community/algorithms/bernstein_vazirani.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "<img src=\"../../images/qiskit-heading.gif\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"500 px\" align=\"left\">"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*The Bernstein-Vazirani Algorithm*_ \n",
    "\n",
    "In this tutorial, we introduce the [Bernstein-Vazirani algorithm](http://epubs.siam.org/doi/abs/10.1137/S0097539796300921), which is one of the earliest algorithms demonstrating the power of quantum computing. Despite its simplicity, it is often used and is the inspiration for many other quantum algorithms even today; it is the basis of the power of the short-depth quantum circuits, as in [Bravyi et al.](https://arxiv.org/abs/1704.00690) that uses its non-oracular version, or in [Linke et al.](http://www.pnas.org/content/114/13/3305.full) that uses it to test the performance of the quantum processors (see also the [talk by Ken Brown](https://www.youtube.com/watch?v=eHV9LTiePrQ) at the ThinkQ 2017 conference). Here, we show the implementation of the Bernstein-Vazirani algorithm **without using entanglement** based on [Du et al.](https://arxiv.org/abs/quant-ph/0012114) on Qiskit and test it on IBM Q systems. \n",
    "\n",
    "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Rudy Raymond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction <a id='introduction'></a>\n",
    "\n",
    "The Bernstein-Vazirani algorithm deals with finding a hidden integer $a \\in \\{0,1\\}^n$ from an oracle $f_a$ that returns a bit $a \\cdot x \\equiv \\sum_i a_i x_i \\mod 2$ upon receiving an input $x \\in \\{0,1\\}^n$. A classical oracle returns $f_a(x) = a \\cdot x \\mod 2$ given an input $x$. Meanwhile, a quantum oracle behaves similarly but can be queried with superposition of input $x$'s. \n",
    "\n",
    "Classically, the hidden integer $a$ can be revealed by querying the oracle with $x = 1, 2, \\ldots, 2^i, \\ldots, 2^{n-1}$, where each query reveals the $i$-th bit of $a$ (or, $a_i$). For example, with $x=1$ one can obtain the least significant bit of $a$, and so on. This turns out to be an optimal strategy; any classical algorithm that finds the hidden integer with high probability must query the oracle $\\Omega(n)$ times. However, given a corresponding quantum oracle, the hidden integer can be found with only $1$ query using the Bernstein-Vazirani algorithm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Algorithm\n",
    "\n",
    "The Bernstein-Vazirani algorithm to find the hidden integer is very simple: start from a $|0\\rangle$ state, apply Hadamard gates, query the oracle, apply Hadamard gates, and measure. The correctness of the algorithm is best explained by looking at the transformation of a quantum register $|a \\rangle$ by $n$ Hadamard gates, each applied to the qubit of the register. It can be shown that\n",
    "\n",
    "$$\n",
    "|a\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle.\n",
    "$$\n",
    "\n",
    "In particular, when we start with a quantum register $|0\\rangle$ and apply $n$ Hadamard gates to it, we have the familiar quantum superposition as below\n",
    "\n",
    "$$\n",
    "|0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} |x\\rangle,\n",
    "$$\n",
    "\n",
    "which is slightly different from the Hadamard transform of the reqister $|a \\rangle$ by the phase $(-1)^{a\\cdot x}$. \n",
    "\n",
    "Now, the quantum oracle $f_a$ returns $1$ on input $x$ such that $a \\cdot x \\equiv 1 \\mod 2$, and returns $0$ otherwise. This means we have the following transformation:\n",
    "\n",
    "$$\n",
    "|x \\rangle \\left(|0\\rangle - |1\\rangle \\right) \\xrightarrow{f_a} | x \\rangle \\left(|0 \\oplus f_a(x) \\rangle - |1 \\oplus f_a(x) \\rangle \\right) = (-1)^{a\\cdot x} |x \\rangle \\left(|0\\rangle - |1\\rangle \\right). \n",
    "$$\n",
    "\n",
    "Notice that the second register $|0\\rangle - |1\\rangle$ in the above does not change and can be omitted for simplicity. In short, the oracle can be used to create $(-1)^{a\\cdot x}|x\\rangle$ from the input $|x \\rangle$. In this tutorial, we follow [Du et al.](https://arxiv.org/abs/quant-ph/0012114) to generate a circuit for a quantum oracle without the need of an ancilla qubit (often used in the standard quantum oracle). \n",
    "\n",
    "The algorithm to reveal the hidden integer follows naturally by querying the quantum oracle $f_a$ with the quantum superposition obtained from the Hadamard transformation of $|0\\rangle$. Namely,\n",
    "\n",
    "$$\n",
    "|0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} |x\\rangle \\xrightarrow{f_a} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle.\n",
    "$$\n",
    "\n",
    "Because the inverse of the $n$ Hadamard gates is again the $n$ Hadamard gates, we can obtain $a$ by\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle \\xrightarrow{H^{\\otimes n}} |a\\rangle.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The (Inner-Product) Oracle <a id='oracle'></a>\n",
    "\n",
    "Here, we describe how to build the oracle used in the Bernstein-Vazirani algorithm. The oracle is also referred to as the [inner-product oracle](https://arxiv.org/pdf/quant-ph/0108095.pdf) (while the oracle of the Grover search is known as the Equivalence, or EQ, oracle). Notice that it transforms $|x\\rangle$ into $(-1)^{a\\cdot x} |x\\rangle$. Clearly, we can observe that\n",
    "\n",
    "$$\n",
    "(-1)^{a\\cdot x} = (-1)^{a_1 x_1} \\ldots (-1)^{a_ix_i} \\ldots (-1)^{a_nx_n} = \\prod_{i: a_i = 1} (-1)^{x_i}. \n",
    "$$\n",
    "\n",
    "Therefore, the inner-product oracle can be realized by the following unitary transformation, which is decomposable as single-qubit unitaries: \n",
    "\n",
    "$$\n",
    "O_{f_a} = O^1 \\otimes O^2 \\otimes \\ldots \\otimes O^i \\otimes \\ldots \\otimes O^n, \n",
    "$$\n",
    "where $O^i = (1 - a_i)I + a_i Z$, where $Z$ is the Pauli $Z$ matrix and $I$ is the identity matrix for $a_i \\in \\{0,1\\}$. \n",
    "\n",
    "Notice that we start from a separable quantum state $|0\\rangle$ and apply a series of transformations that are separable (i.e., can be described by unitaries acting on a single qubit): Hadamard gates to each qubit, followed by the call to the *decomposable* quantum oracle as [Du et al.](https://arxiv.org/abs/quant-ph/0012114), and another Hadamard gate. Hence, there is no entanglement created during the computation. This is in contrast with the circuit at [Linke et al.](http://www.pnas.org/content/114/13/3305.full) that used CNOT gates to realize the oracle and an ancilla qubit to store the answer of the oracle. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Circuit <a id=\"circuit\"></a>\n",
    "\n",
    "We now implement the Bernstein-Vazirani algorithm with Qiskit by first preparing the environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:43.600800Z",
     "start_time": "2018-09-26T15:37:42.133475Z"
    }
   },
   "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 import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:44.514394Z",
     "start_time": "2018-09-26T15:37:43.603203Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load our saved IBMQ accounts.\n",
    "IBMQ.load_accounts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first set the number of qubits used in the experiment, and the hidden integer $a$ to be found by the Bernstein-Vazirani algorithm. The hidden integer $a$ determines the circuit for the quantum oracle. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:45.913084Z",
     "start_time": "2018-09-26T15:37:45.909662Z"
    }
   },
   "outputs": [],
   "source": [
    "nQubits = 14 # number of physical qubits\n",
    "a = 101      # the hidden integer whose bitstring is 1100101\n",
    "\n",
    "# make sure that a can be represented with nQubits\n",
    "a = a % 2**(nQubits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then use Qiskit to program the Bernstein-Vazirani algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:47.277053Z",
     "start_time": "2018-09-26T15:37:47.265832Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0xa12d894e0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating registers\n",
    "# qubits for querying the oracle and finding the hidden integer\n",
    "qr = QuantumRegister(nQubits)\n",
    "# for recording the measurement on qr\n",
    "cr = ClassicalRegister(nQubits)\n",
    "\n",
    "circuitName = \"BernsteinVazirani\"\n",
    "bvCircuit = QuantumCircuit(qr, cr)\n",
    "\n",
    "# Apply Hadamard gates before querying the oracle\n",
    "for i in range(nQubits):\n",
    "    bvCircuit.h(qr[i])\n",
    "    \n",
    "# Apply barrier so that it is not optimized by the compiler\n",
    "bvCircuit.barrier()\n",
    "\n",
    "# Apply the inner-product oracle\n",
    "for i in range(nQubits):\n",
    "    if (a & (1 << i)):\n",
    "        bvCircuit.z(qr[i])\n",
    "    else:\n",
    "        bvCircuit.iden(qr[i])\n",
    "        \n",
    "# Apply barrier \n",
    "bvCircuit.barrier()\n",
    "\n",
    "#Apply Hadamard gates after querying the oracle\n",
    "for i in range(nQubits):\n",
    "    bvCircuit.h(qr[i])\n",
    "    \n",
    "# Measurement\n",
    "bvCircuit.barrier(qr)\n",
    "bvCircuit.measure(qr, cr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:53.798709Z",
     "start_time": "2018-09-26T15:37:49.368851Z"
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   "outputs": [
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa12d725f8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bvCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment with Simulators\n",
    "\n",
    "We can run the above circuit on the simulator. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:38:02.785014Z",
     "start_time": "2018-09-26T15:38:02.562010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa18d07940>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use local simulator\n",
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "shots = 1000\n",
    "results = execute(bvCircuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the result of the measurement is the binary representation of the hidden integer $a$. \n",
    "\n",
    "## Experiment with Real Devices\n",
    "\n",
    "We can run the circuit on the real device as below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:38:07.311126Z",
     "start_time": "2018-09-26T15:38:07.114440Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b23aeaf732044ec9a4c639ad39bec63b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HTML(value=\"<p style='font-size:16px;'>Job Status: job is being initialized </p>\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "backend = IBMQ.get_backend('ibmq_16_melbourne')\n",
    "shots = 1000\n",
    "job_exp = execute(bvCircuit, backend=backend, shots=shots)    \n",
    "job_monitor(job_exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T16:09:52.415375Z",
     "start_time": "2018-09-26T16:09:51.924230Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa18d564a8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = job_exp.result()\n",
    "answer = results.get_counts(bvCircuit)\n",
    "\n",
    "threshold = int(0.01 * shots) #the threshold of plotting significant measurements\n",
    "filteredAnswer = {k: v for k,v in answer.items() if v >= threshold} #filter the answer for better view of plots\n",
    "\n",
    "removedCounts = np.sum([ v for k,v in answer.items() if v < threshold ]) #number of counts removed \n",
    "filteredAnswer['other_bitstrings'] = removedCounts  #the removed counts is assigned to a new index\n",
    "\n",
    "plot_histogram(filteredAnswer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'00000001100100': 45, '00000001101101': 10, '00000000100101': 14, '00000001100101': 381, '00000001000101': 48, '10000001100101': 61, '00000001100111': 21, '00000101100101': 13, '00000001100011': 19, '00000011100101': 33, '00000001110101': 30, '00010001100101': 26, '00000001100001': 44, '00001001100101': 13, 'other_bitstrings': 242}\n"
     ]
    }
   ],
   "source": [
    "print(filteredAnswer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We indeed see that the outcome is the binary representation of the hidden integer $a$ with high probability. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "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": 2
}