week2_en.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Week2: Grover's Algorithm\n",
    "*(This tutorial partially refers to [Grover's algorithm and its Qiskit implementation](https://quantum-computing.ibm.com/support/guides/quantum-algorithms-with-qiskit?page=5cc0d9fd86b50d00642353ca#) under Quantum Algorithms with Qiskit in IBM Q Exprience. The last section \"Qiskit implementation\" was added for this specific challenge.)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Welcome to week 2 !** <br/><br/>\n",
    "For this week, let us learn about a well-known quantum algorithm called Grover's algorithm. <br/> Also, **there is a learning challenge exercise for you to tackle on your own at the end of this tutorial.** <br/>\n",
    "\n",
    "So let's get started.<br/><br/>\n",
    "You may have heard that one of the advantages a quantum computer has over a classical computer is its superior speed searching databases.<br/>\n",
    "Grover's algorithm demonstrates this capability. This algorithm can speed up an unstructured search problem quadratically, but its uses extend beyond that; it can serve as a general trick or subroutine to obtain quadratic run time improvements for a variety of other algorithms. This is called the amplitude amplification trick.\n",
    "\n",
    "This page will walk you through the description of the search problem, building the oracle - the circuit representation of our search problem, and implementing the complete Grover algorithm in Qiskit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unstructured search\n",
    "Suppose you are given a large list of N items. Among these items there is one item with a unique property that we wish to locate; we will call this one the winner w. Think of each item in the list as a box of a particular item. Say all items in the list have grey colored items except the winning item w."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"./fig/unstructured_search.png\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the winning item -- the marked item -- using classical computation, one would have to check on average $N/2$ of these boxes, and in the worst case, all $N$ of them. On a quantum computer, however, we can find the marked item in roughly $\\sqrt{N}$ steps with Grover's amplitude amplification trick. A quadratic speedup is indeed a substantial time-saver for finding marked items in long lists. Additionally, the algorithm does not use the list's internal structure, which makes it generic; this is why it immediately provides a quadratic quantum speed-up for many classical problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating an Oracle that marks the winning item\n",
    "How will the list items be provided to the quantum computer? A common way to encode such a list is in terms of a function 𝑓 that returns $f(x)=0$ for all unmarked items $x$, and $f(w)=1$ for the winner. To use a quantum computer for this problem, we must provide the items in superposition to this function, so we encode the function into a unitary matrix called an **oracle**. First we choose a binary encoding of the items $x,w \\in \\{0,1\\}^n$ so that $N=2^n$. This way, we can represent it in terms of qubits on a quantum computer. We then define the oracle matrix $U_w$ to act on any of the simple, standard basis states $|x>$ by $U_w |x> = (-1)^{f(x)}|x>$\n",
    "\n",
    "We see that if $x$ is an unmarked item, the oracle does nothing to the state. However, when we apply the oracle to the basis state $|w>$, it maps $U_w |w> = -|w>$. Geometrically, this unitary matrix corresponds to a reflection about the origin for the marked item in an $N=2^n$-dimensional vector space.\n",
    "\n",
    "<img src=\"./fig/oracle.png\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Amplitude amplification\n",
    "So how does the algorithm work? Before looking at the list of items, we have no idea where the marked item is. Therefore, any guess of its location is as good as any other. You may have heard the term superposition This can be expressed in terms of a uniform superposition: <br/>\n",
    "$$|s> = \\frac{1}{\\sqrt N}\\sum_{x=0}^{N-1} |x> $$\n",
    "\n",
    "If at this point we were to measure in the standard basis $|x>$, this superposition would collapse to any one of the basis states with the same probability of $\\frac{1}{N} = \\frac{1}{2^{n}} $. Our chances of guessing the right value $|w>$ is therefore $\\frac{1}{2^{n}}$, as could be expected. Hence, on average we would need to try about $N=2^{n}$ times to guess the correct item."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's enter the procedure called amplitude amplification, which is how a quantum computer significantly enhances this probability. This procedure stretches out (amplifies) the amplitude of the marked item, which shrinks the other items' amplitude, so that measuring the final state will return the right item with near-certainty.\n",
    "\n",
    "This algorithm has a nice geometrical interpretation in terms of two reflections, which generate a rotation in a two-dimensional plane. The only two special states we need to consider are the winner $|w>$ and the uniform superposition $|s>$ . These two vectors span a two-dimensional plane in the vector space $\\mathbb C^{N}$ . They are not quite perpendicular because $|w>$ occurs in the superposition with amplitude $N^{-1/2}$ as well.\n",
    "\n",
    "We can, however, introduce an additional state $|s'>$ that is in the span of these two vectors, which is perpendicular to $|w>$ and is obtained from $|s>$ by removing $|w>$ and rescaling.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 0** :\n",
    "The amplitude amplification procedure starts out in the uniform superposition $|s>$ .  (The uniform superposition is easily constructed from $|s> = H^{\\otimes n}|0>^{n}$ At $t=0$ the initial state is $|\\psi_{0}> = |s>$.\n",
    "\n",
    "<img src=\"./fig/step0.png\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step1** :\n",
    "We apply the oracle reflection $U_{w}$ to the state $U_{w}|\\psi_{t}> = |\\psi_{t'}>$.\n",
    "<img src=\"./fig/step1.png\" width=\"700\">\n",
    "Geometrically, this corresponds to a reflection of the state $|\\psi_{t}>$ about  $|s'>$ . This transformation means that the amplitude in front of the $|w>$ state becomes negative, which in turn means that the average amplitude has been lowered. (Note how the dotted line in the right graph is tapering).\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step2**:\n",
    "We now apply an additional reflection $U_{s}$ about the state $|s>$: $U_{s} = 2|s> <s| - 1 $ . This transformation maps the state to $U_{s}|\\psi_{t'}>$ and completes the transformation $|\\psi_{t+1}> = U_{s}U_{w}|\\psi_{t}>$ .（Note how the amplitude at $|w>$ is amplified in the right graph).\n",
    "<img src=\"./fig/step2.png\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two reflections always correspond to a rotation. The transformation $ U_{s}U_{w}$ rotates the initial state $|s>$ closer towards the winner $|w>$ . (Please pay attention to left graph in Step 2. The action of the reflection $U_{s}$ in the amplitude bar diagram can be understood as a reflection about the average amplitude. Since the average amplitude has been lowered by the first reflection, this transformation boosts the negative amplitude of $|w>$ to roughly three times its original value, while it decreases the other amplitudes. We then go to **Step １** to repeat the application. This procedure will be repeated several times to zero in on the winner. \n",
    "\n",
    "After $t$ steps the state will have transformed to $|\\psi_{t}> = (U_{s}U_{w})^{t}|\\psi_{0}>$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many times do we need to apply the rotation? It turns out that roughly $\\sqrt N$ rotations suffice. This becomes clear when looking at the amplitudes of the state $|\\psi_{t}>$ . We can see that the amplitude of $|w>$ grows linearly with the number of applications（$ \\sim tN^{1/2}$）. However, since we are dealing with amplitudes and not probabilities, the vector space's dimension enters as a square root. Therefore it is the amplitude, and not just the probability, that is being amplified in this procedure.\n",
    "\n",
    "In the case that there are multiple solutions, $M$ it can be shown that roughly $\\sqrt{(N/M)}$ rotations will suffice.\n",
    "<img src=\"./fig/grover_algorithm.png\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Qiskit implementation: Grover's algorithm using 2 qubits\n",
    "Now, let's impement Grover's algorithm using Qiskit. In this example, we will use two qubits to find the state |11⟩.\n",
    "\n",
    "First we prepare our environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialization\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, BasicAer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we have seen in Step1, let us create a phase oracle to mark the state |11⟩."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 227.556x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def phase_oracle(circuit, register):\n",
    "    circuit.cz(register[0], register[1])\n",
    "\n",
    "qr = QuantumRegister(2)\n",
    "oracleCircuit = QuantumCircuit(qr)\n",
    "phase_oracle(oracleCircuit, qr)\n",
    "oracleCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we set up the circuit for inversion about the average as we saw in step 2. This circuit is sometimes called an amplitude ampification module or a diffusion circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inversion_about_average(circuit, register):\n",
    "    \"\"\"Apply inversion about the average step of Grover's algorithm.\"\"\"\n",
    "    circuit.h(register)\n",
    "    circuit.x(register)\n",
    "    circuit.h(register[1])\n",
    "    circuit.cx(register[0], register[1])\n",
    "    circuit.h(register[1])\n",
    "    circuit.x(register)\n",
    "    circuit.h(register)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 588.756x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qAverage = QuantumCircuit(qr)\n",
    "inversion_about_average(qAverage, qr)\n",
    "qAverage.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we put the pieces together, with the creation of a uniform superposition at the start of the circuit and a measurement at the end. Note that since there is one solution and four possibilities, we will only need to run one iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 829.556x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(2)\n",
    "cr = ClassicalRegister(2)\n",
    "\n",
    "groverCircuit = QuantumCircuit(qr,cr)\n",
    "groverCircuit.h(qr)\n",
    "\n",
    "phase_oracle(groverCircuit, qr)\n",
    "inversion_about_average(groverCircuit, qr)\n",
    "\n",
    "groverCircuit.measure(qr,cr)\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment with Simulators\n",
    "We now run the above circuit on the simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(groverCircuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the algorithm discovers our marked states."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment with Real Devices\n",
    "We can run the circuit on the real device as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Applications/anaconda3/lib/python3.7/site-packages/qiskit/providers/ibmq/ibmqfactory.py:181: UserWarning: Credentials are already in use. The existing account in the session will be replaced.\n",
      "  warnings.warn('Credentials are already in use. The existing '\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Least busy backend:  ibmq_16_melbourne\n"
     ]
    }
   ],
   "source": [
    "# Load our saved IBMQ accounts and get the least busy backend device\n",
    "\n",
    "# These are compatible with QisKit v0.11.x\n",
    "# IBMQ.load_accounts()\n",
    "# IBMQ.backends()\n",
    "# backend_lb = least_busy(IBMQ.backends(simulator=False))\n",
    "# print(\"Least busy backend: \", backend_lb)\n",
    "\n",
    "# Updated to run on QisKit v0.12.0\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(group='open')\n",
    "backend_lb = least_busy(provider.backends(simulator=False, operational=True))\n",
    "print(\"Least busy backend: \", backend_lb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "\n",
    "backend = backend_lb\n",
    "shots = 1024\n",
    "job_exp = execute(groverCircuit, backend=backend, shots=shots)\n",
    "\n",
    "job_monitor(job_exp, interval = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the results from the computation\n",
    "results = job_exp.result()\n",
    "answer = results.get_counts(groverCircuit)\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Qiskit implementation: 2 qubit Grover's algorithm using ancilla bits\n",
    "We are going to find the state $|11>$ just like in the previous example but this time using an ancilla bit. Ancilla bits bits will allow you to deal with sutations when more qubits are required or implement more complex oracles.\n",
    "\n",
    "Let us prepare the environment first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialization\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "# Importing Qiskit\n",
    "from qiskit import IBMQ, BasicAer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "\n",
    "# Import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will create an oracle that will flip the phase of the answer (in this case $|11>$ ) we are looking for. This time, using the ancilla bit to make the target bit's phase flip when the input state is $|11>$ . Please note that in order to make this phase flip work, you need to prepare the ancilla bit to be $|1>$ by using an x gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 408.156x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def phase_oracle(circuit, register,oracle_register):\n",
    "    circuit.h(oracle_register)\n",
    "    circuit.ccx(register[0], register[1],oracle_register)\n",
    "    circuit.h(oracle_register)\n",
    "    \n",
    "qr = QuantumRegister(3)\n",
    "oracleCircuit = QuantumCircuit(qr)\n",
    "oracleCircuit.x(qr[2])\n",
    "phase_oracle(oracleCircuit, qr,qr[2])\n",
    "oracleCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we prepare the amplitude amplification module/diffusion circuit. Make sure that the circuit does not act on the ancilla bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inversion_about_average(circuit, register):\n",
    "    \"\"\"Apply inversion about the average step of Grover's algorithm.\"\"\"\n",
    "    circuit.h(register)\n",
    "    circuit.x(register)\n",
    "    circuit.h(register[1])\n",
    "    circuit.cx(register[0], register[1])\n",
    "    circuit.h(register[1])\n",
    "    circuit.x(register)\n",
    "    circuit.h(register)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 588.756x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qAverage = QuantumCircuit(qr)\n",
    "inversion_about_average(qAverage, qr[0:2])\n",
    "qAverage.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like we did in the previous example without using the ancilla bit, here we first create a uniform superposition by using the hadamard (H gate) , incorporate the transformation and then take measurement. Again, please make sure that you do not apply the H gate to your ancilla bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 889.756x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(3)\n",
    "cr = ClassicalRegister(3)\n",
    "\n",
    "groverCircuit = QuantumCircuit(qr,cr)\n",
    "groverCircuit.h(qr[0:2])\n",
    "groverCircuit.x(qr[2])\n",
    "\n",
    "phase_oracle(groverCircuit, qr,qr[2])\n",
    "inversion_about_average(groverCircuit, qr[0:2])\n",
    "\n",
    "groverCircuit.measure(qr,cr)\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment with Simulators\n",
    "We now run this circuit on a simulator. Make sure to specify 'qasm_simulator' as your backend. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(groverCircuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see how the state $|11>$ is being amplified just like we saw previously without using the ancilla bit. You can ignore the 1 in the highest order as that comes from the ancilla bit. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Challenge Exercise II\n",
    "\n",
    "Implement Grover's algorithm with 2 qubits to find the answer $|10>$.\n",
    "In doing so, try two different approaches. One without using the ancilla bit and the other with an ancilla bit. *Please note that the higher order number shown in the states correspond to the higher quantum register index.* \n",
    "\n",
    "**Expected Outputs:**<br/>\n",
    "(1)For the **with the ancilla bit approach only**, based on the simulator result, please submit the quantum state (bit string) with the highest probability.<br/> \n",
    "(2)Use the unroller to calculate the quantum costs of your circuit.  <br/>\n",
    "\n",
    "For details on how to use an unroller. Please check out [How to Calculate Quantum Costs](https://github.com/quantum-challenge/2019/blob/master/problems/how_to_calculate_quantum_cost_en.ipynb).\n",
    "\n",
    "**For Submission:**<br/>\n",
    "For submission, create a text file (.txt) showing the above output (1) in first line and (2) in the second line.<br/>\n",
    "For generating (2) you may use the following sample code to output the elementary gate counts (i.e. {“u3”: 20, “cx”: 10}), which is in dictionary format.  After generating the file you can copy paste the answer of (1) in the first line of the file and then [submit](https://angelhack.typeform.com/to/AakobE). \n",
    "\n",
    "```sample_output.py\n",
    "import json\n",
    "dct = qc.count_ops()\n",
    "with open('wk2_output.txt', 'w') as f:\n",
    "    f.write(json.dumps(dct))\n",
    "```\n",
    "\n",
    "Example output:<br/>\n",
    "0000 <br/>\n",
    "{\"u3\": 20, \"cx\": 10}<br/>\n",
    "\n",
    "**Use this [Submission Form](https://angelhack.typeform.com/to/AakobE) to submit your code for learning challenges 1-3.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example Answer\n",
    "## Without an ancilla bit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialization\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, BasicAer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create an Oracle to inverse the sign of $|10>$ state. The oracle can be created by combining CZ gates and X gates. Verify that the oracle inverses only the sign of $|10>$ state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 347.956x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def phase_oracle(circuit, register):\n",
    "    circuit.x(register[0])\n",
    "    circuit.cz(register[0], register[1])\n",
    "    circuit.x(register[0])\n",
    "\n",
    "qr = QuantumRegister(2)\n",
    "oracleCircuit = QuantumCircuit(qr)\n",
    "phase_oracle(oracleCircuit, qr)\n",
    "oracleCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inversion_about_average(circuit, register):\n",
    "    \"\"\"Apply inversion about the average step of Grover's algorithm.\"\"\"\n",
    "    circuit.h(register)\n",
    "    circuit.x(register)\n",
    "    circuit.h(register[1])\n",
    "    circuit.cx(register[0], register[1])\n",
    "    circuit.h(register[1])\n",
    "    circuit.x(register)\n",
    "    circuit.h(register)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 889.756x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(2)\n",
    "cr = ClassicalRegister(2)\n",
    "\n",
    "groverCircuit = QuantumCircuit(qr,cr)\n",
    "groverCircuit.h(qr)\n",
    "\n",
    "phase_oracle(groverCircuit, qr)\n",
    "inversion_about_average(groverCircuit, qr)\n",
    "\n",
    "groverCircuit.measure(qr,cr)\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(groverCircuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## With an ancilla bit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialization\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, BasicAer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 408.156x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def phase_oracle(circuit, register,oracle_register):\n",
    "    circuit.h(oracle_register)\n",
    "    circuit.x(register[0])\n",
    "    circuit.ccx(register[0], register[1],oracle_register)\n",
    "    circuit.x(register[0])\n",
    "    circuit.h(oracle_register)\n",
    "\n",
    "qr = QuantumRegister(3)\n",
    "oracleCircuit = QuantumCircuit(qr)\n",
    "oracleCircuit.x(qr[2])\n",
    "phase_oracle(oracleCircuit, qr,qr[2])\n",
    "oracleCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inversion_about_average(circuit, register):\n",
    "    \"\"\"Apply inversion about the average step of Grover's algorithm.\"\"\"\n",
    "    circuit.h(register)\n",
    "    circuit.x(register)\n",
    "    circuit.h(register[1])\n",
    "    circuit.cx(register[0], register[1])\n",
    "    circuit.h(register[1])\n",
    "    circuit.x(register)\n",
    "    circuit.h(register)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 889.756x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(3)\n",
    "cr = ClassicalRegister(3)\n",
    "\n",
    "groverCircuit = QuantumCircuit(qr,cr)\n",
    "groverCircuit.h(qr[0:2])\n",
    "groverCircuit.x(qr[2])\n",
    "\n",
    "phase_oracle(groverCircuit, qr,qr[2])\n",
    "inversion_about_average(groverCircuit, qr[0:2])\n",
    "\n",
    "groverCircuit.measure(qr,cr)\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(groverCircuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|10> is being amplified just like we saw previously without using the ancilla bit. (You can ignore the highest order bit as it is an ancilla bit.)"
   ]
  }
 ],
 "metadata": {
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}