GraphStates.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "84002f9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import qiskit\n",
    "from qiskit_aer import AerSimulator\n",
    "simulator = AerSimulator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "e9524f96-d9ea-492c-9b45-c1b5cf256f8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "numShots = 1024*4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "2c3ac960-4725-4876-b4a7-cb82c9dde2f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def integerToIndices(integer, numQbits = 15):\n",
    "    indicesOut = [0 for _ in range(numQbits)]\n",
    "    binaryRep = bin(int(integer))[2:]\n",
    "    indicesOut[:len(binaryRep)] = [int(item) for item in binaryRep]\n",
    "    return indicesOut\n",
    "\n",
    "def countsToTensorForm(countsDict, numQbits = 15):\n",
    "    tensorOut = np.zeros((2,)*numQbits)\n",
    "    for key,value in countsDict.items():\n",
    "        indices = integerToIndices(key, numQbits)\n",
    "        tensorOut[tuple(indices)] = value\n",
    "    return tensorOut\n",
    "def qiskitcountsToTensorForm(countsDict, numQbits = 15):\n",
    "    tensorOut = np.zeros((2,)*numQbits)\n",
    "    for key,value in countsDict.items():\n",
    "        indices = [int(item) for item in list(key)]\n",
    "        tensorOut[tuple(int(item) for item in list(key))] = value\n",
    "    return tensorOut\n",
    "\n",
    "def contractEverythingButt(tensorIn,relAxes):\n",
    "    return tensorIn.sum(axis=tuple([item for item in range(len(tensorIn.shape)) if item not in relAxes]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "id": "d6dacdc6-9ca5-4273-b593-e1291071d4bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "numNodes = 4\n",
    "def makeCirc():\n",
    "    n = numNodes\n",
    "    edges = [[0,1],[1,2],[2,3],[3,4],[4,0]]\n",
    "    edges = [[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4]]\n",
    "    edges = [[0,1],[0,2],[0,3],[0,4],[3,5],[4,5]]\n",
    "    # edges = [[0,1],[0,2],[1,2],[0,3],[1,3],[2,3]]\n",
    "    # edges = [[0,1],[2,3]]\n",
    "    # edges = [[0,1],[1,2],[0,2]]#[2,3]]\n",
    "    edges = [[0,1],[1,2]]#[2,3]]\n",
    "    # edges = [[0,1],[1,2],[0,2]]\n",
    "    edges = [[0,1],[1,2],[0,2],[2,3]]\n",
    "    edges = [[0,1],[1,2],[2,3],[0,3]]#,[0,2],[1,3]]\n",
    "    edges = [[0,1],[1,2],[0,3],[1,3]]#,[0,2],[1,3]]\n",
    "    # edges = []\n",
    "    circInner = qiskit.QuantumCircuit(n)\n",
    "    for i in range(n):\n",
    "        circInner.h(i)\n",
    "    for edge in edges:\n",
    "        circInner.cz(edge[0],edge[1])\n",
    "        # circInner.cz(edge[0],edge[1])\n",
    "    # circInner.draw(\"mpl\",style=\"iqp\")\n",
    "    return circInner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "id": "96489757-171d-4e0f-98f1-19528d2b6777",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 538.33x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 269,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circUs = makeCirc()\n",
    "circUs.draw(\"mpl\",style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "id": "2ef9808e-d574-4f9e-b11b-744d4c0171b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "256.0\n",
      "{'1011': 994, '1101': 1052, '0110': 1022, '0000': 1028}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1165.66x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circUs = makeCirc()\n",
    "circUs.cz(1,0)\n",
    "# circUs.cz(1,2)\n",
    "# circUs.cz(1,3)\n",
    "# circUs.cz(1,4)\n",
    "circUs.h(0)\n",
    "circUs.h(1)\n",
    "# circUs.h(2)\n",
    "# circUs.rz(np.pi/2,0)\n",
    "# for i in range(numNodes):\n",
    "#     circUs.h(i)\n",
    "circUs.measure_all()\n",
    "circUs = qiskit.transpile(circUs,simulator)\n",
    "result = simulator.run(circUs,shots=numShots).result()\n",
    "counts = result.get_counts(0)\n",
    "print(numShots/2**numNodes)\n",
    "print(counts)\n",
    "circUs.draw(\"mpl\",style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "5bd2dedf-2ccc-4a5e-8b7f-18d55d1f8021",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[[1032.,  996.],\n",
       "          [   0.,    0.]],\n",
       "\n",
       "         [[   0.,    0.],\n",
       "          [   0.,    0.]]],\n",
       "\n",
       "\n",
       "        [[[   0.,    0.],\n",
       "          [   0.,    0.]],\n",
       "\n",
       "         [[   0.,    0.],\n",
       "          [   0.,    0.]]]],\n",
       "\n",
       "\n",
       "\n",
       "       [[[[   0.,    0.],\n",
       "          [   0.,    0.]],\n",
       "\n",
       "         [[   0.,    0.],\n",
       "          [   0.,    0.]]],\n",
       "\n",
       "\n",
       "        [[[   0.,    0.],\n",
       "          [   0.,    0.]],\n",
       "\n",
       "         [[   0.,    0.],\n",
       "          [1000., 1068.]]]]])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qiskitcountsToTensorForm(counts,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "765da345-5189-425d-a11a-35f1b99af45b",
   "metadata": {},
   "outputs": [],
   "source": [
    "wedgechnode0 = {'011': 2587, '000': 2447, '111': 2466, '100': 2500}\n",
    "chnode1 = {'011': 2529, '110': 2529, '101': 2453, '000': 2489}\n",
    "chnode2 = {'111': 2439, '001': 2518, '110': 2537, '000': 2506}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "dbb7e678-5c51-4f86-bc19-c7f6336645c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'011': 2587, '000': 2447, '111': 2466, '100': 2500}\n"
     ]
    }
   ],
   "source": [
    "circUs = makeCirc()\n",
    "# circUs.cx(0,1)\n",
    "# circUs.cx(0,2)\n",
    "# circUs.cx(0,3)\n",
    "circUs.h(0)\n",
    "# circUs.h(1)\n",
    "# circUs.h(2)\n",
    "# circUs.h(3)\n",
    "circUs.measure_all()\n",
    "circUs = qiskit.transpile(circUs,simulator)\n",
    "result = simulator.run(circUs,shots=numShots).result()\n",
    "counts = result.get_counts(0)\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "59b4ce8d-137e-4c3f-97ea-feb54ffdd2bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 747.609x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circUs.draw(\"mpl\",style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "ab8d8958-97d3-470c-a905-4a5428d613b4",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'circ' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[51], line 8\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# n = 8\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m# edges = [[0,1],[0,2],[1,2],[0,3],[3,4],[4,5],[3,5],[6,7]]\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# circ = qiskit.QuantumCircuit(n)\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;66;03m# for edge in edges:\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;66;03m#     circ.cz(edge[0],edge[1])\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m \u001b[43mcirc\u001b[49m\u001b[38;5;241m.\u001b[39mdraw(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmpl\u001b[39m\u001b[38;5;124m\"\u001b[39m,style\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124miqp\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[0;31mNameError\u001b[0m: name 'circ' is not defined"
     ]
    }
   ],
   "source": [
    "# n = 8\n",
    "# edges = [[0,1],[0,2],[1,2],[0,3],[3,4],[4,5],[3,5],[6,7]]\n",
    "# circ = qiskit.QuantumCircuit(n)\n",
    "# for i in range(n):\n",
    "#     circ.h(i)\n",
    "# for edge in edges:\n",
    "#     circ.cz(edge[0],edge[1])\n",
    "circ.draw(\"mpl\",style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "d27c7906-c241-4dbe-b332-cec941868bf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "output states with nonzero probability is at least:  128\n",
      "output states with nonzero probability is at least:  128\n",
      "output states with nonzero probability is at least:  128\n",
      "output states with nonzero probability is at least:  128\n",
      "output states with nonzero probability is at least:  128\n",
      "output states with nonzero probability is at least:  128\n",
      "output states with nonzero probability is at least:  128\n",
      "output states with nonzero probability is at least:  128\n"
     ]
    }
   ],
   "source": [
    "# THIS TELLS US THAT THERE IS A TEST FOR GRAPH-STATE:\n",
    "#  if applying a hadamard to a qbit, get 2^n / 2 states\n",
    "\n",
    "numShots = 1024*4\n",
    "\n",
    "for i in range(n):\n",
    "    circ = qiskit.QuantumCircuit(n)\n",
    "    for i in range(n):\n",
    "        circ.h(i)\n",
    "    for edge in edges:\n",
    "        circ.cz(edge[0],edge[1])\n",
    "    circ.h(i)\n",
    "    circ.measure_all()\n",
    "    circ = qiskit.transpile(circ,simulator)\n",
    "    result = simulator.run(circ,shots=numShots).result()\n",
    "    counts = result.get_counts(0)\n",
    "    print(\"output states with nonzero probability is at least: \", len(counts))\n",
    "# qiskit.visualization.plot_histogram(counts_ideal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "f026b2a9-6d5b-4468-9f6b-151632be3b86",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[256] [8]\n"
     ]
    }
   ],
   "source": [
    "# TESTING if we can get the existence of a single edge\n",
    "#  if edge, hadamard the two nodes gives 2^n states\n",
    "testEdges = edges\n",
    "supportSizes = []\n",
    "for testEdge in testEdges:\n",
    "    circ = qiskit.QuantumCircuit(n)\n",
    "    for i in range(n):\n",
    "        circ.h(i)\n",
    "    for edge in edges:\n",
    "        circ.cz(edge[0],edge[1])\n",
    "    circ.h(testEdge[0])\n",
    "    circ.h(testEdge[1])\n",
    "    circ.measure_all()\n",
    "    circ = qiskit.transpile(circ,simulator)\n",
    "    result = simulator.run(circ,shots=numShots).result()\n",
    "    counts = result.get_counts()\n",
    "    supportSizes.append(len(counts))\n",
    "    # print(len(counts))\n",
    "unique, counts = np.unique(supportSizes, return_counts=True)\n",
    "print(unique, counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "733bb5e3-1f95-469a-8b18-7aa991e9ee0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20,  0,  0,  0,  0,  0,  0,  0,  0,  8])"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  if not an edge, hadamard the two nodes gives 2^n / 4 states\n",
    "allDyads = [[j,i] for i in range(n) for j in range(i)]\n",
    "supportSizes = []\n",
    "for testEdge in allDyads:\n",
    "    circ = qiskit.QuantumCircuit(n)\n",
    "    for i in range(n):\n",
    "        circ.h(i)\n",
    "    for edge in edges:\n",
    "        circ.cz(edge[0],edge[1])\n",
    "    circ.h(testEdge[0])\n",
    "    circ.h(testEdge[1])\n",
    "    circ.measure_all()\n",
    "    circ = qiskit.transpile(circ,simulator)\n",
    "    result = simulator.run(circ,shots=numShots).result()\n",
    "    counts = result.get_counts()\n",
    "    supportSizes.append(len(counts))\n",
    "    # print(len(counts))\n",
    "np.histogram(supportSizes)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "b0ce4575-2068-4a03-8ecb-0ce1d5ba7798",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "3456549a-d56c-43f2-8491-93571bd3610f",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 12\n",
    "edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,0],[0,2],[0,3]]\n",
    "circ = qiskit.QuantumCircuit(n)\n",
    "for i in range(n):\n",
    "    circ.h(i)\n",
    "for edge in edges:\n",
    "    circ.cz(edge[0],edge[1])\n",
    "circ.h(0)\n",
    "circ.measure_all()\n",
    "circ = qiskit.transpile(circ,simulator)\n",
    "result = simulator.run(circ,shots=numShots).result()\n",
    "counts = result.get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "d82b796a-6608-4439-a8c6-af05af34f21c",
   "metadata": {},
   "outputs": [],
   "source": [
    "tensorCounts = qiskitcountsToTensorForm(counts, numQbits = n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "e26da6bb-500a-4063-b1fe-407f6df1fda3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2054. 2042.]\n",
      "[2050. 2046.]\n",
      "[2076. 2020.]\n",
      "[2078. 2018.]\n",
      "[2073. 2023.]\n",
      "[2032. 2064.]\n",
      "[2076. 2020.]\n",
      "[2052. 2044.]\n",
      "[2072. 2024.]\n",
      "[2054. 2042.]\n",
      "[2099. 1997.]\n",
      "[1997. 2099.]\n"
     ]
    }
   ],
   "source": [
    "for i in range(12):\n",
    "    print(contractEverythingButt(tensorCounts,[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "436de833-d869-408a-8c1f-a4a0b72bccee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integerToIndices('35', numQbits = 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "8d8de053-2512-48b4-a3a0-ace1f5bc7db6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4096.0"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(tensorCounts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "0feab408-2cea-42b6-bf36-8b273f35fa7b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'001': 1004, '100': 1054, '101': 1005, '000': 1033}\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "circ = qiskit.QuantumCircuit(n)\n",
    "circ.h(0)\n",
    "\n",
    "circ.h(1)\n",
    "circ.h(2)\n",
    "### end them, begin us\n",
    "circ.h(1)\n",
    "# circ.h(2)\n",
    "circ.measure_all()\n",
    "circ = qiskit.transpile(circ,simulator)\n",
    "result = simulator.run(circ,shots=numShots).result()\n",
    "counts = result.get_counts()\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "158a255a-c0bd-42b0-9714-92d4945f2758",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'011': 1041, '000': 1012, '110': 1030, '101': 1013}"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7a94172f-d7d1-4ddf-a014-900b4d4b2052",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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