Demonstration_Fault_Tolerance.ipynb

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   "source": [
    "import time\n",
    "import random"
   ]
  },
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    "# Demonstration of Fault-tolerance on the IBM 5Q chip\n",
    "\n",
    "###### Contributor : \n",
    "Christophe Vuillot\n",
    "###### Affiliations :\n",
    "JARA Institute for Quantum Information, RWTH Aachen university\n",
    "\n",
    "### Introduction\n",
    "\n",
    "This notebook uses the IBM 5Q chip to demonstrate fault-tolerant behavior of a small quantum error detection code, the [[4,2,2]] code.\n",
    "The idea is to compare some bare circuits on two qubits with their encoded version in the [[4,2,2]] code.\n",
    "The chosen circuits are ones that have some fault-tolerant implementation in the [[4,2,2]] code.\n",
    "In practice, not all are completely fault-tolerant due to the restricted connectivity of the IBM 5Q chip but close enough to show some improvement  !\n",
    "\n",
    "One can prepare |00>, |0+> or |00>+|11> almost fault-tolerantly :\n",
    "The preparation of |00> and |0+> can suffer an undetected X1.X2 error.\n",
    "\n",
    "The gates X1, X2, Z1, Z2 (Pauli matrices), H1.H2.SWAP (two Hadamards and a SWAP) and CZ (controlled phase) can be done fault tolerantly.\n",
    "\n",
    "More detailed information can be found at https://arxiv.org/abs/1610.03507, and https://arxiv.org/abs/1705.08957."
   ]
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    "### Preparing the circuits\n",
    "In order to fairly compare the encoded implementation to the bare implementation, one has to chose the best two qubits to represent the bare version. The possible pairs are listed below, chose the one with the lowest error rates at the time of doing the experiement."
   ]
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   "source": [
    "possible_pairs = [[0,1],[0,2],[1,2],[3,2],[3,4],[4,2]]\n",
    "cp = 1 #the chosen pair"
   ]
  },
  {
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   "source": [
    "The file Experiment_tools.py contains one function creating all the qasm code circuits depending on the chosen qubits for the bare version."
   ]
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     "text": [
      "Summary of the circuits that will be tested :\n",
      "\n",
      "input state\t|\tGate sequence\n",
      "--------------------------------------\n",
      "|00>     \t|\tX1 HHS CZ X2\n",
      "|00>     \t|\tHHS Z1 CZ   \n",
      "|00>     \t|\tHHS Z1 Z2   \n",
      "|00>     \t|\tHHS Z2 CZ   \n",
      "|00>+|11>\t|\tZ2 X2       \n",
      "|0+>     \t|\tX1 Z2       \n",
      "|00>     \t|\tHHS Z1      \n",
      "|00>     \t|\tHHS CZ      \n",
      "|00>     \t|\tX1 X2       \n",
      "|00>     \t|\tHHS Z2      \n",
      "|00>+|11>\t|\tX1          \n",
      "|0+>     \t|\tX1          \n",
      "|00>     \t|\tHHS         \n",
      "|00>+|11>\t|\tZ2          \n",
      "|0+>     \t|\tZ2          \n",
      "|00>     \t|\tX1          \n",
      "|00>     \t|\tX2          \n",
      "|00>+|11>\t|\t            \n",
      "|0+>     \t|\t            \n",
      "|00>     \t|\t            \n"
     ]
    }
   ],
   "source": [
    "# Creating the circuits with misc info\n",
    "from tools.Experiment_tools import *\n",
    "all_circuits = create_all_circuits(possible_pairs[cp])\n",
    "\n",
    "# Printing summary\n",
    "template = \"{input_state:9}\\t|\\t{circuit_desc:12}\"\n",
    "print('Summary of the circuits that will be tested :\\n')\n",
    "print(template.format(circuit_desc=\"Gate sequence\", input_state=\"input state\"))\n",
    "print('--------------------------------------')\n",
    "for rec in all_circuits: \n",
    "    print(template.format(**rec))\n",
    "\n",
    "# Creating job batches to be run \n",
    "qasm_batch_bare = [{'qasm':c['qasm_bare']} for c in all_circuits]\n",
    "qasm_batch_encoded = [{'qasm':c['qasm_encoded']} for c in all_circuits]"
   ]
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   "source": [
    "### Connecting to the chip\n",
    "Connecting with the IBM 5Q chip\n",
    "(Needs a correct file Qconfig.py with a correct token for the API, see at https://quantumexperience.ng.bluemix.net)"
   ]
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   "cell_type": "code",
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   "source": [
    "from IBMQuantumExperience import IBMQuantumExperience\n",
    "import Qconfig\n",
    "api = IBMQuantumExperience.IBMQuantumExperience(Qconfig.APItoken,Qconfig.config)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Running the experiment\n",
    "Configure on which device you want to run the experiment ('real' is advised to do an actual test but it requires credits from the Quantum Experience).\n",
    "Configure also how many runs for each version and how many shots (< 8192) per run."
   ]
  },
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   "cell_type": "code",
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   "source": [
    "device = 'real'\n",
    "N_bare = 6\n",
    "N_encoded = 6\n",
    "shots = 8192"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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     "text": [
      "\n",
      "Bare circuits running... (can take several minutes)\n",
      "\n",
      "Still 1 running...\n",
      "\n",
      "All completed !\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Running the bare version of the circuits\n",
    "\n",
    "f_bare = open('data/'+device+'_bare_experiment_ids.txt', 'a')\n",
    "\n",
    "# Launching the jobs for the bare circuits onto the chip\n",
    "# The IDs of the jobs together with the index of the chosen pair of qubits\n",
    "# are also stored in the file device_bare_experiment_ids.txt\n",
    "results_bare_list = []\n",
    "for k in range(0,N_bare):\n",
    "    out_tmp = api.run_job(qasm_batch_bare, device = device, shots = shots, max_credits=5)\n",
    "    f_bare.write(out_tmp['id']+','+str(cp)+'\\n')\n",
    "    results_bare_list.append(api.get_job(out_tmp['id']))\n",
    "\n",
    "# Waiting for the jobs to finish\n",
    "i_running = range(0,N_bare)\n",
    "n_running = len(i_running)\n",
    "print('\\nBare circuits running... (can take several minutes)\\n')\n",
    "print('Still '+str(len(i_running))+' running...\\n')\n",
    "while (True in [results_bare_list[k]['status'] == 'RUNNING' for k in i_running]):\n",
    "    i_running = [k for k in i_running if results_bare_list[k]['status'] == 'RUNNING']\n",
    "    if len(i_running)!=n_running:\n",
    "        print('Still '+str(len(i_running))+' running...\\n')\n",
    "        n_running = len(i_running)\n",
    "    time.sleep(3)\n",
    "    for k in i_running:\n",
    "        results_bare_list[k] = api.get_job(results_bare_list[k]['id'])\n",
    "        \n",
    "print('All completed !\\n')\n",
    "f_bare.close()"
   ]
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Encoded circuits running... (can take several minutes)\n",
      "\n",
      "Still 1 running...\n",
      "\n",
      "All completed !\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Running the encoded version of the circuits\n",
    "\n",
    "f_encoded = open('data/'+device+'_encoded_experiment_ids.txt', 'a')\n",
    "\n",
    "\n",
    "# Launching the jobs for the encoded circuits onto the chip\n",
    "# The IDs of the jobs are stored in the file device_encoded_experiment_ids.txt\n",
    "results_encoded_list = []\n",
    "for k in range(0,N_encoded):\n",
    "    out_tmp = api.run_job(qasm_batch_encoded, device = device, shots = shots, max_credits=5)\n",
    "    f_encoded.write(out_tmp['id']+'\\n')\n",
    "    results_encoded_list.append(api.get_job(out_tmp['id']))\n",
    "\n",
    "# Waiting for the jobs to finish\n",
    "i_running = range(0,N_encoded)\n",
    "n_running = len(i_running)\n",
    "print('\\nEncoded circuits running... (can take several minutes)\\n')\n",
    "print('Still '+str(len(i_running))+' running...\\n')\n",
    "while (True in [results_encoded_list[k]['status'] == 'RUNNING' for k in i_running]):\n",
    "    i_running = [k for k in i_running if results_encoded_list[k]['status'] == 'RUNNING']\n",
    "    if len(i_running)!=n_running:\n",
    "        print('Still '+str(len(i_running))+' running...\\n')\n",
    "        n_running = len(i_running)\n",
    "    time.sleep(.1)\n",
    "    for k in i_running:\n",
    "        results_encoded_list[k] = api.get_job(results_encoded_list[k]['id'])\n",
    "        \n",
    "print('All completed !\\n')\n",
    "f_encoded.close()"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Aggregating all the previously ran experiments\n",
    "All the runs are stored using their ids in the files real_bare_experiment_ids.txt and real_encoded_experiment_ids.txt, if you had previously run the circuits their results are also gathered to analyse all the data existing at the same time."
   ]
  },
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     "text": [
      "Fetching all previous experiments for the bare versions of the circuits... (can take minutes)\n",
      "...Done.\n",
      "Fetching all previous experiments for the encoded versions of the circuits...(can take minutes)\n",
      "...Done.\n"
     ]
    }
   ],
   "source": [
    "print('Fetching all previous experiments for the bare versions of the circuits... (can take minutes)')\n",
    "\n",
    "f_bare = open('data/'+device+'_bare_experiment_ids.txt', 'r')\n",
    "\n",
    "results_bare_list = []\n",
    "cps = []\n",
    "for line in f_bare:\n",
    "    id_string, cp_string = line.split(',')\n",
    "    results_bare_list.append(api.get_job(id_string))\n",
    "    cps.append(int(cp_string))\n",
    "\n",
    "f_bare.close()\n",
    "print('...Done.')\n",
    "\n",
    "print('Fetching all previous experiments for the encoded versions of the circuits...(can take minutes)')\n",
    "\n",
    "f_encoded = open('data/'+device+'_encoded_experiment_ids.txt', 'r')\n",
    "\n",
    "results_encoded_list = []\n",
    "for line in f_encoded:\n",
    "    results_encoded_list.append(api.get_job(line.rstrip()))\n",
    "    \n",
    "f_encoded.close()\n",
    "print('...Done.')\n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### Analysing the results\n",
    "For each individual circuit and run we analyse the output distribution and can compare it to the expected one."
   ]
  },
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   "cell_type": "code",
   "execution_count": 9,
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   "source": [
    "analysed_bare = []\n",
    "analysed_encoded = []\n",
    "\n",
    "for j, res in enumerate(results_bare_list):\n",
    "    analysed_bare.append([])\n",
    "    for k in range(0,20):\n",
    "        analysed_bare[j].append(analysis_one_bare_expe(res['qasms'][k],all_circuits[k],possible_pairs[cps[j]]))\n",
    "\n",
    "for j, res in enumerate(results_encoded_list):\n",
    "    analysed_encoded.append([])\n",
    "    for k in range(0,20):\n",
    "        analysed_encoded[j].append(analysis_one_encoded_expe(res['qasms'][k],all_circuits[k]))"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "We can look at random example from the set of runs, for example for the first circuit : X2 CZ HHS X1 |00>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
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vXC3fKczpbF0zUlT1TwAzAbxlnhTZWgLrwjiAe5jL6bCV7FwRkbEi0t9cLx4iciOMG0Ps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\nzEDb658NssIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77a525d048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_one_expe(analysed_bare[random.randrange(len(analysed_bare))][0],analysed_encoded[random.randrange(len(analysed_bare))][0],0.99)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We should see that the encoded version is much more evenly distributed whereas the bare version shows suffering from decay errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "As another example we can look at the circuit : X1 X2 |00>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ERERkhQkiEREREVlhgkhEREREVpggEhEREZEVJohEREREZIUJIhERERFZYYJI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\nAKDkL512mcjarotwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77a525d710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_one_expe(analysed_bare[random.randrange(len(analysed_bare))][8],analysed_encoded[random.randrange(len(analysed_encoded))][8],0.99)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We should see the bare version being much more accurate and note that the most common error for the encoded version is precisely X1.X2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Computing average performances for each circuit\n",
    "We now look at the average performances over all runs for each circuit, comparing the statistical distance of the observed output distribution to the expected one.\n",
    "We show the difference between the statistical distance of the encoded version minus the bare version."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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REZF2pjPt5lRXw7Bh9Fm0CE45pbwTtoiIdGlK2s2pqYEFC1g5dChcddWG17hF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77a525d438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_expe = analyse_all_expe(analysed_bare, analysed_encoded, .99)\n",
    "plot_stat_dist(all_expe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Classifying circuits\n",
    "Finally we can classify the circuits depending on if the encoding actually improve the performances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Circuits better encoded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit that are improved when encoded : \n",
      "-----------------------------------------\n",
      "input state\t|\tGate sequence\n",
      "--------------------------------------\n",
      "|00>     \t|\tX1 HHS CZ X2\n",
      "|00>     \t|\tHHS Z1 CZ   \n",
      "|00>     \t|\tHHS Z1 Z2   \n",
      "|00>     \t|\tHHS Z2 CZ   \n",
      "|00>+|11>\t|\tZ2 X2       \n",
      "|00>     \t|\tHHS Z1      \n",
      "|00>     \t|\tHHS CZ      \n",
      "|00>     \t|\tHHS Z2      \n",
      "|00>+|11>\t|\tX1          \n",
      "|00>     \t|\tHHS         \n",
      "|00>+|11>\t|\tZ2          \n",
      "|00>+|11>\t|\t            \n"
     ]
    }
   ],
   "source": [
    "print('Circuit that are improved when encoded : ')\n",
    "print('-----------------------------------------')\n",
    "template = \"{input_state:9}\\t|\\t{circuit_desc:12}\"\n",
    "print(template.format(circuit_desc=\"Gate sequence\", input_state=\"input state\"))\n",
    "print('--------------------------------------')\n",
    "for rec in [c for c in all_expe if c['bare_mean_stat_dist']>c['encoded_mean_stat_dist']]: \n",
    "    print(template.format(**rec))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Circuits better bare"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Circuit that are better off performed bare : \n",
      "--------------------------------------------\n",
      "input state\t|\tGate sequence\n",
      "--------------------------------------\n",
      "|0+>     \t|\tX1 Z2       \n",
      "|00>     \t|\tX1 X2       \n",
      "|0+>     \t|\tX1          \n",
      "|0+>     \t|\tZ2          \n",
      "|00>     \t|\tX1          \n",
      "|00>     \t|\tX2          \n",
      "|0+>     \t|\t            \n",
      "|00>     \t|\t            \n"
     ]
    }
   ],
   "source": [
    "print('\\n\\nCircuit that are better off performed bare : ')\n",
    "print('--------------------------------------------')\n",
    "template = \"{input_state:9}\\t|\\t{circuit_desc:12}\"\n",
    "print(template.format(circuit_desc=\"Gate sequence\", input_state=\"input state\"))\n",
    "print('--------------------------------------')\n",
    "for rec in [c for c in all_expe if c['bare_mean_stat_dist']<c['encoded_mean_stat_dist']]: \n",
    "    print(template.format(**rec))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can see that the fault-tolerant circuits or the states whose output distribution is unchanged by the eventual X1.X2 errors perform better encoded."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
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}