demos/ZXW_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ZXW demo\n",
    "\n",
    "The ZXW calculus includes the ZX calculus and in addition, it has the Z box and W node as generators.\n",
    "\n",
    "To learn more about the ZXW calculus, check out some of these papers:\n",
    "* [Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus](https://arxiv.org/abs/2302.12135)\n",
    "* [How to Sum and Exponentiate Hamiltonians in ZXW calculus](https://arxiv.org/abs/2212.04462)\n",
    "* [Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning](https://arxiv.org/abs/2201.13250)\n",
    "* [Light-Matter interaction in the ZXW calculus](https://arxiv.org/abs/2306.02114)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys; sys.path.append('..')\n",
    "import pyzx as zx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
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       "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",
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       "    if (t == 0) return \"black\";\n",
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       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
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       "\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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
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       "        .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(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
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       "        .attr(\"font-size\", \"8px\")\n",
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       "        .selectAll(\"tspan\")\n",
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       "        .append(\"tspan\")\n",
       "        .attr(\"x\", \"0\")\n",
       "        .attr(\"dy\", \"1.2em\")\n",
       "        .text(x => x.join(\": \"));\n",
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       "    if (scalar_str != \"\") {\n",
       "        svg.append(\"text\")\n",
       "            .text(scalar_str)\n",
       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
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       "\n",
       "    function update_hboxes() {\n",
       "        if (auto_hbox) {\n",
       "            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",
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       "                        x += d.nhd[i].x;\n",
       "                        y += d.nhd[i].y;\n",
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       "                    pos[[x,y]] = true;\n",
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       "    }\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",
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       "            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",
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       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "            node.filter(function(d) { return d.selected; })\n",
       "                .attr(\"transform\", function(d) {\n",
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       "                    d.y += dy;\n",
       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                });\n",
       "\n",
       "            update_hboxes();\n",
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       "            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",
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       "                .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
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       "            //     .attr(\"x\", function(d) { return d.x; })\n",
       "            //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
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       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
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       "                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",
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       "            }\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-GyIylJ7h',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 90.0, \"y\": 200.0, \"t\": 4, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 200.0, \"t\": 5, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 150, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 3}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1}, {\"source\": \"1\", \"target\": \"4\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1}, {\"source\": \"1\", \"target\": \"7\", \"t\": 1}]}'), 200, 350, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create the W node using the zx.generate.spider method\n",
    "zx.draw(zx.generate.spider(\"W\", 1, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "<div style=\"overflow:auto\" id=\"graph-output-HhuimfX5\"></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",
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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",
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       "\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",
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       "    graph.nodes.forEach(function(d) {\n",
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       "        d.selected = false;\n",
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       "\n",
       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "        return d.t != 3;\n",
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       "\n",
       "    graph.links.forEach(function(d) {\n",
       "        var s = ntab[d.source];\n",
       "        var t = ntab[d.target];\n",
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       "        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 && d.t != 5; })\n",
       "        .append(\"circle\")\n",
       "        .attr(\"r\", function(d) {\n",
       "            if (d.t == 0) return 0.5 * node_size;\n",
       "            else if (d.t == 4) return 0.25 * 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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
       "\n",
       "    // draw a square for Z box: d.t == 6\n",
       "    node.filter(function(d) { return d.t == 6; })\n",
       "        .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-HhuimfX5',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 90.0, \"y\": 150.0, \"t\": 4, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150.0, \"t\": 5, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150.0, \"y\": 275.0, \"t\": 4, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 160.0, \"y\": 275.0, \"t\": 5, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 270.0, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 270.0, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 270.0, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 270.0, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 270.0, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 210.0, \"y\": 375.0, \"t\": 4, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 220.00000000000003, \"y\": 375.0, \"t\": 5, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 270.0, \"y\": 350, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 270.0, \"y\": 400, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 3}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1}, {\"source\": \"1\", \"target\": \"7\", \"t\": 1}, {\"source\": \"1\", \"target\": \"8\", \"t\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 3}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1}, {\"source\": \"6\", \"target\": \"11\", \"t\": 1}, {\"source\": \"6\", \"target\": \"12\", \"t\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 3}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1}]}'), 320.0, 450, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_diagram = zx.generate.spider(\"W\", 1, 3) + \\\n",
    "            (zx.generate.identity(2) @ zx.generate.spider(\"W\", 1, 4)) + \\\n",
    "            (zx.generate.identity(5) @ zx.generate.spider(\"W\", 1, 2))\n",
    "zx.draw(w_diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W fusion: 1. 1.  2 iterations\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-spYnYM9w\"></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",
       "    else if (t == 4) return \"black\";\n",
       "    else if (t == 5) return \"black\";\n",
       "}\n",
       "\n",
       "function edgeColor(t) {\n",
       "    if (t == 1) return \"black\";\n",
       "    else if (t == 2) return \"#08f\";\n",
       "    else if (t == 3) return \"gray\";\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 && d.t != 5; })\n",
       "        .append(\"circle\")\n",
       "        .attr(\"r\", function(d) {\n",
       "            if (d.t == 0) return 0.5 * node_size;\n",
       "            else if (d.t == 4) return 0.25 * 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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\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-spYnYM9w',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 90.0, \"y\": 150.0, \"t\": 4, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150.0, \"t\": 5, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 270.0, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 270.0, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 270.0, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 270.0, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 270.0, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 270.0, \"y\": 350, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 270.0, \"y\": 400, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 3}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"1\", \"target\": \"7\", \"t\": 1}, {\"source\": \"1\", \"target\": \"8\", \"t\": 1}, {\"source\": \"1\", \"target\": \"9\", \"t\": 1}, {\"source\": \"1\", \"target\": \"10\", \"t\": 1}, {\"source\": \"1\", \"target\": \"11\", \"t\": 1}, {\"source\": \"1\", \"target\": \"14\", \"t\": 1}, {\"source\": \"1\", \"target\": \"15\", \"t\": 1}]}'), 320.0, 450, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Apply the simplification based on W fusion\n",
    "zx.simplify.simp(w_diagram, 'W fusion', zx.rules.match_w_fusion, zx.rules.w_fusion)\n",
    "zx.draw(w_diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-NqSuQt8S\"></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",
       "    else if (t == 4) return \"black\";\n",
       "    else if (t == 5) return \"black\";\n",
       "    else if (t == 6) return \"#ccffcc\";\n",
       "}\n",
       "\n",
       "function edgeColor(t) {\n",
       "    if (t == 1) return \"black\";\n",
       "    else if (t == 2) return \"#08f\";\n",
       "    else if (t == 3) return \"gray\";\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 && d.t != 5 && d.t != 6; })\n",
       "        .append(\"circle\")\n",
       "        .attr(\"r\", function(d) {\n",
       "            if (d.t == 0) return 0.5 * node_size;\n",
       "            else if (d.t == 4) return 0.25 * 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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
       "\n",
       "    // draw a square for Z box: d.t == 6\n",
       "    node.filter(function(d) { return d.t == 6; })\n",
       "        .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-NqSuQt8S',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 100, \"y\": 175.0, \"t\": 6, \"phase\": \"(2.2+1.5j)\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 150, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 150, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 150, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"0\", \"target\": \"3\", \"t\": 1}, {\"source\": \"0\", \"target\": \"4\", \"t\": 1}, {\"source\": \"0\", \"target\": \"5\", \"t\": 1}, {\"source\": \"0\", \"target\": \"6\", \"t\": 1}, {\"source\": \"0\", \"target\": \"7\", \"t\": 1}, {\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"0\", \"target\": \"9\", \"t\": 1}]}'), 200, 350, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create the Z box using the zx.generate.spider method\n",
    "zx.draw(zx.generate.spider(\"ZBox\", 4, 5, 2.2 +1.5j))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-XwGBUcGq\"></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",
       "    else if (t == 4) return \"black\";\n",
       "    else if (t == 5) return \"black\";\n",
       "    else if (t == 6) return \"#ccffcc\";\n",
       "}\n",
       "\n",
       "function edgeColor(t) {\n",
       "    if (t == 1) return \"black\";\n",
       "    else if (t == 2) return \"#08f\";\n",
       "    else if (t == 3) return \"gray\";\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 && d.t != 5 && d.t != 6; })\n",
       "        .append(\"circle\")\n",
       "        .attr(\"r\", function(d) {\n",
       "            if (d.t == 0) return 0.5 * node_size;\n",
       "            else if (d.t == 4) return 0.25 * 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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
       "\n",
       "    // draw a square for Z box: d.t == 6\n",
       "    node.filter(function(d) { return d.t == 6; })\n",
       "        .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-XwGBUcGq',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 100, \"y\": 175.0, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 150, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 150, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 150, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"0\", \"target\": \"3\", \"t\": 1}, {\"source\": \"0\", \"target\": \"4\", \"t\": 1}, {\"source\": \"0\", \"target\": \"5\", \"t\": 1}, {\"source\": \"0\", \"target\": \"6\", \"t\": 1}, {\"source\": \"0\", \"target\": \"7\", \"t\": 1}, {\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"0\", \"target\": \"9\", \"t\": 1}]}'), 200, 350, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-e17olkyE\"></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",
       "    else if (t == 4) return \"black\";\n",
       "    else if (t == 5) return \"black\";\n",
       "    else if (t == 6) return \"#ccffcc\";\n",
       "}\n",
       "\n",
       "function edgeColor(t) {\n",
       "    if (t == 1) return \"black\";\n",
       "    else if (t == 2) return \"#08f\";\n",
       "    else if (t == 3) return \"gray\";\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 && d.t != 5 && d.t != 6; })\n",
       "        .append(\"circle\")\n",
       "        .attr(\"r\", function(d) {\n",
       "            if (d.t == 0) return 0.5 * node_size;\n",
       "            else if (d.t == 4) return 0.25 * 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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
       "\n",
       "    // draw a square for Z box: d.t == 6\n",
       "    node.filter(function(d) { return d.t == 6; })\n",
       "        .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-e17olkyE',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 100, \"y\": 175.0, \"t\": 6, \"phase\": \"1j\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 150, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 150, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 150, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"0\", \"target\": \"3\", \"t\": 1}, {\"source\": \"0\", \"target\": \"4\", \"t\": 1}, {\"source\": \"0\", \"target\": \"5\", \"t\": 1}, {\"source\": \"0\", \"target\": \"6\", \"t\": 1}, {\"source\": \"0\", \"target\": \"7\", \"t\": 1}, {\"source\": \"0\", \"target\": \"8\", \"t\": 1}, {\"source\": \"0\", \"target\": \"9\", \"t\": 1}]}'), 200, 350, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the z spider is a special case of the z box and it can be converted using the z to zbox method\n",
    "z_spider = zx.generate.spider(\"Z\", 4, 5, 1//2)\n",
    "zx.draw(z_spider)\n",
    "zx.rules.z_to_z_box(z_spider, zx.rules.match_z_to_z_box(z_spider))\n",
    "zx.draw(z_spider)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-mOEeUEme\"></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",
       "    else if (t == 4) return \"black\";\n",
       "    else if (t == 5) return \"black\";\n",
       "    else if (t == 6) return \"#ccffcc\";\n",
       "}\n",
       "\n",
       "function edgeColor(t) {\n",
       "    if (t == 1) return \"black\";\n",
       "    else if (t == 2) return \"#08f\";\n",
       "    else if (t == 3) return \"gray\";\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 && d.t != 5 && d.t != 6; })\n",
       "        .append(\"circle\")\n",
       "        .attr(\"r\", function(d) {\n",
       "            if (d.t == 0) return 0.5 * node_size;\n",
       "            else if (d.t == 4) return 0.25 * 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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
       "\n",
       "    // draw a square for Z box: d.t == 6\n",
       "    node.filter(function(d) { return d.t == 6; })\n",
       "        .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-mOEeUEme',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 100, \"y\": 125.0, \"t\": 6, \"phase\": \"3.5\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 200, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 200, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 150, \"y\": 250.0, \"t\": 6, \"phase\": \"2\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 200, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 200, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 350, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"0\", \"target\": \"9\", \"t\": 1}, {\"source\": \"0\", \"target\": \"10\", \"t\": 1}, {\"source\": \"0\", \"target\": \"11\", \"t\": 1}, {\"source\": \"6\", \"target\": \"11\", \"t\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 1}, {\"source\": \"11\", \"target\": \"14\", \"t\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1}]}'), 250, 400, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spider_simp: 1.  1 iterations\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-eXX15SwU\"></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",
       "    else if (t == 4) return \"black\";\n",
       "    else if (t == 5) return \"black\";\n",
       "    else if (t == 6) return \"#ccffcc\";\n",
       "}\n",
       "\n",
       "function edgeColor(t) {\n",
       "    if (t == 1) return \"black\";\n",
       "    else if (t == 2) return \"#08f\";\n",
       "    else if (t == 3) return \"gray\";\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 && d.t != 5 && d.t != 6; })\n",
       "        .append(\"circle\")\n",
       "        .attr(\"r\", function(d) {\n",
       "            if (d.t == 0) return 0.5 * node_size;\n",
       "            else if (d.t == 4) return 0.25 * 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",
       "    // draw a triangle for d.t == 5\n",
       "    node.filter(function(d) { return d.t == 5; })\n",
       "        .append(\"path\")\n",
       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "        .attr(\"stroke\", \"black\")\n",
       "        .attr(\"class\", \"selectable\")\n",
       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
       "\n",
       "    // draw a square for Z box: d.t == 6\n",
       "    node.filter(function(d) { return d.t == 6; })\n",
       "        .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-eXX15SwU',\n",
       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 100, \"y\": 125.0, \"t\": 6, \"phase\": \"7.0\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 200, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 200, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 200, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 200, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 350, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1}, {\"source\": \"0\", \"target\": \"2\", \"t\": 1}, {\"source\": \"0\", \"target\": \"9\", \"t\": 1}, {\"source\": \"0\", \"target\": \"10\", \"t\": 1}, {\"source\": \"0\", \"target\": \"12\", \"t\": 1}, {\"source\": \"0\", \"target\": \"13\", \"t\": 1}, {\"source\": \"0\", \"target\": \"14\", \"t\": 1}, {\"source\": \"0\", \"target\": \"15\", \"t\": 1}, {\"source\": \"0\", \"target\": \"6\", \"t\": 1}, {\"source\": \"0\", \"target\": \"8\", \"t\": 1}]}'), 250, 400, 50,\n",
       "  10.0, false, false, '');\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can apply the spider fusion rule to the zbox but now they multiply instead of add\n",
    "zbox_diag = (zx.generate.spider(\"ZBox\", 2, 3, 3.5) @ zx.generate.identity(2)) + \\\n",
    "            (zx.generate.identity(2) @ zx.generate.spider(\"ZBox\", 3, 4, 2))\n",
    "zx.draw(zbox_diag)\n",
    "zx.spider_simp(zbox_diag)\n",
    "zx.draw(zbox_diag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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