qiskit/advanced/ignis/6a_state_tomography.ipynb

{
 "cells": [
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![qiskit_header.png](attachment:qiskit_header.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum State Tomography"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains examples for using the ``ignis.verification.tomography`` state tomography module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:05.692984Z",
     "start_time": "2019-12-10T22:02:02.719087Z"
    }
   },
   "outputs": [],
   "source": [
    "# Needed for functions\n",
    "import numpy as np\n",
    "import time\n",
    "from copy import deepcopy\n",
    "\n",
    "# Import Qiskit classes\n",
    "import qiskit \n",
    "from qiskit import QuantumRegister, QuantumCircuit, ClassicalRegister, Aer\n",
    "from qiskit.quantum_info import state_fidelity\n",
    "from qiskit.providers.aer import noise\n",
    "\n",
    "# Tomography functions\n",
    "from qiskit.ignis.verification.tomography import state_tomography_circuits, StateTomographyFitter\n",
    "import qiskit.ignis.mitigation.measurement as mc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-Qubit state tomography Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the below example we want to perform state tomography on a 2Q Bell state between qubits 3 and 5. To make the reference circuit we generate the expected statevector using ``statevector_simulator`` between qubits 0 and 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:05.715895Z",
     "start_time": "2019-12-10T22:02:05.695482Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         ┌───┐     \n",
      "q0_0: |0>┤ H ├──■──\n",
      "         └───┘┌─┴─┐\n",
      "q0_1: |0>─────┤ X ├\n",
      "              └───┘\n",
      "[0.70710678+0.j 0.        +0.j 0.        +0.j 0.70710678+0.j]\n"
     ]
    }
   ],
   "source": [
    "# Create the expected density matrix\n",
    "q2 = QuantumRegister(2)\n",
    "bell = QuantumCircuit(q2)\n",
    "bell.h(q2[0])\n",
    "bell.cx(q2[0], q2[1])\n",
    "print(bell)\n",
    "\n",
    "job = qiskit.execute(bell, Aer.get_backend('statevector_simulator'))\n",
    "psi_bell = job.result().get_statevector(bell)\n",
    "print(psi_bell)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:05.726381Z",
     "start_time": "2019-12-10T22:02:05.719133Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   \n",
      "q1_0: |0>──────────\n",
      "                   \n",
      "q1_1: |0>──────────\n",
      "                   \n",
      "q1_2: |0>──────────\n",
      "         ┌───┐     \n",
      "q1_3: |0>┤ H ├──■──\n",
      "         └───┘  │  \n",
      "q1_4: |0>───────┼──\n",
      "              ┌─┴─┐\n",
      "q1_5: |0>─────┤ X ├\n",
      "              └───┘\n"
     ]
    }
   ],
   "source": [
    "# Create the actual circuit \n",
    "q2 = QuantumRegister(6)\n",
    "bell = QuantumCircuit(q2)\n",
    "bell.h(q2[3])\n",
    "bell.cx(q2[3], q2[5])\n",
    "print(bell)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we are going to generate and run the state tomography circuits. By only passing in the 2 registers we want to measure the state tomography will only run on that reduced $2^2$ Hilbert space. However, if we pass the whole register in the state tomography module will try and fit the full $2^6$ space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:05.962627Z",
     "start_time": "2019-12-10T22:02:05.729674Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 0.08162879943847656\n"
     ]
    }
   ],
   "source": [
    "# Generate circuits and run on simulator\n",
    "t = time.time()\n",
    "# Generate the state tomography circuits. Only pass in the \n",
    "# registers we want to measure (in this case 3 and 5)\n",
    "qst_bell = state_tomography_circuits(bell, [q2[3],q2[5]])\n",
    "job = qiskit.execute(qst_bell, Aer.get_backend('qasm_simulator'), shots=5000)\n",
    "print('Time taken:', time.time() - t)\n",
    "\n",
    "tomo_bell = StateTomographyFitter(job.result(), qst_bell)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fitter will output a density matrix ordered according to how we passed in the registers to ``state_tomography_circuits``. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:06.222354Z",
     "start_time": "2019-12-10T22:02:05.964786Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit Fidelity = 0.9998367586964225\n"
     ]
    }
   ],
   "source": [
    "# Perform the tomography fit\n",
    "# which outputs a density matrix\n",
    "rho_bell = tomo_bell.fit()\n",
    "F_bell = state_fidelity(psi_bell, rho_bell)\n",
    "print('Fit Fidelity =', F_bell)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Repeat the Example with Measurement Noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:07.149325Z",
     "start_time": "2019-12-10T22:02:06.224483Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit Fidelity (no correction) = 0.571108210311232\n",
      "Fit Fidelity (w/ correction) = 0.9905539409293663\n"
     ]
    }
   ],
   "source": [
    "#Add measurement noise\n",
    "noise_model = noise.NoiseModel()\n",
    "for qi in range(6):\n",
    "    read_err = noise.errors.readout_error.ReadoutError([[0.75, 0.25],[0.1,0.9]])\n",
    "    noise_model.add_readout_error(read_err,[qi])\n",
    "    \n",
    "#generate the calibration circuits\n",
    "meas_calibs, state_labels = mc.complete_meas_cal(qubit_list=[3,5])\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job_cal = qiskit.execute(meas_calibs, backend=backend, shots=15000, noise_model=noise_model)\n",
    "job_tomo = qiskit.execute(qst_bell, backend=backend, shots=15000, noise_model=noise_model)\n",
    "\n",
    "meas_fitter = mc.CompleteMeasFitter(job_cal.result(),state_labels)\n",
    "\n",
    "tomo_bell = StateTomographyFitter(job_tomo.result(), qst_bell)\n",
    "\n",
    "#no correction\n",
    "rho_bell = tomo_bell.fit()\n",
    "F_bell = state_fidelity(psi_bell, rho_bell)\n",
    "print('Fit Fidelity (no correction) =', F_bell)\n",
    "\n",
    "#correct data\n",
    "correct_tomo_results = meas_fitter.filter.apply(job_tomo.result(), method='least_squares')\n",
    "tomo_bell = StateTomographyFitter(correct_tomo_results, qst_bell)\n",
    "rho_bell = tomo_bell.fit()\n",
    "F_bell = state_fidelity(psi_bell, rho_bell)\n",
    "print('Fit Fidelity (w/ correction) =', F_bell)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating and fitting random states\n",
    "\n",
    "We now test the functions on the state generated by a circuit consisting of a layer of random single qubit unitaries u3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:07.158424Z",
     "start_time": "2019-12-10T22:02:07.151860Z"
    }
   },
   "outputs": [],
   "source": [
    "def random_u3_tomo(nq, shots):\n",
    "    \n",
    "    def rand_angles():\n",
    "        return tuple(2 * np.pi * np.random.random(3) - np.pi)\n",
    "    q = QuantumRegister(nq)\n",
    "    circ = QuantumCircuit(q)\n",
    "    for j in range(nq):\n",
    "        circ.u3(*rand_angles(), q[j])\n",
    "    job = qiskit.execute(circ, Aer.get_backend('statevector_simulator'))\n",
    "    psi_rand = job.result().get_statevector(circ)\n",
    "    \n",
    "    qst_circs = state_tomography_circuits(circ, q)\n",
    "    job = qiskit.execute(qst_circs, Aer.get_backend('qasm_simulator'),\n",
    "                         shots=shots)\n",
    "    tomo_data = StateTomographyFitter(job.result(), qst_circs)\n",
    "    rho_cvx = tomo_data.fit(method='cvx')\n",
    "    rho_lstsq = tomo_data.fit(method='lstsq')\n",
    "    \n",
    "    print('F fit (CVX) =', state_fidelity(psi_rand, rho_cvx))\n",
    "    print('F fit (LSTSQ) =', state_fidelity(psi_rand, rho_lstsq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:10.608393Z",
     "start_time": "2019-12-10T22:02:07.162333Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random single-qubit unitaries: set 0\n",
      "F fit (CVX) = 0.9970021426687093\n",
      "F fit (LSTSQ) = 0.9938559982001989\n",
      "Random single-qubit unitaries: set 1\n",
      "F fit (CVX) = 0.9926241507480411\n",
      "F fit (LSTSQ) = 0.9881044594933572\n",
      "Random single-qubit unitaries: set 2\n",
      "F fit (CVX) = 0.9986710986679923\n",
      "F fit (LSTSQ) = 0.99990232375963\n",
      "Random single-qubit unitaries: set 3\n",
      "F fit (CVX) = 0.9942910810880954\n",
      "F fit (LSTSQ) = 0.9911223098568922\n",
      "Random single-qubit unitaries: set 4\n",
      "F fit (CVX) = 0.9982499565955223\n",
      "F fit (LSTSQ) = 0.9966482823050419\n"
     ]
    }
   ],
   "source": [
    "for j in range(5):\n",
    "    print('Random single-qubit unitaries: set {}'.format(j))\n",
    "    random_u3_tomo(3, 5000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5-Qubit Bell State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:18.551117Z",
     "start_time": "2019-12-10T22:02:10.612471Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 7.9116270542144775\n"
     ]
    }
   ],
   "source": [
    "# Create a state preparation circuit\n",
    "q5 = QuantumRegister(5)\n",
    "bell5 = QuantumCircuit(q5)\n",
    "bell5.h(q5[0])\n",
    "for j in range(4):\n",
    "    bell5.cx(q5[j], q5[j + 1])\n",
    "\n",
    "# Get ideal output state\n",
    "job = qiskit.execute(bell5, Aer.get_backend('statevector_simulator'))\n",
    "psi_bell5 = job.result().get_statevector(bell5)\n",
    "\n",
    "# Generate circuits and run on simulator\n",
    "t = time.time()\n",
    "qst_bell5 = state_tomography_circuits(bell5, q5)\n",
    "job = qiskit.execute(qst_bell5, Aer.get_backend('qasm_simulator'), shots=5000)\n",
    "\n",
    "# Extract tomography data so that counts are indexed by measurement configuration\n",
    "tomo_bell5 = StateTomographyFitter(job.result(), qst_bell5)\n",
    "print('Time taken:', time.time() - t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:02:22.223534Z",
     "start_time": "2019-12-10T22:02:18.553830Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Least-Sq Reconstruction\n",
      "Time taken: 3.6655709743499756\n",
      "Fit Fidelity: 0.9942473311097934\n"
     ]
    }
   ],
   "source": [
    "t = time.time()\n",
    "rho_lstsq_bell5 = tomo_bell5.fit(method='lstsq')\n",
    "print('Least-Sq Reconstruction')\n",
    "print('Time taken:', time.time() - t)\n",
    "print('Fit Fidelity:', state_fidelity(psi_bell5, rho_lstsq_bell5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:01.866504Z",
     "start_time": "2019-12-10T22:02:22.225768Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CVX Reconstruction\n",
      "Time taken: 39.63530111312866\n",
      "Fidelity: 0.9999287186828141\n"
     ]
    }
   ],
   "source": [
    "t = time.time()\n",
    "rho_cvx_bell5 = tomo_bell5.fit(method='cvx')\n",
    "print('CVX Reconstruction')\n",
    "print('Time taken:', time.time() - t)\n",
    "print('Fidelity:', state_fidelity(psi_bell5, rho_cvx_bell5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-Qubit Conditional State Tomography "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we have a three qubit system where one of the qubits will be an ancilla for performing state tomography, i.e. only perform tomography when the third qubit is in the state \"1\". The circuit is setup in such a way that after conditional tomography we will get a Bell state on the first two qubits.\n",
    "\n",
    "First make a 3Q GHZ state with no classical measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:01.884883Z",
     "start_time": "2019-12-10T22:03:01.869330Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         ┌───┐               \n",
      "q9_0: |0>┤ H ├──■────────────\n",
      "         └───┘┌─┴─┐          \n",
      "q9_1: |0>─────┤ X ├──■───────\n",
      "              └───┘┌─┴─┐┌───┐\n",
      "q9_2: |0>──────────┤ X ├┤ H ├\n",
      "                   └───┘└───┘\n"
     ]
    }
   ],
   "source": [
    "# Create the actual circuit \n",
    "q2 = QuantumRegister(3)\n",
    "ghz = QuantumCircuit(q2)\n",
    "ghz.h(q2[0])\n",
    "ghz.cx(q2[0], q2[1])\n",
    "ghz.cx(q2[1], q2[2])\n",
    "ghz.h(q2[2])\n",
    "print(ghz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we are going to generate and run the state tomography circuits. Only pass the registers we want to perform state tomography on. The code will generate a new classical register for only those measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:01.903389Z",
     "start_time": "2019-12-10T22:03:01.888165Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         ┌───┐                ░ ┌───┐┌─┐   \n",
      "q9_0: |0>┤ H ├──■─────────────░─┤ H ├┤M├───\n",
      "         └───┘┌─┴─┐           ░ ├───┤└╥┘┌─┐\n",
      "q9_1: |0>─────┤ X ├──■────────░─┤ H ├─╫─┤M├\n",
      "              └───┘┌─┴─┐┌───┐ ░ └───┘ ║ └╥┘\n",
      "q9_2: |0>──────────┤ X ├┤ H ├─░───────╫──╫─\n",
      "                   └───┘└───┘ ░       ║  ║ \n",
      " c8_0: 0 ═════════════════════════════╩══╬═\n",
      "                                         ║ \n",
      " c8_1: 0 ════════════════════════════════╩═\n",
      "                                           \n"
     ]
    }
   ],
   "source": [
    "qst_ghz = state_tomography_circuits(ghz, [q2[0],q2[1]])\n",
    "print(qst_ghz[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now make a copy of this circuit (we will need it for the fitter) and make a new circuit with an ancilla measurement attached (this is what will be run):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:01.915062Z",
     "start_time": "2019-12-10T22:03:01.906411Z"
    }
   },
   "outputs": [],
   "source": [
    "#Make a copy without the ancilla register\n",
    "qst_ghz_no_anc = deepcopy(qst_ghz)\n",
    "ca = ClassicalRegister(1)\n",
    "for qst_ghz_circ in qst_ghz:\n",
    "    qst_ghz_circ.add_register(ca)\n",
    "    qst_ghz_circ.measure(q2[2],ca[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:02.335643Z",
     "start_time": "2019-12-10T22:03:01.919990Z"
    }
   },
   "outputs": [],
   "source": [
    "#Run in Aer\n",
    "job = qiskit.execute(qst_ghz, Aer.get_backend('qasm_simulator'), shots=10000)\n",
    "raw_results = job.result()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before sending the results to the state tomography fitter we must strip the register for the Q2 measurement and only keep the results when that register is 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:02.348493Z",
     "start_time": "2019-12-10T22:03:02.337934Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "new_result = deepcopy(raw_results)\n",
    "\n",
    "for resultidx, _ in enumerate(raw_results.results):\n",
    "    old_counts = raw_results.get_counts(resultidx)\n",
    "    new_counts = {}\n",
    "    \n",
    "    #change the size of the classical register\n",
    "    new_result.results[resultidx].header.creg_sizes = [new_result.results[resultidx].header.creg_sizes[0]]\n",
    "    new_result.results[resultidx].header.clbit_labels = new_result.results[resultidx].header.clbit_labels[0:-1]\n",
    "    new_result.results[resultidx].header.memory_slots = 2\n",
    "    \n",
    "    for reg_key in old_counts:\n",
    "        reg_bits = reg_key.split(' ')\n",
    "        if reg_bits[0]=='1':\n",
    "            new_counts[reg_bits[1]]=old_counts[reg_key]\n",
    "\n",
    "    new_result.results[resultidx].data.counts = \\\n",
    "        new_result.results[resultidx]. \\\n",
    "        data.counts.from_dict(new_counts)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:02.381672Z",
     "start_time": "2019-12-10T22:03:02.350264Z"
    }
   },
   "outputs": [],
   "source": [
    "tomo_bell = StateTomographyFitter(new_result, qst_ghz_no_anc)\n",
    "# Perform the tomography fit\n",
    "# which outputs a density matrix\n",
    "rho_bell = tomo_bell.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:02.390883Z",
     "start_time": "2019-12-10T22:03:02.383619Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.494+0.j   , -0.003+0.002j, -0.001+0.j   , -0.5  +0.003j],\n",
       "       [-0.003-0.002j,  0.   +0.j   ,  0.   +0.j   ,  0.003+0.002j],\n",
       "       [-0.001-0.j   ,  0.   -0.j   ,  0.   +0.j   ,  0.001+0.j   ],\n",
       "       [-0.5  -0.003j,  0.003-0.002j,  0.001-0.j   ,  0.506+0.j   ]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.around(rho_bell,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-10T22:03:02.465096Z",
     "start_time": "2019-12-10T22:03:02.392599Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "<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>3.7.5 (default, Oct 25 2019, 10:52:18) \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'>Tue Dec 10 17:03:02 2019 EST</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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   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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