qu-n-it-byzantine-agreement.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumRegister, QuantumCircuit, execute\n",
    "from qiskit import Aer\n",
    "from qiskit.providers.aer import AerSimulator\n",
    "\n",
    "from qiskit.visualization import plot_histogram\n",
    "import copy, random, itertools\n",
    "import qiskit.providers.aer.noise as noise\n",
    "from qiskit.quantum_info.analysis import hellinger_fidelity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NoiseModel:\n",
      "  Basis gates: ['cx', 'id', 'rz', 'sx', 'u3', 'x']\n",
      "  Instructions with noise: ['cx0', 'x', 'measure', 'rz', 'sx']\n",
      "  All-qubits errors: ['rz', 'sx', 'x', 'cx0', 'measure']\n"
     ]
    }
   ],
   "source": [
    "# noise model for four-general problem\n",
    "# the errors are the averages reported from the real device ibmq-sydney\n",
    "biz_noise_model = noise.NoiseModel()\n",
    "\n",
    "# Error probabilities \n",
    "prob_1 = 0.0005  # 1-qubit gate\n",
    "prob_2 =  0.013  # 2-qubit gate\n",
    "Er0 =  0.075   # readout error P(\"1\"|\"0\")\n",
    "Er1 =  0.11   # readout error P(\"0\"|\"1\")\n",
    "\n",
    "# Depolarizing quantum errors\n",
    "error_1 = noise.depolarizing_error(prob_1, 1)\n",
    "error_2 = noise.depolarizing_error(prob_2, 2)\n",
    "\n",
    "biz_noise_model.add_all_qubit_quantum_error(error_1, ['rz', 'sx', 'x'], warnings=False)\n",
    "biz_noise_model.add_all_qubit_quantum_error(error_2, ['cx0'] , warnings=False)\n",
    "biz_noise_model.add_all_qubit_readout_error([[1 - Er0, Er0], [Er1, 1 - Er1]])\n",
    "\n",
    "print(biz_noise_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters\n",
    "noise = True\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "optimization_level = 2\n",
    "shots = 2**13\n",
    "max_rounds = 500\n",
    "verbose_flag = False\n",
    "\n",
    "# number of generals\n",
    "N_gen = 4\n",
    "\n",
    "# here you can change the backends\n",
    "from qiskit.test.mock import FakeCasablanca as device_3_generals\n",
    "from qiskit.test.mock import FakeSydney as device_4_generals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# adapt to given parameters\n",
    "if N_gen == 3:\n",
    "    perms = list(itertools.permutations(['00','01','10'], r=3))\n",
    "    device = device_3_generals\n",
    "    noise_model = None\n",
    "elif N_gen == 4:\n",
    "    perms = list(itertools.permutations(['00','01','10','11'], r=4))\n",
    "    device = device_4_generals\n",
    "    noise_model = biz_noise_model\n",
    "else: \n",
    "    print(\"only the three and four generals cases considered at this time\")\n",
    "\n",
    "if noise:\n",
    "    backend = AerSimulator.from_backend(device())\n",
    "else: # switch to the ideal device\n",
    "    backend = simulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set device dependant parameter for final agreement algorithm\n",
    "noise_dic = {'qasm_simulator' : 0.0, \n",
    "             'aer_simulator(fake_casablanca)' : 0.05, \n",
    "             'aer_simulator(fake_guadalupe)' : 0.1,\n",
    "             'aer_simulator(fake_sydney)' : 0.12,\n",
    "             'aer_simulator(fake_montreal)' : 0.15,\n",
    "            }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use the simulator to get get the bitstring list\n",
    "circuit = QuantumCircuit(2 * N_gen)\n",
    "circuit.h(circuit.qubits)\n",
    "\n",
    "circuit.measure_active()\n",
    "\n",
    "job = execute(circuit, backend = simulator,shots = 2**13)\n",
    "              \n",
    "result = job.result()\n",
    "counts = result.get_counts(circuit)\n",
    "\n",
    "bitstrings = np.sort(list(counts.keys()))\n",
    "nonorm_init_list= []\n",
    "\n",
    "for bitstring in bitstrings:\n",
    "    flag = 0\n",
    "    for perm in perms:\n",
    "        if bitstring == ''.join(list(perm)):\n",
    "            flag = 1\n",
    "            #break    \n",
    "    nonorm_init_list.append(flag)\n",
    "\n",
    "init_list = np.array(nonorm_init_list) / np.sqrt(np.math.factorial(N_gen))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code used to prepare the equation for the states in the following text\n",
    "bstring_list = []\n",
    "\n",
    "for perm in perms:\n",
    "        bstring_list.append(''.join(list(perm)))\n",
    "\n",
    "state_N_gen = \"(\"\n",
    "for bstring in bstring_list:\n",
    "    state_N_gen += '|' + ''.join(list(bstring)) + \"\\rangle +  \"\n",
    "state_N_gen = state_N_gen[:-1] + \")\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prepare the state:\n",
    "\n",
    "\n",
    "In case of three generals:\n",
    "\n",
    "$$(|000110\\rangle +  |001001\\rangle +  |010010\\rangle +  |011000\\rangle +  |100001\\rangle +  |100100\\rangle) /\\sqrt!3$$\n",
    "\n",
    "\n",
    "In case of four generals:\n",
    "\n",
    "\n",
    "$$(|00011011\\rangle +  |00011110\\rangle +  |00100111\\rangle +  |00101101\\rangle +  |00110110\\rangle +  |00111001\\rangle +  |01001011\\rangle +  |01001110\\rangle +  |01100011\\rangle +  |01101100\\rangle +  |01110010\\rangle +  |01111000\\rangle +  |10000111 \\rangle +  |10001101\\rangle +  |10010011\\rangle +  |10011100\\rangle +  |10110001\\rangle +  |10110100\\rangle +  |11000110\\rangle +  |11001001\\rangle +  |11010010\\rangle +  |11011000\\rangle +  |11100001\\rangle +  |11100100\\rangle) \\ /\\sqrt!4$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x1eafba0f460>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create the quantum circuit\n",
    "circuit = QuantumCircuit(2 * N_gen)\n",
    "\n",
    "circuit.initialize(init_list, circuit.qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 994.294x565.88 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add Pauli-Z measurements and draw the circuit\n",
    "circuit.measure_active()\n",
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# if more details are requested (more .decompose() may be added)\n",
    "#qasm_circuit = circuit.decompose().decompose() \n",
    "#qasm_circuit.draw(output='mpl', fold = 20 - N_gen , plot_barriers=False,\n",
    "                  #style = {'backgroundcolor': 'cyan'})                                             "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## game functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# byzantine traitor game serving function\n",
    "def serve(k_list, t_list, n_its_list, used_list, stop_flag):\n",
    "    flag_1 = True\n",
    "    flag_2 = True\n",
    "    \n",
    "    retry = True\n",
    "    while retry:\n",
    "        k = k_list[-1]\n",
    "        if k in used_list:\n",
    "            k_list.pop()\n",
    "            if k_list == []: \n",
    "                stop_flag = True\n",
    "                return flag_1, flag_2\n",
    "        else:\n",
    "            retry = False\n",
    "            used_list.append(k)\n",
    "    \n",
    "    if k in t_list:\n",
    "        flag_1 = False\n",
    "\n",
    "    if n_its_list[k] < 2:\n",
    "        flag_2 = False\n",
    "\n",
    "    return flag_1, flag_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def traitor_game(players, verbose = False):\n",
    "    # start playing\n",
    "    \n",
    "    game_rounds = 0\n",
    "    toss = random.randrange(2)\n",
    "    head = tail = 0\n",
    "    gen[players[toss]]['failed'] = 0\n",
    "    gen[players[1-toss]]['failed'] = 0\n",
    "    \n",
    "    mat_t = gen[players[toss]]['mat']\n",
    "    n_its_toss = n_its[mat_t:mat_t+1][0]\n",
    "    mat_nt = gen[players[1-toss]]['mat']\n",
    "    n_its_notoss = n_its[mat_nt:mat_nt+1][0]\n",
    "    \n",
    "    flag = np.ones((2, 2), dtype=bool)\n",
    "    used_list = []\n",
    "    stop_flag = False\n",
    "    print(\"\\nByzantine traitor game. First to serve is\", gen[players[toss]]['name'])\n",
    "    print(\"                        Second to serve is\", gen[players[1-toss]]['name'])    \n",
    "    \n",
    "    if verbose:\n",
    "        print( \"shots:\", shots )\n",
    "        print(len(gen[players[toss]]['k_list']), \"in \"  + gen[players[toss]]['name'] + ' list:', \n",
    "                   sorted(gen[players[toss]]['k_list']) )   \n",
    "        print(len(gen[players[1-toss]]['k_list']), \"in \"  + gen[players[1-toss]]['name'] + ' list:', \n",
    "                   sorted(gen[players[1-toss]]['k_list']) )    \n",
    "    \n",
    "    while len(gen[players[toss]]['k_list']) > 0 and game_rounds < max_rounds\\\n",
    "            and len(gen[players[1-toss]]['k_list']) > 0 and not stop_flag:\n",
    "        \n",
    "        game_rounds += 1        \n",
    "        \n",
    "        # first to serve\n",
    "        flag[0][1], flag[1][1] = serve(gen[players[toss]]['k_list'],\n",
    "                                   gen[players[1-toss]]['t_list'],\n",
    "                                   n_its_notoss, used_list, stop_flag)\n",
    "        \n",
    "        if not flag[0][1] or not flag[1][1]:                          \n",
    "            head +=1\n",
    "        \n",
    "        gen[players[toss]]['k_list'].pop()\n",
    "\n",
    "        # second to serve\n",
    "        if not stop_flag: \n",
    "            \n",
    "            flag[0][0], flag[1][0] = serve(gen[players[1-toss]]['k_list'],\n",
    "                                       gen[players[toss]]['t_list'],\n",
    "                                       n_its_toss, used_list, stop_flag)\n",
    "\n",
    "            if not flag[0][0] or not flag[1][0]:                                     \n",
    "                tail += 1\n",
    "\n",
    "            gen[players[1-toss]]['k_list'].pop()    \n",
    "    \n",
    "    if verbose:\n",
    "        print(len(used_list), \"ind in used_list\", sorted(used_list) ) \n",
    "    \n",
    "    print(\"rounds:\", game_rounds)\n",
    "    \n",
    "    print(gen[players[1-toss]]['name'] + \" counted that \" +\\\n",
    "           gen[players[toss]]['name'] + \" failed \" + str(head)\\\n",
    "           + \" times: \" + \"{:.0%}\".format(head / game_rounds))\n",
    "              \n",
    "    \n",
    "    print(gen[players[toss]]['name'] + \" counted that \" +\\\n",
    "           gen[players[1-toss]]['name'] + \" failed \" + str(tail)\\\n",
    "           + \" times: \" + \"{:.0%}\".format(tail / game_rounds))\n",
    "    \n",
    "    return game_rounds, head, tail, toss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Start experiments\n",
    "### distribute entaglement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hellinger fidelity: 42.6%\n"
     ]
    }
   ],
   "source": [
    "# distribute entanglement \n",
    "if noise:\n",
    "    job_ideal = execute(circuit, backend = simulator, shots = shots,                \n",
    "                optimization_level = optimization_level)\n",
    "    \n",
    "    res_ideal = job_ideal.result()\n",
    "    counts_ideal = res_ideal.get_counts(circuit)\n",
    "\n",
    "    if shots <= 200: # for checks\n",
    "        verbose_flag = True\n",
    "\n",
    "    if N_gen == 3:    \n",
    "        job = execute(circuit, backend = backend, shots = shots,\n",
    "        memory=True,     \n",
    "        optimization_level = optimization_level)\n",
    "        figsize = (16,7)\n",
    "        \n",
    "    elif N_gen == 4:\n",
    "        job = execute(circuit, backend = backend, shots = shots,\n",
    "        noise_model = noise_model,\n",
    "        memory=True,\n",
    "        optimization_level = optimization_level)\n",
    "        figsize = (100,30) \n",
    "   \n",
    "    else: \n",
    "        job = None\n",
    "        print(\"only the three and four generals cases considered at this time\")\n",
    "\n",
    "    results = job.result()\n",
    "    memory = results.get_memory(circuit)\n",
    "    counts = results.get_counts(circuit)\n",
    "    legend_to_plot = [simulator, backend.name()]\n",
    "    counts_to_plot = [counts_ideal,counts]\n",
    "    print('hellinger fidelity: {:.1%}'.format(\n",
    "        hellinger_fidelity(counts_ideal,counts)))\n",
    "else:\n",
    "    job_ideal = execute(circuit, backend = simulator, shots = shots,\n",
    "                        memory = True,\n",
    "                        optimization_level = optimization_level)\n",
    "    results = job_ideal.result()\n",
    "    memory = results.get_memory(circuit)\n",
    "    counts = results.get_counts(circuit)\n",
    "    legend_to_plot = [backend.name()]\n",
    "    counts_to_plot = [counts]\n",
    "    figsize = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 7200x2160 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(counts_to_plot, bar_labels = False,\n",
    "                   figsize = figsize,\n",
    "                   legend = legend_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get an array of shape((N_gen,shots))\n",
    "n_its = np.zeros((N_gen,shots)).astype(int)\n",
    "\n",
    "# convert bitstrings to n_its and store them \n",
    "# '00'--> 2  '01'--> 1  '10'--> 0  '11' --> 3\n",
    "n_it_vals = [2, 1, 0, 3]\n",
    "\n",
    "for j, bitstring in enumerate(memory):\n",
    "    for pos in range(N_gen):\n",
    "        n_its[pos][j] = n_it_vals[int(bitstring[2*pos:2*pos+2],2)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###   check if the entangled states are not corrupt\n",
    "\n",
    "Mutual verification that no n_it value of a list occupies the same place in one of the other lists.\n",
    "\n",
    "Here it is not simulated because not really relevant for the demonstration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### use the results to solve the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define scenario\n",
    "gen = { 'A': { \"mat\" : 0, 'name': 'Alice', 'faithful': False, 'target': None},\n",
    "        'B': { \"mat\" : 1, 'name': 'Bob', 'faithful': True, 'target': False},\n",
    "        'C': { \"mat\" : 2, 'name': 'Charlie', 'faithful': True, 'target': True} }\n",
    "if N_gen == 4 :       \n",
    "        gen['D'] = { \"mat\" : 3,'name': 'Dave', 'faithful': False, 'target': False} "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scenario with 4 generals and 2 traitor(s)\n"
     ]
    }
   ],
   "source": [
    "# check here the number of traitors\n",
    " \n",
    "for key in list(gen.keys())[1:N_gen]:\n",
    "    if not gen[key]['faithful'] and gen[key]['target']:           \n",
    "        print(\"A lieutenant cannot be traitor himself and target of a traitorous commander\") \n",
    "        print(\"Please correct the scenario\")\n",
    "\n",
    "traitor_counter = 0\n",
    "for key in list(gen.keys())[0:N_gen]:    \n",
    "    if not gen[key]['faithful']:\n",
    "        traitor_counter += 1\n",
    "\n",
    "print(\"Scenario with \" + str(N_gen) + \" generals and \" + str(traitor_counter) + \" traitor(s)\")\n",
    "\n",
    "if traitor_counter > N_gen -2 :\n",
    "    print(\"No more than \" + str(N_gen-2) + \" traitor(s) allowed for \"\\\n",
    "          + str(N_gen) + \" generals, even with quantum power\") \n",
    "    print(\"Please correct the scenario\")    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scenario run on aer_simulator(fake_sydney)\n",
      "generals: ['Alice', 'Bob', 'Charlie', 'Dave']\n",
      "faithful:   [False, True, True, False]\n",
      "  target:   [None, False, True, False]\n",
      "\n",
      "Byzantine traitor game. First to serve is Bob\n",
      "                        Second to serve is Charlie\n",
      "rounds: 500\n",
      "Charlie counted that Bob failed 136 times: 27%\n",
      "Bob counted that Charlie failed 149 times: 30%\n",
      "\n",
      "Byzantine traitor game. First to serve is Dave\n",
      "                        Second to serve is Bob\n",
      "rounds: 500\n",
      "Bob counted that Dave failed 218 times: 44%\n",
      "Dave counted that Bob failed 180 times: 36%\n",
      "\n",
      "No game between Charlie and Dave\n",
      "They say they got the same order from Alice\n",
      "\n",
      "Final agreement:\n",
      "\n",
      "Dave and Alice are traitors\n",
      "Bob and Charlie agree with a common strategy\n"
     ]
    }
   ],
   "source": [
    "print(\"Scenario run on \" + backend.name())\n",
    "print(\"generals:\", list(map(lambda v: v[\"name\"],gen.values()))[0:N_gen])\n",
    "print(\"faithful:  \", list(map(lambda v: v[\"faithful\"],gen.values()))[0:N_gen])\n",
    "print(\"  target:  \", list(map(lambda v: v[\"target\"],gen.values()))[0:N_gen])\n",
    "\n",
    "# Alice determine the message: 0 for retreat, 1 for attack\n",
    "m = 0\n",
    "gen['A']['message'] = m\n",
    "# Alice establishes the corresponding list of indices \n",
    "# and the corresponding cheating list\n",
    "\n",
    "j_list_A = []\n",
    "j_list_Ac = []\n",
    "mat = gen['A']['mat']\n",
    "for k in range(shots):\n",
    "    val_it = n_its[mat:mat+1][0][k]\n",
    "    if val_it == m:\n",
    "        j_list_A.append(k)\n",
    "    elif val_it == 1 - m:\n",
    "        j_list_Ac.append(k)\n",
    "\n",
    "# Alice send her messages and corresponding lists \n",
    "# by pairwise authenticated classical and quantum channels  \n",
    "\n",
    "# first equalize lists lengths\n",
    "\n",
    "random.shuffle(j_list_A)\n",
    "while len(j_list_A) > len(j_list_Ac):\n",
    "    j_list_A.pop()\n",
    "j_list_A.sort()\n",
    "random.shuffle(j_list_Ac)\n",
    "while len(j_list_Ac) > len(j_list_A):\n",
    "    j_list_Ac.pop()\n",
    "j_list_Ac.sort()\n",
    "gen['A']['j_list'] = copy.deepcopy(j_list_A) \n",
    "\n",
    "for key in list(gen.keys())[1:N_gen]:\n",
    "    if (not gen['A']['faithful']) and gen[key]['target']:\n",
    "        gen[key]['message'] = 1 - m    \n",
    "        gen[key]['j_list'] = copy.deepcopy(j_list_Ac )\n",
    "    else:\n",
    "        gen[key]['message'] = m    \n",
    "        gen[key]['j_list'] = copy.deepcopy(j_list_A) \n",
    "            \n",
    "# test of consistency by the lieutenants (compare j_list and message)\n",
    "for key in list(gen.keys())[1:N_gen]:\n",
    "    gen[key]['flag_y'] = gen[key]['message']\n",
    "\n",
    "# false flag by traitors:\n",
    "for key in list(gen.keys())[1:N_gen]:\n",
    "    if gen[key]['faithful']:\n",
    "        gen[key]['t_list'] = copy.deepcopy(gen[key]['j_list'])\n",
    "    else:\n",
    "        gen[key]['flag_y'] = 1 - gen[key]['flag_y']\n",
    "        gen[key]['t_list'] = list( set(range(shots)) - set(gen[key]['j_list']) )\n",
    "\n",
    "# prepare for treator game\n",
    "\n",
    "p_list = []\n",
    "    \n",
    "for key in list(gen.keys())[1:N_gen]:\n",
    "\n",
    "    # add to player's list:            \n",
    "    if gen[key]['flag_y'] != 3: \n",
    "        p_list.append(key)\n",
    "\n",
    "# check if treator game possible\n",
    "if len(p_list) == 1:\n",
    "    print(\"Only one lieutenant has consistent order\") \n",
    "\n",
    "elif len(p_list) == 0:\n",
    "    print(\"No lieutenant has consistent order\")\n",
    "    \n",
    "else: # treator game:\n",
    "        \n",
    "    res_traitor = {}\n",
    "    \n",
    "    for players in list(itertools.combinations(p_list, r=2)):\n",
    "        \n",
    "        if gen[players[0]]['flag_y'] == gen[players[1]]['flag_y']:\n",
    "            print(\"\\nNo game between \" + gen[players[0]]['name']\\\n",
    "             + \" and \" + gen[players[1]]['name'] + \"\\nThey say they got the same order from \" + gen['A']['name'])\n",
    "            res_traitor[players[0] + players[1]] = -1.0\n",
    "            res_traitor[players[1] + players[0]] = -1.0\n",
    "        \n",
    "        else:\n",
    "            # prepare indices list\n",
    "            for key in players:\n",
    "                gen[key]['k_list'] = []                        \n",
    "                mat = gen[key]['mat']\n",
    "                \n",
    "                for k in range(shots):\n",
    "                    n_it = n_its[mat:mat+1][0][k]\n",
    "                    if (k in gen[key]['t_list']) and (n_it == 1 - gen[key]['flag_y']):\n",
    "                        gen[key]['k_list'].append(k)    \n",
    "\n",
    "                    random.shuffle(gen[key]['k_list'])\n",
    "                \n",
    "            game_rounds, head, tail, toss = traitor_game(players, verbose_flag)\n",
    "            res_traitor[players[1-toss] + players[toss]] = head / game_rounds\n",
    "            res_traitor[players[toss] + players[1-toss]] = tail / game_rounds    \n",
    "                \n",
    "    print(\"\\nFinal agreement:\\n\")\n",
    "    \n",
    "    sorted_res = dict(sorted(res_traitor.items()))\n",
    "    res_val = list(sorted_res.values())\n",
    "    test_val = np.round(np.array(res_val) + noise_dic[backend.name()])\n",
    "        \n",
    "    if N_gen == 3 :  # three generals with traitor game\n",
    "                \n",
    "        if np.sum(test_val) == - 2:\n",
    "            print(\"No traitor detected\")\n",
    "            print(\"Both lieutenants follow the order of \", gen['A']['name'])\n",
    "    \n",
    "        elif np.sum(test_val) == 0:\n",
    "            print(gen['A']['name'] + \" is a traitor\")\n",
    "            print(gen['B']['name'] + \" and \" + gen['C']['name'] + \" agree with a common strategy\")        \n",
    "        \n",
    "        elif test_val[0] == [1.] and test_val[1] == [0.]:\n",
    "            print(gen['C']['name'] + \" is a traitor\")\n",
    "            print(gen['B']['name'] + \" follows the order of \" +  gen['A']['name'])\n",
    "        \n",
    "        elif test_val[0] == [0.] and test_val[1] == [1.]:\n",
    "            print(gen['B']['name'] + \" is a traitor\")\n",
    "            print(gen['C']['name'] + \" follows the order of \" +  gen['A']['name'])\n",
    "            \n",
    "        else:\n",
    "            print(\"Something wrong\")\n",
    "\n",
    "    if N_gen == 4 :  # four generals with traitor game\n",
    "        \n",
    "        if np.sum(test_val) == - 6:\n",
    "            print(\"No traitor detected\")\n",
    "            print(\"All lieutenants follow \"+ gen['A']['name'] +\"'s order\")\n",
    "        else:\n",
    "            uncovered = []\n",
    "            discoverer = []\n",
    "\n",
    "            for i, (j, k) in enumerate(sorted_res):\n",
    "    \n",
    "                if test_val[i] == 1.0:\n",
    "                    uncovered.append(gen[k]['name'])\n",
    "                    discoverer.append(gen[j]['name'])\n",
    "\n",
    "            if np.sum(test_val) == -2 and len(uncovered) == 0:\n",
    "                print(\"The commanding general is a traitor\")\n",
    "                print(\"All lieutenants follow a majority strategy\") \n",
    "\n",
    "            elif np.sum(test_val) == 0 and len(uncovered) == 2:\n",
    "\n",
    "                if uncovered[0] != uncovered[1]:\n",
    "                    print(uncovered[0]+\" and \"+uncovered[1]+\" are traitors\")\n",
    "                    print(discoverer[0]+\" follows \"+ gen['A']['name'] +\"'s order\")\n",
    "                else:\n",
    "                    print(uncovered[0]+\" is a traitor\")\n",
    "                    print(discoverer[0]+\" and \"+discoverer[1]+\" follow \"+ gen['A']['name'] +\"'s order\")\n",
    "\n",
    "            elif np.sum(test_val) == -1 and len(uncovered) == 1:\n",
    "                    print(uncovered[0]+\" and \"+ gen['A']['name'] +\" are traitors\")\n",
    "\n",
    "                    # who was the targed of the traitor?\n",
    "                    for key in list(gen.keys())[1:N_gen]:\n",
    "                        if gen[key]['name'] != uncovered[0] and gen[key]['name'] != discoverer[0]:\n",
    "                            t_target = gen[key]['name'] \n",
    "\n",
    "                    print(discoverer[0] +\" and \"+ t_target +\" agree with a common strategy\")\n",
    "            else:\n",
    "                print(\"Something wrong\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}