demos/Optimizing almost-Clifford circuits.ipynb

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    "# Optimizing almost-Clifford circuits\n",
    "\n",
    "In this Notebook we will produce some comparisons for how the PyZX Clifford simplification procedure fares in comparison to more naive approaches."
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   "source": [
    "First we import all the necessary libraries"
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   "source": [
    "import sys; sys.path.append('..')\n",
    "import random, math, os\n",
    "import pyzx as zx\n",
    "from fractions import Fraction\n",
    "from functools import reduce\n",
    "import numpy as np"
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   "cell_type": "markdown",
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   "source": [
    "Now we define some useful functions for generating our data and optimizing circuits"
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    "def generate_clifford_circuit(qubits, depth, p_cnot=0.3, p_t=0):\n",
    "    p_s = 0.5*(1.0-p_cnot-p_t)\n",
    "    p_had = 0.5*(1.0-p_cnot-p_t)\n",
    "    c = zx.Circuit(qubits)\n",
    "    for _ in range(depth):\n",
    "        r = random.random()\n",
    "        if r > 1-p_had:\n",
    "            c.add_gate(\"HAD\",random.randrange(qubits))\n",
    "        elif r > 1-p_had-p_s:\n",
    "            c.add_gate(\"S\",random.randrange(qubits))\n",
    "        elif r > 1-p_had-p_s-p_t:\n",
    "            c.add_gate(\"T\",random.randrange(qubits))\n",
    "        else:\n",
    "            tgt = random.randrange(qubits)\n",
    "            while True:\n",
    "                ctrl = random.randrange(qubits)\n",
    "                if ctrl!=tgt: break\n",
    "            c.add_gate(\"CNOT\",tgt,ctrl)\n",
    "    return c"
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   "cell_type": "markdown",
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   "source": [
    "For the naive approach, we introduce a function that splits the circuit when a T gate is encountered and a function for merging circuits back together."
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    "def split_circ_on_T(c):\n",
    "    \"\"\"Produces a list of circuits whose odd elements are T-free circuits and\n",
    "    whose even elements are circuits consisting only of T gates. Note it expects\n",
    "    the circuit to only have basic gates (i.e. at most 1 control).\"\"\"\n",
    "    q = c.qubits\n",
    "    \n",
    "    # keep lists of T-free and T-only circuits\n",
    "    cs0 = [zx.Circuit(q)]\n",
    "    cs1 = [zx.Circuit(q)]\n",
    "    after = zx.Circuit(q)\n",
    "    blocked = set()\n",
    "    blocked2 = set()\n",
    "    for g in c.gates:\n",
    "        if g.name == 'T':\n",
    "            if g.target in blocked2:\n",
    "                cs0.append(after)\n",
    "                after = zx.Circuit(q)\n",
    "                cs1.append(zx.Circuit(q))\n",
    "                blocked.clear()\n",
    "                blocked2.clear()\n",
    "                cs1[-1].gates.append(g)\n",
    "                blocked.add(g.target)\n",
    "            else:\n",
    "                cs1[-1].gates.append(g)\n",
    "                blocked.add(g.target)\n",
    "        else:\n",
    "            if g.name in ('CNOT','HAD') and g.target in blocked: \n",
    "                after.gates.append(g)\n",
    "                blocked2.add(g.target)\n",
    "                if g.name == 'CNOT': \n",
    "                    blocked.add(g.control)\n",
    "            elif g.target in blocked2 or (g.name == 'CNOT' and g.control in blocked2):\n",
    "                after.gates.append(g)\n",
    "                if g.name == 'CNOT': \n",
    "                    blocked.add(g.target)\n",
    "                    blocked2.add(g.target)\n",
    "            else:\n",
    "                cs0[-1].gates.append(g)\n",
    "    cs = []\n",
    "    for i,c0 in enumerate(cs0):\n",
    "        cs.append(c0)\n",
    "        cs.append(cs1[i])\n",
    "    cs.append(after)\n",
    "    return cs\n",
    "def merge_circ(cs):\n",
    "    c0 = zx.Circuit(cs[0].qubits)\n",
    "    for c in cs:\n",
    "        c0.add_circuit(c)\n",
    "    return c0"
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   "cell_type": "markdown",
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   "source": [
    "Testing circuit generation and split/merge code."
   ]
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   "execution_count": 4,
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{\"name\": \"68\", \"x\": 400, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"69\", \"x\": 380, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"70\", \"x\": 420, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"71\", \"x\": 420, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"72\", \"x\": 320, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"73\", \"x\": 440, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"74\", \"x\": 440, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"75\", \"x\": 460, \"y\": 120, \"t\": 2, \"phase\": \"\"}, {\"name\": \"76\", \"x\": 460, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"77\", \"x\": 480, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"78\", \"x\": 500, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"79\", \"x\": 500, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"80\", \"x\": 340, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"81\", \"x\": 420, \"y\": 60, \"t\": 2, \"phase\": \"\"}, {\"name\": \"82\", \"x\": 420, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"83\", \"x\": 520, \"y\": 120, \"t\": 2, \"phase\": \"\"}, {\"name\": \"84\", \"x\": 520, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"85\", \"x\": 440, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"86\", \"x\": 460, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"87\", \"x\": 520, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"88\", \"x\": 540, \"y\": 140, \"t\": 2, \"phase\": \"\"}, {\"name\": \"89\", \"x\": 540, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"90\", \"x\": 560, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"91\", \"x\": 580, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"92\", \"x\": 600, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"93\", \"x\": 440, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"94\", \"x\": 440, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"95\", \"x\": 540, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"96\", \"x\": 560, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"97\", \"x\": 560, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"98\", \"x\": 460, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"99\", \"x\": 620, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"100\", \"x\": 580, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"101\", \"x\": 600, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"102\", \"x\": 480, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"103\", \"x\": 480, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"104\", \"x\": 500, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"105\", \"x\": 620, \"y\": 140, \"t\": 2, \"phase\": \"\"}, {\"name\": \"106\", \"x\": 620, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"107\", \"x\": 640, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"108\", \"x\": 520, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"109\", \"x\": 540, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"110\", \"x\": 640, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"111\", \"x\": 640, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"112\", \"x\": 660, \"y\": 60, \"t\": 2, \"phase\": \"\"}, {\"name\": \"113\", \"x\": 660, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"114\", \"x\": 680, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"115\", \"x\": 680, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"116\", \"x\": 560, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"117\", \"x\": 680, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"118\", \"x\": 700, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"119\", \"x\": 700, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"120\", \"x\": 720, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"121\", \"x\": 740, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"122\", \"x\": 700, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"123\", \"x\": 720, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"124\", \"x\": 720, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"125\", \"x\": 760, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"126\", \"x\": 760, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"127\", \"x\": 720, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"128\", \"x\": 700, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"129\", \"x\": 780, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"130\", \"x\": 780, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"131\", \"x\": 800, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"132\", \"x\": 800, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"133\", \"x\": 740, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"134\", \"x\": 760, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"135\", \"x\": 580, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"136\", \"x\": 820, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"137\", \"x\": 840, \"y\": 40, \"t\": 0, \"phase\": \"\"}, {\"name\": \"138\", \"x\": 840, \"y\": 60, \"t\": 0, \"phase\": \"\"}, {\"name\": \"139\", \"x\": 840, \"y\": 80, \"t\": 0, \"phase\": \"\"}, {\"name\": \"140\", \"x\": 840, \"y\": 100, \"t\": 0, \"phase\": \"\"}, {\"name\": \"141\", \"x\": 840, \"y\": 120, \"t\": 0, \"phase\": \"\"}, {\"name\": \"142\", \"x\": 840, \"y\": 140, \"t\": 0, \"phase\": \"\"}], \"links\": [{\"source\": \"0\", \"target\": \"12\", \"t\": 1}, {\"source\": \"1\", \"target\": \"24\", \"t\": 1}, {\"source\": \"2\", \"target\": \"9\", \"t\": 2}, {\"source\": \"3\", \"target\": \"17\", \"t\": 2}, {\"source\": \"4\", \"target\": \"7\", \"t\": 2}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1}, {\"source\": \"6\", \"target\": \"8\", \"t\": 1}, {\"source\": \"7\", \"target\": \"14\", \"t\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 2}, {\"source\": \"10\", \"target\": \"16\", \"t\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1}, {\"source\": \"11\", \"target\": \"31\", \"t\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1}, {\"source\": \"13\", \"target\": \"18\", \"t\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1}, {\"source\": \"15\", \"target\": \"19\", \"t\": 1}, {\"source\": \"16\", \"target\": \"26\", \"t\": 1}, {\"source\": \"17\", \"target\": \"22\", \"t\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1}, {\"source\": \"20\", \"target\": \"32\", \"t\": 2}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1}, {\"source\": \"21\", \"target\": \"23\", \"t\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1}, {\"source\": \"23\", \"target\": \"29\", \"t\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 2}, {\"source\": \"26\", \"target\": \"38\", \"t\": 1}, {\"source\": \"27\", \"target\": \"30\", \"t\": 2}, {\"source\": \"28\", \"target\": \"39\", \"t\": 2}, {\"source\": \"29\", \"target\": \"40\", \"t\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 1}, {\"source\": \"31\", \"target\": \"35\", \"t\": 2}, {\"source\": \"32\", \"target\": \"34\", \"t\": 1}, {\"source\": \"33\", \"target\": \"34\", \"t\": 1}, {\"source\": \"33\", \"target\": \"37\", \"t\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1}, {\"source\": \"36\", \"target\": \"42\", \"t\": 1}, {\"source\": \"37\", \"target\": \"38\", \"t\": 1}, {\"source\": \"37\", \"target\": \"43\", \"t\": 2}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1}, {\"source\": \"39\", \"target\": \"59\", \"t\": 2}, {\"source\": \"40\", \"target\": \"52\", \"t\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1}, {\"source\": \"41\", \"target\": \"45\", \"t\": 2}, {\"source\": \"42\", \"target\": \"44\", \"t\": 1}, {\"source\": \"43\", \"target\": \"46\", \"t\": 1}, {\"source\": \"44\", \"target\": \"48\", \"t\": 1}, {\"source\": \"45\", \"target\": \"47\", \"t\": 1}, {\"source\": \"46\", \"target\": \"72\", \"t\": 2}, {\"source\": \"47\", \"target\": \"48\", \"t\": 1}, {\"source\": \"47\", \"target\": \"54\", \"t\": 1}, {\"source\": \"48\", \"target\": \"50\", \"t\": 1}, {\"source\": \"49\", \"target\": \"51\", \"t\": 1}, {\"source\": \"50\", \"target\": \"65\", \"t\": 1}, {\"source\": \"51\", \"target\": \"53\", \"t\": 1}, {\"source\": \"52\", \"target\": \"53\", \"t\": 1}, {\"source\": \"52\", \"target\": \"55\", \"t\": 2}, {\"source\": \"53\", \"target\": \"62\", \"t\": 1}, {\"source\": \"54\", \"target\": \"56\", \"t\": 1}, {\"source\": \"55\", \"target\": \"57\", \"t\": 1}, {\"source\": \"56\", \"target\": 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{\"source\": \"86\", \"target\": \"89\", \"t\": 1}, {\"source\": \"87\", \"target\": \"95\", \"t\": 2}, {\"source\": \"88\", \"target\": \"89\", \"t\": 1}, {\"source\": \"88\", \"target\": \"97\", \"t\": 1}, {\"source\": \"89\", \"target\": \"90\", \"t\": 1}, {\"source\": \"90\", \"target\": \"91\", \"t\": 2}, {\"source\": \"91\", \"target\": \"92\", \"t\": 1}, {\"source\": \"92\", \"target\": \"99\", \"t\": 1}, {\"source\": \"93\", \"target\": \"103\", \"t\": 1}, {\"source\": \"94\", \"target\": \"98\", \"t\": 1}, {\"source\": \"95\", \"target\": \"96\", \"t\": 1}, {\"source\": \"96\", \"target\": \"97\", \"t\": 1}, {\"source\": \"96\", \"target\": \"100\", \"t\": 1}, {\"source\": \"97\", \"target\": \"105\", \"t\": 1}, {\"source\": \"98\", \"target\": \"102\", \"t\": 1}, {\"source\": \"99\", \"target\": \"111\", \"t\": 1}, {\"source\": \"100\", \"target\": \"101\", \"t\": 1}, {\"source\": \"101\", \"target\": \"106\", \"t\": 1}, {\"source\": \"102\", \"target\": \"103\", \"t\": 1}, {\"source\": \"102\", \"target\": \"104\", \"t\": 1}, {\"source\": \"103\", \"target\": \"110\", \"t\": 1}, {\"source\": \"104\", \"target\": \"108\", \"t\": 2}, {\"source\": \"105\", \"target\": \"106\", \"t\": 1}, {\"source\": \"105\", \"target\": \"113\", \"t\": 1}, {\"source\": \"106\", \"target\": \"107\", \"t\": 1}, {\"source\": \"107\", \"target\": \"124\", \"t\": 1}, {\"source\": \"108\", \"target\": \"114\", \"t\": 1}, {\"source\": \"109\", \"target\": \"116\", \"t\": 2}, {\"source\": \"110\", \"target\": \"111\", \"t\": 1}, {\"source\": \"110\", \"target\": \"119\", \"t\": 1}, {\"source\": \"111\", \"target\": \"112\", \"t\": 1}, {\"source\": \"112\", \"target\": \"113\", \"t\": 1}, {\"source\": \"112\", \"target\": \"115\", \"t\": 1}, {\"source\": \"113\", \"target\": \"117\", \"t\": 1}, {\"source\": \"114\", \"target\": \"115\", \"t\": 1}, {\"source\": \"114\", \"target\": \"118\", \"t\": 1}, {\"source\": \"115\", \"target\": \"128\", \"t\": 2}, {\"source\": \"116\", \"target\": \"135\", \"t\": 1}, {\"source\": \"117\", \"target\": \"122\", \"t\": 1}, {\"source\": \"118\", \"target\": \"119\", \"t\": 1}, {\"source\": \"118\", \"target\": \"120\", \"t\": 1}, {\"source\": \"119\", \"target\": \"123\", \"t\": 1}, {\"source\": \"120\", \"target\": \"121\", \"t\": 1}, {\"source\": \"121\", \"target\": \"126\", \"t\": 1}, {\"source\": \"122\", \"target\": \"127\", \"t\": 2}, {\"source\": \"123\", \"target\": \"124\", \"t\": 1}, {\"source\": \"123\", \"target\": \"125\", \"t\": 1}, {\"source\": \"124\", \"target\": \"139\", \"t\": 1}, {\"source\": \"125\", \"target\": \"126\", \"t\": 1}, {\"source\": \"125\", \"target\": \"130\", \"t\": 1}, {\"source\": \"126\", \"target\": \"129\", \"t\": 1}, {\"source\": \"127\", \"target\": \"133\", \"t\": 1}, {\"source\": \"128\", \"target\": \"138\", \"t\": 1}, {\"source\": \"129\", \"target\": \"130\", \"t\": 1}, {\"source\": \"129\", \"target\": \"131\", \"t\": 2}, {\"source\": \"130\", \"target\": \"132\", \"t\": 1}, {\"source\": \"131\", \"target\": \"136\", \"t\": 1}, {\"source\": \"132\", \"target\": \"140\", \"t\": 1}, {\"source\": \"133\", \"target\": \"134\", \"t\": 2}, {\"source\": \"134\", \"target\": \"142\", \"t\": 1}, {\"source\": \"135\", \"target\": \"141\", \"t\": 1}, {\"source\": \"136\", \"target\": \"137\", \"t\": 1}]}'), 860, 180, 20, 4.0, true, false);\n",
       "});\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = generate_clifford_circuit(6,100,p_t=0.1)\n",
    "zx.draw(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "True\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"overflow:auto\" id=\"graph-output-2\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "require.config({baseUrl: \"../pyzx/js\",paths: {d3: \"d3.v5.min\"} });\n",
       "require.undef('zx_viewer');\n",
       "\n",
       "define('zx_viewer', ['d3'], function(d3) {\n",
       "    \n",
       "    // styling functions\n",
       "    function nodeColor(t) {\n",
       "        if (t == 0) return \"black\";\n",
       "        else if (t == 1) return \"green\";\n",
       "        else if (t == 2) return \"red\";\n",
       "        else if (t == 3) return \"yellow\";\n",
       "    }\n",
       "\n",
       "    function edgeColor(t) {\n",
       "        if (t == 1) return \"black\";\n",
       "        else if (t == 2) return \"#08f\";\n",
       "    }\n",
       "\n",
       "    function nodeStyle(selected) {\n",
       "        return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
       "    }\n",
       "\n",
       "    return {\n",
       "    showGraph: function(tag, graph, width, height, scale, node_size, auto_hbox, show_labels) {\n",
       "        var ntab = {};\n",
       "\n",
       "        graph.nodes.forEach(function(d) {\n",
       "            ntab[d.name] = d;\n",
       "            d.selected = false;\n",
       "            d.previouslySelected = false;\n",
       "            d.nhd = [];\n",
       "        });\n",
       "\n",
       "        var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
       "            return d.t != 3;\n",
       "        });\n",
       "\n",
       "        graph.links.forEach(function(d) {\n",
       "            var s = ntab[d.source];\n",
       "            var t = ntab[d.target];\n",
       "            d.source = s;\n",
       "            d.target = t;\n",
       "            s.nhd.push(t);\n",
       "            t.nhd.push(s);\n",
       "        });\n",
       "\n",
       "        var shiftKey;\n",
       "\n",
       "        // SETUP SVG ITEMS\n",
       "\n",
       "        var svg = d3.select(tag)\n",
       "            //.attr(\"tabindex\", 1)\n",
       "            .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
       "            //.each(function() { this.focus(); })\n",
       "            .append(\"svg\")\n",
       "            .attr(\"style\", \"max-width: none; max-height: none\")\n",
       "            .attr(\"width\", width)\n",
       "            .attr(\"height\", height);\n",
       "\n",
       "        var link = svg.append(\"g\")\n",
       "            .attr(\"class\", \"link\")\n",
       "            .selectAll(\"line\")\n",
       "            .data(graph.links)\n",
       "            .enter().append(\"line\")\n",
       "            .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
       "            .attr(\"style\", \"stroke-width: 1.5px\");\n",
       "\n",
       "        var brush = svg.append(\"g\")\n",
       "            .attr(\"class\", \"brush\");\n",
       "\n",
       "        var node = svg.append(\"g\")\n",
       "            .attr(\"class\", \"node\")\n",
       "            .selectAll(\"g\")\n",
       "            .data(graph.nodes)\n",
       "            .enter().append(\"g\")\n",
       "            .attr(\"transform\", function(d) {\n",
       "                return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "            });\n",
       "\n",
       "        node.filter(function(d) { return d.t != 3; })\n",
       "            .append(\"circle\")\n",
       "            .attr(\"r\", function(d) {\n",
       "               if (d.t == 0) return 0.5 * node_size;\n",
       "               else return node_size;\n",
       "            })\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\");\n",
       "\n",
       "        var hbox = node.filter(function(d) { return d.t == 3; });\n",
       "\n",
       "        hbox.append(\"rect\")\n",
       "            .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
       "            .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
       "            .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
       "            .attr(\"stroke\", \"black\");\n",
       "\n",
       "        node.filter(function(d) { return d.phase != ''; })\n",
       "            .append(\"text\")\n",
       "            .attr(\"y\", 0.7 * node_size + 14)\n",
       "            .text(function (d) { return d.phase })\n",
       "            .attr(\"text-anchor\", \"middle\")\n",
       "            .attr(\"font-size\", \"12px\")\n",
       "            .attr(\"font-family\", \"monospace\")\n",
       "            .attr(\"fill\", \"#00d\")\n",
       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
       "\n",
       "        if (show_labels) {\n",
       "            node.append(\"text\")\n",
       "                .attr(\"y\", -0.7 * node_size - 5)\n",
       "                .text(function (d) { return d.name; })\n",
       "                .attr(\"text-anchor\", \"middle\")\n",
       "                .attr(\"font-size\", \"8px\")\n",
       "                .attr(\"font-family\", \"monospace\")\n",
       "                .attr(\"fill\", \"#ccc\")\n",
       "                .attr('style', 'pointer-events: none; user-select: none;');\n",
       "        }\n",
       "\n",
       "        function update_hboxes() {\n",
       "            if (auto_hbox) {\n",
       "                var pos = {};\n",
       "                hbox.attr(\"transform\", function(d) {\n",
       "                    // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
       "                    // to the NE.\n",
       "                    var x=0,y=0,sz=0;\n",
       "                    for (var i = 0; i < d.nhd.length; ++i) {\n",
       "                        if (d.nhd[i].t != 3) {\n",
       "                            sz++;\n",
       "                            x += d.nhd[i].x;\n",
       "                            y += d.nhd[i].y;\n",
       "                        }\n",
       "                    }\n",
       "\n",
       "                    offset = 0.25 * scale;\n",
       "\n",
       "                    if (sz != 0) {\n",
       "                        x = (x/sz) + offset;\n",
       "                        y = (y/sz) - offset;\n",
       "\n",
       "                        while (pos[[x,y]]) {\n",
       "                            x += offset;\n",
       "                        }\n",
       "                        d.x = x;\n",
       "                        d.y = y;\n",
       "                        pos[[x,y]] = true;\n",
       "                    }\n",
       "\n",
       "                    return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
       "                });\n",
       "            }\n",
       "        }\n",
       "\n",
       "        update_hboxes();\n",
       "\n",
       "        link.attr(\"x1\", function(d) { return d.source.x; })\n",
       "            .attr(\"y1\", function(d) { return d.source.y; })\n",
       "            .attr(\"x2\", function(d) { return d.target.x; })\n",
       "            .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "        // EVENTS FOR DRAGGING AND SELECTION\n",
       "\n",
       "        node.on(\"mousedown\", function(d) {\n",
       "                if (shiftKey) {\n",
       "                    d3.select(this).select(\":first-child\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
       "                    d3.event.stopImmediatePropagation();\n",
       "                } else if (!d.selected) {\n",
       "                    node.select(\":first-child\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
       "                }\n",
       "            })\n",
       "            .call(d3.drag().on(\"drag\", function(d) {\n",
       "                var dx = d3.event.dx;\n",
       "                var dy = d3.event.dy;\n",
       "                // node.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
       "                //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
       "                node.filter(function(d) { return d.selected; })\n",
       "                    .attr(\"transform\", function(d) {\n",
       "                        d.x += dx;\n",
       "                        d.y += dy;\n",
       "                        return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
       "                    });\n",
       "\n",
       "                update_hboxes();\n",
       "\n",
       "                link.filter(function(d) { return d.source.selected ||\n",
       "                                            (auto_hbox && d.source.t == 3); })\n",
       "                    .attr(\"x1\", function(d) { return d.source.x; })\n",
       "                    .attr(\"y1\", function(d) { return d.source.y; });\n",
       "\n",
       "                link.filter(function(d) { return d.target.selected ||\n",
       "                                            (auto_hbox && d.target.t == 3); })\n",
       "                    .attr(\"x2\", function(d) { return d.target.x; })\n",
       "                    .attr(\"y2\", function(d) { return d.target.y; });\n",
       "\n",
       "                // text.filter(function(d) { return d.selected; })\n",
       "                //     .attr(\"x\", function(d) { return d.x; })\n",
       "                //     .attr(\"y\", function(d) { return d.y + 0.7 * node_size + 14; });\n",
       "            }));\n",
       "\n",
       "        brush.call(d3.brush().keyModifiers(false)\n",
       "            .extent([[0, 0], [width, height]])\n",
       "            .on(\"start\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    node.select(\":first-child\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(\n",
       "                            d.selected = d.previouslySelected = shiftKey &&\n",
       "                            d.selected);\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"brush\", function() {\n",
       "                if (d3.event.sourceEvent.type !== \"end\") {\n",
       "                    var selection = d3.event.selection;\n",
       "                    node.select(\":first-child\").attr(\"style\", function(d) {\n",
       "                        return nodeStyle(d.selected = d.previouslySelected ^\n",
       "                            (selection != null\n",
       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
       "                    });\n",
       "                }\n",
       "            })\n",
       "            .on(\"end\", function() {\n",
       "                if (d3.event.selection != null) {\n",
       "                    d3.select(this).call(d3.event.target.move, null);\n",
       "                }\n",
       "            }));\n",
       "    }};\n",
       "});\n",
       "\n",
       "</script>\n",
       "<script type=\"text/javascript\">\n",
       "require(['zx_viewer'], function(zx_viewer) {\n",
       "    zx_viewer.showGraph('#graph-output-2',\n",
       "    JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 20, \"y\": 40, \"t\": 0, \"phase\": \"\"}, {\"name\": \"1\", \"x\": 20, \"y\": 60, \"t\": 0, \"phase\": \"\"}, {\"name\": \"2\", \"x\": 20, \"y\": 80, \"t\": 0, \"phase\": \"\"}, {\"name\": \"3\", \"x\": 20, \"y\": 100, \"t\": 0, \"phase\": \"\"}, {\"name\": \"4\", \"x\": 20, \"y\": 120, \"t\": 0, \"phase\": \"\"}, {\"name\": \"5\", \"x\": 20, \"y\": 140, \"t\": 0, \"phase\": \"\"}, {\"name\": \"6\", \"x\": 40, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"7\", \"x\": 40, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"8\", \"x\": 60, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"9\", \"x\": 40, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"10\", \"x\": 60, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"11\", \"x\": 80, \"y\": 140, \"t\": 2, \"phase\": \"\"}, {\"name\": \"12\", \"x\": 80, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"13\", \"x\": 100, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"14\", \"x\": 100, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"15\", \"x\": 120, \"y\": 120, \"t\": 2, \"phase\": \"\"}, {\"name\": \"16\", \"x\": 120, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"17\", \"x\": 40, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"18\", \"x\": 140, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"19\", \"x\": 140, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"20\", \"x\": 160, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"21\", \"x\": 160, \"y\": 120, \"t\": 2, \"phase\": \"\"}, {\"name\": \"22\", \"x\": 160, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"23\", \"x\": 180, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"24\", \"x\": 180, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"25\", \"x\": 180, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"26\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"27\", \"x\": 40, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"28\", \"x\": 200, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"29\", \"x\": 220, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"30\", \"x\": 100, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"31\", \"x\": 180, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"32\", \"x\": 240, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"33\", \"x\": 240, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"34\", \"x\": 120, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"35\", \"x\": 140, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"36\", \"x\": 260, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"37\", \"x\": 260, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"38\", \"x\": 260, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"39\", \"x\": 260, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"40\", \"x\": 280, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"41\", \"x\": 280, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"42\", \"x\": 280, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"43\", \"x\": 300, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"44\", \"x\": 300, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"45\", \"x\": 280, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"46\", \"x\": 320, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"47\", \"x\": 300, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"48\", \"x\": 320, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"49\", \"x\": 340, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"50\", \"x\": 360, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"51\", \"x\": 60, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"52\", \"x\": 220, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"53\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"54\", \"x\": 80, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"55\", \"x\": 320, \"y\": 120, \"t\": 2, \"phase\": \"\"}, {\"name\": \"56\", \"x\": 320, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"57\", \"x\": 340, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"58\", \"x\": 360, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"59\", \"x\": 100, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"60\", \"x\": 340, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"61\", \"x\": 380, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"62\", \"x\": 380, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"63\", \"x\": 380, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"64\", \"x\": 320, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"65\", \"x\": 340, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"66\", \"x\": 120, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"67\", \"x\": 360, \"y\": 60, \"t\": 2, \"phase\": \"\"}, {\"name\": \"68\", \"x\": 360, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"69\", \"x\": 380, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"70\", \"x\": 400, \"y\": 60, \"t\": 2, \"phase\": \"\"}, {\"name\": \"71\", \"x\": 400, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"72\", \"x\": 420, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"73\", \"x\": 420, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"74\", \"x\": 440, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"75\", \"x\": 440, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"76\", \"x\": 460, \"y\": 120, \"t\": 2, \"phase\": \"\"}, {\"name\": \"77\", \"x\": 460, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"78\", \"x\": 480, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"79\", \"x\": 500, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"80\", \"x\": 500, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"81\", \"x\": 420, \"y\": 60, \"t\": 2, \"phase\": \"\"}, {\"name\": \"82\", \"x\": 420, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"83\", \"x\": 520, \"y\": 120, \"t\": 2, \"phase\": \"\"}, {\"name\": \"84\", \"x\": 520, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"85\", \"x\": 440, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"86\", \"x\": 460, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"87\", \"x\": 520, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"88\", \"x\": 540, \"y\": 140, \"t\": 2, \"phase\": \"\"}, {\"name\": \"89\", \"x\": 540, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"90\", \"x\": 440, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"91\", \"x\": 440, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"92\", \"x\": 540, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"93\", \"x\": 560, \"y\": 80, \"t\": 2, \"phase\": \"\"}, {\"name\": \"94\", \"x\": 560, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"95\", \"x\": 460, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"96\", \"x\": 580, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"97\", \"x\": 600, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"98\", \"x\": 480, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"99\", \"x\": 480, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"100\", \"x\": 500, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"101\", \"x\": 620, \"y\": 140, \"t\": 2, \"phase\": \"\"}, {\"name\": \"102\", \"x\": 620, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"103\", \"x\": 640, \"y\": 80, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"104\", \"x\": 520, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"105\", \"x\": 540, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"106\", \"x\": 560, \"y\": 120, \"t\": 1, \"phase\": \"\"}, {\"name\": \"107\", \"x\": 640, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"108\", \"x\": 660, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"109\", \"x\": 560, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"110\", \"x\": 580, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"111\", \"x\": 600, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"112\", \"x\": 620, \"y\": 60, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"113\", \"x\": 640, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"114\", \"x\": 640, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"115\", \"x\": 680, \"y\": 60, \"t\": 2, \"phase\": \"\"}, {\"name\": \"116\", \"x\": 680, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"117\", \"x\": 700, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"118\", \"x\": 700, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"119\", \"x\": 720, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"120\", \"x\": 720, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"121\", \"x\": 740, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"122\", \"x\": 760, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"123\", \"x\": 740, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"124\", \"x\": 740, \"y\": 80, \"t\": 1, \"phase\": \"\"}, {\"name\": \"125\", \"x\": 780, \"y\": 100, \"t\": 2, \"phase\": \"\"}, {\"name\": \"126\", \"x\": 780, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"127\", \"x\": 700, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"128\", \"x\": 720, \"y\": 60, \"t\": 1, \"phase\": \"\"}, {\"name\": \"129\", \"x\": 800, \"y\": 40, \"t\": 2, \"phase\": \"\"}, {\"name\": \"130\", \"x\": 800, \"y\": 100, \"t\": 1, \"phase\": \"\"}, {\"name\": \"131\", \"x\": 820, \"y\": 40, \"t\": 1, \"phase\": \"\"}, {\"name\": \"132\", \"x\": 720, \"y\": 140, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"133\", \"x\": 740, \"y\": 140, \"t\": 1, \"phase\": \"\"}, {\"name\": \"134\", \"x\": 580, \"y\": 120, \"t\": 1, \"phase\": \"\\u03c0/2\"}, {\"name\": \"135\", \"x\": 820, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"136\", \"x\": 840, \"y\": 40, \"t\": 1, \"phase\": \"\\u03c0/4\"}, {\"name\": \"137\", \"x\": 860, \"y\": 40, \"t\": 0, \"phase\": \"\"}, {\"name\": \"138\", \"x\": 860, \"y\": 60, \"t\": 0, \"phase\": \"\"}, {\"name\": \"139\", \"x\": 860, \"y\": 80, \"t\": 0, \"phase\": \"\"}, {\"name\": \"140\", \"x\": 860, \"y\": 100, \"t\": 0, \"phase\": \"\"}, {\"name\": \"141\", \"x\": 860, \"y\": 120, \"t\": 0, \"phase\": \"\"}, {\"name\": \"142\", \"x\": 860, \"y\": 140, \"t\": 0, \"phase\": \"\"}], \"links\": [{\"source\": \"0\", \"target\": \"12\", \"t\": 1}, {\"source\": \"1\", \"target\": \"27\", \"t\": 1}, {\"source\": \"2\", \"target\": \"9\", \"t\": 2}, {\"source\": \"3\", \"target\": \"17\", \"t\": 2}, {\"source\": \"4\", \"target\": \"7\", \"t\": 2}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1}, {\"source\": \"6\", \"target\": \"8\", \"t\": 1}, {\"source\": \"7\", \"target\": \"14\", \"t\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 2}, {\"source\": \"10\", \"target\": \"16\", \"t\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1}, {\"source\": \"11\", \"target\": \"30\", \"t\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1}, {\"source\": \"13\", \"target\": \"18\", \"t\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1}, {\"source\": \"15\", \"target\": \"19\", \"t\": 1}, {\"source\": \"16\", \"target\": \"25\", \"t\": 1}, {\"source\": \"17\", \"target\": \"22\", \"t\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1}, {\"source\": \"20\", \"target\": \"31\", \"t\": 2}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1}, {\"source\": \"21\", \"target\": \"23\", \"t\": 1}, {\"source\": \"22\", \"target\": \"24\", \"t\": 1}, {\"source\": \"23\", \"target\": \"28\", \"t\": 1}, {\"source\": \"24\", \"target\": \"25\", \"t\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 2}, {\"source\": \"25\", \"target\": \"37\", \"t\": 1}, {\"source\": \"26\", \"target\": \"29\", \"t\": 2}, {\"source\": \"27\", \"target\": \"51\", \"t\": 1}, {\"source\": \"28\", \"target\": \"52\", \"t\": 1}, {\"source\": \"29\", \"target\": \"32\", \"t\": 1}, {\"source\": \"30\", \"target\": \"34\", \"t\": 2}, {\"source\": \"31\", \"target\": \"33\", \"t\": 1}, {\"source\": \"32\", \"target\": \"33\", \"t\": 1}, {\"source\": \"32\", \"target\": \"36\", \"t\": 1}, {\"source\": \"33\", \"target\": \"38\", \"t\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1}, {\"source\": \"35\", \"target\": \"39\", \"t\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1}, {\"source\": \"36\", \"target\": \"40\", \"t\": 2}, {\"source\": \"37\", \"target\": \"45\", \"t\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1}, {\"source\": \"38\", \"target\": \"42\", 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   "source": [
    "cs = split_circ_on_T(c)\n",
    "print(len(cs))\n",
    "#zx.d3.draw(cs[4])\n",
    "c2 = merge_circ(cs)\n",
    "print(zx.compare_tensors(c,c2))\n",
    "g = c2.to_graph(False)\n",
    "zx.draw(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def opt_circuit(c):\n",
    "    g = c.to_graph()\n",
    "    zx.simplify.interior_clifford_simp(g,quiet=True)\n",
    "    c2 = zx.extract_circuit(g)\n",
    "    return zx.optimize.basic_optimization(c2.to_basic_gates()).to_basic_gates()\n",
    "def part_opt_circuit(c):\n",
    "    cs = split_circ_on_T(c)\n",
    "    for i in range(len(cs)):\n",
    "        if i % 2 == 0:\n",
    "            cs[i] = opt_circuit(cs[i])\n",
    "    return zx.optimize.basic_optimization(merge_circ(cs)).to_basic_gates()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_dataset(qubits,depth,cnot_prob,t_prob,reps=50,two_q=False):\n",
    "    \"\"\"Generates a set of `reps` circuits consisting of `layers` amount of Clifford circuits,\n",
    "    interspersed with T gates that appear with probability `t_prob` on every qubit.\n",
    "    Each Clifford layer has `depth` amount of gates.\"\"\"\n",
    "    stats = []\n",
    "    \n",
    "    count = [0,0,0,0]\n",
    "    count2 = [0,0,0,0]\n",
    "    for _ in range(reps):\n",
    "        c = generate_clifford_circuit(qubits,depth,p_cnot=cnot_prob,p_t=t_prob)\n",
    "        c0 = c.copy()\n",
    "        c0 = zx.optimize.basic_optimization(c0).to_basic_gates()\n",
    "        c1 = part_opt_circuit(c)\n",
    "        c2 = opt_circuit(c)\n",
    "        \n",
    "        count[0] += len(c.gates)\n",
    "        count[1] += len(c0.gates)\n",
    "        count[2] += len(c1.gates)\n",
    "        count[3] += len(c2.gates)\n",
    "        \n",
    "        count2[0] += c.twoqubitcount()\n",
    "        count2[1] += c0.twoqubitcount()\n",
    "        count2[2] += c1.twoqubitcount()\n",
    "        count2[3] += c2.twoqubitcount()\n",
    "        \n",
    "\n",
    "    for i in range(4):\n",
    "        count[i] /= reps\n",
    "        count2[i] /= reps\n",
    "    \n",
    "    return (count, count2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we generate some data comparing the different optimization methods when we vary the gate count per Clifford block"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0;0.015;0.03;0.045;0.06;0.075;0.09;0.105;0.12;0.135;0.15;"
     ]
    }
   ],
   "source": [
    "random.seed(42)\n",
    "xs = [0.015*i for i in range(11)]\n",
    "\n",
    "yys = [[],[],[],[]]\n",
    "zzs = [[],[],[],[]]\n",
    "qubits = 8\n",
    "reps = 20\n",
    "for t_prob in xs:\n",
    "    print(t_prob, end=';')\n",
    "    depth = 800\n",
    "    ys,zs = generate_dataset(qubits,depth,cnot_prob=0.3,t_prob=t_prob,reps=reps)\n",
    "    for i,y in enumerate(ys): yys[i].append(y)\n",
    "    for i,z in enumerate(zs): zzs[i].append(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we plot the resulting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "colors = ['#53257f', '#bc1b73', '#f8534a', '#ffa600']\n",
    "names = ['original','original+','naive', 'pyzx']\n",
    "styles = ['-','--','-.',':']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "for i, ys in enumerate(yys):\n",
    "    ax1.plot(xs, ys, c=colors[i], marker=\"o\",markersize=3, linestyle=styles[i], label=names[i])\n",
    "\n",
    "ax1.set_ylabel(\"total gate count\")\n",
    "ax1.set_xlabel(\"$p_t$\")\n",
    "plt.legend(loc='upper left');\n",
    "plt.grid(color='#EEEEEE')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     },
     "metadata": {},
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   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "for i, zs in enumerate(zzs):\n",
    "    ax1.plot(xs, zs, c=colors[i], marker=\"o\",markersize=3, linestyle=styles[i], label=names[i])\n",
    "\n",
    "ax1.set_ylabel(\"2-qubit gate count\")\n",
    "ax1.set_xlabel(\"$p_t$\")\n",
    "plt.legend(loc='upper left');\n",
    "plt.grid(color='#EEEEEE')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen, both of the extraction methods, the one that only acts on the block of Cliffords, and the full extraction, saturate in the amount of 2-qubit gates, but the full extraction saturates at a much lower total gate count, showing that it indeed performs better than naive Clifford optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig(r'/home/aleks/git/papers/cliff-simp/graphics/gatecount-2q.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen, as the amount of T gates between the layers increases, the full method starts performing more comparably to the block extraction method. This is to be expected as the T gates act as obstructions to our simplification method."
   ]
  }
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