\": \"11\", \"target\": \"23\", \"t\": 2}, {\"source\": \"11\", \"target\": \"37\", \"t\": 2}, {\"source\": \"16\", \"target\": \"32\", \"t\": 2}, {\"source\": \"16\", \"target\": \"45\", \"t\": 2}, {\"source\": \"21\", \"target\": \"43\", \"t\": 2}, {\"source\": \"21\", \"target\": \"23\", \"t\": 2}, {\"source\": \"21\", \"target\": \"37\", \"t\": 2}, {\"source\": \"32\", \"target\": \"37\", \"t\": 2}, {\"source\": \"32\", \"target\": \"44\", \"t\": 1}, {\"source\": \"37\", \"target\": \"42\", \"t\": 2}]}'), 250, 300, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g.normalize() # Reposition nodes horizontally to look nicer\n",
    "zx.draw(g) # This draw function by default uses the D3 Javascript library to draw the diagram. If it doesn't work, use draw_matplotlib() instead"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The blue lines represent edges that have a Hadamard gate on them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to see in a bit more detail what goes into rewriting this circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e75ad7fbf62840398ee6a59c0d712a76",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='rewrite', layout=Layout(width='700px'), max=13), Output(…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import widgets\n",
    "from IPython.display import display, Markdown\n",
    "\n",
    "from pyzx.simplify import clifford_iter\n",
    "\n",
    "graph = circ.copy()\n",
    "graphs = [zx.draw_matplotlib(graph)]\n",
    "names = [\"start\"]\n",
    "for gs, n in clifford_iter(graph):\n",
    "    graphs.append(zx.draw_matplotlib(gs))\n",
    "    names.append(n)\n",
    "zx.drawing.pack_circuit_nf(gs,'grg')\n",
    "graphs.append(zx.draw_matplotlib(gs))\n",
    "names.append(\"reposition\")\n",
    "\n",
    "def plotter(rewrite):\n",
    "    display(Markdown(\"Rewrite step: \" + names[rewrite]))\n",
    "    display(graphs[rewrite])\n",
    "\n",
    "w = widgets.interactive(plotter, rewrite=(0,len(graphs)-1))\n",
    "slider = w.children[0]\n",
    "slider.layout.width = \"{!s}px\".format(min(800,50*len(graphs)))\n",
    "output = w.children[-1]\n",
    "output.layout.height = \"{!s}px\".format(200+qubit_amount*20)\n",
    "slider.value = 0\n",
    "w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the first few steps are **spider fusion**, where adjacent red nodes and adjacent green nodes are fused together (and their phases added). The next step is to convert all red nodes to green nodes by changing regular edges to hadamard edges.\n",
    "\n",
    "Now come the steps that do most of the work. These steps are a round of **pivots** followed by **local complementations** and then a round of pivots again. The local complementation rules looks for green nodes with a phase of $\\frac\\pi2$ or $\\frac{3\\pi}2$. By doing a local complementation on this node we can remove the node from the graph. This process is done until no more suitable candidates are found. A pivot consists of a series of three local complementations that is done on two neighboring vertices that have a zero or $\\pi$ phase. A pivot move allows us to remove these two nodes.\n",
    "\n",
    "Finally we do a round of **identity** simplification which removes phaseless nodes that are connected to precisely two neighbors.\n",
    "\n",
    "**Note**: Depending on the circuit that was generated, any of these steps might not have been done."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though this graph is a lot compacter than the one we started out with, it no longer looks like a circuit. To fix this we need to be clever and *extract* a circuit from the ZX-diagram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-qtyimpMh\"></div>\n",
       "<script type=\"module\">\n",
       "var d3;\n",
       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\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",
       "// 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",
       "function showGraph(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",
       "showGraph('#graph-output-qtyimpMh',\n",
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       "  7.272727272727273, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circ2 = g.copy()\n",
    "circ2.normalize()\n",
    "circ2 = zx.extract_circuit(circ2)\n",
    "zx.draw(circ2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that this circuit is still equal to the original circuit, we can transform them into numpy tensors and compare these tensors for equality:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1 = circ.to_tensor()\n",
    "t2 = circ2.to_tensor()\n",
    "# This checks whether t1 and t2 are equal up to some number: t1 == z*t2 for some complex number z\n",
    "zx.compare_tensors(t1,t2,preserve_scalar=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can represent the circuit in one of several quantum circuit description languages, such as that of QASM:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OPENQASM 2.0;\n",
      "include \"qelib1.inc\";\n",
      "qreg q[4];\n",
      "cx q[2], q[3];\n",
      "cx q[3], q[2];\n",
      "cx q[2], q[3];\n",
      "cx q[0], q[1];\n",
      "cx q[1], q[0];\n",
      "cx q[0], q[1];\n",
      "h q[2];\n",
      "h q[0];\n",
      "cz q[0], q[1];\n",
      "h q[1];\n",
      "cz q[1], q[2];\n",
      "cz q[0], q[2];\n",
      "rz(0.5*pi) q[2];\n",
      "h q[2];\n",
      "cz q[2], q[3];\n",
      "cz q[1], q[3];\n",
      "cz q[0], q[3];\n",
      "rz(1.0*pi) q[0];\n",
      "h q[3];\n",
      "h q[0];\n",
      "cz q[2], q[3];\n",
      "cz q[0], q[2];\n",
      "cz q[0], q[1];\n",
      "rz(1.0*pi) q[3];\n",
      "h q[3];\n",
      "rz(1.0*pi) q[2];\n",
      "rz(1.0*pi) q[1];\n",
      "h q[1];\n",
      "rz(0.5*pi) q[0];\n",
      "h q[0];\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(circ2.to_qasm())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets try the same thing with a more complicated Clifford+T circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-VOCO455z\"></div>\n",
       "<script type=\"module\">\n",
       "var d3;\n",
       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\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",
       "// 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",
       "function showGraph(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",
       "showGraph('#graph-output-VOCO455z',\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\": 20, \"y\": 140, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 40, \"y\": 40, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 40, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 40, \"y\": 80, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 40, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 40, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 40, \"y\": 140, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 60, \"y\": 140, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 60, \"y\": 80, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 80, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 100, \"y\": 140, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 120, \"y\": 140, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 140, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 140, \"y\": 140, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 160, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 180, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 200, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 220, \"y\": 60, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 220, \"y\": 140, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 240, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 260, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 260, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 280, \"y\": 120, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 300, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 320, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 340, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 360, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 380, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 400, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 420, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 440, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 460, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 480, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 500, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 500, \"y\": 40, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 520, \"y\": 40, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 540, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 560, \"y\": 80, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 580, \"y\": 60, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 600, \"y\": 60, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 620, \"y\": 120, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 620, \"y\": 140, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 640, \"y\": 80, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 640, \"y\": 140, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 660, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 680, \"y\": 80, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 700, \"y\": 120, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 720, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 740, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, 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       "  4.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qubit_amount = 6\n",
    "depth = 70\n",
    "random.seed(1338)\n",
    "circ = zx.generate.cliffordT(qubit_amount, depth,p_t=0.2)\n",
    "zx.draw(circ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-Y20PZNir\"></div>\n",
       "<script type=\"module\">\n",
       "var d3;\n",
       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\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",
       "// 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",
       "function showGraph(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",
       "showGraph('#graph-output-Y20PZNir',\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\": 50, \"y\": 350, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 100, \"y\": 250, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, 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{\"name\": \"82\", \"x\": 350, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"83\", \"x\": 400, \"y\": 350, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"86\", \"x\": 400, \"y\": 300, \"t\": 1, \"phase\": \"3\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"88\", \"x\": 400, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"97\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"104\", \"x\": 450, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"105\", \"x\": 450, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"106\", \"x\": 450, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"107\", \"x\": 450, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": 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\"77\", \"t\": 2}, {\"source\": \"44\", \"target\": \"82\", \"t\": 2}, {\"source\": \"50\", \"target\": \"83\", \"t\": 2}, {\"source\": \"54\", \"target\": \"71\", \"t\": 2}, {\"source\": \"54\", \"target\": \"77\", \"t\": 2}, {\"source\": \"71\", \"target\": \"82\", \"t\": 2}, {\"source\": \"71\", \"target\": \"106\", \"t\": 2}, {\"source\": \"77\", \"target\": \"83\", \"t\": 2}, {\"source\": \"77\", \"target\": \"107\", \"t\": 1}, {\"source\": \"77\", \"target\": \"86\", \"t\": 2}, {\"source\": \"77\", \"target\": \"82\", \"t\": 2}, {\"source\": \"82\", \"target\": \"88\", \"t\": 2}, {\"source\": \"83\", \"target\": \"109\", \"t\": 2}, {\"source\": \"83\", \"target\": \"97\", \"t\": 2}, {\"source\": \"86\", \"target\": \"108\", \"t\": 1}, {\"source\": \"88\", \"target\": \"104\", \"t\": 2}, {\"source\": \"97\", \"target\": \"105\", \"t\": 1}]}'), 500, 400, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = circ.copy()\n",
    "zx.clifford_simp(g, quiet=True)\n",
    "g.normalize()\n",
    "zx.draw(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, let us extract a circuit from this diagram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit  on 6 qubits with 62 gates.\n",
      "        8 is the T-count\n",
      "        54 Cliffords among which\n",
      "        28 2-qubit gates (2 CNOT, 26 other) and\n",
      "        22 Hadamard gates.\n"
     ]
    }
   ],
   "source": [
    "g2 = g.copy()\n",
    "c = zx.extract_circuit(g2)\n",
    "print(c.stats())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert this back into a PyZX-graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-OuGZVa4r\"></div>\n",
       "<script type=\"module\">\n",
       "var d3;\n",
       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\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",
       "// 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",
       "function showGraph(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",
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       "            .attr(\"fill\", \"#999\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "    }\n",
       "\n",
       "    // Display the chosen data fields over the node.\n",
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       "        .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",
       "showGraph('#graph-output-OuGZVa4r',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 21.05263157894737, \"y\": 42.10526315789474, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 21.05263157894737, \"y\": 63.15789473684211, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 21.05263157894737, \"y\": 84.21052631578948, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 21.05263157894737, \"y\": 105.26315789473685, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 21.05263157894737, \"y\": 126.31578947368422, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 21.05263157894737, \"y\": 147.3684210526316, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 42.10526315789474, \"y\": 147.3684210526316, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 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       "  4.210526315789474, false, false, '');\n",
       "</script>"
      ],
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "zx.draw(c.to_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And verify that it is still equal to the original graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can just feed the Circuit objects directly to compare_tensors\n",
    "zx.compare_tensors(c, circ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets represent this circuit in the QASM circuit description language:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(c.to_basic_gates().to_qasm())"
   ]
  }
 ],
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