qiskit/fundamentals/4_quantum_circuit_properties.ipynb

{
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-05T15:02:24.868454Z",
     "start_time": "2019-08-05T15:02:24.863831Z"
    }
   },
   "source": [
    "![qiskit_header.png](attachment:qiskit_header.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of contents\n",
    "\n",
    "1) [Introduction](#introduction)\n",
    "\n",
    "\n",
    "2) [Circuit Depth](#depth)\n",
    "\n",
    "\n",
    "3) [Circuit Unitary Factors](#unitary)\n",
    "\n",
    "\n",
    "4) [Circuits with Classical Registers](#classical)\n",
    "\n",
    "\n",
    "5) [Gate Set Dependence of Depth](#gate_dependence)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:41.150575Z",
     "start_time": "2019-08-09T13:41:38.833301Z"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction <a name='introduction'></a>\n",
    "\n",
    "When constructing quantum circuits, there are several properties that help quantify the \"size\" of the circuits, and their ability to be run on a noisy quantum device.  Some of these, like number of qubits, are straightforward to understand, while others like depth and number of tensor components require a bit more explanation.  Here we will explain all of these properties, and, in preparation for understanding how circuits change when run on actual devices, highlight the conditions under which they change.\n",
    "\n",
    "\n",
    "### Basics\n",
    "Consider the following circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:41.750753Z",
     "start_time": "2019-08-09T13:41:41.158135Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">         ┌───┐                                                           \n",
       " q_0: |0>┤ H ├──■────────────────────────────────────────────────────────\n",
       "         ├───┤  │                                                        \n",
       " q_1: |0>┤ H ├──┼────■───────────────────■────■─────────■────────────────\n",
       "         ├───┤  │    │                   │    │         │                \n",
       " q_2: |0>┤ H ├──┼────┼────■──────────────┼────┼─────────┼────────────────\n",
       "         ├───┤  │    │    │              │    │         │                \n",
       " q_3: |0>┤ H ├──┼────┼────┼────■─────────┼────┼─────────┼────────────────\n",
       "         ├───┤  │    │    │    │         │    │         │                \n",
       " q_4: |0>┤ H ├──┼────┼────┼────┼────■────┼────┼─────────┼────────────────\n",
       "         └───┘┌─┴─┐  │    │    │    │    │    │         │                \n",
       " q_5: |0>─────┤ X ├──┼────┼────┼────┼────┼────┼─────────┼────────────────\n",
       "              └───┘┌─┴─┐  │    │    │    │    │         │           ┌───┐\n",
       " q_6: |0>──────────┤ X ├──┼────┼────┼────┼────┼─────────┼───X──X──X─┤ X ├\n",
       "                   └───┘┌─┴─┐  │    │  ┌─┴─┐  │  ┌───┐  │   │  │  │ └───┘\n",
       " q_7: |0>───────────────┤ X ├──┼────┼──┤ X ├──┼──┤ X ├──┼───┼──┼──┼──────\n",
       "                        └───┘┌─┴─┐  │  ├───┤  │  └───┘  │   │  │  │      \n",
       " q_8: |0>────────────────────┤ X ├──┼──┤ X ├──┼─────────┼───┼──┼──┼──────\n",
       "                             └───┘┌─┴─┐└───┘┌─┴─┐       │   │  │  │      \n",
       " q_9: |0>─────────────────────────┤ X ├─────┤ X ├───────┼───┼──X──┼──────\n",
       "                                  └───┘     └───┘       │   │     │      \n",
       "q_10: |0>───────────────────────────────────────────────┼───┼─────X──────\n",
       "                                                      ┌─┴─┐ │            \n",
       "q_11: |0>─────────────────────────────────────────────┤ X ├─X────────────\n",
       "                                                      └───┘              </pre>"
      ],
      "text/plain": [
       "<qiskit.visualization.text.TextDrawing at 0x19297550f48>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(12)\n",
    "\n",
    "for idx in range(5):\n",
    "    qc.h(idx)\n",
    "    qc.cx(idx, idx+5)\n",
    "\n",
    "qc.cx(1, 7)\n",
    "qc.x(8)\n",
    "qc.cx(1, 9)\n",
    "qc.x(7)\n",
    "qc.cx(1, 11)\n",
    "qc.swap(6, 11)\n",
    "qc.swap(6, 9)\n",
    "qc.swap(6, 10)\n",
    "qc.x(6)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot, it is easy to see that this circuit has 12 qubits, and a collection of Hadamard, CNOT, X, and SWAP gates.  But how to quantify this programmatically? Because we can do single-qubit gates on all the qubits simultaneously, the number of qubits in this circuit is equal to the **width** of the circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:41.770638Z",
     "start_time": "2019-08-09T13:41:41.766728Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.width()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "<b>Warning:</b> For a quantum circuit composed from just qubits, the circuit width is equal to the number of qubits.  This is the definition used in quantum computing.  However, for more complicated circuits with classical registers, and classically controlled gates, this equivalence breaks down.  As such, from now on we will <b>not</b> refer to the number of qubits in a quantum circuit as the width.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also just get the number of qubits directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:43.168268Z",
     "start_time": "2019-08-09T13:41:43.165353Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.n_qubits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also straightforward to get the number and type of the gates in a circuit using `count_ops()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:44.253551Z",
     "start_time": "2019-08-09T13:41:44.249665Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('cx', 8), ('h', 5), ('x', 3), ('swap', 3)])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.count_ops()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also get just the raw count of operations by computing the circuits **size**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:45.551875Z",
     "start_time": "2019-08-09T13:41:45.548211Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Circuit Depth <a name=\"depth\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A particularly important circuit property is known as the **depth**.  The depth of a quantum circuit is a measure of how many \"layers\" of quantum gates, executed in parallel, it takes to complete the computation defined by the circuit.  Because quantum gates take time to implement, the depth of a circuit roughly corresponds to the amount of time it takes the quantum computer to execute the circuit.  Thus, the depth of a circuit is one important quantity used to measure if a quantum circuit can be run on a device.\n",
    "\n",
    "The depth of a quantum circuit has a mathematical definition as the longest path in a directed acyclic graph (DAG).  However, such a definition is a bit hard to grasp, even for experts.  Fortunately, the depth of a circuit can be easily understood by anyone familiar with playing [Tetris](https://en.wikipedia.org/wiki/Tetris).  To understand this, let us redraw the circuit with the first five CNOT gates colored differently for clarity:"
   ]
  },
  {
   "attachments": {
    "depth_1.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![depth_1.png](attachment:depth_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute the depth, we turn the circuit counterclockwise so that the beginning of the circuit is at the bottom.  We then let the gates fall to the bottom.  Later gates stack on earlier gates, and multi-qubit gate components must be stacked at the same height.  For the current circuit of interest, this stacking looks like:"
   ]
  },
  {
   "attachments": {
    "depth_2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-05T16:39:59.435226Z",
     "start_time": "2019-08-05T16:39:59.429815Z"
    }
   },
   "source": [
    "![depth_2.png](attachment:depth_2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the first five CNOT gates all collapsed down on top of each other, and are stacked on top of the initial set of Hadamard gates.  The remaining gates stack on top of the CNOT layer as shown.  The stack of gates can be partitioned into \"layers\", where each layer represents a set of gates that can be executed in parallel on a quantum device (Hardware limitations may restrict the number and/or type of gates that can be run in parallel).  The **depth** of the circuit is just the number of layers in the circuit;  The depth is equal to the height of the stack of gates.  This computation is done for you in qiskit, and we can verify our visual method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:54.651583Z",
     "start_time": "2019-08-09T13:41:54.647492Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.depth()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unitary Factors <a name=\"unitary\"></a>\n",
    "\n",
    "The circuit we are focusing on here is a 12-qubit circuit.  However, does this circuit actually require a 12-qubit quantum computer to run?  That is to say, can we compute  the same result by running a collection of smaller circuits individually?\n",
    "\n",
    "In the limit where only single-qubit gates are performed, it should be clear that each qubit is controlled independently of the rest, and thus we can run each qubit independently and still get the desired result.  Thus, the question becomes are there enough entangling gates in the circuit to have all qubits interacting?  Again, this is best understood in terms of diagrams.  Below, we track the sets of qubits that interact amongst themselves via CNOT gates at each layer in the circuit."
   ]
  },
  {
   "attachments": {
    "tensor_factors_1.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-05T17:23:58.305508Z",
     "start_time": "2019-08-05T17:23:58.301385Z"
    }
   },
   "source": [
    "![tensor_factors_1.png](attachment:tensor_factors_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that at the end of the computation there are three independent sets of qubits.  Thus, our 12-qubit computation is actual two two-qubit calculations and a single eight-qubit computation.  We can verify this via qiskit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:56.134319Z",
     "start_time": "2019-08-09T13:41:56.129574Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.num_unitary_factors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circuits with Classical Registers and Measurements <a name=\"classical\"></a>\n",
    "\n",
    "Several of the circuit properties introduced so far change when adding classical registers and measurements.\n",
    "\n",
    "Let's add measurements to the circuit above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:57.804795Z",
     "start_time": "2019-08-09T13:41:57.175649Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">         ┌───┐                                                            ░ ┌─┐»\n",
       " q_0: |0>┤ H ├──■─────────────────────────────────────────────────────────░─┤M├»\n",
       "         ├───┤  │                                                         ░ └╥┘»\n",
       " q_1: |0>┤ H ├──┼────■───────────────────■────■─────────■─────────────────░──╫─»\n",
       "         ├───┤  │    │                   │    │         │                 ░  ║ »\n",
       " q_2: |0>┤ H ├──┼────┼────■──────────────┼────┼─────────┼─────────────────░──╫─»\n",
       "         ├───┤  │    │    │              │    │         │                 ░  ║ »\n",
       " q_3: |0>┤ H ├──┼────┼────┼────■─────────┼────┼─────────┼─────────────────░──╫─»\n",
       "         ├───┤  │    │    │    │         │    │         │                 ░  ║ »\n",
       " q_4: |0>┤ H ├──┼────┼────┼────┼────■────┼────┼─────────┼─────────────────░──╫─»\n",
       "         └───┘┌─┴─┐  │    │    │    │    │    │         │                 ░  ║ »\n",
       " q_5: |0>─────┤ X ├──┼────┼────┼────┼────┼────┼─────────┼─────────────────░──╫─»\n",
       "              └───┘┌─┴─┐  │    │    │    │    │         │           ┌───┐ ░  ║ »\n",
       " q_6: |0>──────────┤ X ├──┼────┼────┼────┼────┼─────────┼───X──X──X─┤ X ├─░──╫─»\n",
       "                   └───┘┌─┴─┐  │    │  ┌─┴─┐  │  ┌───┐  │   │  │  │ └───┘ ░  ║ »\n",
       " q_7: |0>───────────────┤ X ├──┼────┼──┤ X ├──┼──┤ X ├──┼───┼──┼──┼───────░──╫─»\n",
       "                        └───┘┌─┴─┐  │  ├───┤  │  └───┘  │   │  │  │       ░  ║ »\n",
       " q_8: |0>────────────────────┤ X ├──┼──┤ X ├──┼─────────┼───┼──┼──┼───────░──╫─»\n",
       "                             └───┘┌─┴─┐└───┘┌─┴─┐       │   │  │  │       ░  ║ »\n",
       " q_9: |0>─────────────────────────┤ X ├─────┤ X ├───────┼───┼──X──┼───────░──╫─»\n",
       "                                  └───┘     └───┘       │   │     │       ░  ║ »\n",
       "q_10: |0>───────────────────────────────────────────────┼───┼─────X───────░──╫─»\n",
       "                                                      ┌─┴─┐ │             ░  ║ »\n",
       "q_11: |0>─────────────────────────────────────────────┤ X ├─X─────────────░──╫─»\n",
       "                                                      └───┘               ░  ║ »\n",
       "  c_0: 0 ════════════════════════════════════════════════════════════════════╩═»\n",
       "                                                                               »\n",
       "  c_1: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_2: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_3: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_4: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_5: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_6: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_7: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_8: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "  c_9: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       " c_10: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       " c_11: 0 ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                               »\n",
       "«                                       \n",
       "« q_0: ─────────────────────────────────\n",
       "«      ┌─┐                              \n",
       "« q_1: ┤M├──────────────────────────────\n",
       "«      └╥┘┌─┐                           \n",
       "« q_2: ─╫─┤M├───────────────────────────\n",
       "«       ║ └╥┘┌─┐                        \n",
       "« q_3: ─╫──╫─┤M├────────────────────────\n",
       "«       ║  ║ └╥┘┌─┐                     \n",
       "« q_4: ─╫──╫──╫─┤M├─────────────────────\n",
       "«       ║  ║  ║ └╥┘┌─┐                  \n",
       "« q_5: ─╫──╫──╫──╫─┤M├──────────────────\n",
       "«       ║  ║  ║  ║ └╥┘┌─┐               \n",
       "« q_6: ─╫──╫──╫──╫──╫─┤M├───────────────\n",
       "«       ║  ║  ║  ║  ║ └╥┘┌─┐            \n",
       "« q_7: ─╫──╫──╫──╫──╫──╫─┤M├────────────\n",
       "«       ║  ║  ║  ║  ║  ║ └╥┘┌─┐         \n",
       "« q_8: ─╫──╫──╫──╫──╫──╫──╫─┤M├─────────\n",
       "«       ║  ║  ║  ║  ║  ║  ║ └╥┘┌─┐      \n",
       "« q_9: ─╫──╫──╫──╫──╫──╫──╫──╫─┤M├──────\n",
       "«       ║  ║  ║  ║  ║  ║  ║  ║ └╥┘┌─┐   \n",
       "«q_10: ─╫──╫──╫──╫──╫──╫──╫──╫──╫─┤M├───\n",
       "«       ║  ║  ║  ║  ║  ║  ║  ║  ║ └╥┘┌─┐\n",
       "«q_11: ─╫──╫──╫──╫──╫──╫──╫──╫──╫──╫─┤M├\n",
       "«       ║  ║  ║  ║  ║  ║  ║  ║  ║  ║ └╥┘\n",
       "« c_0: ═╬══╬══╬══╬══╬══╬══╬══╬══╬══╬══╬═\n",
       "«       ║  ║  ║  ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "« c_1: ═╩══╬══╬══╬══╬══╬══╬══╬══╬══╬══╬═\n",
       "«          ║  ║  ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "« c_2: ════╩══╬══╬══╬══╬══╬══╬══╬══╬══╬═\n",
       "«             ║  ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "« c_3: ═══════╩══╬══╬══╬══╬══╬══╬══╬══╬═\n",
       "«                ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "« c_4: ══════════╩══╬══╬══╬══╬══╬══╬══╬═\n",
       "«                   ║  ║  ║  ║  ║  ║  ║ \n",
       "« c_5: ═════════════╩══╬══╬══╬══╬══╬══╬═\n",
       "«                      ║  ║  ║  ║  ║  ║ \n",
       "« c_6: ════════════════╩══╬══╬══╬══╬══╬═\n",
       "«                         ║  ║  ║  ║  ║ \n",
       "« c_7: ═══════════════════╩══╬══╬══╬══╬═\n",
       "«                            ║  ║  ║  ║ \n",
       "« c_8: ══════════════════════╩══╬══╬══╬═\n",
       "«                               ║  ║  ║ \n",
       "« c_9: ═════════════════════════╩══╬══╬═\n",
       "«                                  ║  ║ \n",
       "«c_10: ════════════════════════════╩══╬═\n",
       "«                                     ║ \n",
       "«c_11: ═══════════════════════════════╩═\n",
       "«                                       </pre>"
      ],
      "text/plain": [
       "<qiskit.visualization.text.TextDrawing at 0x19297594bc8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2 = QuantumCircuit(12, 12)\n",
    "\n",
    "for idx in range(5):\n",
    "    qc2.h(idx)\n",
    "    qc2.cx(idx, idx+5)\n",
    "\n",
    "qc2.cx(1, 7)\n",
    "qc2.x(8)\n",
    "qc2.cx(1, 9)\n",
    "qc2.x(7)\n",
    "qc2.cx(1, 11)\n",
    "qc2.swap(6, 11)\n",
    "qc2.swap(6, 9)\n",
    "qc2.swap(6, 10)\n",
    "qc2.x(6)\n",
    "qc2.barrier()\n",
    "qc2.measure(range(12), range(12))\n",
    "qc2.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **width** of the circuit now includes the number of qubits _and_ number of classical bits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:58.770816Z",
     "start_time": "2019-08-09T13:41:58.767090Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2.width()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of operations has increased because of the measurements and the barrier we used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:41:59.668505Z",
     "start_time": "2019-08-09T13:41:59.664485Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('measure', 12),\n",
       "             ('cx', 8),\n",
       "             ('h', 5),\n",
       "             ('x', 3),\n",
       "             ('swap', 3),\n",
       "             ('barrier', 1)])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2.count_ops()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the **size** of the circuit has grown:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:42:00.542953Z",
     "start_time": "2019-08-09T13:42:00.539335Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-05T17:39:12.011784Z",
     "start_time": "2019-08-05T17:39:12.008688Z"
    }
   },
   "source": [
    "The **depth** of the circuit has now increased because measurements are included in the depth computation as they perform physical operations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:42:01.831318Z",
     "start_time": "2019-08-09T13:42:01.827625Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2.depth()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Barriers and other special commands like snapshots do not count towards the depth directly. However, gates cannot pass through them and must therefore start stacking on top."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dependence of Depth on Gate Selection <a name=\"gate_dependence\"></a>\n",
    "\n",
    "We close by highlighting a very important point.  The **depth** of a quantum circuit, and thus the ability to run said circuit on noisy quantum hardware depends on the choice of gates used to implement that circuit.  The original circuit used in this tutorial had a depth of 9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:42:04.879677Z",
     "start_time": "2019-08-09T13:42:04.875785Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.depth()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, the SWAP gates used in the construction of that circuit are not native to the IBM Q devices.  A decomposition that runs on the devices is a decomposition in terms of three CNOT gates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:42:06.185935Z",
     "start_time": "2019-08-09T13:42:06.047374Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">             ┌───┐     \n",
       "q_0: |0>──■──┤ X ├──■──\n",
       "        ┌─┴─┐└─┬─┘┌─┴─┐\n",
       "q_1: |0>┤ X ├──■──┤ X ├\n",
       "        └───┘     └───┘</pre>"
      ],
      "text/plain": [
       "<qiskit.visualization.text.TextDrawing at 0x1e90a8ca608>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc3 = QuantumCircuit(2)\n",
    "qc3.swap(0,1)\n",
    "qc3.decompose().draw() # This decomposes the swap gate into the gates we want"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the exact same circuit could be written as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:42:07.332409Z",
     "start_time": "2019-08-09T13:42:06.871793Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">         ┌───┐                                                                 »\n",
       " q_0: |0>┤ H ├──■──────────────────────────────────────────────────────────────»\n",
       "         ├───┤  │                                                              »\n",
       " q_1: |0>┤ H ├──┼────■───────────────────■────■─────────■──────────────────────»\n",
       "         ├───┤  │    │                   │    │         │                      »\n",
       " q_2: |0>┤ H ├──┼────┼────■──────────────┼────┼─────────┼──────────────────────»\n",
       "         ├───┤  │    │    │              │    │         │                      »\n",
       " q_3: |0>┤ H ├──┼────┼────┼────■─────────┼────┼─────────┼──────────────────────»\n",
       "         ├───┤  │    │    │    │         │    │         │                      »\n",
       " q_4: |0>┤ H ├──┼────┼────┼────┼────■────┼────┼─────────┼──────────────────────»\n",
       "         └───┘┌─┴─┐  │    │    │    │    │    │         │                      »\n",
       " q_5: |0>─────┤ X ├──┼────┼────┼────┼────┼────┼─────────┼──────────────────────»\n",
       "              └───┘┌─┴─┐  │    │    │    │    │         │       ┌───┐          »\n",
       " q_6: |0>──────────┤ X ├──┼────┼────┼────┼────┼─────────┼────■──┤ X ├──■────■──»\n",
       "                   └───┘┌─┴─┐  │    │  ┌─┴─┐  │  ┌───┐  │    │  └─┬─┘  │    │  »\n",
       " q_7: |0>───────────────┤ X ├──┼────┼──┤ X ├──┼──┤ X ├──┼────┼────┼────┼────┼──»\n",
       "                        └───┘┌─┴─┐  │  ├───┤  │  └───┘  │    │    │    │    │  »\n",
       " q_8: |0>────────────────────┤ X ├──┼──┤ X ├──┼─────────┼────┼────┼────┼────┼──»\n",
       "                             └───┘┌─┴─┐└───┘┌─┴─┐       │    │    │    │  ┌─┴─┐»\n",
       " q_9: |0>─────────────────────────┤ X ├─────┤ X ├───────┼────┼────┼────┼──┤ X ├»\n",
       "                                  └───┘     └───┘       │    │    │    │  └───┘»\n",
       "q_10: |0>───────────────────────────────────────────────┼────┼────┼────┼───────»\n",
       "                                                      ┌─┴─┐┌─┴─┐  │  ┌─┴─┐     »\n",
       "q_11: |0>─────────────────────────────────────────────┤ X ├┤ X ├──■──┤ X ├─────»\n",
       "                                                      └───┘└───┘     └───┘     »\n",
       "«                                    \n",
       "« q_0: ──────────────────────────────\n",
       "«                                    \n",
       "« q_1: ──────────────────────────────\n",
       "«                                    \n",
       "« q_2: ──────────────────────────────\n",
       "«                                    \n",
       "« q_3: ──────────────────────────────\n",
       "«                                    \n",
       "« q_4: ──────────────────────────────\n",
       "«                                    \n",
       "« q_5: ──────────────────────────────\n",
       "«      ┌───┐          ┌───┐     ┌───┐\n",
       "« q_6: ┤ X ├──■────■──┤ X ├──■──┤ X ├\n",
       "«      └─┬─┘  │    │  └─┬─┘  │  └───┘\n",
       "« q_7: ──┼────┼────┼────┼────┼───────\n",
       "«        │    │    │    │    │       \n",
       "« q_8: ──┼────┼────┼────┼────┼───────\n",
       "«        │  ┌─┴─┐  │    │    │       \n",
       "« q_9: ──■──┤ X ├──┼────┼────┼───────\n",
       "«           └───┘┌─┴─┐  │  ┌─┴─┐     \n",
       "«q_10: ──────────┤ X ├──■──┤ X ├─────\n",
       "«                └───┘     └───┘     \n",
       "«q_11: ──────────────────────────────\n",
       "«                                    </pre>"
      ],
      "text/plain": [
       "<qiskit.visualization.text.TextDrawing at 0x1e90a8ca648>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc4 = QuantumCircuit(12)\n",
    "\n",
    "for idx in range(5):\n",
    "    qc4.h(idx)\n",
    "    qc4.cx(idx, idx+5)\n",
    "\n",
    "qc4.cx(1, 7)\n",
    "qc4.x(8)\n",
    "qc4.cx(1, 9)\n",
    "qc4.x(7)\n",
    "qc4.cx(1, 11)\n",
    "\n",
    "qc4.cx(6, 11)\n",
    "qc4.cx(11, 6)\n",
    "qc4.cx(6, 11)\n",
    "\n",
    "qc4.cx(6, 9)\n",
    "qc4.cx(9, 6)\n",
    "qc4.cx(6, 9)\n",
    "\n",
    "qc4.cx(6, 10)\n",
    "qc4.cx(10, 6)\n",
    "qc4.cx(6, 10)\n",
    "\n",
    "qc4.x(6)\n",
    "qc4.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-05T17:57:54.296659Z",
     "start_time": "2019-08-05T17:57:54.291924Z"
    }
   },
   "source": [
    "That has a depth approaching twice that of the original circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-09T13:42:08.282431Z",
     "start_time": "2019-08-09T13:42:08.278588Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc4.depth()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This simple example is meant to illustrate a very important point: **When running circuits on actual quantum devices, the circuit that gets run is in general not the same circuit that you constructed**.  In addition, the depth of that new circuit is likely to be larger, and in some cases much larger, than the original one.  Fortunately, often times one can reduce this overhead through smart circuit rewriting toolchains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T23:38:16.528901Z",
     "start_time": "2019-08-08T23:38:16.523169Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>0.14.0</td></tr><tr><td>Terra</td><td>0.11.0</td></tr><tr><td>Aer</td><td>0.3.4</td></tr><tr><td>Ignis</td><td>0.2.0</td></tr><tr><td>Aqua</td><td>0.6.1</td></tr><tr><td>IBM Q Provider</td><td>0.4.4</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.7.4 (default, Aug  9 2019, 18:34:13) [MSC v.1915 64 bit (AMD64)]</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td>CPUs</td><td>2</td></tr><tr><td>Memory (Gb)</td><td>7.9987335205078125</td></tr><tr><td colspan='2'>Tue Dec 10 15:37:44 2019 Eastern Standard Time</td></tr></table>"
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      "text/plain": [
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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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   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
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   "metadata": {},
   "outputs": [],
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