qiskit/fundamentals/5_using_the_transpiler.ipynb

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   "source": [
    "<img src=\"../../images/qiskit_header.png\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" align=\"middle\">"
   ]
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   "cell_type": "markdown",
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    "# Circuit Rewriting using the Transpiler\n",
    "\n",
    "Previously we have performed basic operations on circuits, and ran those circuits on real quantum devices using the `execute` function.  `execute` is a helper function that performs three tasks for the user:\n",
    "\n",
    "1) Circuits are rewritten to match the constraints of a given backend and optimized.\n",
    "\n",
    "2) The rewritten circuits are packaged for submission.\n",
    "\n",
    "3) The packaged circuits are submitted to the device.\n",
    "\n",
    "The first step is called transpilation, and is the fundamental step required for running circuits on real quantum devices.  The qiskit function that does this is `transpile`, which takes a single, or list of input circuits, as well as a collection of parameters, and returns a modified list of circuits.  Using this `transpile` function is the goal of this tutorial.\n",
    "\n",
    "For those wishing to bypass this in-depth discussion of what happens during the transpilation process, we note that the standard way of calling the `transpile` function is:\n",
    "\n",
    "```python\n",
    "new_circuits = transpile(circuits, backend, optimization_level=1)\n",
    "```\n",
    "\n",
    "where `circuits` is a single or list of input circuits, `backend` is the target device, and `optimization_level` selects between four different `[0,1,2,3]` preset methods of circuit rewriting and optimization.  By default, `optimization_level=1`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T14:50:04.434271Z",
     "start_time": "2019-08-09T14:50:04.429464Z"
    }
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   "source": [
    "# Table of contents\n",
    "\n",
    "1) [Introduction](#introduction)\n",
    "\n",
    "\n",
    "2) [Basis Gates](#basis)\n",
    "\n",
    "\n",
    "3) [Initial Layout](#layout)\n",
    "\n",
    "\n",
    "4) [Mapping Circuits to Hardware](#mapping)\n",
    "\n",
    "\n",
    "5) [Optimizing Gates](#optimizing)\n",
    "\n",
    "\n",
    "6) [User Defined Topologies](#topology)\n",
    "\n",
    "\n",
    "7) [Passing Transpiled Circuits to Devices](#passing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:51.084814Z",
     "start_time": "2019-08-09T13:47:48.486326Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit import *\n",
    "from qiskit.visualization import plot_histogram, plot_gate_map, plot_circuit_layout\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:53.454349Z",
     "start_time": "2019-08-09T13:47:51.092457Z"
    }
   },
   "outputs": [],
   "source": [
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(group='open')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction <a name='introduction'></a>\n",
    "\n",
    "Consider the following circuit that creates a five-qubit GHZ state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:53.996090Z",
     "start_time": "2019-08-09T13:47:53.463668Z"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 626.08x294.626 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghz = QuantumCircuit(5, 5)\n",
    "ghz.h(0)\n",
    "for idx in range(1,5):\n",
    "    ghz.cx(0,idx)\n",
    "ghz.barrier(range(5))\n",
    "ghz.measure(range(5), range(5))\n",
    "ghz.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We would like to take this circuit and run it on an IBM Q quantum device.  However, in its original form, this circuit cannot be run.  This circuit, as is the case with most circuits, must undergo a series of transformations that make it compatible with a given target device, and optimize it to reduce the effects of noise on the resulting outcomes.\n",
    "\n",
    "As we will see, rewriting quantum circuits to match hardware constraints and optimize for performance can be far from trivial.  The flow of logic in the rewriting tool chain need not be linear, and can often have iterative sub-loops, conditional branches, and other complex behaviors.  That being said, the basic building blocks follow the structure given below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-06T09:28:13.270334Z",
     "start_time": "2019-08-06T09:28:13.266618Z"
    }
   },
   "source": [
    "<img src=\"images/transpiling_core_steps.png\" style=\"width=auto;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In what follows we highlight the key steps in this workflow, and show how they modifey circuits based on the value of keyword arguments passed to the `transpile` function.  The `transpile` function has many input arguments:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:54.015108Z",
     "start_time": "2019-08-09T13:47:54.011066Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Signature (circuits, backend=None, basis_gates=None, coupling_map=None, backend_properties=None, initial_layout=None, seed_transpiler=None, optimization_level=None, pass_manager=None, callback=None, output_name=None, log_level=20)>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import inspect\n",
    "inspect.signature(transpile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we focus only on the most important ones: `basis_gates`, `initial_layout` `optimization_level` and `coupling_map'`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basis Gates <a name='basis'></a>\n",
    "\n",
    "When writing a quantum circuit you are free to use any quantum gate (unitary operator) that you like, along with a collection of non-gate operations such as qubit measurements and reset operations.  However, when running a circuit on a real quantum device one no longer has this flexibility.  Due to limitations in, for example, the physical interactions between qubits, difficulty in implementing multi-qubit gates, control electronics etc, a quantum computing device can only natively support a handful of quantum gates and non-gate operations. In the present case of IBM Q devices, the native gate set can be found by querying the devices themselves, and looking for the corresponding attribute in their configuration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:54.451253Z",
     "start_time": "2019-08-09T13:47:54.037172Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<IBMQBackend('ibmqx4') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmqx2') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_16_melbourne') from IBMQ(hub='ibm-q', group='open', project='main')>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "provider = IBMQ.get_provider(group='open')\n",
    "provider.backends(simulator=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:54.470643Z",
     "start_time": "2019-08-09T13:47:54.466317Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['u1', 'u2', 'u3', 'cx', 'id']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = provider.get_backend('ibmqx4')\n",
    "backend.configuration().basis_gates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-05T18:44:17.399097Z",
     "start_time": "2019-08-05T18:44:17.383113Z"
    }
   },
   "source": [
    "We see that the `ibmqx4` device supports five native gates: three single-qubit gates (`u1`, `u2`, `u3`, and `id`) and one two-qubit entangling gate `cx`.  In addition, the device supports qubit measurements (otherwise we can not read out an answer!).  Although we have queried only a single device, all IBM Q devices support this gate set.\n",
    "\n",
    "The `u*` gates represent arbitrary single-qubit rotations of one, two, and three angles.  The `u1` gates are single-parameter rotations that represent generalized phase gates of the form\n",
    "\n",
    "$$\n",
    "U_{1}(\\lambda) = \\begin{bmatrix}\n",
    "1 & 0 \\\\\n",
    "0 & e^{i\\lambda}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "This set includes common gates such as $Z$, $T$, $T^{\\dagger}$, $S$, and $S^{\\dagger}$.  It turns out that these gates do not actually need to be performed on hardware, but instead, can be implemented in software as \"virtual gates\".  These virtual gates are called \"frame changes\" and take zero time, and have no associated error; they are free gates on hardware.\n",
    "\n",
    "Two-angle rotations, $U_{2}(\\phi,\\lambda)$, are actually two frame changes with a single $X_{\\pi/2}$ gate in between them, and can be used to synthesize gates like the Hadamard ($U_{2}(0,\\pi)$) gate.  As the only actual gate performed is the $X_{\\pi/2}$ gate, the error and gate time associated with any $U_{2}$ gate is the same as an $X_{\\pi/2}$ gate.  Similarly, $U_{3}(\\theta,\\phi,\\lambda)$ gates are formed from three frame changes with two $X_{\\pi/2}$ gates in between them.  The errors and gate times are twice those of a single $X_{\\pi/2}$.  The identity gate, $id$, is straightforward, and is a placeholder gate with a fixed time-interval. \n",
    "\n",
    "The only entangling gate supported by the IBM Q devices is the CNOT gate (`cx`) that, in the computational basis, can be written as:\n",
    "\n",
    "$$\n",
    "\\mathrm{CNOT}(0,1) = \\begin{bmatrix}\n",
    "1 & 0 & 0 & 0 \\\\\n",
    "0 & 0 & 0 & 1 \\\\\n",
    "0 & 0 & 1 & 0 \\\\\n",
    "0 & 1 & 0 & 0\n",
    "\\end{bmatrix}\n",
    "$$,\n",
    "\n",
    "where we see that the matrix form follows from the specific bit-ordering convention used in Qiskit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Every quantum circuit run on a IBM Q device must be expressed using only these basis gates.  For example, suppose one wants to run a simple phase estimation circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:54.684874Z",
     "start_time": "2019-08-09T13:47:54.491476Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 303.833x156.52 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2, 1)\n",
    "\n",
    "qc.h(0)\n",
    "qc.x(1)\n",
    "qc.cu1(np.pi/4, 0, 1)\n",
    "qc.h(0)\n",
    "qc.measure([0], [0])\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have $H$, $X$, and controlled-$U_{1}$ gates, all of which are not in our devices basis gate set, and must be expanded.  This expansion is taken care of for us in the `execute` function.  However, we can decompose the circuit to show what it would look like in the native gate set of the IBM Q devices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:54.920353Z",
     "start_time": "2019-08-09T13:47:54.699157Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaEAAACECAYAAAA5vpTzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAcjUlEQVR4nO3deViU5f748fcM+yogsiMooCwCuS9pHmwz83wz29Tq19G09JidMjvZ6agZl22anfqerqKsb8vRPLmdbDt+c8nsqx3REFFMVEAW2QJZBYSZ+f0xSYxsAwzzzIyf13VxXXDP89zzee57Hj7Pcs/9qHQ6nQ4hhBBCAWqlAxBCCHHtkiQkhBBCMZKEhBBCKEaSkBBCCMVIEhJCCKEYSUJCCCEUI0lICCGEYiQJCSGEUIwkISGEEIqRJCSEEEIxkoSEEEIoRpKQEEIIxUgSEkIIoRhJQkIIIRQjSUgIIYRiJAkJIYRQjCQhIYQQipEkJIQQQjGShIQQQijGXukArFnT058qHYLiHNbOblOmRLu0F4ewfLIPtf3sqlQqReLQ6XSKvK+cCQkhhFCMJCEhhBCKkSQkhBBCMZKErEBpXRWO6+ZwrDTXoPx8VRmO6+ZwqrxQmcB6yNa2R1g++cxZLklCVuBIcTbO9g4M8w01KE8tPoeHowtDfQIViqxnbG17hOWTz5zlkiRkBY6WZHOdXzj2ajuD8iNF5xjhPwi1yrq60da2R1g++cxZLhmibQWOFmczKmBwm/LU4nOMDoxUIKLesbXtEZbPlj9zERERjBw5koEDB6JWqykvLyctLY2MjAyampraLD9gwADWr1/P448/zsWLFxWI2JAkISuQVpLDPdHjDcq0Oi1pJbksGn4LPxVn8+Tej7FTq7FXqXnn1gUM9vJXKNqudbU9AFM/W0N62XmWjLiNv4y/U4kwhQ2xtX2oX79+zJ8/n4ULFxIZ2X4Sraqq4uOPP+bvf/87WVlZgD4B7dmzh/j4eNRqNffff785w26X1SUhrVbL+vXrSUlJIT8/n6FDh/Lmm2/yyCOPMHnyZN59912lQzSpwpoKiuoqGeE/yKA8vfQ8tU0NjA2Mwl6t5su7n8HD0YVvstN44eA2Ppz2R4Ui7pwx2wOw4baF7D1/goKaCrPF1qyB9HxIz4OGJvByhXERMGgAKPT9QYtQVgMHz8CFi6BWw9AAGDMYXJ2Ujsw4trYPTZ8+nZSUFIKCggAoLS3l8OHDnD59Go1GQ3BwMKNGjWLo0KEsWbKEhQsXkpyczIYNG9i1axfx8fFkZmby5JNPKrwlelaXhObNm8eOHTtYsWIFI0eO5ODBg8yePZuysjKWLl2qdHgmV1ir/yfs5eRqUL751EHGBkYS6tnfoNzRzh57C76+bez2hHj0b7NuX/qlBt7eA+V1+oSj04EKOJwNw0LgoYngYNdlNTbnf0/A1+m//a0CTl3Ql829AWKCFAvNaLa0D61evZqVK1cCcOjQIdasWcM333yDVqtts2xCQgJPPPEEc+fO5YUXXuDPf/4z7u7uZGZmkpSURGlpqbnDb5dltnQHNm3axEcffcTOnTtZtmwZSUlJPPfcc4wfP57m5mZGjhwJQElJCbfccguurq4kJiaSlpamcOQ9F+0TRD8nV9Ye3kllQx0V9bW8e2w37xz7ljU3GE73UXe5gee+38yTo6crFG3XurM95nK5Gd7aAxWX9H9fmb3kyiQmJwpgy2FFQlPUj2cNExD81iZNGtiwH4oqzR5Wt9nKPvTss8+ycuVKmpubWbp0KRMnTuSrr75qNwEBHD9+nHnz5nHnnXfS1NSEu7s7dXV13HzzzRaTgMDKktBLL73E1KlTmTx5skF5ZGQkDg4OxMfHA7Bo0SKio6MpLy9n8eLF3H333Wg0GiVC7jVPJ1f+decyjhbnMCjlMeI/WMa/zqTy5V3PcENoTMtylzXNzP7iDZ4dN4M43xAFI+6csdtjTj/lwsW635JPe1KzoaLWbCEpTquFXRkdv677dZl9p8wWUo/Zwj40duxYkpOT0Wq1zJkzh9dff73D5NPagAEDeOGFF3BwcKCpqQk3NzfmzZtnhoiNp9IpNWtdNxUUFBAaGsr777/fphFnz57Nzz//TFpaGjU1Nfj6+lJYWIivry8A4eHhbNy4keuvv77XcbSeXPDysk29rs8UNFotc754k1sHJTIvIcms7+24bk6bMlO1y8cn9lNQU2HUwIT24jDWncu/JSQ2CbW68+ttBz59mp++Wtfj97EmAZHjuO/5Q10u19zUwFvzXDvP4J2Qfajrz65areb48ePExcXxyiuvsHz5cqPqbT0IITMzk7/+9a9s376dy5cvEx8f3zJYoS8Zk16s5kyooKAAgICAAIPy+vp69u/f33Ip7syZM/Tv378lAQEtnWCrtmb9yP/mprMp8wdu2pzME3s+VDqkXlvw7xReS/2ST05+z4zta/v0vVw8fLtMQDqdFmc3nz6Nw5I4uxu3rfYOztg7uvRxNH3PkvehW2+9lbi4OHJzc1m1apVR61ydgJKSktixYwcffPABjo6OPPbYY30ctfGsZmDClaSSlZXFtGnTWspfffVVioqKGDFiBAB1dXV4enoarOvp6UltrWmupbTO7JYyDf190RO4L3qCIu/d3pGOKdrlvamP9joOY6Xsg58v/Ha/oz0qlZoXVz/L5H8+2+P3sSYFFbDum66Xc7KHy/V1PR49KPtQ28/u1Y9yWLBgAQBvv/02jY2NXdbXXgK6cg/ob3/7G/PmzeOhhx5i2bJlXL58ucM4zMVqktDgwYNJSEjgxRdfxMfHh+DgYLZu3crXX38N0HIm5ObmRk1NjcG61dXVuLu7mz1mYR3GDtaP+OqMWgUjw80SjkUI9oaAflBS1XlyHhtxbQ9fN4eJEycCsGXLli6X7SwBAWRkZHDq1CliYmKIj4/n6NGjfRa3sazmcpxarWbLli3ExcWxaNEi5s6di6+vL4sXL8be3p6EhAQAoqKi+OWXXygvL29Z98SJE8TGxioVurBw8aEQ6qMfftyRpBhwdzZbSIpTqWD6dR0nIJUKXB3hd9FmDeuaExwczIABAygvLycnJ6fTZbtKQFdcSTxXrh4pzWqSEMCQIUPYt28fdXV15OXlkZycTEZGBjExMbi46K9Le3h4cPvtt5OcnExDQwMbNmxApVIxbtw4haMXlspODY8mwWC/tq+pVPoEdPt15o9LacNC4IEJ4NjO7TIvF1h8E/jIBYY+5ebmxpkzZ7o8Y/Hy8jIqAQGcPHmSc+fO9UW4PWI1l+M6cuTIkTYJ5u233+aBBx7A29ubqKgotm3bhp3dNfhNQ2E0d2dYcjPklcP6f+vLpiXqZwbwcu18XVs2apA+GR3NgS2p+rL5kyE2SD97guhbWVlZDBkypMvlqqurOXr0KHZ2dl1+EfXll1/m5ZdfNmWYvWLVH6Pa2lqysrLanFb6+/vz7bffUl9fz/Hjxxk+fLhCEfbc+tQvSSvJBWDZvk9I+nQ1S/d+1K060kvP89rhL/ogup5rvV1XK6yp4Km9H3OpqZE7tr3KTZuTmbnjNRqbm8y2LQNbfXn+lmHXdgK6wtkBrm/1f3BYiHUkIFvdh9qj1Wp5+OGHmThxokV9EdUYVvBR6pi7uzsajYYlS5YoHYpJaXVaDhZmMdw/nLSSHOqaGtg3exWXNc0cKTL+NDrRL4xDF86g1XX9pTZzaL1d7dlzPoMbw+LZlZPO6MBIds9awejACHblplvctgjLZqv7UGe0Wq1FzIrdXVZ/Oc4WpZfmEeKh/57GjxfOMGWgfiaIKWHx/KfoLKMCI9qssz8vk3s+X0/CgDByq8pI9A9j24yniPQOIL30PMOvmrxRCa23q714vZzceOPGP3CusoSfSvQ3Yasa6ujvrL/xYEnbIiybre5Dtsiqz4Rs1dmLxYR5DgCgsvESnk76QRf9nFy42FDX7jqTQqMZHRjB7lkrmBQazZs3zgVgcD8/fq7oYvyxmbTervbivdTUiLujM1HeAaQWnSXxf57maEkO44P114IsaVuEZbPVfcgWSRKyQLpWA2O9nFypbqwHoLqxHi/n9m9SZFeWMqiffnhXQU0Fwb8eBerQoep08LH5tN6uq+Mtq68mwS8MgE9Ofs/N4Qmkz13LbYOvY2PmDy3rW8q2CMtmq/uQLZIkZIGivAM5X10GwLigKPblnQBg7/kTjA2MpFmroaSuymCdzPICYvuHoNFqUbf69mBOVRlDfQLNF3wnWm/X1fHuzs3gprBhgH4aMh8X/SU4XxePln8glrQtwrLZ6j5kiyQJWaBEv4Hk1+i/bDvcfxDO9g4kfboatUrF6MBIcqvKWPXDZwbrZP5SQKxvCI2aJkovVVNUq79BmVVRROKvZxhKa71dV8e7L+8EI399/PKsmAlsPf0jN21O5tNT/8fsGP3Es5a0LcKy2eo+ZItkYIIFUqvUXB88lLSSXIb7h7N+ykMGrx8vy+O+GMN5rpaPm9Hye9ofXgH0w0vHB0WhtpAHdLXerqvj3fLzjy1xejm78dXdhnO0Wdq2CMtmq/uQLZIkZKGWdvJQrZlDxhhVR6JfmMUdwXW0XfdEdz6jhSVui7BstroP2RpJQr3gsFaZJ4FaOmkXYSz5rLTVk9msl7/yLgAvP/OIwe/WQM4xhRBCKEaSkBBCCMVIEhJCCKEYSUJCCCEUIwMTesFSHk2sJLmxbBylPivXQv9I21o3ORMSQgihGElCQgghFCNJSIhWNK0eG1Ndr5/HTsClxt9+v9ysXBzC9sg9IXHNq2uEw9lwPA8KWj0TbOV2cHOCsP4wejDEh4D9NfKUeJ0Ossvg0FnILoWKVk8/WP4Z+PeD6ECYEAUDPJSLU1g/OROyAqV1VTium8Ox0lyD8vNVZTium8Op8kJlArNyGi38+zis2gGf/wQ5v0CTxnCZukbIvAAf/QDJn0NGft/FYyn9fOEivL4L/vtbOJJjmIAAtDooqoR9p2DNTvjk/6C2wSyh9ZiltK1oS86ErMCR4myc7R0Y5htqUJ5afA4PRxeZZr4HKi/Bhu8Mz3y6UlUP738PYyPg3jFgZ+JDOEvo5+9Pw+dHQdONy5BHc+F0McydBBF+fRZar1hC24r2yZmQFThaks11fuHYqw2vBR0pOscI/0Eyw283VV7SH+V3JwG19p9z+jOj1vePTEHpft6bCduPdC8BXVHbAO/shXMlpo/LFJRuW9ExaXkrcLQ4m1G/PmuntdTicy3P4BHG0erg4x+gvLbjZf52v/6nM8fz4duTpo1NyX7OKoadaZ0v01W7NGnggwNQY4GX5mQfslyShKxAWkkOIwMiDMq0Oi1pJbmMChjML5eqmbRxJTdufoHxn/yV3bkZCkVq+Q6c1t9wN4VvM/T3T0ylq34GmPrZGgLfeoQXD+0w2fs2NsGnP5qmrrpG2JpqmrpMSam2FV2zuiSk1WpZt24dUVFRODs7k5iYyP79+xk6dCiPPGIdU5d3R2FNBUV1lYzwH2RQnl56ntqmBsYGRuHt7M53s59nz6yVfDL9MVYc+KdC0Vq2Zo1pz140OtPVZ0w/A2y4bSGvTO7iNK2bDmfDxbqulzNWep5+4IKlULJtRdesLgnNmzeP5ORkHn30Ub755hvuvfdeZs+eTXZ2NiNHjlQ6PJMrrK0AwMvJ1aB886mDjA2MJNSzP3ZqNXZqfVfWXG4gwW+g2eO0Bun5ph/FdTxf/32i3jKmnwFCPPr3/s1a0enghyyTVgn0TZ09pVTbCuNYVRLatGkTH330ETt37mTZsmUkJSXx3HPPMX78eJqbm1uS0KpVq4iNjUWtVrN161aFo+6daJ8g+jm5svbwTiob6qior+XdY7t559i3rLnht7mrcipL+d2nz3P71pf4r8hRCkZsuU5dMH2dGi2cKe59Pcb2s6ldrIOSatPX+3OR6evsKaXaVhjHqoZov/TSS0ydOpXJkycblEdGRuLg4EB8fDwAUVFRvPHGG6xYsUKJME3K08mVf925jL98v5lBKY/hau9Eol8YX971DJNCY1qWG+Tlx3eznye3qoyb/5nM7REjFIzaMuWX9029eRUwclDXy3XG2H42tfyKvqm3vFZ/f8jNqW/q7w6l2lYYx2qSUEFBASdOnODJJ59s81peXh5xcXE4Oek/8Q888AAAa9asMXkcKpWq5ffLyzaZvP72XB8Szf45z3f4emNzE072DgB4Orrg7uhilrjAsD0s3R/fr8Oh1SWZrkbAdfT6ExsN/37/k+3MHHVXp3UZ81npqp97oqv+GX7bk9xw/3qDMlO1y6Chwyk7f6yrEHvNUtvWnJ55OQXQx9T6d6UZ86hyq0pCAAEBAQbl9fX17N+/n2nTpikRlkVIK83hL99vxk6lplmr4bWkB5UOySKp1H0z505f1dueBf9O4XDRWS5rmjlcdJZ/zXy6V/X1ZezmbBdTMHXbCuNYTRLy9fUFICsryyDhvPrqqxQVFTFihHkuP7XO7JbyPKFxQUPYO2ulIu9tzJGOpVi5DapbDUy4+sj9iitH+h29frXZ99zBF+s7bwdTfVbem/pot5bvqn8OnYV//sewzFTtcjL9CL5mmFfOUtvWnJa/8i6gj6n179bAapLQ4MGDSUhI4MUXX8THx4fg4GC2bt3K119/DWCTI+OEaQX7QHUfDE4I9jZ9neYS0kexOztAf/e+qVvYFqsZHadWq9myZQtxcXEsWrSIuXPn4uvry+LFi7G3tychIUHpEIWFGzTAuuo1h0AvcOqDQ9FwX7CAWxLCCljNmRDAkCFD2Ldvn0HZgw8+SExMDC4uv92Mb2pqQqPRoNVqaWpqoqGhAScnJ4u4USeUM2awftZsrQmvUgR5Q6iP6eozN3s7GD0Ifjhj2nrHRZq2PmG7rOZMqCNHjhxpcyluwYIFuLi4cODAAebMmYOLiwvnz59XKEJhKbxcIdHE3+OdPNT6j/gnDgW1CbfBx03/7CUhjGHVSai2tpasrKw2gxI+/PBDdDqdwU94eLgyQRphfeqXpJXkdmudZfs+IenT1Szd+1G31ksvPc9rh7/o1jq2ZMZIcHE0TV1R/vqH3fVET/oc9FPQPLX3Yy41NXLHtle5aXMyM3e8RmNzU4/7NqAf3BTX7dU6NGuc6R9z0VOdtXNftKXoPgv5qPSMu7s7Go2GJUuWKB1Kj2l1Wg4WZjHcP9zoddJKcqhramDf7FVc1jRzpOic0esm+oVx6MIZtDoTP4fASvRzgdnjoLMD/yc2dj0CzMNZX09PziB60udX7DmfwY1h8ezKSWd0YCS7Z61gdGAEu3LTe9W3twzr+t6WMe0yJQaGBHS+jLl01c591Zaie6zqnpAtSi/NI8RDf1Nhf14m93y+noQBYeRWlZHoH8a2GU+1WefHC2eYMlA/O8SUsHj+U3SWUYERbZbrqL5I7wDSS88z3L+XX/O3UgmhcP8E2HSoZ/eHPF1g0RTw6eHor9Z93pGO+m5//ineuPEPnKss4aeSHACqGuro76wPpqd9a28HC34H7+3TP2G2JyYOgd8P79m6faGrfcvLya1P2lJ0j1WfCdmCsxeLCfPUH4JOCo1mdGAEu2etYFJoNG/eOLfddSobL+HppB+I0c/JhYsN7U+B3FF9g/v58XNFH4xVtiKjBsHjt4CfZ/fWGxYCy27TjyrrqdZ93pH2+k6n03GpqRF3R2eivANILTpL4v88zdGSHMYHDwF617eujvDHm+DG2M7PFK/m4ggPTIC7RlnW/bGu9q2+bEthPDkTUpiO3w7FsytLGdRP/3zkgpoKgjs4WvZycqW6UT91c3VjPV7Oru0u11F9OnSouvVvxjaF++oTyuFs/azPxVXtL6cCooNg0hCICer9P9rWfV5cV8kDX/y3wev+bv1YPfHeNn13rDSXBL8wAD45+T03hyfw1Jjfsz71SzZm/sCDcTf0um8d7PRnMyPC9Y/6PpqrfwRGezycYXyk/gzI03wzRRmts32rrL66z9tSGEeSkMKivAM5WHgagMzyAmL7h6DRalGrVDRrNZTX1+Lv1s9gnXFBUbyXvod7osex9/wJ/t+wG9pd9ur6rsipKuO+aBlDC+Bor/8nen0UlNXoJ/Qsq4Zmrf77M0HeMNAHPEz4T7Z1nwe4ebF7VtuJdneePdKm73bnZnBT2DBA/wgGHxf9ZSNfF4+WgxJT9W2wt/6e150joaBC/1PXqE/A3m4Q4gNBXpYzAKE9ne1b5mxL0TlJQgpL9BtIfo1+eufMXwoYFxRFo6aJ0kvV/HjhDP84eYB3bl1gsM5w/0E42zuQ9OlqEgYMZHRgJGcvFrPu8BcGy15dX1HtRQLdvcmqKCLx16NAoadS6S/NdffyXE+07vOOtNd3P5XksHT07QDMipnA/V++ycaTP+BgZ8fG6Y8DmLxvnR0g0l//Y20627f25Z0we1uK9kkSUphapeb64KGkleSyfNyMlvK0P7zC9qzD3Bczod311k95yODv42V5bZa9uj7QD9EeHxSFWmXBh7A2rnWfdzRyq72+uzNqTEu/eTm78dXdzxqsI31rqLN9a8vPP0pbWghJQhZg6ejp7ZbPHDLG6DqMXTbRL0yO7ixAR33emXuix3X6uvRtWx21s7Sl5ZAk1AsOa+WpjMI48lnpO9K21k3ONYUQQihGkpAQQgjFSBISQgihGElCQgghFCNJSAghhGIkCQkhhFCMJCEhhLjGfPfdd8TFxREZGcn8+fPRaDqYINAMJAkJIcQ1RKvVMn/+fLZs2cLZs2eprq7mH//4h2LxyJdVhRDCypzNLaSisrpN+eFjp9r8bmdnx4hhUah+nQg3NTWVoKAgYmNjAXj44Yd56623eOihh9rUZw6ShIQQwtqoYPuuA22KW5dd+f2GMQktCQigoKCA0NDQlr8HDhxIfn5+HwbbObkcJ4QQViYyLJjYqPAul3NzdWbKhBEGZTqdziAp6XQ9eLywCUkSEkIIKzQtaSx26s7/hd8yaTTOTo4GZaGhoeTl5bX8nZ+fT0hISJ/EaAxJQkIIYYV8vftx/ahhHb4eMMCH0QlD25SPGjWKwsJCMjMzAXj//feZOXNmn8XZFUlCQghhpaZMGIGbq3O7r/3+xgmo2zlTsrOz47333uPuu+8mIiICd3d3Hnzwwb4OtUM2l4Q+//xzpk+fjp+fH05OToSFhTFnzhwyMjKUDk0IIUzK2cmRWyaNblMeGxVORFhQh+tNmTKFzMxMzp07xwcffIC9vXJj1GwmCTU3NzNr1ixmzJhBeno6M2fO5E9/+hPDhw9n27ZtFBYWKh2iEEKY3OiEoQQM8Gn5206tZlrSWAUj6h6VTumhESaycOFCUlJSWLBgAa+//jpubm4tr+Xn5+Pl5YWHh0ev32f5K+/2ug4hhLgWvPzMI10uYxPfEzpw4AApKSlMnTqVlJQUg+GHgMGYeCGEEJbDJs6E7rrrLrZv386xY8dITExUOhwhhDC7Xy5WkVtQzKj4tiPiLJlNJCFPT0/69+9PTk5On7+XXI4TQgjjGHM5zuoHJlRWVlJTU0N4eLjSoQghhOgmqz8TunjxIj4+PsTGxnLy5EmlwxFCCNENVn8m5O3tTUREBKdOnWL37t1tXj99+rQCUQkhhDCG1Z8JAXz22Wfcd9992NnZcccddxAZGUlpaSkHDx4kNjaWHTt2KB2iEEKIdthEEgLYtWsXa9euJTU1lYaGBvz8/BgzZgxPPPEEkyZNUjo8IYQQ7bCZJCSEEML6WP09ISGEENZLkpAQQgjFSBISQgihGElCQgghFCNJSAghhGIkCQkhhFCMJCEhhBCKkSQkhBBCMZKEhBBCKEaSkBBCCMVIEhJCCKEYSUJCCCEUI0lICCGEYiQJCSGEUIwkISGEEIqRJCSEEEIxkoSEEEIoRpKQEEIIxUgSEkIIoRhJQkIIIRQjSUgIIYRi/j/sPCPlr2to1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 534.009x156.52 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_basis = qc.decompose()\n",
    "qc_basis.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A few things to highlight.  One, as mentioned in [Part 4: Quantum Circuit Properties](4_quantum_circuit_properties.ipynb), the circuit has gotten longer with respect to the initial one.  This can be verified by checking the depth of the circuits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:54.941745Z",
     "start_time": "2019-08-09T13:47:54.937994Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 , 7\n"
     ]
    }
   ],
   "source": [
    "print(qc.depth(), ',', qc_basis.depth())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second, although we had a single controlled gate, the fact that it was not in the basis set means that, when expanded, it requires more than a single `cx` gate to implement. All said, unrolling to the basis set of gates leads to an increase in the depth of a quantum circuit and the number of gates.  It is important to highlight two special cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SWAP Gate Decomposition\n",
    "\n",
    "A SWAP gate is not a native gate on the IBM Q devices, and must be decomposed into three CNOT gates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:47:57.053386Z",
     "start_time": "2019-08-09T13:47:56.919376Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 257.798x110.485 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "swap_circ = QuantumCircuit(2)\n",
    "swap_circ.swap(0, 1)\n",
    "swap_circ.decompose().draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a product of three CNOT gates, SWAP gates are expensive operations to perform on a noisy quantum devices.  However, such operations are usually necessary for embedding a circuit into the limited entangling gate connectivities of actual devices.  Thus, minimizing the number of SWAP gates in a circuit is a primary goal in the transpilation process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Toffoli Gate Decomposition\n",
    "\n",
    "A Toffoli, or controlled-controlled-not gate is a three qubit gate.  Given that our basis gate set includes only single- and two-qubit gates, it is obvious that this gate must be decomposed.  This decomposition is quite costly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:00:00.098589Z",
     "start_time": "2019-08-09T00:59:59.884584Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 626.08x156.52 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ccx_circ = QuantumCircuit(3)\n",
    "ccx_circ.ccx(0, 1, 2)\n",
    "ccx_circ.decompose().draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For every Toffoli gate in a quantum circuit, the IBM Q hardware may execute up to six CNOT gates, and a handful of single-qubit gates.  From this example, it should be clear that any algorithm that makes use of multiple Toffoli gates will end up as a circuit with large depth and with therefore be appreciably affected by noise and gate errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial Layout <a name='layout'></a>\n",
    "\n",
    "Quantum circuits are abstract entities whose qubits are \"virtual\" representations of actual qubits used in computations.  We need to be able to map these virtual qubits in a one-to-one manner to the \"physical\" qubits in an actual quantum device."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/mapping.png\" style=\"width=auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, qiskit will do this mapping for you.  The choice of mapping depends on the properties of the circuit, the particular device you are targeting, and the optimization level that is chosen.  The basic mapping strategies are the following:\n",
    "\n",
    "- **Trivial layout**: Map virtual qubits to the same numbered physical qubit on the device, i.e. `[0,1,2,3,4]` -> `[0,1,2,3,4]` (default in `optimization_level=0`).\n",
    "\n",
    "\n",
    "- **Dense layout**: Find the sub-graph of the device with same number of qubits as the circuit with the greatest connectivity (default in `optimization_level=1`).\n",
    "\n",
    "\n",
    "- **Noise adaptive layout**: Uses the noise properties of the device, in concert with the circuit properties, to generate the layout with the best noise properties (default in `optimization_level=2` and `optimization_level=3`).\n",
    "\n",
    "The choice of initial layout is extremely important when:\n",
    "\n",
    "1) Computing the number of SWAP operations needed to map the input circuit onto the device topology.\n",
    "\n",
    "2) Taking into account the noise properties of the device.\n",
    "\n",
    "As we will see, the choice of `initial_layout` can mean the difference between getting a result, and getting nothing but noise.\n",
    "\n",
    "To begin, lets see what layouts are automatically picked at various optimization levels.  The modified circuits returned by `transpile` have this initial layout information in them, and we can view this layout selection graphically using `plot_circuit_layout`.  Let us pick the `ibmq_16_melbourne` device:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:50:51.640655Z",
     "start_time": "2019-08-09T13:50:51.520404Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = provider.get_backend('ibmq_16_melbourne')\n",
    "plot_gate_map(backend, plot_directed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Layout using `optimization_level=0`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:50:53.338042Z",
     "start_time": "2019-08-09T13:50:52.836642Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = provider.get_backend('ibmq_16_melbourne')\n",
    "new_circ_lv0 = transpile(ghz, backend=backend, optimization_level=0)\n",
    "\n",
    "plot_circuit_layout(new_circ_lv0, backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Layout using `optimization_level=3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:50:54.050445Z",
     "start_time": "2019-08-09T13:50:53.775606Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 13\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_circuit_layout\n",
    "\n",
    "backend = provider.get_backend('ibmq_16_melbourne')\n",
    "new_circ_lv3 = transpile(ghz, backend=backend, optimization_level=3)\n",
    "\n",
    "print('Depth:', new_circ_lv3.depth())\n",
    "plot_circuit_layout(new_circ_lv3, backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now execute this level 3 circuit, and get the counts.  Note that the circuit has already been rewritten to match the target backend.  Therefore, the circuit will go unmodified by `execute` and be directly packaged and sent to the device."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:51:39.195545Z",
     "start_time": "2019-08-09T13:50:54.994602Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "job1 = execute(new_circ_lv3, backend)\n",
    "job_monitor(job1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specifying an Initial Layout\n",
    "\n",
    "It is completely possible to specify your own initial layout.  To do so we can pass a list of integers to `transpile` via the `initial_layout` keyword argument, where the index labels the virtual qubit in the circuit and the corresponding value is the label for the physical qubit to map onto.  For example, lets map our GHZ circuit onto `ibmq_16_melbourne` in two different ways results:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Good choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:51:53.183029Z",
     "start_time": "2019-08-09T13:51:53.011406Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 16\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Virtual -> physical\n",
    "#    0    ->    11\n",
    "#    1    ->    12\n",
    "#    2    ->    10\n",
    "#    3    ->    2\n",
    "#    4    ->    4\n",
    "\n",
    "good_ghz = transpile(ghz, backend, initial_layout=[11,12,10,2,4])\n",
    "print('Depth:', good_ghz.depth())\n",
    "plot_circuit_layout(good_ghz, backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:52:57.307300Z",
     "start_time": "2019-08-09T13:51:53.267947Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "job2 = execute(good_ghz, backend)\n",
    "job_monitor(job2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bad choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:52:57.671042Z",
     "start_time": "2019-08-09T13:52:57.391975Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 40\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Virtual -> physical\n",
    "#    0    ->    0\n",
    "#    1    ->    6\n",
    "#    2    ->    10\n",
    "#    3    ->    13\n",
    "#    4    ->    7\n",
    "\n",
    "bad_ghz = transpile(ghz, backend, initial_layout=[0,6,10,13,7])\n",
    "print('Depth:', bad_ghz.depth())\n",
    "plot_circuit_layout(bad_ghz, backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:54:13.845012Z",
     "start_time": "2019-08-09T13:52:57.815605Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "job3 = execute(bad_ghz, backend)\n",
    "job_monitor(job3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:54:14.254191Z",
     "start_time": "2019-08-09T13:54:13.969361Z"
    }
   },
   "outputs": [],
   "source": [
    "counts1 = job1.result().get_counts()\n",
    "counts2 = job2.result().get_counts()\n",
    "counts3 = job3.result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:54:15.151337Z",
     "start_time": "2019-08-09T13:54:14.380235Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram([counts1, counts2, counts3],\n",
    "               figsize=(15,6),\n",
    "               legend=['level3', 'good', 'bad'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the figure it is clear that the choice of initial layout is an extremely important step, and can mean the difference between a good answer and one dominated by noise.  Although the 'good' circuit has a smaller depth, the level 3 circuit generated results are are more in line with the expected answer.  This is because our manual layout selection did not take into account the noise properties of the device.  Noise affects each qubit differently, and qubit measurement errors can also corrupt the answer.  The noise adaptive layout in `optimization_level=2` and `optimization_level=3` takes this into account, and the benefits are obvious."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Being a bit Smarter\n",
    "\n",
    "Picking a good `initial_layout` is critical, but it is not the only step in optimizing a circuit on a quantum device.  Often it is beneficial to rewrite a circuit, with the goal of targeting a specific device.  Our GHZ circuit can be perfectly mapped to the `ibmq_16_melbourne` device provided that we reformulate the gate sequence as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:31:29.549091Z",
     "start_time": "2019-08-09T01:31:29.281965Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 580.045x294.626 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghz2 = QuantumCircuit(5, 5)\n",
    "ghz2.h(2)\n",
    "ghz2.cx(2, 1)\n",
    "ghz2.cx(1, 0)\n",
    "ghz2.cx(2, 3)\n",
    "ghz2.cx(3, 4)\n",
    "ghz2.barrier(range(5))\n",
    "ghz2.measure(range(5), range(5))\n",
    "ghz2.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This circuit can now be mapped exactly onto the device topology using `initial_layout=[10,4,5,6,8]`.  This can be verified by once again computing the depth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:31:29.646031Z",
     "start_time": "2019-08-09T01:31:29.552835Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 5\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exact_ghz = transpile(ghz2, backend, initial_layout=[10,4,5,6,8])\n",
    "print('Depth:', exact_ghz.depth())\n",
    "plot_circuit_layout(exact_ghz, backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:41:09.732117Z",
     "start_time": "2019-08-09T01:31:29.648616Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "job4 = execute(exact_ghz, backend)\n",
    "job_monitor(job4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:41:10.408469Z",
     "start_time": "2019-08-09T01:41:09.734297Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts4 = job4.result().get_counts()\n",
    "plot_histogram([counts1, counts4],\n",
    "               figsize=(15,6),\n",
    "               legend=['level3', 'exact'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mapping Circuits to Hardware Topology <a name='mapping'></a>\n",
    "\n",
    "Our original GHZ circuit consists of a single qubit (`0`) coupled to the others via CNOT gates.  If implemented directly, this would require hardware that has a single qubit coupled to four other qubits.  Looking at the gate maps of the public IBM Q hardware we see that there are two devices that fit this description."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:41:10.472262Z",
     "start_time": "2019-08-09T01:41:10.410598Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = provider.get_backend('ibmqx2')\n",
    "plot_gate_map(backend, plot_directed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:41:10.537942Z",
     "start_time": "2019-08-09T01:41:10.473878Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = provider.get_backend('ibmqx4')\n",
    "plot_gate_map(backend, plot_directed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and one that does not:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:41:10.645877Z",
     "start_time": "2019-08-09T01:41:10.539381Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = provider.get_backend('ibmq_16_melbourne')\n",
    "plot_gate_map(backend, plot_directed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems our circuit is a good match to the `ibmqx2` and `ibmqx4` topologies provided that we map virtual qubit `0` to physical qubit `2`.  The arrows on the graphs above indicate that CNOT gates are only allowed in one direction.  However, flipping the direction of a CNOT gate is relatively trivial, and does not greatly affect the fidelity of the computation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`ibmq_16_melbourne` represents a problem.  There is no qubit anywhere that is connected to four others via CNOT gates.  In order to implement a CNOT gate between qubits that are not directly connected, one or more SWAP gates must be inserted into the circuit to move the qubit states around until they are adjacent on the device gate map.  Our choice of `initial_layout` in `job3` above was purposely designed to take many SWAP gates to make adjacent. As we have seen previously, each SWAP gate is decomposed into three CNOT gates on the IBM Q devices, and represents an expensive and noisy operation to perform.  Thus, finding the minimum number of SWAP gates needed to map a circuit onto a given device, is an important step (if not the most important) in the whole execution process.\n",
    "\n",
    "As with many important things in life, finding the optimal SWAP mapping is hard.  In fact it is in a class of problems called NP-Hard, and is thus is prohibitively expensive to compute for all but the smallest quantum devices and input circuits.  To get around this, by default Qiskit uses a stochastic heuristic algorithm called `StochasticSwap` to compute a good, but not necessarily minimal SWAP count.  The use of a stochastic method means the circuits generated by `transpile` (or `execute` that calls `transpile` internally) are not guaranteed to be the same over repeated runs.  Indeed, running the same circuit repeatedly will in general result in a distribution of circuit depths and gate counts at the output.\n",
    "\n",
    "In order to highlight this, we run the GHZ circuit 100 times, using the \"bad\" (disconnected) `initial_layout` from the previous section:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:02.418909Z",
     "start_time": "2019-08-09T13:55:55.996117Z"
    }
   },
   "outputs": [],
   "source": [
    "bad_circs = transpile([ghz]*100, backend, initial_layout=[0,6,10,13,7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:12.152254Z",
     "start_time": "2019-08-09T13:56:11.936337Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "depths = [circ.depth() for circ in bad_circs]\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.hist(depths, bins=list(range(39,56)), align='left', color='#648fff')\n",
    "plt.xlabel('Depth', fontsize=14)\n",
    "plt.ylabel('Counts', fontsize=14);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This distribution is quite wide, signaling the difficultly the SWAP mapper is having in computing the best mapping.  Most circuits will have a distribution of depths, perhaps not as wide as this one, due to the stochastic nature of the default SWAP mapper.  Of course, we want the best circuit we can get, especially in cases where the depth is critical to success or failure.  In cases like this, it is best to `transpile` a circuit several times, e.g. 10, and take the one with the lowest depth.  The `transpile` function will automatically run in parallel mode, making this procedure relatively speedy in most cases.\n",
    "\n",
    "Just to highlight the difference when running on a different device, we show the same distribution when using the `ibmqx4` backend with the default settings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:19.396948Z",
     "start_time": "2019-08-09T13:56:16.884565Z"
    }
   },
   "outputs": [],
   "source": [
    "backend = provider.get_backend('ibmqx4')\n",
    "qx4_circs = transpile([ghz]*100, backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:24.008482Z",
     "start_time": "2019-08-09T13:56:23.828800Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "depths = [circ.depth() for circ in qx4_circs]\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.hist(depths, bins=list(range(12,22)), align='left', color='#648fff')\n",
    "plt.xlabel('Depth', fontsize=14)\n",
    "plt.ylabel('Counts', fontsize=14);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimizing Single- and Multi-Qubit Gates\n",
    "\n",
    "Decomposing quantum circuits into the basis gate set of the IBM Q devices, and the addition of SWAP gates needed to match hardware topology, conspire to increase the depth and gate count of quantum circuits.  Fortunately many routines for optimizing circuits by combining or eliminating gates exist.  In some cases these methods are so effective the output circuits have lower depth than the inputs.  In other cases, not much can be done, and the computation may be difficult to perform on noisy devices.  Different gate optimizations are turned on with different `optimization_level` values.  Below shows the benefits gained from setting the optimization level higher:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    <b>Remember:</b> The output from <code>transpile</code> varies due to the stochastic swap mapper.  So the numbers below will likely change each time you run the code.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:26.038494Z",
     "start_time": "2019-08-09T13:56:26.035734Z"
    }
   },
   "outputs": [],
   "source": [
    "backend = provider.get_backend('ibmq_16_melbourne')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:26.353081Z",
     "start_time": "2019-08-09T13:56:26.248097Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 25\n",
      "Gate counts: OrderedDict([('u2', 29), ('cx', 19), ('measure', 5), ('barrier', 1)])\n"
     ]
    }
   ],
   "source": [
    "circ0 = transpile(ghz, backend, optimization_level=0)\n",
    "print('Depth:', circ0.depth())\n",
    "print('Gate counts:', circ0.count_ops())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:26.649019Z",
     "start_time": "2019-08-09T13:56:26.509400Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 22\n",
      "Gate counts: OrderedDict([('u2', 25), ('cx', 17), ('measure', 5), ('barrier', 1)])\n"
     ]
    }
   ],
   "source": [
    "circ1 = transpile(ghz, backend, optimization_level=1)\n",
    "print('Depth:', circ1.depth())\n",
    "print('Gate counts:', circ1.count_ops())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:26.948413Z",
     "start_time": "2019-08-09T13:56:26.829380Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 13\n",
      "Gate counts: OrderedDict([('u2', 9), ('cx', 7), ('measure', 5), ('barrier', 1)])\n"
     ]
    }
   ],
   "source": [
    "circ2 = transpile(ghz, backend, optimization_level=2)\n",
    "print('Depth:', circ2.depth())\n",
    "print('Gate counts:', circ2.count_ops())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:27.479648Z",
     "start_time": "2019-08-09T13:56:27.271226Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth: 10\n",
      "Gate counts: OrderedDict([('u2', 9), ('cx', 7), ('measure', 5), ('barrier', 1)])\n"
     ]
    }
   ],
   "source": [
    "circ3 = transpile(ghz, backend, optimization_level=3)\n",
    "print('Depth:', circ3.depth())\n",
    "print('Gate counts:', circ3.count_ops())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transpiling for User Defined Topologies <a name='topology'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Up to now, we have focused on rewriting and optimizing circuits for the IBM Q set of devices.  However, `transpile` is much more general than that, and can be used to map circuits onto user defined device topologies.  The topology is encoded in what qiskit calls the `coupling_map`, and the coupling map for a device can be obtained from its `configuration`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:31.152071Z",
     "start_time": "2019-08-09T13:56:31.148319Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 0], [2, 0], [2, 1], [3, 2], [3, 4], [4, 2]]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = provider.get_backend('ibmqx4')\n",
    "backend.configuration().coupling_map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the elements of this list are `[control, target]` pairs that indicate that a CNOT gate can be performed using those qubits.  The coupling map is in essence an adjacency matrix characterizing the entangling gate coupling of the device:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:31.604159Z",
     "start_time": "2019-08-09T13:56:31.509046Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPUAAAD8CAYAAACvvuKtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAJsUlEQVR4nO3dS4hcBR6F8XMmplHoARddCzFh2oXIiDAKhQjZBYX4QLcKuhKyGSGCIApuhKzFjZug4oCiCLoQcZAGFREcteILM1EIohgUUkFEszGoZxbdoDjdqVuVe6vq/vP9oKEfl1uHtr++leqy20kEoI6/LHoAgHYRNVAMUQPFEDVQDFEDxRA1UEwvorZ9wPYXtk/YfmjRe87F9tO2T9n+bNFbJrG91/abto/bPmb70KI37cT2xbbft/3J1tZHF72pCdu7bH9k+9V53ebSR217l6QnJN0s6WpJd9m+erGrzukZSQcWPaKhXyQ9kOTvkm6Q9M8l/tz+LGl/kn9IulbSAds3LHhTE4ckHZ/nDS591JKul3QiyZdJzkp6QdIdC960oyRvS/p+0TuaSPJdkg+3Xv9Jm198ly921fay6czWm7u3Xpb6mVO290i6VdKT87zdPkR9uaRv/vD2SS3pF16f2V6XdJ2k9xa7ZGdbd2U/lnRK0kaSpd265XFJD0r6bZ432oeovc37lvo7dN/YXpX0kqT7k/y46D07SfJrkmsl7ZF0ve1rFr1pJ7Zvk3QqydF533Yfoj4pae8f3t4j6dsFbSnH9m5tBv1ckpcXvaeJJD9IekvL/djFPkm32/5Km/9k3G/72XnccB+i/kDSlbavsL0i6U5Jryx4Uwm2LekpSceTPLboPedie2D70q3XL5F0o6TPF7tqZ0keTrInybo2v2bfSHL3PG576aNO8ouk+yS9rs0Hcl5Mcmyxq3Zm+3lJ70q6yvZJ2/cuetM57JN0jzavIh9vvdyy6FE7uEzSm7Y/1eY3+o0kc/sxUZ+Y//USqGXpr9QApkPUQDFEDRRD1EAxRA0U05uobR9c9IZp9Glvn7ZK/dq7iK29iVpSb/5DbunT3j5tlfq1l6gBnJ9OnnyytraW9fX1Vs85Ho81GAxaPWeX+rS3T1ulfu3tauvRo0dPJ9n2xBe1fmuS1tfXNRqNujg1AEm2v97pY9z9BoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgmEZR2z5g+wvbJ2w/1PUoALObGLXtXZKekHSzpKsl3WX76q6HAZhNkyv19ZJOJPkyyVlt/q3dO7qdBWBWTaK+XNI3f3j75Nb7ACyhJlF7m/f9368gtX3Q9sj2aDwen/8yADNpEvVJSXv/8PYeSd/++aAkR5IMkwz78utbgYqaRP2BpCttX2F7RdKdkl7pdhaAWU38vd9JfrF9n6TXJe2S9HSSY50vAzCTRr/MP8lrkl7reAuAFvCMMqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgmIsWPWA7w8MbOn3m7MTj1lZXNHrkpjksAvpj4pXa9tO2T9n+bB6DJDUKeprjgAtJk7vfz0g60PEOAC2ZGHWStyV9P4ctAFrAA2VAMa1Fbfug7ZHt0Xg8buu0AKbUWtRJjiQZJhkOBoO2TgtgStz9Bopp8iOt5yW9K+kq2ydt39v9LACzmvjkkyR3zWMIgHYs5d3vtdWVVo8DLiRL+TRRnvoJzG4pr9QAZkfUQDFEDRRD1EAxRA0UQ9RAMUQNFEPUQDFEDRRD1EAxRA0UQ9RAMUQNFEPUQDFEDRRD1EAxRA0UQ9RAMUQNFEPUQDFEDRRD1EAxRA0UQ9RAMUQNFEPUQDFEDRRD1EAxRA0UQ9RAMUQNFEPUQDFL+Ufnh4c3dPrM2YnHra2uLMUfqO/bXtQ28Upte6/tN20ft33M9qGuRzUJZJrjuta3vaityZX6F0kPJPnQ9l8lHbW9keS/HW8DMIOJV+ok3yX5cOv1nyQdl3R518MAzGaqB8psr0u6TtJ7XYwBcP4aR217VdJLku5P8uM2Hz9oe2R7NB6P29wIYAqNora9W5tBP5fk5e2OSXIkyTDJcDAYtLkRwBSaPPptSU9JOp7kse4nATgfTa7U+yTdI2m/7Y+3Xm7peBeAGU38kVaSdyR5DlsAtGApnya6trrS6nFd69te1OYkrZ90OBxmNBq1fl4Am2wfTTLc7mNLeaUGMDuiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoJiLFj0A8zU8vKHTZ85OPG5tdUWjR26aw6I6luVzO/FKbfti2+/b/sT2MduPdrYGnWvyRTfNcfjdsnxum1ypf5a0P8kZ27slvWP730n+0+kyADOZGHWSSDqz9eburZd0OQrA7Bo9UGZ7l+2PJZ2StJHkvW5nAZhVo6iT/JrkWkl7JF1v+5o/H2P7oO2R7dF4PG57J4CGpvqRVpIfJL0l6cA2HzuSZJhkOBgMWpoHYFpNHv0e2L506/VLJN0o6fOuhwGYTZNHvy+T9C/bu7T5TeDFJK92OwvArJo8+v2ppOvmsAVAC3ia6AVmbXWl1ePwu2X53Hrzx9DtGg6HGY1GrZ8XwCbbR5MMt/sYV2qgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGirlo0QMwX8PDGzp95uzE49ZWVzR65KY5LELbGl+pbe+y/ZHtV7schG41CXqa47B8prn7fUjS8a6GAGhHo6ht75F0q6Qnu50D4Hw1vVI/LulBSb91uAVACyZGbfs2SaeSHJ1w3EHbI9uj8Xjc2kAA02lypd4n6XbbX0l6QdJ+28/++aAkR5IMkwwHg0HLMwE0NTHqJA8n2ZNkXdKdkt5IcnfnywDMhCefAMVM9eSTJG9JequTJQBawZX6ArO2utLqcVg+PE30AsNTP+vjSg0UQ9RAMUQNFEPUQDFEDRRD1EAxRA0UQ9RAMUQNFEPUQDFEDRRD1EAxRA0UQ9RAMU7S/kntsaSvWz7tmqTTLZ+zS33a26etUr/2drX1b0m2/WWAnUTdBdujJMNF72iqT3v7tFXq195FbOXuN1AMUQPF9CnqI4seMKU+7e3TVqlfe+e+tTf/pgbQTJ+u1AAaIGqgGKIGiiFqoBiiBor5H5afThkRznEAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.sparse import coo_matrix\n",
    "cmap = backend.configuration().coupling_map\n",
    "rows = [c[0] for c in cmap]\n",
    "cols = [c[1] for c in cmap]\n",
    "data = np.ones_like(rows)\n",
    "adj_matrix = coo_matrix((data,(rows,cols)),shape=(5,5))\n",
    "plt.spy(adj_matrix);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If it is possible to perform CNOT gates in both directions on all pairs of qubits, then this matrix is symmetric.\n",
    "\n",
    "We are free to construct our own device topology by defining our own `coupling_map` and using it in `transpile`.  For example, a five qubit linear nearest-neighbor (LNN) topology supporting bi-direction CNOT gates is written as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:31.854550Z",
     "start_time": "2019-08-09T13:56:31.851114Z"
    }
   },
   "outputs": [],
   "source": [
    "lnn5 = [[0,1], [1,0], [1,2], [2,1], [2,3], [3,2], [3,4], [4,3]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:32.182267Z",
     "start_time": "2019-08-09T13:56:32.092850Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPUAAAD8CAYAAACvvuKtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAJ80lEQVR4nO3dT2icBR7G8efZtEEhCx5mDtKUjQeRLcIqvBSht2Kh/kGvCnoSelmhgiAKvQg9ixcvRcUFRRH0IOIiAS0iuOobrWI3CkUUi0IniGguhupvDzPQ0k0670zed955f/1+IJA0L+88TPPtO51MU0eEAOTxl7YHAKgXUQPJEDWQDFEDyRA1kAxRA8l0ImrbR21/Y/uc7Sfb3nM1tl+0fcH2V21vGcf2ftvv2163fdb28bY37cT2dbY/sf3FaOvTbW+qwvaC7c9tvz2r25z7qG0vSHpO0l2SDkh60PaBdldd1UuSjrY9oqKLkh6PiL9LukPSP+f4vv1d0uGI+Iek2yQdtX1Hy5uqOC5pfZY3OPdRSzoo6VxEfBsRW5Jek3R/y5t2FBEfSPq57R1VRMRPEfHZ6P3fNPzi29fuqu3F0Obow72jt7l+5ZTtZUn3SHp+lrfbhaj3Sfrhso/Pa06/8LrM9oqk2yV93O6SnY0eyp6RdEHSakTM7daRZyU9IenPWd5oF6L2Nr82139Cd43tJUlvSHosIn5te89OIuKPiLhN0rKkg7ZvbXvTTmzfK+lCRKzN+ra7EPV5Sfsv+3hZ0o8tbUnH9l4Ng34lIt5se08VEfGLpNOa7+cuDkm6z/Z3Gv6V8bDtl2dxw12I+lNJN9u+yfaipAckvdXyphRsW9ILktYj4pm291yN7b7tG0bvXy/pTklft7tqZxHxVEQsR8SKhl+z70XEQ7O47bmPOiIuSnpU0rsaPpHzekScbXfVzmy/KukjSbfYPm/7kbY3XcUhSQ9reBU5M3q7u+1RO7hR0vu2v9TwD/rViJjZt4m6xPzTSyCXub9SA5gMUQPJEDWQDFEDyRA1kExnorZ9rO0Nk+jS3i5tlbq1t42tnYlaUmd+I0e6tLdLW6Vu7SVqALvTyItPer1erKys1HrOwWCgfr9f6zmb1KW9XdoqdWtvU1vX1tY2ImLbE++p/dYkraysqCzLJk4NQJLt73f6HA+/gWSIGkiGqIFkiBpIhqiBZIgaSIaogWSIGkiGqIFkiBpIhqiBZIgaSIaogWSIGkiGqIFkGvn31Nea4uSqNja3xh7XW1pUeeLIDBbhWlbpSm37qO1vbJ+z/WTTo7qmStCTHAfsxtiobS9Iek7SXZIOSHrQ9oGmhwGYTpUr9UFJ5yLi24jY0vD/2r2/2VkAplUl6n2Sfrjs4/OjXwMwh6pE7W1+7f9+BKntY7ZL2+VgMNj9MgBTqRL1eUn7L/t4WdKPVx4UEaciooiIois/vhXIqErUn0q62fZNthclPSDprWZnAZjW2O9TR8RF249KelfSgqQXI+Js48sATKXSi08i4h1J7zS8BUANeJloDXpLi7UeB+wGLxOtAS/9xDzhSg0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kM5f/P3VxclUbm1tjj+stLfJ/Q0+I+za/sVdq2y/avmD7q1kMklTpi26S43AJ921+VR5+vyTpaMM7ANRkbNQR8YGkn2ewBUANeKIMSKa2qG0fs13aLgeDQV2nBTCh2qKOiFMRUURE0e/36zotgAnx8BtIpsq3tF6V9JGkW2yft/1I87MATGvsi08i4sFZDAFQj7l8+N1bWqz1OFzCfZufI6L2kxZFEWVZ1n5eAEO21yKi2O5zc3mlBjA9ogaSIWogGaIGkiFqIBmiBpIhaiAZogaSIWogGaIGkiFqIBmiBpIhaiAZogaSIWogGaIGkiFqIBmiBpIhaiAZogaSIWogGaIGkiFqIBmiBpIhaiAZogaSIWogGaIGkiFqIBmiBpIhaiAZogaS2dP2gAyKk6va2Nwae1xvaVHliSMzWJQH9+3kxl6pbe+3/b7tddtnbR+fxbAuqfJFN8lxuIT7dnJVrtQXJT0eEZ/Z/qukNdurEfHfhrcBmMLYK3VE/BQRn43e/03SuqR9TQ8DMJ2JniizvSLpdkkfNzEGwO5Vjtr2kqQ3JD0WEb9u8/ljtkvb5WAwqHMjgAlUitr2Xg2DfiUi3tzumIg4FRFFRBT9fr/OjQAmUOXZb0t6QdJ6RDzT/CQAu1HlSn1I0sOSDts+M3q7u+FdAKY09ltaEfGhJM9gC4Aa8DLRGvSWFms9Dpdw307OEVH7SYuiiLIsaz8vgCHbaxFRbPc5rtRAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMnvaHoDZKk6uamNza+xxvaVFlSeOzGBRHvNy3469Utu+zvYntr+wfdb2042tQeOqfNFNchwumZf7tsqV+ndJhyNi0/ZeSR/a/ndE/KfRZQCmMjbqiAhJm6MP947eoslRAKZX6Yky2wu2z0i6IGk1Ij5udhaAaVWKOiL+iIjbJC1LOmj71iuPsX3Mdmm7HAwGde8EUNFE39KKiF8knZZ0dJvPnYqIIiKKfr9f0zwAk6ry7Hff9g2j96+XdKekr5seBmA6VZ79vlHSv2wvaPiHwOsR8XazswBMq8qz319Kun0GWwDUgJeJXmN6S4u1HodL5uW+9fDb0PUqiiLKsqz9vACGbK9FRLHd57hSA8kQNZAMUQPJEDWQDFEDyRA1kAxRA8kQNZAMUQPJEDWQDFEDyRA1kAxRA8kQNZAMUQPJEDWQDFEDyRA1kAxRA8kQNZAMUQPJEDWQDFEDyRA1kAxRA8kQNZAMUQPJEDWQDFEDyRA1kAxRA8kQNZDMnrYHAFdTnFzVxubW2ON6S4sqTxyZwaL5V/lKbXvB9ue2325yEHC5KkFPcty1YJKH38clrTc1BEA9KkVte1nSPZKeb3YOgN2qeqV+VtITkv5scAuAGoyN2va9ki5ExNqY447ZLm2Xg8GgtoEAJlPlSn1I0n22v5P0mqTDtl++8qCIOBURRUQU/X6/5pkAqhobdUQ8FRHLEbEi6QFJ70XEQ40vAzAVXnwCJDPRi08i4rSk040sAVALrtSYa72lxVqPuxbwMlHMNV76OTmu1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0kQ9RAMkQNJEPUQDJEDSRD1EAyRA0k44io/6T2QNL3NZ+2J2mj5nM2qUt7u7RV6tbeprb+LSK2/WGAjUTdBNtlRBRt76iqS3u7tFXq1t42tvLwG0iGqIFkuhT1qbYHTKhLe7u0VerW3plv7czfqQFU06UrNYAKiBpIhqiBZIgaSIaogWT+B9JNcRfd0M1RAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = [c[0] for c in lnn5]\n",
    "cols = [c[1] for c in lnn5]\n",
    "data = np.ones_like(rows)\n",
    "adj_matrix = coo_matrix((data,(rows,cols)),shape=(5,5))\n",
    "plt.spy(adj_matrix);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then use this `coupling_map` in place of an actual backend as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:32.784373Z",
     "start_time": "2019-08-09T13:56:32.392714Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 948.327x294.626 with 1 Axes>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lnn5_circ = transpile(ghz, backend=None, coupling_map=lnn5)\n",
    "lnn5_circ.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or we can write a directional five qubit '+' shaped topology, with all directional CNOT gates pointing to the center as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:35.162158Z",
     "start_time": "2019-08-09T13:56:35.159222Z"
    }
   },
   "outputs": [],
   "source": [
    "plus = [[0,2], [1,2], [3,2], [4,2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:35.578426Z",
     "start_time": "2019-08-09T13:56:35.484158Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = [c[0] for c in plus]\n",
    "cols = [c[1] for c in plus]\n",
    "data = np.ones_like(rows)\n",
    "adj_matrix = coo_matrix((data,(rows,cols)),shape=(5,5))\n",
    "plt.spy(adj_matrix);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:56:37.342535Z",
     "start_time": "2019-08-09T13:56:36.761977Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1270.57x616.873 with 1 Axes>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plus_circ = transpile(ghz, backend=None, coupling_map=plus)\n",
    "plus_circ.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above examples we can see that a Hadamard gate is still in the circuit.  This is because with `backend=None` we also need to specify the `basis_gates` if we want a specific gate set at the end."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Passing Transpiled Circuits to a Backend <a name='passing'></a>\n",
    "\n",
    "Now that we have transpiled circuits, the final step is to pass them to a backend for execution.  There are two ways of doing this:\n",
    "\n",
    "1) Pass the circuits to `execute` as done before.\n",
    "\n",
    "2) Use the `assemble` function to package them, and then call the backend directly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using `execute` with transpiled circuits\n",
    "\n",
    "Typically one is interested in transpiling circuits for the same backend that they intend to run their circuits on.  In this case, the circuits have already been mapped to the backend and optimized so calling:\n",
    "\n",
    "```\n",
    "job = execute(transpiled_circuits, backend, **kwargs)\n",
    "```\n",
    "Will simply package the circuits up, and send them to the target backend.  The exeception to this rule is if the level of optimization is different than what the circuits were originally transpiled with.  That is to say setting `optimization_level=3` in `execute` while passing circuits transpiled under `optimization_level=1` (the default) will undergo further optimization before being sent to the device."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Packaging Circuits with `assemble`\n",
    "\n",
    "It is also possible to skip the `execute` function and bundle the transpiled circuits using the `assemble` function.  The `assemble` function is designed to take both circuits and pulse schedules and has lots of input arguments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T14:06:50.694252Z",
     "start_time": "2019-08-09T14:06:50.690385Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Signature (experiments, backend=None, qobj_id=None, qobj_header=None, shots=1024, memory=False, max_credits=None, seed_simulator=None, qubit_lo_freq=None, meas_lo_freq=None, qubit_lo_range=None, meas_lo_range=None, schedule_los=None, meas_level=2, meas_return='avg', meas_map=None, memory_slot_size=100, rep_time=None, parameter_binds=None, **run_config)>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect.signature(assemble)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "but many of them overlap with those in `execute`.  Here `experiments` is the circuit or list of circuits to be run, and `backend` is of course the backend you are targeting.  The other important ones are:\n",
    "\n",
    "- **shots** - Number of times to execute each circuit.\n",
    "\n",
    "- **memory** - Return the resulting bitstring for each shot rather than collecting counts.\n",
    "\n",
    "A standard call to `assemble` would look like:\n",
    "\n",
    "```\n",
    "qobj = assemble(transpiled_circuits, backend, shots=2048)\n",
    "```\n",
    "\n",
    "where `qobj` is the container format used in sending circuits (and pulse experiments) to the devices.  This `qobj` can be run by calling the `backend` directly:\n",
    "\n",
    "```\n",
    "job = backend.run(qobj)\n",
    "```\n",
    "\n",
    "that will return a `job` just like `execute`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T01:41:22.751335Z",
     "start_time": "2019-08-09T01:41:22.745919Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>None</td></tr><tr><td>Terra</td><td>0.9.0</td></tr><tr><td>Aer</td><td>0.3.0</td></tr><tr><td>Ignis</td><td>0.2.0</td></tr><tr><td>Aqua</td><td>0.5.6</td></tr><tr><td>IBM Q Provider</td><td>0.3.1</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.7.3 (default, Mar 27 2019, 16:54:48) \n",
       "[Clang 4.0.1 (tags/RELEASE_401/final)]</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>4</td></tr><tr><td>Memory (Gb)</td><td>16.0</td></tr><tr><td colspan='2'>Thu Aug 08 21:41:22 2019 EDT</td></tr></table>"
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       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>&copy; Copyright IBM 2017, 2019.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
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       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
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   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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