diff --git a/demos/PauliWebs.ipynb b/demos/PauliWebs.ipynb
index 75c05e97..d3d1b54d 100644
--- a/demos/PauliWebs.ipynb
+++ b/demos/PauliWebs.ipynb
@@ -44,7 +44,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-MkhojJ4d\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-F1RwiHXP\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -407,7 +407,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-MkhojJ4d',\n",
+       "showGraph('#graph-output-F1RwiHXP',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -440,7 +440,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Qlp6stwV\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-E2MyRITo\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -803,7 +803,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Qlp6stwV',\n",
+       "showGraph('#graph-output-E2MyRITo',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -818,7 +818,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qWMB22nJ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-GenGnixe\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1181,7 +1181,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-qWMB22nJ',\n",
+       "showGraph('#graph-output-GenGnixe',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1196,7 +1196,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-omk09KlE\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-4SDKzu9I\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1559,7 +1559,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-omk09KlE',\n",
+       "showGraph('#graph-output-4SDKzu9I',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1574,7 +1574,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wW2HjYCA\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-BuJtQylO\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1937,7 +1937,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-wW2HjYCA',\n",
+       "showGraph('#graph-output-BuJtQylO',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1966,7 +1966,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-r6IidzxG\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-tcd1SPH8\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2329,7 +2329,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-r6IidzxG',\n",
+       "showGraph('#graph-output-tcd1SPH8',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -2344,7 +2344,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-RsQtsuBn\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-d75ol2PF\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2707,7 +2707,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-RsQtsuBn',\n",
+       "showGraph('#graph-output-d75ol2PF',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -2735,7 +2735,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-sDHG9pqb\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-EMHLX8Cb\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3098,7 +3098,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-sDHG9pqb',\n",
+       "showGraph('#graph-output-EMHLX8Cb',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 300, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3135,7 +3135,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-WP22uqEC\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-lcuJRjgD\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3498,7 +3498,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-WP22uqEC',\n",
+       "showGraph('#graph-output-lcuJRjgD',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 4, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 4, \"t\": \"X\"}, {\"source\": 9, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 9, \"t\": \"X\"}]}'), 300, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3513,7 +3513,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-7oJvrLPn\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qKnhF9cG\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3876,7 +3876,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-7oJvrLPn',\n",
+       "showGraph('#graph-output-qKnhF9cG',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 6, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}]}'), 300, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3891,7 +3891,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-KuLidNJt\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-IF3E9BeN\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -4254,7 +4254,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-KuLidNJt',\n",
+       "showGraph('#graph-output-IF3E9BeN',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 8, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 4, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 4, \"t\": \"X\"}]}'), 300, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -4269,7 +4269,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-dEbN96bU\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-95Q2RRa9\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -4632,7 +4632,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-dEbN96bU',\n",
+       "showGraph('#graph-output-95Q2RRa9',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"I\"}, {\"source\": 0, \"target\": 4, \"t\": \"I\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 7, \"t\": \"Z\"}]}'), 300, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -4647,7 +4647,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-oUQDUZXv\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-HhIttM6S\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5010,7 +5010,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-oUQDUZXv',\n",
+       "showGraph('#graph-output-HhIttM6S',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 10, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 10, \"t\": \"Z\"}]}'), 300, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5025,7 +5025,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-cCRJ28GH\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-jZUurX4I\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5388,7 +5388,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-cCRJ28GH',\n",
+       "showGraph('#graph-output-jZUurX4I',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 11, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 11, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}]}'), 300, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5418,7 +5418,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-zbkpu55T\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-vrSFfIuv\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5781,7 +5781,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-zbkpu55T',\n",
+       "showGraph('#graph-output-vrSFfIuv',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -5796,7 +5796,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-VIxPEAam\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-hgOTveJS\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6159,7 +6159,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-VIxPEAam',\n",
+       "showGraph('#graph-output-hgOTveJS',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6190,7 +6190,7 @@
     "\n",
     "# Adjacent spiders of the same color need to be fused for the Pauli web computation to work.\n",
     "# We can accomplish this with spider_simp:\n",
-    "zx.spider_simp(g, quiet=True)\n",
+    "zx.spider_simp(g)\n",
     "\n",
     "# This is not a fundamental problem, it just requires more case distinctions for compute_pauli_webs\n",
     "# to handle unfused spiders.\n",
@@ -6208,7 +6208,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-snIpKXz5\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-BxFBIlM8\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6571,7 +6571,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-snIpKXz5',\n",
+       "showGraph('#graph-output-BxFBIlM8',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 15, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 15, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"I\"}, {\"source\": 1, \"target\": 3, \"t\": \"I\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"I\"}, {\"source\": 2, \"target\": 5, \"t\": \"I\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6586,7 +6586,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-i3lQpKxn\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-zcJUoo0I\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6949,7 +6949,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-i3lQpKxn',\n",
+       "showGraph('#graph-output-zcJUoo0I',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 16, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6964,7 +6964,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-rd7rs7d5\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-lX3JBUh5\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -7327,7 +7327,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-rd7rs7d5',\n",
+       "showGraph('#graph-output-lX3JBUh5',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 10, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 10, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"I\"}, {\"source\": 2, \"target\": 5, \"t\": \"I\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -7342,7 +7342,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-1V9ngvb6\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-lhwg0eza\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -7705,7 +7705,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-1V9ngvb6',\n",
+       "showGraph('#graph-output-lhwg0eza',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 13, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 13, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -7720,7 +7720,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-XWa50rKo\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ooP6NXhd\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8083,7 +8083,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-XWa50rKo',\n",
+       "showGraph('#graph-output-ooP6NXhd',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 9, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 9, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"I\"}, {\"source\": 0, \"target\": 4, \"t\": \"I\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8098,7 +8098,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wHaPWXJ7\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-MhzNFqQY\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8461,7 +8461,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-wHaPWXJ7',\n",
+       "showGraph('#graph-output-MhzNFqQY',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"I\"}, {\"source\": 0, \"target\": 4, \"t\": \"I\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}, {\"source\": 17, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 17, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8491,7 +8491,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Foib6n1h\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-jadx1ruW\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8854,7 +8854,1555 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Foib6n1h',\n",
+       "showGraph('#graph-output-jadx1ruW',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 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; background-color: white\" id=\"graph-output-GGtdVGHT\"></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 webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\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",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\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 web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\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",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\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 || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\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-GGtdVGHT',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Next, we'll look at a single H gate\n",
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[1];\n",
+    "h q[0];\n",
+    "\"\"\")\n",
+    "g = c.to_graph()\n",
+    "\n",
+    "# PyZX renders this as a single H-edge connected to an identity spider\n",
+    "zx.draw(g)\n",
+    "\n",
+    "# we don't really need this id-spider, so we can remove it with id_simp\n",
+    "zx.id_simp(g)\n",
+    "zx.draw(g, labels=True)\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-2jhENXOh\"></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 webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\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",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\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 web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\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",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\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 || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\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-2jhENXOh',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 2, \"t\": \"X\"}]}'), 200, 150, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-FPOmK1Hr\"></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 webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\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",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\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 web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\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",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\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 || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\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-FPOmK1Hr',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 2, \"t\": \"Z\"}]}'), 200, 150, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# The single output has two Pauli webs\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[2])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[2])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-8KXFUU87\"></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 webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\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",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\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 web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\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",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\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 || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\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-8KXFUU87',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 26.666666666666668, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 26.666666666666668, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 26.666666666666668, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 53.333333333333336, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 53.333333333333336, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 80.0, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 80.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 106.66666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 106.66666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 133.33333333333334, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 160.0, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 160.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 186.66666666666669, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 186.66666666666669, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 186.66666666666669, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 213.33333333333334, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 213.33333333333334, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 240.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 240.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 240.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 266.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 266.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 293.33333333333337, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 293.33333333333337, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 266.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 320.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 320.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 346.6666666666667, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 346.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 373.33333333333337, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 373.33333333333337, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 373.33333333333337, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 400.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 400.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 426.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 426.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 453.33333333333337, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 453.33333333333337, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 480.0, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 480.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 480.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 506.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 506.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 533.3333333333334, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 560.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 586.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 613.3333333333334, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 613.3333333333334, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 640.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 640.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 666.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 506.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 533.3333333333334, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 666.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 560.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 586.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 693.3333333333334, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 693.3333333333334, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 720.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 720.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"60\", \"x\": 746.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 746.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 773.3333333333334, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 773.3333333333334, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 773.3333333333334, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"49\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"50\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"53\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"60\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"57\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"62\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"61\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 133.33333333333334, 26.666666666666668,\n",
        "  5.333333333333334, false, false, '');\n",
        "</script>"
@@ -8877,13 +10425,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-w4Z8BbjY\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9mJlC0E8\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -9246,7 +10794,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-w4Z8BbjY',\n",
+       "showGraph('#graph-output-9mJlC0E8',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 350, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -9278,7 +10826,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -9316,7 +10864,7 @@
        " (58, 14): 'X'}"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -9328,13 +10876,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-m5O9iHKS\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ADWaFseO\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -9697,7 +11245,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-m5O9iHKS',\n",
+       "showGraph('#graph-output-ADWaFseO',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 16, \"t\": \"Y\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 16, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 16, \"t\": \"Y\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 54, \"t\": \"Z\"}, {\"source\": 54, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 3, \"t\": \"Y\"}, {\"source\": 5, \"target\": 43, \"t\": \"X\"}, {\"source\": 43, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 54, \"t\": \"X\"}, {\"source\": 54, \"target\": 5, \"t\": \"Z\"}, {\"source\": 14, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 14, \"t\": \"X\"}]}'), 350, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -9727,13 +11275,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-4UnBIBHv\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-KsdZrqT4\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10096,7 +11644,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-4UnBIBHv',\n",
+       "showGraph('#graph-output-KsdZrqT4',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -10111,7 +11659,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-n2FqkzWZ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Ue0FdeJP\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10474,7 +12022,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-n2FqkzWZ',\n",
+       "showGraph('#graph-output-Ue0FdeJP',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -10511,13 +12059,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-U2vZXqTu\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-klPW5dEe\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10880,7 +12428,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-U2vZXqTu',\n",
+       "showGraph('#graph-output-klPW5dEe',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 250, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -10895,7 +12443,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-tSoikvKv\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-fchAVTws\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -11258,7 +12806,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-tSoikvKv',\n",
+       "showGraph('#graph-output-fchAVTws',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 110.00000000000001, \"y\": 300.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 80.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 16, \"t\": \"Z\"}, {\"source\": 17, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 17, \"t\": \"Z\"}, {\"source\": 16, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 16, \"t\": \"Z\"}, {\"source\": 18, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 18, \"t\": \"Z\"}, {\"source\": 16, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 16, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}]}'), 400, 350, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
diff --git a/pyzx/circuit/graphparser.py b/pyzx/circuit/graphparser.py
index 1ccea9e6..500873c5 100644
--- a/pyzx/circuit/graphparser.py
+++ b/pyzx/circuit/graphparser.py
@@ -129,7 +129,7 @@ def circuit_to_graph(c: Circuit, compress_rows:bool=True, backend:Optional[str]=
             except ValueError:
                 raise ValueError("PostSelect label {} is not in use".format(str(l)))
             v = g.add_vertex(VertexType.Z, q, r)
-            g.add_edge(g.edge(u,v),EdgeType.SIMPLE)
+            g.add_edge((u,v),EdgeType.SIMPLE)
         else:
             if not compress_rows: #or not isinstance(gate, (ZPhase, XPhase, HAD)):
                 r = max(q_mapper.max_row(), c_mapper.max_row())
@@ -148,7 +148,7 @@ def circuit_to_graph(c: Circuit, compress_rows:bool=True, backend:Optional[str]=
             v = g.add_vertex(VertexType.BOUNDARY, o, r)
             outputs.append(v)
             u = mapper.prev_vertex(l)
-            g.add_edge(g.edge(u,v))
+            g.add_edge((u,v))
 
     g.set_inputs(tuple(inputs))
     g.set_outputs(tuple(outputs))
diff --git a/pyzx/pauliweb.py b/pyzx/pauliweb.py
index 9908d382..ff9e8d08 100644
--- a/pyzx/pauliweb.py
+++ b/pyzx/pauliweb.py
@@ -93,7 +93,7 @@ def transpose_corrections(c: Dict[VT, Set[VT]]) -> Dict[VT, Set[VT]]:
 def compute_pauli_webs(g: BaseGraph[VT,ET]) -> Tuple[Dict[VT, int], Dict[VT, PauliWeb[VT,ET]], Dict[VT, PauliWeb[VT,ET]]]:
     g1 = g.clone()
     out_edge: Dict[VT, Tuple[VT,VT]] = dict()
-    for j,o in enumerate(g1.outputs()):
+    for o in g1.outputs():
         e = g1.incident_edges(o)[0]
         v = next(iter(g1.neighbors(o)))
         vt = g1.type(v)
@@ -103,8 +103,7 @@ def compute_pauli_webs(g: BaseGraph[VT,ET]) -> Tuple[Dict[VT, int], Dict[VT, Pau
             (vt == VertexType.X and et == EdgeType.HADAMARD)):
             v0 = g1.add_vertex(VertexType.X)
             v1 = g1.add_vertex(VertexType.Z)
-        if ((vt == VertexType.X and et == EdgeType.SIMPLE) or
-            (vt == VertexType.Z and et == EdgeType.HADAMARD)):
+        else:
             v0 = g1.add_vertex(VertexType.Z)
             v1 = g1.add_vertex(VertexType.X)
         g1.add_edge((v, v0), et)
@@ -150,5 +149,12 @@ def compute_pauli_webs(g: BaseGraph[VT,ET]) -> Tuple[Dict[VT, int], Dict[VT, Pau
         elif g.type(v) == VertexType.X:
             pw.add_edge((v, i), 'X')
             xwebs[v] = pw
+        elif g.type(v) == VertexType.BOUNDARY:
+            pw.add_edge((v, i), 'X')
+            xwebs[v] = pw
+            pw1 = PauliWeb(g)
+            pw1.add_edge((v, i), 'Z')
+            zwebs[v] = pw1
+
 
     return (order, zwebs, xwebs)
\ No newline at end of file