32QRAC.ipynb

{
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    "## _*(3, 2, 1/2+$\\sqrt{6}/6$)-QRAC*_ \n",
    "Namely, encoding three bits into 2 qubits so that any one of three bits can be recovered with probability at least $1/2 + \\sqrt{6}/6$\n",
    "***\n",
    "### Contributors\n",
    "Rudy Raymond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "The $(3,2)$-QRAC is a protocol to encode 3 bits of information using 2 qubits. The encoding states are as the following.\n",
    "\n",
    "\\begin{eqnarray}\n",
    "|\\psi_{000}\\rangle &=& |00\\rangle\\\\ \n",
    "|\\psi_{001}\\rangle &=& \\frac{1}{\\sqrt{3}}\\left(|00\\rangle + |01\\rangle + |10\\rangle \\right)\\\\\n",
    "|\\psi_{010}\\rangle &=& \\frac{1}{\\sqrt{3}}\\left(|00\\rangle - |01\\rangle + |11\\rangle \\right)\\\\\n",
    "|\\psi_{011}\\rangle &=& |01\\rangle\\\\\n",
    "|\\psi_{100}\\rangle &=& \\frac{1}{\\sqrt{3}}\\left(-|00\\rangle + |10\\rangle + |11\\rangle \\right)\\\\\n",
    "|\\psi_{101}\\rangle &=& |10\\rangle\\\\\n",
    "|\\psi_{110}\\rangle &=& |11\\rangle\\\\\n",
    "|\\psi_{111}\\rangle &=& \\frac{1}{\\sqrt{3}}\\left(|01\\rangle - |10\\rangle + |11\\rangle \\right)\\\\\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "The decoding of the $(3,2)$-QRAC is the projective measurements as follows.\n",
    "\n",
    "\\begin{eqnarray}\n",
    "E_{0}^{1} &=& \\left\\{ \\sqrt{p}|00\\rangle + \\sqrt{\\frac{1-p}{2}}\\left(|10\\rangle + |11\\rangle \\right),  \n",
    "-\\sqrt{p}|01\\rangle + \\sqrt{\\frac{1-p}{2}}\\left(-|10\\rangle + |11\\rangle \\right)\\right\\}\\\\\n",
    "E_{0}^{2} &=& \\left\\{ -\\sqrt{p}|00\\rangle + \\sqrt{\\frac{1-p}{2}}\\left(-|01\\rangle + |11\\rangle \\right),  \n",
    "\\sqrt{p}|10\\rangle + \\sqrt{\\frac{1-p}{2}}\\left(|01\\rangle + |11\\rangle \\right)\\right\\}\\\\\n",
    "E_{0}^{3} &=& \\left\\{ -\\sqrt{p}|00\\rangle + \\sqrt{\\frac{1-p}{2}}\\left(|01\\rangle + |10\\rangle \\right),  \n",
    "\\sqrt{p}|11\\rangle + \\sqrt{\\frac{1-p}{2}}\\left(-|01\\rangle + |10\\rangle \\right)\\right\\}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Here $p \\equiv 1/2 + \\sqrt{6}/6$, which is the success probability of obtaining the correct bit. We can check the success probability by numpy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Please input your token and hit enter: ········\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "if sys.version_info < (3,0):\n",
    "    raise Exception(\"Please use Python version 3 or greater.\")\n",
    "\n",
    "# useful additional packages \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "# useful math functions\n",
    "from math import pi, cos, acos, sqrt\n",
    "\n",
    "# importing the QISKit\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit import available_backends, execute, register, get_backend\n",
    "\n",
    "try:\n",
    "    import Qconfig\n",
    "    qx_config = {\n",
    "        \"APItoken\": Qconfig.APItoken,\n",
    "        \"url\": Qconfig.config['url']}\n",
    "except:\n",
    "    import getpass\n",
    "    APItoken = getpass.getpass('Please input your token and hit enter: ')\n",
    "    qx_config = {\n",
    "        \"APItoken\": APItoken,\n",
    "        \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}\n",
    "    \n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We check the success probability by calculating the projections of encoding by the decoding. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "encoding = dict()\n",
    "encoding[\"000\"] = np.array( [1., 0., 0. , 0. ] )\n",
    "encoding[\"001\"] = (1.0/sqrt(3.)) * np.array( [1., 1., 1., 0.] )\n",
    "encoding[\"010\"] = (1.0/sqrt(3.)) * np.array( [1., -1., 0., 1.] ) \n",
    "encoding[\"011\"] = np.array( [0., 1., 0., 0.] )\n",
    "encoding[\"100\"] = (1.0/sqrt(3.)) * np.array( [-1., 0., 1., 1.] )\n",
    "encoding[\"101\"] = np.array( [0., 0., 1., 0.] )\n",
    "encoding[\"110\"] = np.array( [0., 0., 0., 1.] )\n",
    "encoding[\"111\"] = (1.0/sqrt(3.)) * np.array( [0., 1., -1., 1.] )\n",
    "\n",
    "p = 1.0/2.0 + sqrt(6)/6.0\n",
    "decoding = dict()\n",
    "decoding[\"First\"] = [ np.array( [sqrt(p), 0, sqrt((1-p)/2.), sqrt((1-p)/2.)] ) , \n",
    "                     np.array( [0, -sqrt(p), -sqrt((1-p)/2.), sqrt((1-p)/2.)] ) ]\n",
    "decoding[\"Second\"] = [ np.array( [-sqrt(p), -sqrt((1-p)/2.), 0, sqrt((1-p)/2.)] ) , \n",
    "                      np.array( [0, sqrt((1-p)/2.), sqrt(p), sqrt((1-p)/2.)] ) ]\n",
    "decoding[\"Third\"] = [ np.array( [-sqrt(p), sqrt((1-p)/2.), sqrt((1-p)/2.), 0] ) , \n",
    "                     np.array( [0, -sqrt((1-p)/2.), sqrt((1-p)/2.), sqrt(p)] ) ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The succes probabilities of observing \"0\" by each pair of encoding and decoding are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical success probability: 0.9082482904638629\n",
      "Encoding  000  , Decoding  First  obtaining 0 w.p.  0.9082482904638629 , and 1 w.p.  0.0917517095361371\n",
      "Encoding  000  , Decoding  Second  obtaining 0 w.p.  0.9082482904638629 , and 1 w.p.  0.0917517095361371\n",
      "Encoding  000  , Decoding  Third  obtaining 0 w.p.  0.9082482904638629 , and 1 w.p.  0.0917517095361371\n",
      "\n",
      "Encoding  001  , Decoding  First  obtaining 0 w.p.  0.9082482904638632 , and 1 w.p.  0.09175170953613676\n",
      "Encoding  001  , Decoding  Second  obtaining 0 w.p.  0.9082482904638632 , and 1 w.p.  0.09175170953613676\n",
      "Encoding  001  , Decoding  Third  obtaining 0 w.p.  0.09175170953613686 , and 1 w.p.  0.9082482904638631\n",
      "\n",
      "Encoding  010  , Decoding  First  obtaining 0 w.p.  0.9082482904638632 , and 1 w.p.  0.09175170953613676\n",
      "Encoding  010  , Decoding  Second  obtaining 0 w.p.  0.09175170953613686 , and 1 w.p.  0.9082482904638631\n",
      "Encoding  010  , Decoding  Third  obtaining 0 w.p.  0.9082482904638632 , and 1 w.p.  0.09175170953613676\n",
      "\n",
      "Encoding  011  , Decoding  First  obtaining 0 w.p.  0.9082482904638629 , and 1 w.p.  0.0917517095361371\n",
      "Encoding  011  , Decoding  Second  obtaining 0 w.p.  0.09175170953613711 , and 1 w.p.  0.9082482904638629\n",
      "Encoding  011  , Decoding  Third  obtaining 0 w.p.  0.09175170953613711 , and 1 w.p.  0.9082482904638629\n",
      "\n",
      "Encoding  100  , Decoding  First  obtaining 0 w.p.  0.09175170953613686 , and 1 w.p.  0.9082482904638631\n",
      "Encoding  100  , Decoding  Second  obtaining 0 w.p.  0.9082482904638632 , and 1 w.p.  0.09175170953613676\n",
      "Encoding  100  , Decoding  Third  obtaining 0 w.p.  0.9082482904638632 , and 1 w.p.  0.09175170953613676\n",
      "\n",
      "Encoding  101  , Decoding  First  obtaining 0 w.p.  0.09175170953613711 , and 1 w.p.  0.9082482904638629\n",
      "Encoding  101  , Decoding  Second  obtaining 0 w.p.  0.9082482904638629 , and 1 w.p.  0.0917517095361371\n",
      "Encoding  101  , Decoding  Third  obtaining 0 w.p.  0.09175170953613711 , and 1 w.p.  0.9082482904638629\n",
      "\n",
      "Encoding  110  , Decoding  First  obtaining 0 w.p.  0.09175170953613711 , and 1 w.p.  0.9082482904638629\n",
      "Encoding  110  , Decoding  Second  obtaining 0 w.p.  0.09175170953613711 , and 1 w.p.  0.9082482904638629\n",
      "Encoding  110  , Decoding  Third  obtaining 0 w.p.  0.9082482904638629 , and 1 w.p.  0.0917517095361371\n",
      "\n",
      "Encoding  111  , Decoding  First  obtaining 0 w.p.  0.09175170953613686 , and 1 w.p.  0.9082482904638631\n",
      "Encoding  111  , Decoding  Second  obtaining 0 w.p.  0.09175170953613686 , and 1 w.p.  0.9082482904638631\n",
      "Encoding  111  , Decoding  Third  obtaining 0 w.p.  0.09175170953613686 , and 1 w.p.  0.9082482904638631\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(\"Theoretical success probability:\", p)\n",
    "for k1 in encoding.keys():\n",
    "    for k2 in decoding.keys():\n",
    "        succProb = 0.0\n",
    "        for v in decoding[k2]:\n",
    "            succProb += np.sum(v*encoding[k1])**2\n",
    "        print(\"Encoding \", k1, \" , Decoding \", k2, \" obtaining 0 w.p. \", succProb, \", and 1 w.p. \", 1.0-succProb)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that each bit can be retrieved with success probability $p \\approx 0.908$. Now, we work on designing circuits to realize the above $(3,2)$-QRAC. \n",
    "\n",
    "## Circuits of $(3,2)$-QRAC\n",
    "\n",
    "The core of the encoding circuits is how to create the following superposition.\n",
    "$$\n",
    "\\frac{1}{\\sqrt{3}} \\left( |00\\rangle + |01\\rangle + |10\\rangle \\right)\n",
    "$$\n",
    "\n",
    "We can create it by the following series of transformation.\n",
    "\n",
    "$$\n",
    "|00\\rangle \\xrightarrow{u3} \\frac{\\sqrt{2}}{\\sqrt{3}}|00\\rangle + \\frac{1}{\\sqrt{3}}|10\\rangle \\xrightarrow{cH}  \\frac{1}{\\sqrt{3}} \\left( |00\\rangle + |01\\rangle + |10\\rangle \\right)\n",
    "$$\n",
    "\n",
    "The phase can be adjusted by using controlled-Z. Similarly, the core of decoding circuits is how to create the following superposition. \n",
    "\n",
    "$$\n",
    "\\sqrt{p}|00\\rangle + \\sqrt{\\frac{1-p}{2}}\\left(|10\\rangle + |11\\rangle \\right)\n",
    "$$\n",
    "\n",
    "We can create it by the following series of transformation.\n",
    "\n",
    "$$\n",
    "|00\\rangle \\xrightarrow{u3} \\sqrt{p} |00\\rangle + \\sqrt{1-p} |10\\rangle \\xrightarrow{cH}  \\sqrt{p} |00\\rangle + \\frac{\\sqrt{1-p}}{\\sqrt{2}} \\left( |10\\rangle + |11\\rangle \\right)\n",
    "$$\n",
    "\n",
    "However, because we must perform measurement in the standard computational basis, what we need is a circuit that perform the inverse of the transformation above.\n",
    "\n",
    "Here is the encoding circuits by IBM Q. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "def ch(qProg, a, b):\n",
    "    \"\"\" Controlled-Hadamard gate \"\"\"\n",
    "    qProg.h(b)\n",
    "    qProg.sdg(b)\n",
    "    qProg.cx(a, b)\n",
    "    qProg.h(b)\n",
    "    qProg.t(b)\n",
    "    qProg.cx(a, b)\n",
    "    qProg.t(b)\n",
    "    qProg.h(b)\n",
    "    qProg.s(b)\n",
    "    qProg.x(b)\n",
    "    qProg.s(a)\n",
    "    return qProg\n",
    "\n",
    "def encoding000(qProg, a, b):\n",
    "    return qProg\n",
    "\n",
    "def encoding011(qProg, a, b):\n",
    "    qProg.x(b)\n",
    "    return qProg\n",
    "\n",
    "def encoding101(qProg, a, b):\n",
    "    qProg.x(a)\n",
    "    return qProg\n",
    "    \n",
    "def encoding110(qProg, a, b):\n",
    "    qProg.x(a)\n",
    "    qProg.x(b)\n",
    "    return qProg\n",
    "\n",
    "p = 1.0/2.0 + sqrt(6.0)/6.0 \n",
    "theta1 = 2.0*acos(sqrt(1.0/3.0))\n",
    "theta2 = 2.0*acos(sqrt(2.0/3.0))\n",
    "\n",
    "lambda1 = 2.0*acos(sqrt(p))\n",
    "lambda2 = 2.0*acos(sqrt(1.0-p))\n",
    "\n",
    "\n",
    "def encoding001(qProg, a, b):\n",
    "    qProg.u3(theta2, 0, 0, a)\n",
    "    qProg.x(a)\n",
    "    qProg = ch(qProg, a, b)\n",
    "    qProg.x(a)\n",
    "    return qProg\n",
    "    \n",
    "def encoding010(qProg, a, b):\n",
    "    qProg.u3(theta2, 0, 0, a)\n",
    "    qProg.x(b)\n",
    "    qProg.x(a)\n",
    "    qProg = ch(qProg, a, b)\n",
    "    qProg.x(a)\n",
    "    return qProg\n",
    "\n",
    "def encoding100(qProg, a, b):\n",
    "    qProg.u3(theta1, 0, 0, a)\n",
    "    qProg = ch(qProg, a, b)\n",
    "    qProg.x(a)\n",
    "    qProg.x(b)\n",
    "    qProg.cz(a, b)\n",
    "    qProg.x(a)\n",
    "    qProg.x(b)\n",
    "    return qProg\n",
    "\n",
    "def encoding111(qProg, a, b):\n",
    "    qProg.u3(theta1, 0, 0, a)\n",
    "    qProg.x(b)\n",
    "    qProg = ch(qProg, a, b)\n",
    "    qProg.cx(a, b)\n",
    "    return qProg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inverse of controlled-Hadamard is controlled-Hadamard, and the inverse of $u3(\\theta, 0, 0)$ is $u3(2\\pi - \\theta, 0, 0)$. So, we have the following decoding circuits. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def decodingFirst(qProg, a, b, cbit):\n",
    "    \"\"\" the following circuit is the inverse of \n",
    "    u3_1(lambda1, 0, 0) --> cH(1,2)\n",
    "    |00> is mapped to the first measurement basis\n",
    "    |01> is mapped to the second measurement basis\n",
    "    \"\"\"\n",
    "    qProg = ch(qProg, a, b)\n",
    "    qProg.u3(2*pi - lambda1, 0, 0, a)\n",
    "    qProg.measure(a, cbit) #measurement\n",
    "    return qProg\n",
    "\n",
    "def decodingSecond(qProg, a, b, cbit):\n",
    "    \"\"\" the following circuit is the inverse of\n",
    "    SWAP(1,2) --> u3_2(lambda1, 0, 0) --> cH(2,1) --> cZ(1,2)\n",
    "    |00> is mapped to the first measurement basis\n",
    "    |01> is mapped to the second measurement basis\n",
    "    \"\"\"\n",
    "    qProg.cz(a, b)\n",
    "    qProg = ch(qProg, b, a)\n",
    "    qProg.u3(2*pi - lambda1, 0, 0, b)\n",
    "    qProg.cx(a, b)\n",
    "    qProg.cx(b, a)\n",
    "    qProg.cx(a, b)\n",
    "    qProg.measure(a, cbit) #measurement\n",
    "    return qProg\n",
    "\n",
    "lambda3 = 2.0*acos(-sqrt(p))\n",
    "def decodingThird(qProg, a, b, cbit):\n",
    "    \"\"\" the following circuit is the inverse of\n",
    "    SWAP(1,2) --> u3_2(lambda3, 0, 0) --> cH(2,1) --> cx(1,2)\n",
    "    \"\"\"\n",
    "    qProg.cx(a, b)\n",
    "    qProg = ch(qProg, b, a)\n",
    "    qProg.u3(2*pi - lambda3, 0, 0, b)\n",
    "    qProg.cx(a, b)\n",
    "    qProg.cx(b, a)\n",
    "    qProg.cx(a, b)\n",
    "    qProg.measure(a, cbit)#measurement\n",
    "    return qProg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having defined the encoding and decoding circuits, we can now experiment with simulator and real devices.\n",
    "\n",
    "## Experimenting with Simulators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding000DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083d3240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding000DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108457d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding000DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10842d8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding001DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10834c6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding001DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108321a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding001DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10859d3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding010DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108648588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding010DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10878d208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding010DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1087a7748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding011DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1087d8080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding011DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108919550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding011DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a2a9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding100DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a7bda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding100DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108b32710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding100DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108bd47f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding101DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108cef320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding101DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108bbb400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding101DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108df54a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding110DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e9b828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding110DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d4d978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding110DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10842dc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding111DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083eb6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding111DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10834e518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,2)-QRAC for  Encoding111DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1084229b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating registers\n",
    "# qubits for encoding 7 bits of information with qr[0] kept by the sender\n",
    "qr = QuantumRegister(2)\n",
    "# bits for recording the measurement. we  only need 1 bit of information at a time\n",
    "cr = ClassicalRegister(1)\n",
    "\n",
    "encodingFunctions = {\n",
    "    \"000\": encoding000,\n",
    "    \"001\": encoding001,\n",
    "    \"010\": encoding010,\n",
    "    \"011\": encoding011,\n",
    "    \"100\": encoding100,\n",
    "    \"101\": encoding101,\n",
    "    \"110\": encoding110,\n",
    "    \"111\": encoding111\n",
    "}\n",
    "\n",
    "decodingFunctions = {\n",
    "    \"First\": decodingFirst,\n",
    "    \"Second\": decodingSecond,\n",
    "    \"Third\": decodingThird\n",
    "}\n",
    "\n",
    "circuitNames = []\n",
    "circuits = []\n",
    "for xstring in encodingFunctions.keys():\n",
    "    for pos in decodingFunctions.keys():\n",
    "        circuitName = \"Encoding\"+xstring+\"Decoding\"+pos    \n",
    "        aCircuit = QuantumCircuit(qr, cr, name=circuitName)\n",
    "        aCircuit = encodingFunctions[xstring](aCircuit, qr[0], qr[1])\n",
    "        aCircuit = decodingFunctions[pos](aCircuit, qr[0], qr[1], cr[0])\n",
    "        circuits.append(aCircuit)\n",
    "        circuitNames.append(circuitName)\n",
    "        \n",
    "backend = \"local_qasm_simulator\"\n",
    "shots = 8000\n",
    "\n",
    "job = execute(circuits, backend=backend, shots=shots)\n",
    "results = job.result()\n",
    "for i, each in enumerate(circuitNames):\n",
    "    print(\"(3,2)-QRAC for \", each)\n",
    "    plot_histogram(results.get_counts(circuits[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimenting with Real Devices\n",
    "\n",
    "We first list all available real-device backends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['ibmq_16_rueschlikon', 'ibmq_5_tenerife', 'ibmq_5_yorktown']\n"
     ]
    }
   ],
   "source": [
    "register(qx_config[\"APItoken\"], qx_config[\"url\"]) #need to register the token to use real-device backends\n",
    "list_of_backends = available_backends({'local': False, 'simulator': False})\n",
    "print(list_of_backends)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Noting that `ibmqx5` is available, we use it to perform experiments on $(3,2)$-QRACs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status @ 0 seconds\n",
      "{'job_id': None, 'status': <JobStatus.INITIALIZING: 'job is being initialized'>, 'status_msg': 'Job is initializing. Please, wait a moment.'}\n",
      "Status @ 10 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 84}\n",
      "Status @ 20 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 84}\n",
      "Status @ 30 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 84}\n",
      "Status @ 40 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 84}\n",
      "Status @ 50 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 84}\n",
      "Status @ 60 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 81}\n",
      "Status @ 70 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 81}\n",
      "Status @ 80 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 81}\n",
      "Status @ 90 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 81}\n",
      "Status @ 100 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 81}\n",
      "Status @ 110 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 78}\n",
      "Status @ 120 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 78}\n",
      "Status @ 130 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 78}\n",
      "Status @ 140 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 78}\n",
      "Status @ 150 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 78}\n",
      "Status @ 160 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 78}\n",
      "Status @ 170 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 180 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 190 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 200 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 210 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 220 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 230 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 240 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 250 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 260 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 75}\n",
      "Status @ 270 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 72}\n",
      "Status @ 280 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 72}\n",
      "Status @ 290 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 72}\n",
      "Status @ 300 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 72}\n",
      "Status @ 310 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 72}\n",
      "Status @ 320 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 72}\n",
      "Status @ 330 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 69}\n",
      "Status @ 340 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 69}\n",
      "Status @ 350 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 69}\n",
      "Status @ 360 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 69}\n",
      "Status @ 370 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 69}\n",
      "Status @ 380 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 69}\n",
      "Status @ 390 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 66}\n",
      "Status @ 400 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 66}\n",
      "Status @ 410 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 66}\n",
      "Status @ 420 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 66}\n",
      "Status @ 430 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 66}\n",
      "Status @ 440 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 66}\n",
      "Status @ 450 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 460 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 470 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 480 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 490 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 500 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 510 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status @ 520 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 530 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 540 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 550 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 63}\n",
      "Status @ 560 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 60}\n",
      "Status @ 570 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 60}\n",
      "Status @ 580 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 60}\n",
      "Status @ 590 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 60}\n",
      "Status @ 600 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 60}\n",
      "Status @ 610 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 60}\n",
      "Status @ 620 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 57}\n",
      "Status @ 630 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 57}\n",
      "Status @ 640 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 57}\n",
      "Status @ 650 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 57}\n",
      "Status @ 660 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 57}\n",
      "Status @ 670 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 54}\n",
      "Status @ 680 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 54}\n",
      "Status @ 690 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 54}\n",
      "Status @ 700 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 54}\n",
      "Status @ 710 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 54}\n",
      "Status @ 720 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 54}\n",
      "Status @ 730 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 740 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 750 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 760 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 770 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 780 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 790 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 800 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 810 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 820 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 51}\n",
      "Status @ 830 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 48}\n",
      "Status @ 840 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 48}\n",
      "Status @ 850 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 48}\n",
      "Status @ 860 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 48}\n",
      "Status @ 870 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 48}\n",
      "Status @ 880 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 48}\n",
      "Status @ 890 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 45}\n",
      "Status @ 900 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 45}\n",
      "Status @ 910 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 45}\n",
      "Status @ 920 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 45}\n",
      "Status @ 930 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 45}\n",
      "Status @ 940 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 45}\n",
      "Status @ 950 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 42}\n",
      "Status @ 960 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 42}\n",
      "Status @ 970 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 42}\n",
      "Status @ 980 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 42}\n",
      "Status @ 990 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 42}\n",
      "Status @ 1000 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1010 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1020 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1030 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status @ 1040 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1050 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1060 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1070 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1080 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1090 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 39}\n",
      "Status @ 1100 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 36}\n",
      "Status @ 1110 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 36}\n",
      "Status @ 1120 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 36}\n",
      "Status @ 1130 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 36}\n",
      "Status @ 1140 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 36}\n",
      "Status @ 1150 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 36}\n",
      "Status @ 1160 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 33}\n",
      "Status @ 1170 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 33}\n",
      "Status @ 1180 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 33}\n",
      "Status @ 1190 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 33}\n",
      "Status @ 1200 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 33}\n",
      "Status @ 1210 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 33}\n",
      "Status @ 1220 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 30}\n",
      "Status @ 1230 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 30}\n",
      "Status @ 1240 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 30}\n",
      "Status @ 1250 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 30}\n",
      "Status @ 1260 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 30}\n",
      "Status @ 1270 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 30}\n",
      "Status @ 1280 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 27}\n",
      "Status @ 1290 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 27}\n",
      "Status @ 1300 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 27}\n",
      "Status @ 1310 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 27}\n",
      "Status @ 1320 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 27}\n",
      "Status @ 1330 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 27}\n",
      "Status @ 1340 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 27}\n",
      "Status @ 1350 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 24}\n",
      "Status @ 1360 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 24}\n",
      "Status @ 1370 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 24}\n",
      "Status @ 1380 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 24}\n",
      "Status @ 1390 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 24}\n",
      "Status @ 1400 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 24}\n",
      "Status @ 1410 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 21}\n",
      "Status @ 1420 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 21}\n",
      "Status @ 1430 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 21}\n",
      "Status @ 1440 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 21}\n",
      "Status @ 1450 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 21}\n",
      "Status @ 1460 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 21}\n",
      "Status @ 1470 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 18}\n",
      "Status @ 1480 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 18}\n",
      "Status @ 1490 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 18}\n",
      "Status @ 1500 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 18}\n",
      "Status @ 1510 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 18}\n",
      "Status @ 1520 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 15}\n",
      "Status @ 1530 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 15}\n",
      "Status @ 1540 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 15}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status @ 1550 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 15}\n",
      "Status @ 1560 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 15}\n",
      "Status @ 1570 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 15}\n",
      "Status @ 1580 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 15}\n",
      "Status @ 1590 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 12}\n",
      "Status @ 1600 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 12}\n",
      "Status @ 1610 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 12}\n",
      "Status @ 1620 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 12}\n",
      "Status @ 1630 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 12}\n",
      "Status @ 1640 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 12}\n",
      "Status @ 1650 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 9}\n",
      "Status @ 1660 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 9}\n",
      "Status @ 1670 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 9}\n",
      "Status @ 1680 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 9}\n",
      "Status @ 1690 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 9}\n",
      "Status @ 1700 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 6}\n",
      "Status @ 1710 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 6}\n",
      "Status @ 1720 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 6}\n",
      "Status @ 1730 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 6}\n",
      "Status @ 1740 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 6}\n",
      "Status @ 1750 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 6}\n",
      "Status @ 1760 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1770 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1780 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1790 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1800 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1810 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1820 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1830 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1840 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1850 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1860 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1870 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1880 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.QUEUED: 'job is queued'>, 'status_msg': 'job is queued', 'queue_position': 3}\n",
      "Status @ 1890 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1900 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1910 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1920 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1930 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1940 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1950 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1960 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1970 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1980 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 1990 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2000 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2010 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2020 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2030 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2040 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2050 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2060 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status @ 2070 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2080 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2090 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "Status @ 2100 seconds\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.RUNNING: 'job is actively running'>, 'status_msg': 'job is actively running'}\n",
      "{'job_id': '5b3f4fbd34d1a900432db630', 'status': <JobStatus.DONE: 'job has successfully run'>, 'status_msg': 'job has successfully run'}\n",
      "REAL-DEVICE: (3,2)-QRAC for  Encoding000DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1082eea90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding000DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e8ecf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding000DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108331780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding001DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108b2bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding001DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10846f518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding001DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083c2240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding010DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1084246a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding010DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c79080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding010DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108636278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding011DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d26080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding011DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108cf85f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding011DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e6a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding100DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c57208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding100DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108ad15f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding100DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108b4e208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding101DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108cac518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding101DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1020c28d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding101DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f6be48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding110DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108ad60f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding110DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x109894080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding110DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1020a9198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding111DecodingFirst\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c73710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding111DecodingSecond\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108b699e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REAL-DEVICE: (3,2)-QRAC for  Encoding111DecodingThird\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108ad6278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "backend = \"ibmq_5_tenerife\"\n",
    "shots = 8000\n",
    "\n",
    "job_exp = execute(circuits, backend=backend, shots=shots, max_credits=100)\n",
    "\n",
    "lapse = 0\n",
    "interval = 10\n",
    "while not job_exp.done:\n",
    "    print('Status @ {} seconds'.format(interval * lapse))\n",
    "    print(job_exp.status)\n",
    "    time.sleep(interval)\n",
    "    lapse += 1\n",
    "print(job_exp.status)\n",
    "\n",
    "results = job_exp.result()\n",
    "for i, each in enumerate(circuitNames):\n",
    "    print(\"REAL-DEVICE: (3,2)-QRAC for \", each)\n",
    "    plot_histogram(results.get_counts(circuits[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## About Quantum Random Access Coding\n",
    "$(n, m)$-QRACs exist for $ n \\le 2^{2m}-1$ that can be realized with mixed states as shown [here](http://link.springer.com/chapter/10.1007/978-3-540-73420-8_12)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name: qiskit\n",
      "Version: 0.5.6\n",
      "Summary: Software for developing quantum computing programs\n",
      "Home-page: https://github.com/QISKit/qiskit-terra\n",
      "Author: QISKit Development Team\n",
      "Author-email: qiskit@us.ibm.com\n",
      "License: Apache 2.0\n",
      "Location: /Users/rraymondhp/miniconda3/envs/QISKitenv/lib/python3.6/site-packages\n",
      "Requires: numpy, networkx, matplotlib, IBMQuantumExperience, pillow, ply, sympy, scipy\n",
      "Required-by: \n"
     ]
    }
   ],
   "source": [
    "!pip show qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "QISKitenv",
   "language": "python",
   "name": "qiskitenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}