zh-simplify-bug.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e5006fcf-7aff-48b8-ae67-ec6b894e9ff7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "Collecting git+https://github.com/Quantomatic/pyzx.git#master\n",
      "  Cloning https://github.com/Quantomatic/pyzx.git to /tmp/pip-req-build-nss9kdaf\n",
      "  Running command git clone -q https://github.com/Quantomatic/pyzx.git /tmp/pip-req-build-nss9kdaf\n",
      "  Resolved https://github.com/Quantomatic/pyzx.git to commit bc6967e889baa718fdaa467c3810ccb914e326bc\n",
      "Requirement already satisfied: typing_extensions>=3.7.4 in ./anaconda3/lib/python3.8/site-packages (from pyzx==0.6.4) (3.10.0.2)\n",
      "Requirement already satisfied: numpy>=1.14 in ./.local/lib/python3.8/site-packages (from pyzx==0.6.4) (1.19.4)\n",
      "Requirement already satisfied: pyperclip>=1.8.1 in ./anaconda3/lib/python3.8/site-packages (from pyzx==0.6.4) (1.8.2)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from builtins import *\n",
    "#import cytoolz as tl\n",
    "import itertools as it\n",
    "import functools as ft\n",
    "\n",
    "%pip install -U git+https://github.com/Quantomatic/pyzx.git#master\n",
    "import pyzx as zx\n",
    "from pyzx import VertexType as VT\n",
    "from pyzx import EdgeType as ET\n",
    "from fractions import Fraction as F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ea2877ae-1779-401d-a117-d3b314644b7b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph(14 vertices, 13 edges)\n"
     ]
    }
   ],
   "source": [
    "i=2\n",
    "Q = {}\n",
    "g = zx.Graph()\n",
    "g.set_inputs([])\n",
    "g.set_outputs([])\n",
    "\n",
    "def rnd(n=20):\n",
    "    return -(np.random.randint(n)+1)\n",
    "\n",
    "@ft.lru_cache(None)\n",
    "def atom(a):\n",
    "    q=abs(a)\n",
    "    input = g.add_vertex(VT.BOUNDARY, qubit=q, row=0)\n",
    "    g.inputs().append(input)\n",
    "    internal = g.add_vertex(VT.Z, qubit=q, row=1, phase=0)\n",
    "    g.add_edge((input, internal), ET.SIMPLE)\n",
    "    output = g.add_vertex(VT.BOUNDARY, qubit=q, row=2)\n",
    "    g.outputs().append(output)\n",
    "    g.add_edge((internal, output), ET.SIMPLE)\n",
    "    return internal\n",
    "\n",
    "def not_gate(n):\n",
    "    global i\n",
    "    i+=1\n",
    "    res = g.add_vertex(VT.X, phase=1, row=i, qubit=rnd())\n",
    "    g.add_edge((n, res), ET.SIMPLE)\n",
    "    return(res)\n",
    "\n",
    "def lit(l):\n",
    "    n = atom(abs(l))\n",
    "    if l < 0:\n",
    "        res = not_gate(n)\n",
    "    else:\n",
    "        res = n\n",
    "    return res\n",
    "\n",
    "def and_gate(nodes):\n",
    "    nodes = list(nodes)\n",
    "    global i\n",
    "    i+=1\n",
    "    h = g.add_vertex(VT.H_BOX, row=i, qubit=rnd())\n",
    "    for n in nodes:\n",
    "        g.add_edge((n, h), ET.SIMPLE)\n",
    "    i+=1\n",
    "    h2 = g.add_vertex(VT.H_BOX, row=i, qubit=rnd())\n",
    "    g.add_edge((h, h2))\n",
    "    return h2\n",
    "\n",
    "def or_gate(nodes):\n",
    "    return not_gate(and_gate(map(not_gate, nodes)))\n",
    "\n",
    "def clause(c):\n",
    "    return or_gate(map(lit, c))\n",
    "\n",
    "def cnf(frm):\n",
    "    global i\n",
    "    out = and_gate(map(clause, frm))\n",
    "    i+=1\n",
    "    res = g.add_vertex(VT.X, phase=1, row=i, qubit=rnd())\n",
    "    g.add_edge((out, res), ET.SIMPLE)\n",
    "    return res\n",
    "\n",
    "cnf1= [\n",
    "    #[-1 ,-2],\n",
    "    #[-1, 2],\n",
    "    #[1, -2],\n",
    "    [1, 2]\n",
    "]\n",
    "\n",
    "cnf(cnf1)\n",
    "\n",
    "print(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bdebd88d-0d1b-4304-a439-013337e4eebc",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 2160x720 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.normalize()\n",
    "zx.draw_matplotlib(g, labels=True, h_edge_draw='box', show_scalar=True, figsize=(30,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8c7fe7fd-cb71-42e5-9049-5518f8f9d875",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[ 0.        +0.j, -0.        -0.j],\n",
       "         [ 0.        +0.j,  0.        -0.j]],\n",
       "\n",
       "        [[ 0.        +0.j,  5.65685425-0.j],\n",
       "         [ 0.        +0.j,  0.        -0.j]]],\n",
       "\n",
       "\n",
       "       [[[-0.        +0.j,  0.        +0.j],\n",
       "         [ 5.65685425-0.j, -0.        +0.j]],\n",
       "\n",
       "        [[-0.        +0.j,  0.        +0.j],\n",
       "         [-0.        -0.j,  5.65685425-0.j]]]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.to_tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ad872b78-491a-4c47-a9d1-02fb8d53a162",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "id_simp: 2.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "hpivot: 1.  1 iterations\n",
      "par_hbox_intro_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n",
      "copy_simp: 1.  1 iterations\n",
      "spider_simp: 1.  1 iterations\n",
      "id_simp: 1.  1 iterations\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zx.hsimplify.zh_simp(g, quiet=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "416dde5d-cb97-4d45-bbbc-2e0efd674350",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph(4 vertices, 2 edges)\n"
     ]
    }
   ],
   "source": [
    "print(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5468ba73-de34-4342-9c25-4db470992fb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x720 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zx.draw_matplotlib(g, labels=True, h_edge_draw='box', show_scalar=True, figsize=(30,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cfa2bbbc-0fab-4eac-a981-f317b72ad82b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[2.82842712+0.j, 0.        +0.j],\n",
       "         [0.        +0.j, 0.        +0.j]],\n",
       "\n",
       "        [[0.        +0.j, 2.82842712+0.j],\n",
       "         [0.        +0.j, 0.        +0.j]]],\n",
       "\n",
       "\n",
       "       [[[0.        +0.j, 0.        +0.j],\n",
       "         [2.82842712+0.j, 0.        +0.j]],\n",
       "\n",
       "        [[0.        +0.j, 0.        +0.j],\n",
       "         [0.        +0.j, 2.82842712+0.j]]]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
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   "id": "5bdc08d7-eae4-4958-8993-e7f50dbe3963",
   "metadata": {},
   "outputs": [],
   "source": []
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