reference/qis/superposition_and_entanglement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../../images/QISKit.gif\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"250 px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*Superposition and Entanglement*_ \n",
    "\n",
    "\n",
    "The latest version of this notebook is available on https://github.com/QISKit/qiskit-tutorial.\n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Jay Gambetta, Antonio Córcoles, Andrew Cross, Anna Phan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "Many people tend to think quantum physics is hard math, but this is not actually true. Quantum concepts are very similar to those seen in the linear algebra classes you may have taken as a freshman in college, or even in high school. The challenge of quantum physics is the necessity to accept counter-intuitive ideas, and its lack of a simple underlying theory. We believe that if you can grasp the following two Principles, you will have a good start: \n",
    "1. [A physical system in a perfectly definite state can still behave randomly.](#section1)\n",
    "2. [Two systems that are too far apart to influence each other can nevertheless behave in ways that, though individually random, are somehow strongly correlated.](#section2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting Started\n",
    "Please see [Getting Started with QISKit](../tools/getting_started.ipynb) if you would like to understand how to get started with QISKit. This tutorial will be giving an introduction to superposition and entanglement. Note that all the examples will be run on a simulator to avoid the queues for running on a quantum processor, however, all examples can be run on real devices, see [this tutorial](../tools/working_with_backends.ipynb) to find out how. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "try:\n",
    "    sys.path.append(\"../../\") # go to parent dir\n",
    "    import Qconfig\n",
    "    qx_config = {\n",
    "        \"APItoken\": Qconfig.APItoken,\n",
    "        \"url\": Qconfig.config['url']}\n",
    "except:\n",
    "    qx_config = {\n",
    "        \"APItoken\":\"YOUR_TOKEN_HERE\",\n",
    "        \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# useful additional packages \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from pprint import pprint\n",
    "\n",
    "# importing the QISKit\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit import QuantumProgram\n",
    "from qiskit.backends import discover_local_backends, discover_remote_backends\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram, circuit_drawer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lowest_pending_jobs(api):\n",
    "    \"\"\"Returns the backend with lowest pending jobs.\"\"\"\n",
    "    remote_backends = discover_remote_backends(api)\n",
    "    remote_backends.remove('ibmqx_hpc_qasm_simulator')\n",
    "    remote_backends.remove('ibmqx_qasm_simulator')\n",
    "    device_status = [api.backend_status(backend) for backend in remote_backends]\n",
    "\n",
    "    best = min([x for x in device_status if x['available'] is True],\n",
    "               key=lambda x: x['pending_jobs'])\n",
    "    return best['backend'] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IBMQuantumExperience import IBMQuantumExperience\n",
    "api = IBMQuantumExperience(token=qx_config['APItoken'], config={'url': qx_config['url']})\n",
    "\n",
    "#backend = lowest_pending_jobs(api)\n",
    "#print(\"the best backend is \" + backend)\n",
    "\n",
    "backend = 'local_qasm_simulator' # the backend to run on\n",
    "shots = 1024    # the number of shots in the experiment "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum States - Basis States and Superpositions<a id='section1'></a>\n",
    "\n",
    "The first Principle above tells us that the results of measuring a quantum state may be random or deterministic, depending on what basis is used. To demonstrate, we will first introduce the computational (or standard) basis for a qubit. \n",
    "\n",
    "The computational basis is the set containing the ground and excited state $\\{|0\\rangle,|1\\rangle\\}$, which also corresponds to the following vectors: \n",
    "\n",
    "$$|0\\rangle =\\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}$$\n",
    "$$|1\\rangle =\\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$$\n",
    "\n",
    "In Python these are represented by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "zero = np.array([[1],[0]])\n",
    "one = np.array([[0],[1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our quantum processor system (and many other physical quantum processors) it is natural for all qubits to start in the $|0\\rangle$ state, known as the ground state. To make the $|1\\rangle$ (or excited) state, we use the operator \n",
    "\n",
    "$$ X =\\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}.$$\n",
    "\n",
    "This $X$ operator is often called a bit-flip because it exactly implements the following:\n",
    "\n",
    "$$X: |0\\rangle  \\rightarrow  |1\\rangle$$\n",
    "$$X: |1\\rangle \\rightarrow |0\\rangle.$$\n",
    "\n",
    "In Python this can be represented by the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0]\n",
      " [1]]\n",
      "[[1]\n",
      " [0]]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[0,1],[1,0]])\n",
    "print(np.dot(X,zero))\n",
    "print(np.dot(X,one))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we give the two quantum circuits for preparing and measuring a single qubit in the ground and excited states using QISKit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._measure.Measure at 0x104fb8cc0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating registers\n",
    "qr = QuantumRegister('qr', 1)\n",
    "cr = ClassicalRegister('cr', 1)\n",
    "\n",
    "# Quantum circuit ground \n",
    "qc_ground = QuantumCircuit(qr, cr)\n",
    "qc_ground.measure(qr[0], cr[0])\n",
    "\n",
    "# Quantum circuit excited \n",
    "qc_excited = QuantumCircuit(qr, cr)\n",
    "qc_excited.x(qr)\n",
    "qc_excited.measure(qr[0], cr[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=172x121 at 0x109B8BE80>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(qc_ground)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=281x121 at 0x10ACC0DA0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(qc_excited)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have created two jobs with different quantum circuits; the first to prepare the ground state, and the second to prepare the excited state. Now we can run the prepared jobs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "circuits = ['ground', 'excited']\n",
    "Q_program = QuantumProgram()\n",
    "Q_program.add_circuit('ground',qc_ground)\n",
    "Q_program.add_circuit('excited',qc_excited)\n",
    "Q_program.get_qasms(circuits)\n",
    "result = Q_program.execute(circuits, backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the run has been completed, the data can be extracted from the API output and plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aca6cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_histogram(result.get_counts('ground'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b029518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_histogram(result.get_counts('excited'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that the qubit is in the $|0\\rangle$ state with 100% probability for the first circuit and in the $|1\\rangle$ state with 100% probability for the second circuit. If we had run on a quantum processor rather than the simulator, there would be a difference from the ideal perfect answer due to a combination of measurement error, preparation error, and gate error (for the $|1\\rangle$ state). \n",
    "\n",
    "Up to this point, nothing is different from a classical system of a bit. To go beyond, we must explore what it means to make a superposition. The operation in the quantum circuit language for generating a superposition is the Hadamard gate, $H$. Let's assume for now that this gate is like flipping a fair coin. The result of a flip has two possible outcomes, heads or tails, each occurring with equal probability. If we repeat this simple thought experiment many times, we would expect that on average we will measure as many heads as we do tails. Let heads be $|0\\rangle$ and tails be $|1\\rangle$. \n",
    "\n",
    "Let's run the quantum version of this experiment. First we prepare the qubit in the ground state $|0\\rangle$. We then apply the Hadamard gate (coin flip). Finally, we measure the state of the qubit. Repeat the experiment 1024 times (shots). As you likely predicted, half the outcomes will be in the $|0\\rangle$ state and half will be in the $|1\\rangle$ state.\n",
    "\n",
    "Try the program below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=280x121 at 0x10B26ADD8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quantum circuit superposition \n",
    "qc_superposition = QuantumCircuit(qr, cr)\n",
    "qc_superposition.h(qr)\n",
    "qc_superposition.measure(qr[0], cr[0])\n",
    "\n",
    "circuit_drawer(qc_superposition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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exVRekhtKz4K4tsPLg4E/dHtVkqSa68ptruufBLcDGz4VLik9Z/rL3VyTJKkX6DQgMvMigIj4ZWZ+q+dLkiT1Bp3NgxiUmUvKuz+JiMLbWTNzcXcXJkmqrc7OIJ4Ddi1vL6J0WSk69ElKjxGVJG1DOpsHsWu77UrueJIkbeX8pS9JKtTZGMSTlC4hbVZmntBtFUmSeoXOxiDuqUoVkqRep7MxiPurVYgkqXfp7BLTP2TmA+XtT22qX2be292FSZJqq7NLTBOBB8rb/7CJPknp6XKSpG1IZ5eYPtRue1OL9UmStkGVPJOaiNgdOBPYD3gZ+GFmvtEThUmSaquS50GcAiwBPgscDXwGWBIRY7p4/NiIeDEiFkXElQWv/1NEPBcR8yPi5xExoqu1SZK6XyVnEN8AJmXmI+sbIuJjwDTgkM0dGBF9yv1OBVqAORHRmJkL23V7KDPvKvcfB9wCjK2gPklSN6pkJvV+wGMd2v4v8L4uHHsMsCgzF2fmamA6cFb7Dpm5st3uznRhgp4kqedUEhAPAJd2aPtfwH904dj+lJ4dsV5LuW0DEXFpRPweuJHSpayNRMSkiGiKiKbW1tYuFS5JqtxmAyIinoyIJyLiCeAI4OaIaImIX0VEC6XLQEd0VzGZOS0zDwKuAL60iT53Z2ZDZjbU19d310dLkjqodKmNd/vAoOVs+DS6AeW2TZkO3PkuP0uS1A2qtdTGHGBoRBxIKRgmAOe37xARQzPzpfLumcBLSJJqptJ5EH9LacB5b9o9OKizpTYyc21ETAZmUXq40L2ZuSAirgWaMrMRmBwRHwTWAK8DF1b0TSRJ3arLARERHwX+D6X/2Y8EFgCjgJ/ThaU2MnMGMKND29Xttv+5q7VIknpeJXcx/TtwUWYeAawq/z0JmNsjlUmSaqqSgBiYmf/Zoe1+4IJurEeS1EtUEhCvlscgoLTExvuBgyiNKUiStjGVBMS3gL8rb98K/BT4DXBHdxclSaq9Lg9SZ+YN7bb/IyJ+Buycmc/3RGGSpNqq9DbXPsBx/HW576d7oihJUu1VcpvraOC7wI6U1lIaAPxPRPx9Zv6mh+qTJNVIJWMQ91Jasrt/Zh5DabG9b+DjRiVpm1RJQAwDbsvMBCj//XVgaE8UJkmqrUoCYgYwrkPbR4Afdl85kqTeYrNjEBHxAH99cE8fYHpEzKX0bIf9gaOA7/VohZKkmuhskHpRh/3fttteSGnxPUnSNqiz5b7/d7UKkST1LpXOgziJ0tpL/Sk91+GBzPxpD9QlSaqxLg9SR8QlwCPAfwGPA68AD0fEP/ZQbZKkGqrkDGIqcGr7SXER8R3gMd79o0glSb1UJbe57kVpYLq9F4E9u68cSVJvUUlA/By4JSJ2AoiInYGvAb/sicIkSbVVSUD8EzAaeDMi/gi8ARwGfLonCpMk1VaXxiAiIoC/AcYA76O8mmtmtvRgbZKkGupSQGRmRsRzwK7lUDAYJGkbV8klpnmUFuyTJG0HKrnN9WfAjyLiPkprMa1fo4nMdMlvSdrGVBIQHwCagRM7tCc+E0KStjmdBkT5ttYvAX8Gfg18JTPf7unCJEm11ZUxiGmUnvvwPHAOcFOPViRJ6hW6EhBjgdMycypwBvDhd/NBETE2Il6MiEURcWXB65+PiIUR8WxE/CQiDng3nyNJ6h5dCYidM/MVgMxcBuxW6YdERB9KZyJnACOAiRExokO3eUBDZo4GHgVurPRzJEndpyuD1HURcTIQm9gnM2d38h7HAIsyczFAREwHzqLd2k4dlg1/GvhEF2qTJPWQrgTEq2x4l9KKDvsJDO7kPfpTujV2vRbg2M30vxiYWfRCREwCJgEMHDiwk4+VJL1bnQZEZg6qQh1tIuITQAMb3067vp67gbsBGhoasqiPJGnLVfREuS2wHNi/3f6ActsGIuKDwL8CJ3orrSTVViVLbWyJOcDQiDgwIvoBE4DG9h0i4gjgm8C4zHy1SnVJkjahKgGRmWuBycAsSvMpHsnMBRFxbUSMK3f7GrAL8J8RMT8iGjfxdpKkKqjWJSYycwYwo0Pb1e22P1itWiRJnavWJSZJ0lbGgJAkFTIgJEmFDAhJUiEDQpJUyICQJBUyICRJhQwISVIhA0KSVMiAkCQVMiAkSYUMCElSIQNCklTIgJAkFTIgJEmFDAhJUiEDQpJUyICQJBUyICRJhQwISVIhA0KSVMiAkCQVMiAkSYUMCElSIQNCklTIgJAkFTIgJEmFqhYQETE2Il6MiEURcWXB6ydExK8jYm1EjK9WXZKkYlUJiIjoA0wDzgBGABMjYkSHbkuBTwIPVaMmSdLm1VXpc44BFmXmYoCImA6cBSxc3yEzl5Rfe6dKNUmSNqNal5j6A8va7beU2yoWEZMioikimlpbW7ulOEnSxra6QerMvDszGzKzob6+vtblSNI2q1oBsRzYv93+gHKbJKmXqlZAzAGGRsSBEdEPmAA0VumzJUnvQlUCIjPXApOBWcDzwCOZuSAiro2IcQARcXREtAAfA74ZEQuqUZskqVi17mIiM2cAMzq0Xd1uew6lS0+SpF5gqxukliRVhwEhSSpkQEiSChkQkqRCBoQkqZABIUkqZEBIkgoZEJKkQgaEJKmQASFJKmRASJIKGRCSpEIGhCSpkAEhSSpkQEiSChkQkqRCBoQkqZABIUkqZEBIkgoZEJKkQgaEJKmQASFJKmRASJIKGRCSpEIGhCSpkAEhSSpUtYCIiLER8WJELIqIKwtef09EfKf8+q8iYlC1apMkbawqARERfYBpwBnACGBiRIzo0O1i4PXMHALcCtxQjdokScWqdQZxDLAoMxdn5mpgOnBWhz5nAfeXtx8FxkREVKk+SVIHdVX6nP7Asnb7LcCxm+qTmWsj4k1gL+C19p0iYhIwqbz754h4sUcqrr296fDde4u4/Du1LkGqhl77Mwhb/HN4QFc6VSsguk1m3g3cXes6elpENGVmQ63rkLZX/gxW7xLTcmD/dvsDym2FfSKiDtgNWFGV6iRJG6lWQMwBhkbEgRHRD5gANHbo0whcWN4eD8zOzKxSfZKkDqpyiak8pjAZmAX0Ae7NzAURcS3QlJmNwLeBByJiEfDflEJke7bNX0aTernt/mcw/E+6JKmIM6klSYUMCElSIQNCklTIgJAkFTIgepmI+Jta1yBJ4F1MvUJEDKO0fMjelEK7ldItwT92LohUPRGxA5D+3JUYEL1ARDwP/Bx4HVhJaZ2UwcAS4GuZ+ULtqpO2T4aFAVFzEXE6MK28zPn6pdH3BY4Ezqa0LMknMvO/aleltG2LiKOBzwGzgf+XmYvavRaZmRGxW2a+WbMia8AxiNrbGfhjROwPkJnrMrOlPLv8X4B1lJ6jIannfBFoAE4GboyIWyJifETsWw6HeuArtS2x+jyDqLHyMy8epbQEyeczc3GH1+8A+mTmp2tRn7StK5+1zwS+A7wIHAUMB/YB1gJPAX8PvJaZZ9eqzlrY6pb73taU/3fyL8DNwLyIeJZSYMwGTgTGUVq8UFLP6EfpYWWLM/Mp4OcR8T7gCEqXeocDfwccXbsSa8MziF4kIo6k9GS9symNQ8wGfpSZ99a0MGk7EBE7ZOY768cc2rVPAq7PzL1qWF5NGBC9VHk+RL/tbVBM6i3aDU7/G7BDZv5rrWuqNgNCkjYjIvYGVmXmX2pdS7UZEJKkQt7mKkkqZEBIkgoZEJKkQgaEJKmQASFJKvT/AYyYG55hul9PAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10af66588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuits = ['superposition']\n",
    "Q_program.add_circuit('superposition', qc_superposition)\n",
    "result = Q_program.execute(circuits, backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)\n",
    "\n",
    "plot_histogram(result.get_counts('superposition'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, much like a coin flip, the results are close to 50/50 with some non-ideality due to errors (again due to state preparation, measurement, and gate errors). So far, this is still not unexpected. Let's run the experiment again, but this time with two $H$ gates in succession. If we consider the $H$ gate to be analog to a coin flip, here we would be flipping it twice, and still expecting a 50/50 distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=436x121 at 0x10B83B278>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quantum circuit two Hadamards \n",
    "qc_twohadamard = QuantumCircuit(qr, cr)\n",
    "qc_twohadamard.h(qr)\n",
    "qc_twohadamard.barrier()\n",
    "qc_twohadamard.h(qr)\n",
    "qc_twohadamard.measure(qr[0], cr[0])\n",
    "\n",
    "circuit_drawer(qc_twohadamard)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b7036a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuits = ['twohadamard']\n",
    "Q_program.add_circuit('twohadamard', qc_twohadamard)\n",
    "result= Q_program.execute(circuits, backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)\n",
    "\n",
    "plot_histogram(result.get_counts('twohadamard'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time, the results are surprising. Unlike the classical case, with high probability the outcome is not random, but in the $|0\\rangle$ state. *Quantum randomness* is not simply like a classical random coin flip. In both of the above experiments, the system (without noise) is in a definite state, but only in the first case does it behave randomly. This is because, in the first case, via the $H$ gate, we make a uniform superposition of the ground and excited state, $(|0\\rangle+|1\\rangle)/\\sqrt{2}$, but then follow it with a measurement in the computational basis. The act of measurement in the computational basis forces the system to be in either the $|0\\rangle$ state or the $|1\\rangle$ state with an equal probability (due to the uniformity of the superposition). In the second case, we can think of the second $H$ gate as being a part of the final measurement operation; it changes the measurement basis from the computational basis to a *superposition* basis. The following equations illustrate the action of the $H$ gate on the computational basis states:\n",
    "$$H: |0\\rangle  \\rightarrow  |+\\rangle=\\frac{|0\\rangle+|1\\rangle}{\\sqrt{2}}$$\n",
    "$$H: |1\\rangle \\rightarrow |-\\rangle=\\frac{|0\\rangle-|1\\rangle}{\\sqrt{2}}.$$\n",
    "We can redefine this new transformed basis, the superposition basis, as the set {$|+\\rangle$, $|-\\rangle$}. We now have a different way of looking at the second experiment above. The first $H$ gate prepares the system into a superposition state, namely the $|+\\rangle$ state. The second $H$ gate followed by the standard measurement changes it into a measurement in the superposition basis. If the measurement gives 0, we can conclude that the system was in the $|+\\rangle$ state before the second $H$ gate, and if we obtain 1, it means the system was in the $|-\\rangle$ state. In the above experiment we see that the outcome is mainly 0, suggesting that our system was in the $|+\\rangle$ superposition state before the second $H$ gate. \n",
    "\n",
    "\n",
    "The math is best understood if we represent the quantum superposition state $|+\\rangle$ and $|-\\rangle$ by: \n",
    "\n",
    "$$|+\\rangle =\\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 \\\\ 1 \\end{pmatrix}$$\n",
    "$$|-\\rangle =\\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 \\\\ -1 \\end{pmatrix}$$\n",
    "\n",
    "A standard measurement, known in quantum mechanics as a projective or von Neumann measurement, takes any superposition state of the qubit and projects it to either the state $|0\\rangle$ or the state $|1\\rangle$ with a probability determined by:\n",
    "\n",
    "$$P(i|\\psi) = |\\langle i|\\psi\\rangle|^2$$ \n",
    "\n",
    "where $P(i|\\psi)$ is the probability of measuring the system in state $i$ given preparation $\\psi$.\n",
    "\n",
    "We have written the Python function ```state_overlap``` to return this: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_overlap = lambda state1, state2: np.absolute(np.dot(state1.conj().T,state2))**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a simple way of going from a state to the probability distribution of a standard measurement, we can go back to the case of a superposition made from the Hadamard gate. The Hadamard gate is defined by the matrix:\n",
    "\n",
    "$$ H =\\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}$$\n",
    "\n",
    "The $H$ gate acting on the state $|0\\rangle$ gives:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1033b9978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Hadamard = np.array([[1,1],[1,-1]],dtype=complex)/np.sqrt(2)\n",
    "psi1 = np.dot(Hadamard,zero)\n",
    "P0 = state_overlap(zero,psi1)\n",
    "P1 = state_overlap(one,psi1)\n",
    "plot_histogram({'0' : P0.item(0), '1' : P1.item(0)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is the ideal version of the first superposition experiment. \n",
    "\n",
    "The second experiment involves applying the Hadamard gate twice. While matrix multiplication shows that the product of two Hadamards is the identity operator (meaning that the state $|0\\rangle$ remains unchanged), here (as previously mentioned) we prefer to interpret this as doing a measurement in the superposition basis. Using the above definitions, you can show that $H$ transforms the computational basis to the superposition basis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.70710678+0.j]\n",
      " [0.70710678+0.j]]\n",
      "[[ 0.70710678+0.j]\n",
      " [-0.70710678+0.j]]\n"
     ]
    }
   ],
   "source": [
    "print(np.dot(Hadamard,zero))\n",
    "print(np.dot(Hadamard,one))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entanglement<a id='section2'></a>\n",
    "\n",
    "The core idea behind the second Principle is *entanglement*. Upon reading the Principle, one might be inclined to think that entanglement is simply strong correlation between two entitities -- but entanglement goes well beyond mere perfect (classical) correlation. If you and I read the same paper, we will have learned the same information. If a third person comes along and reads the same paper they <i>also</i> will have learned this information. All three persons in this case are perfectly correlated, and they will remain correlated even if they are separated from each other. \n",
    "\n",
    "The situation with quantum entanglement is a bit more subtle. In the quantum world, you and I could read the same quantum paper, and yet we will not learn what information is actually contained in the paper until we get together and share our information. However, when we are together, we find that we can unlock more information from the paper than we initially thought possible. Thus, quantum entanglement goes much further than perfect correlation.\n",
    "\n",
    "To demonstrate this, we will define the controlled-NOT (CNOT) gate and the composition of two systems. The convention we use in the Quantum Experience is to label states by writing the first qubit's name in the rightmost position, thereby allowing us to easily convert from binary to decimal. As a result, we define the tensor product between operators $q_0$ and $q_1$ by $q_1\\otimes q_0$. \n",
    "\n",
    "Taking $q_0$ as the control and $q_1$ as the target, the CNOT with this representation is given by\n",
    "\n",
    "$$ CNOT =\\begin{pmatrix} 1 & 0 & 0 & 0\\\\ 0 & 0 & 0 & 1\\\\0& 0& 1 & 0\\\\0 & 1 & 0 & 0 \\end{pmatrix},$$\n",
    "\n",
    "which is non-standard in the quantum community, but more easily connects to classical computing, where the least significant bit (LSB) is typically on the right. An entangled state of the two qubits can be made via an $H$ gate on the control qubit, followed by the CNOT gate. This generates a particular maximally entangled two-qubit state known as a Bell state, named after John Stewart Bell ([learn more about Bell and his contributions to quantum physics and entanglement](https://en.wikipedia.org/wiki/John_Stewart_Bell)). \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To explore this, we can prepare an entangled state of two qubits, and then ask questions about the qubit states. The questions we can ask are:\n",
    "* What is the state of the first qubit in the standard basis?\n",
    "* What is the state of the first qubit in the superposition basis?\n",
    "* What is the state of the second qubit in the standard basis?\n",
    "* What is the state of the second qubit in the superposition basis?\n",
    "* What is the state of both qubits in the standard basis?\n",
    "* what is the state of both qubits in the superposition basis?\n",
    "\n",
    "Below is a program with six such circuits for these six questions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._measure.Measure at 0x10b1b8160>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_program = QuantumProgram()\n",
    "\n",
    "# Creating registers\n",
    "q2 = QuantumRegister('q2', 2)\n",
    "c2 = ClassicalRegister('c2', 2)\n",
    "\n",
    "# quantum circuit to make an entangled bell state \n",
    "bell = QuantumCircuit(q2, c2)\n",
    "bell.h(q2[0])\n",
    "bell.cx(q2[0], q2[1])\n",
    "\n",
    "# quantum circuit to measure q0 in the standard basis\n",
    "measureIZ = QuantumCircuit(q2, c2)\n",
    "measureIZ.measure(q2[0], c2[0])\n",
    "\n",
    "# quantum circuit to measure q0 in the superposition basis \n",
    "measureIX = QuantumCircuit(q2, c2)\n",
    "measureIX.h(q2[0])\n",
    "measureIX.measure(q2[0], c2[0])\n",
    "\n",
    "# quantum circuit to measure q1 in the standard basis\n",
    "measureZI = QuantumCircuit(q2, c2)\n",
    "measureZI.measure(q2[1], c2[1])\n",
    "\n",
    "# quantum circuit to measure q1 in the superposition basis \n",
    "measureXI = QuantumCircuit(q2, c2)\n",
    "measureXI.h(q2[1])\n",
    "measureXI.measure(q2[1], c2[1])\n",
    "\n",
    "# quantum circuit to measure q in the standard basis \n",
    "measureZZ = QuantumCircuit(q2, c2)\n",
    "measureZZ.measure(q2[0], c2[0])\n",
    "measureZZ.measure(q2[1], c2[1])\n",
    "\n",
    "# quantum circuit to measure q in the superposition basis \n",
    "measureXX = QuantumCircuit(q2, c2)\n",
    "measureXX.h(q2[0])\n",
    "measureXX.h(q2[1])\n",
    "measureXX.measure(q2[0], c2[0])\n",
    "measureXX.measure(q2[1], c2[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=395x261 at 0x10B0122B0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(bell+measureIZ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=487x261 at 0x10B023358>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(bell+measureIX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5eXmurq7kyRO0XvMTGYrL5fJ4PCE1m5qacEF4hrp48aJAIFi6dOnEiROpClL+ke/R2Gy2uEuLSLmFOgAjEm8ZigULFpSUlDx8+BD/4TUyMnJxcSE6m3g8HrG/i7q6Orlznez06dN4kIE0iAyFEKqqqhpuWDmPx6uoqMBlIRmKz+dHRkaiUdZHjv5vipk+fTr5f1UUittNDhSF2AvlsFis2bNnE2ukkOXn5xNjO2fOnCnxKjyiMDY2VlFRwXdwxcXFw2WoyspKoqdcyHirv//+++XLlwYGBosXL6YhWPklTYoZsIW6wnWTA4VA5RhZmd3iIYRUVFSIDdNLSkqGq1ZaWooLqqqq5IWJB8Dj2j/44ANas6ockuZJXGFhIXkQLFxDATpQmaHIb3cZvF+JMQHkdgfIycnBBUdHx+HGdjY2Nt6+fRshNHqmCmNlZWWvX78mXkozVlNTU1Pc+cYAiEJRr6EQQv7+/rjwxx9/DLfaFrHwnpDp7D///HNfX5+bm5uQvWffSOQUo66uLuQac8TDJdhCHQBRUPau6u7uJrZO0NPTE7IiClW8vLzwUjBNTU3kvT8J6enp+FPE4XA2bdo03HnwTBex1mx7M6xdu5YYdTJgw2FRnDlzhjg8MTGRpiDBKEdZhsrJyeFyubgsm05TDoeze/duXN63b9+AiTgdHR3btm0TCAQIofXr1w+3rFV2dnZeXp6GhgbeDx0AIFcoy1AyvsXDgoKC3N3dEULNzc0+Pj4xMTG9vb2dnZ2JiYmzZ8/Ozc1FCOnr64eHhw93BnwB5e/vL+6DdgCADFD26IqcoWT2WIfNZkdGRvr4+Dx//ry+vt7Pz4/NZrNYLGIM5/jx46OiooZbFa+np+fq1ato9A2DAkBRUHYNNaDflKrTjmjSpElZWVmrVq3C8xX4fD6RnubMmZOWloYvsoZ069atlpYWS0tLIXUAAAyi5RpK+PwSymlra0dFRZWWlt64ceP58+c8Hs/CwmLx4sUjXsqNwuU0AVAsSnhjOPyvNGSclQabPHlyaGio6PVbW1uTkpKEP+YDADBLydfXV01NTQaDA+SNpqamt7f3rFmzjI2NmY4FADA0lgD2elVkWlpaHR0dVVVVJiYmTMcilfLycgsLi3HjxhFrUTBi/Pjxzc3NZWVlo2enHzkH44ABAPILMhQAQH5BhgIAyC/IUAAA+TW6lkN68+DhqUeOHFH0WTt4m3tiaicAGDzLU2wcDoe85a+i43A4zCYpeJYnb+AaSrGFhoZmZ2fb29szHQgFHj9+POTq0qPN3LlzU1NTmY5CLnh6ekKGUmwHDx5kOgRAsaqqKqZDkBeVlZWQoQCQL5MnT66srPzpp5+WLl3KdCyMiYmJ2bJli6WlJWQoAOSRpqbmuHHjmI6CMcRMYRhtAACQX5ChAADyCzIUAEB+QYYCAMgvyFAAAPnFvnTpUkBAALG296iyc+dOvBAwAIAOTU1NaWlp0pyB/d133507d66iooKqmBRFc3PzyZMnAwMD6+rqmI4FgDeQQCDw9fWdM2dOenq6xCdht7S0IISam5spi0tBjBs3zs3Nrbe39/Lly0zHAsAbKCoq6sGDB9ra2paWlhKfZFT3Q+FdXi5evMh0IAC8afr6+vDOJqGhoRMmTJD4PMyPKefxeKmpqUlJSRUVFa2trXp6esbGxl5eXq6urmw2vQnU398/KCioqKjo4cOHMtuFFIDRICIiorS01MTEJCgoSJrzMJyhoqOjQ0NDS0pKBnx93759hoaGe/fuDQgI4HA4NLWuqam5evXqixcvXrhwATLUqCUQCCoqKkpKSqqrq7u7uxFCN27csLW1nTp1qoWFhZIS83/FFU5zc/ORI0cQQkePHlVXV5fqXPgWMSsrSyBzn3766YjhOTs719XV0RfDvXv3EEJjx47t6uqirxUgh7q6uq5cubJ69Wo9Pb3h3n6amppLliz57rvvXr9+LbPA5s+fjxC6efOmzFqkXHBwMELI0dGRx+NJdoYbN24ghHx8fBjLUHv27CHeB8rKyu7u7hs2bFi+fPn06dMHvEsmT55cU1NDXyRTpkxBCP3888/0NQHkSm1t7c6dO8eOHUu8x8aMGePg4LB8+XJ8xYQ3rCZP3FVRUdm4cWNhYaEMwlP0DFVaWqqqqooQSkhIkPgkDGeo5ORkFouFf/dbt24d8AeqoKBgwLoT3t7efD6fpmAOHz6Mm6Dp/EB+9Pb2/utf/xozZgx+X02bNu3QoUMZGRlcLhdXwFmprKwMvywsLIyIiHB1dcX12Wx2YGBgc3MzrUEqeoZauXIlQsjPz0+akzCcoZydnfGvfM+ePcPV2bt3LzlJXbhwgaZgXr58yeFwWCxWeXk5TU0AeVBcXOzg4IDfTp6envHx8YPrDMhQhLy8vLVr1+I/q0ZGRsnJyfTFqdAZKi0tjcViKSkpSXm9yWSGysnJwe8SS0vLvr4+ITVXrFhBZCgrKyuJ72lH9M477yCEvvzyS5rODxgXGxuLN5swNDSMiooartpwGQp78OCBnZ0dQojD4Zw+fZqmUBU3Q/H5fDc3N4RQUFCQlKciMhQD46HOnTuHC2FhYcrKykJqnjx5kniQV1xcnJGRQVNIeGDUpUuXBLCvxJvol19+WbZsWXt7+8KFC3Nzc1etWiXZeVxdXTMyMv75z3/yeLygoKCvvvqK2jgV3Y0bN1JTU7W0tD7//HOqzslAhoqPj0cImZub4/tVIczMzPDfEywhIYGmkJYtW6arq/vixYukpCSamgBMSUxMfP/99/v6+t5///3ff/994sSJ0pxNTU3tzJkzp06dYrPZ+/fvP3nyJFVxKrq+vr4vvvgCIfTFF1/o6+tTdVoGMlRERASLxfL19RWlMr6oxvLz82kKSUVFZcOGDQjGl79xKioq/P39e3t7N2zYEBkZKfyaXXTBwcEREREIoV27dsXFxVFyTkVH1RDNARjIUIsWLQoJCVm2bJkola2trYlyQ0MDbUGhDz/8ECEUHR3d1tZGXytAlrhcrr+/f1NT0/z58y9dukTtFIVPPvnkk08+4fP5GzdufPXqFYVnVkRUDtH8v5iZl3f48GEPDw9Rakozo0csDg4Ojo6O3d3duIsOvAG+/fbbzMzMiRMnXrlyhY6h4V9//fXbb79dX1+/e/duyk+uWA4cONDU1OTo6Lh27Vpqzyztr62rqys2NraoqKi6utrc3NzGxmbRokX43cDlcgMCAnDfs6mp6YEDB4ijVFRURDw/eWkUureB3bJlS1BQ0IULF7Zu3UprQ0AGmpub9+/fjxA6fvy4oaEhHU2oqqqeO3fOxcXl0qVL27dvf/vtt+loRf6VlZWdOXMGIXTixAnq59JKPNqgra1t9+7d48ePH3BCMzOzK1euCASCR48eEV/cuHGjZA8dycni6NGjkp1ERI2NjXgsrGyGDgNa4b+Izs7OYo31FT7aYEj4QfCKFSvEj3FoCjfagJIhmgNIO9ogIyPDwcHh6NGjTU1NA75VUVGxYcOG/fv3P3z4kPiiZPNyeTxebGwsLrNYLH9/f8miFdH48ePfe+89hNClS5dobQjQjcvlfv/99wih0NBQYvYCTfbs2cPhcGJiYkbnXsHp6ek3b95UUlL617/+Rcf5JclQv//++9y5c8vKyoivcDgcPK1p1qxZ+A7uq6++OnHiBFHBxcVFgoYiIyOJ3/qCBQvovstD/zsw6qeffuJyuXS3Bejz119/1dfXGxsbi/jIWBqWlpYLFizg8/k///wz3W3JG4FAsHPnToFAsG3btsEzaikhdoZKSkpatWpVf38/fqmqqvr555+/ePEiJyfn1q1b6enp6enpZmZmCKHS0lJcR0VFZcaMGeI21NfXR4yI43A4x44dE/HA9PT0qVOnZmdni9siQmjhwoUmJiZ1dXXEtRtQRHfu3EEIrVmzhr6le8jWr19PNDqq0DFEcwDxMlRdXZ2/v39PTw9+OW3atNzc3EOHDpmYmBB1HB0df/zxR/JRDg4OoneNE7755hti9fSdO3cSM6qEaG9vP378uIeHx7NnzyS7CGKz2R988AGCgVEKDo+89fHxkU1zCxcuZLFYmZmZ7e3tsmlRHtA0RHMgsXrKydfMM2bMaGhoGK6mra0tUXP79u3i9pOlpKQQg+vc3d37+/uHrNbZ2VlcXPzgwYNz58599NFH5PU00tPTxW0Ue/bsGUJIWVn51atXkp0BMKu9vZ3FYrFYrLa2NnGPlaCnHJs8eTJCKDU1VdwDB1OUnvLjx48jhExMTOhYW02SnvLffvuNuI4dN25cTEyMkKW/5syZQ5TF7Savqanx9/fHN5J2dnYxMTHDDWa5du2alZXVnDlztm7dev78eUoGW1paWs6bN6+/v38Udiu8GUpKSgQCgbGxMZ4qLBvTpk1DCBUXF8usRWbRN0RzADEyVFhYGFH+5ptvzM3NhVRubW0lymJ1k7e2tvr6+uJhUNOmTYuPjx88oGEwNps9e/bskJAQ0RsSAnZYUGj19fUIIXLPgwy89dZbRNOjAX1DNAcS8S6PvOOVtbX1iAuhWFhY4Mo6OjqiD0hpb2+fPXs2EVh1dbXw+k+fPr1x40ZiYiJeA488vFPiuzyBQNDR0aGpqYkQysvLk/gkQtTW1gq5/AQAIUTf6i5YT09PQUHBrVu3jh07tnXrVk9PT0dHRwsLCz09PWKFPy0trYkTJ1pYWMyYMWPBggUff/zx8ePHb9269eeff0q/iqZwxF2eqGPKo6OjiXJgYKDwkaMNDQ3EWARnZ2cRB6R0d3cvXboUp0Jra+v4+PgRhwJbWVlZWVmJcnKxqKqqamhodHR00DRHTyAQ8Pl8Os4MgBCdnZ1paWn3799PTU1NSUnp7e0VXr+9vb29vZ2YD4tXJSHo6Oj8+uuvjY2NCxYsIK+YTC1RM9Rff/1FlEccY0K+4BLxFq+vr8/Pz+/u3bsIoRkzZsTFxTF4lfHnn3/W19ebmpoSy79Sy9DQsK6ublQ995Gl+Pj41atXOzs7k9+0IrKwsGhpacnJycEjZkT3P//zPxcvXty3b9+OHTvEbXSA9957LyUlxdjYWMrzEF6+fHn9+vWoqKjs7Gwej0d8XU9Pb8qUKVOnTp06deqUKVN0dXXHjh07duxYDQ0N3LXU0dHR09PT1tbW0dFRU1NTWlr67NmznJycJ0+eIIRaWloiIiIiIiI4HI6zs/PatWv9/f2NjIyoChsTKUO1tLTk5eXhsr6+vqmpqfD65AwlSjc5l8tds2YNfj85ODgkJCSI0vdEn/PnzyOENm/eTN+GfUpKSvT92Rnl8GO12tpaCf6H8fW+tra2uMfiHihzc3Ppf61UTXJuamr65Zdfrl69mpKSgq/ZWSyWtbW1h4fHvHnzPDw8RrxHGfyzCAQCd3d3hNDmzZu9vb1TUlJSUlKKiorwQMiQkBAPD49169atWrWKsre3KP1QBQUFRH0HB4cR7yE9PT2J+rW1tcIr83i8devW4cr29vbSbPtDST9UXV2dkpISi8WS4JEzkAcw2uD58+cff/yxmpoa/ixwOJyFCxdevHhRyPAgEV2/fh0hpKWlRd4jrr6+/syZM56ensRfdA0NjU8//VSahf/FW6ecvLilo6Oj8FNzuVwNDQ1c2dTUVHhlPp//0Ucf4cq2trZSDkGiJEPhUR5eXl7SRAKYNXXqVIRQbGysuAdKlqFqamrw9gES5MTBpMlQWVlZq1evJkbSOzs7nzp1asSrBBH19vbiRDzcHP7q6urw8HAnJyfcupKS0tq1a7OzsyVoS7zxUHgjVuz58+fCK+fn53d2duLyiJ1QwcHB+JbKxsYmMTFRZqtBCXHhwgX0vwMOgILy8vJCCMls9cu4uDiBQODs7CzLEVgDFBcXL1myxMnJ6T//+Y9AIPDz80tLS8vIyAgODjYwMKCkiRFX0TQyMtqxY0dmZua9e/d8fX15PN7169dnzpzp5+dHnsYrFpEyFB7rgbW3twufw52cnEyUhXdC7dmz5/Tp0wih6dOnJyQkyMMD+PT09KKiIm1tbfI2M0Dh4Ic5169fJ3cM0+fq1asIIRGXjaVcR0fH7t277e3t8SCAjz76qLCw8ObNm8TAHUqINUTT3d399u3b+fn5W7ZsUVFRiYmJsbGx+eKLL4hrFzGIcpfX0tJCPmTHjh3D1SwrKyMn7Lt37w5X8+DBg7iOlZUVVVeh0t/l4eWoPv74Y0riAUzp7+/HM8Vu3bol1oES3OU9e/aMw+Gw2ezKykrxohyG6Hd5fD7/ypUrxOOzlStXvnjxgpIYBpN4o/OSkhJig14TE5Pr16+LcpTY++XZ2NgQH35VVdXHjx8PrlNQUEB+RMpms9vb24c8G7FDxpQpU0Yclik6KTNUZ2cnntmXkZFBVUiAKV9++SVCyMnJ6U1dwa6lpWX16tX43T516tQ//viDqgAGk36j8/j4eCKHrFy5sqmpSXh9sUdsBgYGfvLJJ7jc29vr5uZ25swZf39/vGhBQ0PDmTNnjhw5Qix7gBCysbHBI7MHuHr1KjE95d1337127RrxLR6P19PTQyztMoCRkdG2bdtEDFgCv/zyS1tbm42NDbElMlBcn376aXh4eFZW1uXLlzdt2kRTK9nZ2ZGRkSwWi77lR4Z0//799evXV1VVqaurHzx48NNPP6VqG5shffbZZ729vX5+friDTwLe3t6PHj0KDw/fv39/dHT0o0ePrl69KtJ9qIjXUO3t7To6OgOOVVVVdXZ2trW1xSM42Gw2efOojz76aMhTbd++XbIf0snJSXiQUl5D4c0dvv76a3EPBPLp1KlTCCE9Pb2amhoRDxHrGqqnpwevTf7hhx9KEeZAwq+h+Hz+qVOncD6aPn36kHcz1KJqo3MsPz8fL3yipKS0f/9+Lpc7ZDVJdkX/9ddfhYxgtLa2fvDgAXlA7dmzZ4c8j3xmqOfPn7NYLGVl5fr6erEOBHKrv78fXw7Pnz+/r69PlEPEylD4rsLAwED6cUZkQjJUR0fHkiVL8Dt869atdCx7MgCFG50T2tvbN2/ejH+KFStWdHd3D64jSYYSCARxcXG4PoHD4Xh5eUVHR+NciH8YLDc3d8iTyGeGwlfp1K4GDxhXUVGB5yds2LBBlC5e0TPUt99+ixBis9l///03FZH+f8NlqFevXuGH41paWjdu3KC20eEMOUSTEleuXMFTlN3d3Qd3S0mYoQQCAZ/PT0tLu3z58uXLlxMSEsh94Vwul3gMqa6uPtyyc/SROEPxeDy8WMedO3foCw8wIjExEffybty4ccQrKREzFN4VHSEUHh5OWaD/a8gM9eLFC7wElb6+vmRjICUw4hBNKT18+BCPMbK2tq6oqCB/S/IMJURubi6RIObOnSv9CcUlcYb6888/EUIGBgayz6pABqKiovAjnYULFwq/ix8xQ3V3dwcEBOD32JdffklDsENkqCdPnuCn5JMnT3727BkdjQ6J1lU0saKiIrzSnImJSVFREfF1aXejGlJmZiZRlmxzF6bgce0ffPABHTvTAsatWrXqzp07WlpacXFxDg4OUVFRkp3nwYMHLi4uZ8+e5XA43377Ld4xVAa2b99eXV3t6Oh4//79Ad0s9JHNKprTpk178OCBg4PDy5cv8cdwACozVEZGBlGWbIM8RjQ2Nt6+fRshRPTegTePj49Pdna2g4NDbW3t6tWrPT09B6x2JFxeXt7atWvnzp375MkTIyOjxMREYvCNDAQHBwcFBSUnJ1M1f0UUMltF09DQ8N69e999993OnTuH+DaFd3nk7VikmdYsMcnu8vAzaTc3N1pjA/Kgt7f38OHDxBqSVlZWBw8efPjwIfHMe8BdXkFBwalTp4hlwjgcTmBgYHNzM61BysNOCtIP0ZQS9f1QXV1dxC2Snp4eJVGKS7IMZW9vjxD68ccfaY0NyI/a2tqdO3eSdwYaM2YM3pIWv4ffeeedWbNmkVc4UlFR2bhxIyUDgkYkDxlq1apVCKH33nuPqQDEHlM+opycHGKLOgXqhMrOzs7Ly9PQ0CAmEIA3noGBwfHjx7/66quYmJiYmJjk5OSGhobc3FziUQ9+coIQ0tTUnDdv3rvvvrtmzRpdXV3GIpYtPp9/584dFRWVo0ePMh2LyKsAj4iRbvJXr159//33xMuOjg6i/OOPP5L3DV67du2QK5rjtVb8/f0ZXDcDMEJdXX3dunXr1q0TCAQVFRUlJSXV1dX5+fnNzc1z5swxMDCYOnWqhYXFKHx4wmaz79y5w2az6dgEQFy0ZCiZdZM3NDTgCaKDDd73ePB/d09PD143A1aDGs1YLJa5ubnw3dVGm4ULFzIdwn9R9iyP/CBPUWbe3rp1q6WlxdLSEi+9DACQN7RcQ2lra1N1WuFsbGwEAoHEh8NymgDIOSW8pjixsrjEZJaVqNLa2pqUlMThcOhbmgMAICUlX19fNTW1UXgTrqmp6e3tPWvWLAo3JgMAUEvp4MGDxIK8owqHw5Fgx0cAgCzRtWMlAABIDzIUAEB+QYYCAMgvyFAAAPkFGQoAIL9G3ZwjABRCR0dHc3Mz01EwhtidmCXNmGwAAOXMzMwqKyuZjkIuWFhYwF0eAPIFhhATTExM4BoKAPBfVVVVpqamWlpabW1tCCENDY2urq7q6mojIyOmQoJrKACA/IIMBQCQX5ChAADyCzIUAEB+QYYCAMgvyFAAAPkFGQoAIL8gQwEA5BdkKACA/FLsmcM8Hi81NTUpKamioqK1tVVPT8/Y2NjLy8vV1ZXNhuQLgMJT4AwVHR0dGhpaUlIy4Ov79u0zNDTcu3dvQEAAh8NhJDYAACUU9UIjODh41apVg9MTVltbGxgY6OrqWl9fL+PAAAAUUshrqNDQ0IiICFxWVlaePXu2qalpZ2dncXFxUVERUS0zM9PNzS0lJcXQ0JChSAEA0hEomuTkZBaLhYPfunXr69evyd8tKChYunQp+Qf09vbm8/lMRQuAAsHrUmlpaeGXY8aMQQhVV1czGJLi3eXt2rVLIBAghPbs2XP27FldXV3yd62tre/cubN3717iKwkJCZcuXZJxkAAASijY+lC5ubmOjo4IIUtLy8LCQmVl5eFqrly58ubNm7hsZWVVWFgIT/cAEA7Wh5LWuXPncCEsLExIekIInTx5kniQV1xcnJGRQXtwAACqKViGio+PRwiZm5uvXLlSeE0zM7P58+cTLxMSEuiNDABAAwXLUBERESwWy9fXV5TKdnZ2RDk/P5+2oAAAdFGw0QaLFi0KCQlZvHixKJWtra2JckNDA21BAQDoomAZCiF0+PBhYrSBcBMmTKA7GAAArZjPUJWVlVFRUSUlJS9evGhoaNDQ0NDT05sxY8bSpUudnJwG11dRURHxzHV1dUR50qRJ1IQLAJAhJjNUUlLSkSNHEhIS+Hz+gG/FxMQcOHBg5syZX3/9tYeHh2Tnf/ToEVGeOnWq5IECABjCTE95a2trQECAt7d3XFzc4PREyM7O9vT0LCwslKAJHo8XGxuLyywWy9/fX8JYAQDMYeAaqrq62tvbu7i4mPjKvHnz7O3tzc3NuVxuQ0NDVlZWamoqj8dDCNnY2JA7vEUXGRlZVVWFywsWLIC7PAAUkawzVEVFhZeXV1lZGX65fPnyw4cPT58+fUC1qqqq48ePf/fdd//4xz8kaKWvr++rr77CZQ6Hc+zYMSGVuVzutWvXbt269ezZs46ODnNz8/fee+/999+HjnYAmCfLSYA9PT0ODg5E08eOHRNePz09fcDEYBGRU9Lu3buF1Hz06NGQl1c6Ojq//vqrBE0DoLjkcOawTDPUp59+SqSAvXv30tRKSkoKMSHG3d29v79fSE0tLS1cU1VV1cnJyd3dfezYsfgrLBbr7NmzNAUJgBySwwwlu5nDmZmZLi4uuIyXbRJxWJNYampqZs6ciccZ2NnZJScnjx8/fsiaHR0dNjY2+Ffi6+v7ww8/GBsbI4S6urpCQkL+/e9/I4TU1dWzs7MH34RKr7W1tbGxkfLT0qSnp4fFYqmqqjIdCO24XG5fXx/+ZI5CtbW1c+fO1dDQyMvLMzIy0tXVZXzmsOyuoZYsWYJbZLFY2dnZdDTR0tLy9ttv41amTZtWX18vpPKuXbtwzfnz5/f29g747rZt2/B358yZQ3mclZWVo/YzABSFpaXlKLqGevz4MdEDNX/+/MTERMqb6OjoWLhwYXp6OkLI0tLy7t27QhJ/T0+PoaFhS0sLi8V6/PgxeQYf1traamlp+fr1a4RQYWEhtZdRjY2N7u7u5AGlcq6jowMhpKmpyXQgtOvs7OTz+cS9/2jD5/NbW1tZLJaOjo6Li0tKSspouYb64osviBYjIyMpP39XVxcxsNPa2rqmpkZ4/Z9//hlXfuedd4arQ1xk7dmzh+p4AZBHctgPJaMRm7dv3ybKXl5e1J68r6/Pz8/v7t27CKEZM2YkJyePuDD533//jQs+Pj7D1SHiJAcPAJAlWYyH6u3tzcvLw2UDAwMTExMKT87lctesWfPXX38hhBwcHBISEobrGid78OABLsyaNWu4OlZWVrjw9OnTnp4eNTU1KuJFCKHXr1/PmTMH30IqhPb2doTQaLj36ezs5PF4xPPc0QZP8Ojo6Bg/fjzRpcswGVynlZeXE805OjpSeGYej7du3Tp8Znt7exEHT/X29hLxCLkf5PF4RFbKysqiLmpBVVXVaOjTAQrNyspKHu7yZHENRV6bSUmJshYFAkFAQMC1a9cQQra2tgkJCQN2VRhOa2srUdbX1x+uGpvNtrCwwLMCy8vLZ86cKXXI/2ViYtLQ0NDT00PVCenW19fHYrGEL7v8ZuByuTwebzSMqxhSdXW1nZ2dpqZmZWWlpqamjo4O0xHJ5C6PfHdAzHeRXnBw8Pnz5xFCNjY2iYmJok9SaWlpwQUVFRXh2ysQkeOHWRRSV1dXV1en9pwASAm/z1ks1rhx45iO5b9k0VNuYmJCbGrQ2NhIyUjFPXv2nD59GiE0ffr0hIQEPT090Y8lZyjhNYmrBsozFABAFLLIUFpaWngLKeybb74Z8ZDc3Fwh3z106FBYWBhCyMrKKjExUcid2pBEz1BEBdxVDACQMRmNNti0aRNRPnHihJB9DUpLS9evXy9kJfLw8HC8YeeUKVMSExMNDAzEDYbIUCN2ihEVIEMBwAgZrb6yZcuW48eP4wWburu7XVxcjhw5smbNGpxf+vr6Xr58mZiYeOvWrbi4uP7+fvI1F9nVq1dDQkJw+d1338Xd5BiPx+vp6env7x/yQCMjI2IiCzEfcLjKBKIChR38AADRyeiDp6Ghcfny5YULF+LPfHd3944dO3bs2DFhwgQlJSU8gY5cf7gxU2lpaUT51KlTogfg5OREZCjiSX9fX5/wo4gMNWoHyADALNmtAuzh4RETE6OhoUH+4uvXr+vq6sjpycjIKCws7PLly/RFQjyhIw+MGhKRwrS1temLBwAwHJmuU75kyZKnT59u3rx58HhFNTU1T0/P8+fPl5eX7969m9aMQGQoPPhFSM2mpiZcgAwFACNktz4UWU9PT2ZmZk1NTXd394QJE/T19e3t7WU2TK68vNzCwoIom5ubD1mNx+Opq6vjG73Y2NhFixbJJjwAmFJVVWVqaqqlpdXW1oYQ0tDQYHxtA2Y6gNXU1Nzd3RlpGiFkbGysoqKC7+CKi4uHy1CVlZVEP5RY460AAFRhZjcqZqmoqBD7x5SUlAxXrbS0FBdUVVVtbW1lERkA4P8ajRkKIeTs7IwLGRkZw9XJycnBBUdHR9E3OgYAUGiUZihig88//viju7t7yDrR0dG4sHz5ctlEBQAYYJRmKC8vL7zKXVNTE55+PEB6ejq+vOJwOOQB8QAAWRqlGYrD4ezevRuX9+3bRyywh3V0dGzbtg0/5Vy/fv2IK3YCAGgySjMUQigoKAg/T2xubvbx8YmJient7e3s7ExMTJw9ezaeuqyvrx8eHs5woACMYqN3uhmbzY6MjPTx8Xn+/Hl9fb2fnx+bzWaxWMQYzvHjx0dFRYm4Kh4AgA6j9xoKITRp0qSsrKxVq1bhucR8Pp9IT3PmzElLS2Nw0BYAAI3mayhMW1s7KiqqtLT0xo0bz58/5/F4FhYWixcvFrLDAgBAZkZ7hsImT54cGhrKdBQAgIFG9V0eAEDOQYYCAMgvyFAAAPkFGQoAIL8gQwEA5BdkKACA/IIMBQCQX5ChAADyCzIUAEB+QYYCAMgvyFAAAPkFGQoAIL8gQwEA5BdkKACA/IIMBQCQX5ChAADyCzIUAEB+QYYCAMgvyFAAAPkFGQoAIL8gQwEA5Jdi7/XC4/FSU1OTkpIqKipaW1v19PSMjY29vLxcXV3ZbEi+ACg8Bc5Q0dHRoaGhJSUlA76+b98+Q0PDvXv3BgQEcDgcRmIDAFBCUS80goODV61aNTg9YbW1tYGBga6urvX19TIODABAIYW8hgoNDY2IiMBlZWXl2bNnm5qadnZ2FhcXFxUVEdUyMzPd3NxSUlIMDQ0ZihQAIB2BoklOTmaxWDj4rVu3vn79mvzdgoKCpUuXkn9Ab29vPp/PVLQAKJDKykqEkJaWFn45ZswYhFB1dTWDISneXd6uXbsEAgFCaM+ePWfPntXV1SV/19ra+s6dO3v37iW+kpCQcOnSJRkHCQCgBAt/2hVFbm6uo6MjQsjS0rKwsFBZWXm4mitXrrx58yYuW1lZFRYWwtM9AISrqqoyNTXV0tJqa2tDCGloaHR1dVVXVxsZGTEVkoJ9aM+dO4cLYWFhQtITQujkyZPEg7zi4uKMjAzagwMAUE3BMlR8fDxCyNzcfOXKlcJrmpmZzZ8/n3iZkJBAb2QAABooWIaKiIhgsVi+vr6iVLazsyPK+fn5tAUFAKCLgo02WLRoUUhIyOLFi0WpbG1tTZQbGhpoCwoAQBcFy1AIocOHDxOjDYSbMGEC3cEAAGjFfIaqrKyMiooqKSl58eJFQ0ODhoaGnp7ejBkzli5d6uTkNLi+ioqKiGeuq6sjypMmTaImXACADDGZoZKSko4cOZKQkMDn8wd8KyYm5sCBAzNnzvz66689PDwkO/+jR4+I8tSpUyUPFADAEGZ6yltbWwMCAry9vePi4ganJ0J2dranp2dhYaEETfB4vNjYWFxmsVj+/v4SxgoAYA4D11DV1dXe3t7FxcXEV+bNm2dvb29ubs7lchsaGrKyslJTU3k8HkLIxsaG3OEtusjIyKqqKlxesGAB3OUBoJBkPMvmxYsXFhYWROvLly8vLCwcXK2ysjIoKIjNZoeHh0vQSm9vr5mZGW6Cw+Hk5OSIeGBaWtqUKVOysrIkaBQARSeH8/JkmqF6enocHByI9HTs2DHh9dPT0wdMDBbRsWPHiFZ2794tyiFtbW3Hjh3D3fDp6ekSNAqAopPDDCXTu7zPPvssNzcXl/fu3btr1y7h9WfNmiVBK/fv3//8889x2d3d/dChQ0NW6+rqevnyZWNjY0FBQXp6elRUFJ6LBACQH7LLUJmZmcSiTm5ubgcOHKCjlZqaGn9///7+foSQnZ1dTEyMktLQP+O1a9f+8Y9/0BGDKJqbm5ubm5lqXVzd3d0IIXV1daYDoV1fX19/f7+GhgbTgTCjtrYWIcTn88vKygwMDJgOByEkw36oJUuW4BZZLFZ2djYdTbS0tLz99tu4lWnTptXX1wup/OOPP+KabDZ79uzZISEhxP8J3Xd5FRUVo+HTDhTapEmTRtFd3uPHj//44w9c9vT0JPIIhTo6OhYvXozHQFlaWiYkJEycOFFI/blz5964cUNPT8/e3l5XV7e+vv7kyZOURzUkDQ2NyZMnV1dXy6Y56XV0dCCENDU1mQ6Edp2dnXw+X0tLi+lAmMHn81tbW1kslo6OjrW1tTwsoi2jDPXLL78Q5c2bN1N+/u7u7qVLl6anpyOErK2t4+PjR1z518rKysrKivJIRKGrq/vkyRNGmgZACLw+lKamZlNTE0JIHu52ZZShbt++TZS9vLyoPXlfX5+fn9/du3cRQjNmzIiLi9PT06O2CQBGg4kTJ1pZWU2ePBm/dHd3r6ysZHh+qwzuJHt6eojmDAwMqD15f3//8uXL8ckdHBwaGxslOw95Eh/d/VANDQ2mpqYy/kUDIJZ58+bR+ikQkSxmveAHBBi1267w+fxNmzbFxMQghOzt7ePj48ePH0/h+WnS19fX0tLCdBQACPPq1SuBHCwRLou7PPLaTMM9+5eAQCAICAi4du0aQsjW1jYhIWHArgpyy9jYuL6+Hj/CVwhcLhdR+ruTWzwej8fjib5+xhtMS0tLxGWOaCWL9xz5yUhZWRlVpw0ODj5//jxCyMbGJjExUbFWg1JTU1NTU2M6CgDknSzu8kxMTIhNDRobGxsbG6U/5549e06fPo0Qmj59ekJCAnSNA/BGkkWG0tLSwltIYd98882IhxCTY4Z06NChsLAwhJCVlVViYqK+vr7UMQIA5JGM1ofatGkTUT5x4oSQfQ1KS0vXr18vZCXy8PBwvGHnlClTEhMT5WVsPgCABjLa0bOzs3P69OnEgk3q6upHjhxZs2YNzi99fX0vX75MTEy8detWXFxcf3+/o6MjeYVMwtWrVzds2IDLO3bsMDExIb7F4/F6enrwjLzBjIyMtm3bJiTC+vp6Itmlp6dLNmkZAEAxmY1rSE5OHrwH54QJEwwMDAY/MvD19R3yJNu3b5fsx3RychIenizHQwEARCS7VYA9PDxiYmIGjKN//fp1XV2dgHQdZ2RkFBYWdvnyZZkFBgCQWzJdp3zJkiVPnz7dvHnz4Dmoampqnp6e58+fLy8v3717t7a2tiwDAwDIJxn1Qw3Q09OTmZlZU1PT3d09YcIEfX19e3t7VVVV2UdCgH4oAOQQM6OE1dTU3N3dGWkaAKBAmNmNCgAARAEZCgAgvyBDAQDkF2QoAID8ggwFAJBfb/6KP8N59erV999/T7zEmwVgP/74Y2xsLPFy7dq1TK1oDsAox8x4KHlQUFBga2srSs2YmJj33nuP7ngAAIPBXR4AQH79P4sQUkX5GLRHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=395x260 at 0x109AFE1D0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(bell+measureZI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=487x260 at 0x109B1FD68>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(bell+measureXI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=506x261 at 0x10AC76F60>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(bell+measureZZ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=623x261 at 0x10AC4CBE0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(bell+measureXX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's begin by running just the first two questions, looking at the results of the first qubit ($q_0$) using a computational and then a superposition measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CvNDpVUmSaq4jt7m+u47DLmy8pkNSWiXubzu5JklSN9BuQGTmdICI+NfMvK7rS5IkdQftPQcxODOfL+/eGRGFt7Nm5rLOLkySVFvtnUH8jtJyoABLKV1WijZ9ktIiQJKkHUh7z0Hs1mq7kjueJEnbOf/RlyQVam8M4l5Kl5C2KDOP6LSKJEndQntjENdXpQpJUrfT3hjEj6tViCSpe2nvEtOpmXlLefv0zfXLzBs6uzBJUm21d4npZOCW8vapm+mTlFaXkyTtQNq7xHRsq+3NTdYnSdoBVbImNRHRFzgO2A94EZiTmX/sisIkSbVVyXoQRwLPA18GDgO+BDwfEUd1TWmSpFqq5EG5HwBnZebhmfnpzBwHnAlc3ZGDI2JSRDwVEUsj4sKC178QEb+LiEcj4r6IGF5BbZKkTlZJQOwHzG7Tdjuwb3sHRkQdpSA5BhgOnFwQADMzc2RmjgG+C1xVQW2SpE5WSUDcApzdpu0vgZs7cOxYYGlmLsvMtcAsYErrDpn5Wqvd3nTgCW5JUtepZKqNXYAvRMT5wAqgHtgHeLADn1NPaXGhdzUDhxd83tnA14CewJGbqeks4CyAQYMGdeCjJUlbo9KpNrp0waDMvBq4OiI+A/wNcFpBn2uBawEaGxs9y5CkLlKtqTZWsPFypQPLbZszC/hhJ322JGkrVPocxD6UxhP60WrhoA5MtbEQGBoRB1IKhmnAZ9q899DMfKa8exzwDJKkmulwQETEJ4CfUPqHewSwGDgEuI92ptrIzJaIOAeYT2n1uRsyc3FEXAYsyswm4JyI+DiwDlhNweUlSVL1VHIG8U1gemb+IiJWZ+b7I2I6pbBoV2bOBea2aZvRavsrFdQiSepildzmOigzf9Gm7cfA/+jEeiRJ3UQlAfGH8hgElKbY+CDwXkqXjCRJO5hKAuI64CPl7e8BdwOPAdd0dlGSpNrr8BhEZn6n1fbNEXEP0Dszl3RFYZKk2qr0Ntc6YBx/nu67I09RS5K2Q5Xc5joK+CXQi9JUGQOBtyPik5n5WBfVJ0mqkUrGIG6gNCNrfWaOpTS/0g9wuVFJ2iFVEhDDgL/PzAQo//0PwNCuKEySVFuVBMRcYHKbthOAOZ1XjiSpu2hvuu9b+PN033XArIh4mNLU3fsDhwJ3dGmFkqSaaG+Qemmb/SdabT9JaW4lSdIOqL3pvi+tViGSpO6l0ucgxlOae6me0rTdt2Tm3V1QlySpxjo8SB0RZwA/B/4duA1YCfwsIs7sotokSTVUyRnE+cDE1g/FRcStwGy6eClSSVL1VXKb616UBqZbewrYs/PKkSR1F5UExH3AVRHxXwAiojfwd8C/dkVhkqTaqiQgvgCMAl6NiJeAPwKjgf/ZFYVJkmqrQ2MQERHAXwBHAftSns01M5u7sDZJUg11KCAyMyPid8Bu5VAwGCRpB1fJJaZHKE3YJ0naCVRym+s9wLyIuInSXEzvztFEZjrltyTtYCoJiA8DzwEfa9OeuCaEJO1w2g2I8m2tfwO8AfwW+N+ZuaarC5Mk1VZHxiCuprTuwxLgU8AVXVqRJKlb6EhATAL+W2aeDxwDHN+1JUmSuoOOBETvzFwJkJnLgT225oMiYlJEPBURSyPiwoLXvxYRT0bE4xFxZ0QcsDWfI0nqHB0ZpO4REROA2Mw+mXnXlt4gIuooXaqaSOkZioUR0ZSZred2egRozMw/RcRfAt8FTur4jyJJ6kwdCYg/sPFdSq+02U9gSDvvMRZYmpnLACJiFjCFVpP/tVlX4kHglA7UJknqIu0GRGYO7oTPqaf07MS7moHDt9D/88C/FL0QEWcBZwEMGjSoE0qTJBWp5EnqqoiIU4BGSjPFbiIzr83Mxsxs7N+/f3WLk6SdSEVLjm6DFcD+rfYHlts2EhEfBy4GPuazFpJUW9U6g1gIDI2IAyOiJzANaGrdISLeD/wImJyZf6hSXZKkzahKQGRmC3AOMJ/SA3c/z8zFEXFZREwud/s7oA/wi4h4NCKaNvN2kqQqqNYlJjJzLjC3TduMVtsfr1YtkqT2dbtBaklS92BASJIKGRCSpEIGhCSpkAEhSSpkQEiSChkQkqRCBoQkqZABIUkqZEBIkgoZEJKkQgaEJKmQASFJKmRASJIKGRCSpEIGhCSpkAEhSSpkQEiSChkQkqRCBoQkqZABIUkqZEBIkgoZEJKkQgaEJKmQASFJKmRASJIKVS0gImJSRDwVEUsj4sKC14+IiN9GREtETK1WXZKkYlUJiIioA64GjgGGAydHxPA23f4N+Bwwsxo1SZK2rEeVPmcssDQzlwFExCxgCvDkux0y8/nya+urVJMkaQuqdYmpHljear+53FaxiDgrIhZFxKJVq1Z1SnGSpE1td4PUmXltZjZmZmP//v1rXY4k7bCqFRArgP1b7Q8st0mSuqlqBcRCYGhEHBgRPYFpQFOVPluStBWqEhCZ2QKcA8wHlgA/z8zFEXFZREwGiIjDIqIZ+O/AjyJicTVqkyQVq9ZdTGTmXGBum7YZrbYXUrr0JEnqBra7QWpJUnUYEJKkQgaEJKmQASFJKmRASJIKGRCSpEIGhCSpkAEhSSpkQEiSChkQkqRCBoQkqZABIUkqZEBIkgoZEJKkQgaEJKmQASFJKmRASJIKGRCSpEIGhCSpkAEhSSpkQEiSChkQkqRCBoQkqZABIUkqZEBIkgoZEJKkQlULiIiYFBFPRcTSiLiw4PX3RMSt5dd/ExGDq1WbJGlTVQmIiKgDrgaOAYYDJ0fE8DbdPg+szsyDgO8B36lGbZKkYtU6gxgLLM3MZZm5FpgFTGnTZwrw4/L2PwFHRURUqT5JUhs9qvQ59cDyVvvNwOGb65OZLRHxKrAX8HLrThFxFnBWefeNiHiqSyquvX60+dm7i/irW2tdglQN3fY7CNv8PTygI52qFRCdJjOvBa6tdR1dLSIWZWZjreuQdlZ+B6t3iWkFsH+r/YHltsI+EdED2AN4pSrVSZI2Ua2AWAgMjYgDI6InMA1oatOnCTitvD0VuCszs0r1SZLaqMolpvKYwjnAfKAOuCEzF0fEZcCizGwC/hG4JSKWAv9BKUR2Zjv8ZTSpm9vpv4Phf9IlSUV8klqSVMiAkCQVMiAkSYUMCElSIQOim3h3WhGnF5HUXRgQ3URmZkT08dkPSd2Ft7l2AxHRAJwAnETpCfK5wBzgvsx8s5a1SfqziKjLzHdqXUe1GBDdQETcA7wE3ArsRulJ8kOBfwdmZOY/R0R4diF1nYj4e0qT8/0kM59v1b5LZq6vWWE1ZEDUWETsDSzLzD5t2ncHzqP0RPn0zLy/FvVJO4OI2AdYCSwDDgQeAq4HbsvM1eU+M4FfZObtNSu0yhyDqL1ewMKIOL51Y2a+lpkzKK2NcWZE7FqT6qSdw5HAr4BhlKbCvgf4BvBiRNweEZMp/WftiZpVWAMGRO0tB+4Hvh4RX4yIERHxF61eXwwMz8x1tSlP2iksBG4G+mVmc2ZelJn7ARMoXf79JXB/Zj5TyyKrbbtbD2JHU7576evAeuAI4H3Ayoh4i9KA9bHAT2pYorTDy8ylEbEM6Nmm/UHgwYhopLQS5k7FMYgaiohhlFbH24PS2dx7gfdQWnHvZWAEcA2l6547zZ0TUjVFxMHAGUB/St/DVcA84Nfl/8DtVW7bPTPfqF2l1WdA1FBELAHuBV4DVgP/ldKiSWuAazPzvhqWJ+0UWn0P/wi8CgwGhgDPA1eVlybolZlv16zIGjEgaiQijgauzsyDyvs9KK3LfShwHKWg+Fxmvli7KqUdW8H3sA4YAHwAOJHSd3J6ZjbXrsracZC6dnoDL0XE/lBaVCkzX8jM24BLgASOrmWB0k6g7ffwnfIgdRPw15TGBifWssBaMiBq53ZKD8L9n4gY0vqF8lnDs8C4WhQm7UT8Hm6BAVEj5aei/5rSnWSPRMS9EfGViBhZXp51MnBjTYuUdnB+D7fMMYhuICI+AEyhdM1zAHAXMC8zb6hpYdJOxO/hpgyIbqb8kFzPzHy11rVIOyu/hyUGhCSpkGMQkqRCBoQkqZABIUkqZEBIkgoZEJKkQgaEJKnQfwKcgT3e5pe+8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac36c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q_program.add_circuit(\"bell_measureIZ\", bell+measureIZ )\n",
    "Q_program.add_circuit(\"bell_measureIX\", bell+measureIX )\n",
    "Q_program.add_circuit(\"bell_measureZI\", bell+measureZI )\n",
    "Q_program.add_circuit(\"bell_measureXI\", bell+measureXI )\n",
    "Q_program.add_circuit(\"bell_measureZZ\", bell+measureZZ )\n",
    "Q_program.add_circuit(\"bell_measureXX\", bell+measureXX )\n",
    "\n",
    "circuits = [\"bell_measureIZ\", \"bell_measureIX\", \"bell_measureZI\", \"bell_measureXI\", \"bell_measureZZ\", \"bell_measureXX\"]\n",
    "result = Q_program.execute(circuits[0:2], backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)\n",
    "plot_histogram(result.get_counts(\"bell_measureIZ\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'counts': {'00': 495, '01': 529}}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.get_data(\"bell_measureIZ\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that the result is random. Half the time $q_0$ is in  $|0\\rangle$, and the other half it is in the $|1\\rangle$ state. You may wonder whether this is like the superposition from earlier in the tutorial. Maybe the qubit has a perfectly definite state, and we are simply measuring in another basis.  What would you expect if you did the experiment and measured in the superposition basis? Recall we do this by adding an $H$ gate before the measurement...which is exactly what we have checked with the second question."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109b236d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_histogram(result.get_counts(\"bell_measureIX\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, we see that the result is still random, regardless of whether we measure in the computational or the superposition basis. This tells us that we actually know nothing about the first qubit. What about the second qubit, $q_1$? The next lines will run experiments measuring the second qubit in both the computational and superposition bases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b05d7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ae65828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = Q_program.execute(circuits[2:4], backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)\n",
    "plot_histogram(result.get_counts(\"bell_measureZI\"))\n",
    "plot_histogram(result.get_counts(\"bell_measureXI\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, all the experiments give random outcomes. It seems we know nothing about either qubit in our system! In our previous analogy, this is equivalent to two readers separately reading a quantum paper and extracting no information whatsoever from it on their own.\n",
    "\n",
    "What do you expect, however, when the readers get together?  Below we will measure both in the joint computational basis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = Q_program.execute(circuits[4:6], backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aff6780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_histogram(result.get_counts(\"bell_measureZZ\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that with high probability, if $q_0$ is in state 0, $q_1$ will be in 0 as well; the same goes if $q_0$ is in state 1. They are perfectly correlated.\n",
    "\n",
    "What about if we measure both in the superposition basis?  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ae5bcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_histogram(result.get_counts(\"bell_measureXX\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that the system **also** has perfect correlations (accounting for experimental noise). Therefore, if $q_0$ is measured in state $|0\\rangle$, we know $q_1$ is in this state as well; likewise, if $q_0$ is measured in state $|+\\rangle$, we know $q_1$ is also in this state. These correlations have led to much confusion in science, because any attempt to relate the unusual behavior of quantum entanglement to our everyday experiences is a fruitless endeavor. \n",
    "\n",
    "Finally, we need to point out that having correlated outcomes does not necessarily imply that what we are observing is an entangled state. What would we observe, for example, if we prepared half of our shots in the $|00\\rangle$ state and half of the shots in the $|11\\rangle$ state? Let's have a look"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=290x261 at 0x109B0ED68>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# quantum circuit to make a mixed state \n",
    "mixed1 = QuantumCircuit(q2, c2)\n",
    "mixed2 = QuantumCircuit(q2, c2)\n",
    "mixed2.x(q2)\n",
    "mixed1.measure(q2[0], c2[0])\n",
    "mixed1.measure(q2[1], c2[1])\n",
    "mixed2.measure(q2[0], c2[0])\n",
    "mixed2.measure(q2[1], c2[1])\n",
    "\n",
    "circuit_drawer(mixed1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=467x261 at 0x10AF706D8>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(mixed2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ae41c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mixed_state = [\"mixed1\", \"mixed2\"]\n",
    "Q_program.add_circuit(\"mixed1\", mixed1 )\n",
    "Q_program.add_circuit(\"mixed2\", mixed2 )\n",
    "result = Q_program.execute(mixed_state, backend=backend, shots=shots, max_credits=3, wait=10, timeout=240)\n",
    "counts1 = result.get_counts(mixed_state[0])\n",
    "counts2 = result.get_counts(mixed_state[1])\n",
    "from collections import Counter\n",
    "ground = Counter(counts1)\n",
    "excited = Counter(counts2)\n",
    "plot_histogram(ground+excited)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do see the same kind of correlation indeed as we observed in the \"bell_measureZZ\" circuit. But we know this is not an entangled state! All we have done is leave the qubits in their ground state for some of the shots and flip both qubits for some of the shots. This is called a mixed state and it is a classical state. Now, would we observe a similar outcome if we measured this mixed state in the superposition basis? We will leave this for the reader to try.\n",
    "\n",
    "This is just a taste of what happens in the quantum world. Please continue to [Entanglement revisited](entanglement_revisited.ipynb) to explore further!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h2>Version information</h2>\n",
       "<p>Please note that this tutorial is targeted to the <b>stable</b> version of the QISKit. The following versions of the packages are recommended:</p>\n",
       "<table>\n",
       "<tr><th>Package</th><th colspan=\"2\">Version</th></tr>\n",
       "<tr><td>QISKit</td><td> 0.4.10</td></tr>\n",
       "<tr><td>IBMQuantumExperience</td><td>&gt;= 1.8.26</td></tr>\n",
       "<tr><td>numpy</td><td>&gt;= 1.13, &lt; 1.14</td></tr>\n",
       "<tr><td>scipy</td><td>&gt;= 0.19, &lt; 0.20</td></tr>\n",
       "<tr><td>matplotlib</td><td>&gt;= 2.0, &lt; 2.1</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run \"../../version.ipynb\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}