experiment2-2-real-device-elementwise-error.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "designed-heater",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>0.25.0</td></tr><tr><td>Terra</td><td>0.17.0</td></tr><tr><td>Aer</td><td>0.8.0</td></tr><tr><td>Ignis</td><td>0.6.0</td></tr><tr><td>Aqua</td><td>0.9.0</td></tr><tr><td>IBM Q Provider</td><td>0.12.2</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.6.9 (default, Oct  8 2020, 12:12:24) \n",
       "[GCC 8.4.0]</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>10</td></tr><tr><td>Memory (Gb)</td><td>31.088565826416016</td></tr><tr><td colspan='2'>Sun Sep 19 00:01:01 2021 UTC</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "def warn(*args, **kwargs):\n",
    "    pass\n",
    "warnings.warn = warn\n",
    "\n",
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "#%qiskit_copyright"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "square-aruba",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumCircuit, Aer, IBMQ\n",
    "from qiskit.aqua import QuantumInstance\n",
    "from qiskit.providers.aer import QasmSimulator\n",
    "from qiskit.providers.aer.noise import NoiseModel\n",
    "from qiskit.test import mock\n",
    "from xbm import get_all_meas_circs_bits_coefs\n",
    "from pauli import get_all_meas_circs_bits_coefs_pauli\n",
    "from utils import eval_expectation_listed\n",
    "import time\n",
    "import copy\n",
    "import random\n",
    "import yaml\n",
    "import pickle\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "skilled-destination",
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 42\n",
    "shots = 8192\n",
    "\n",
    "nb_qubits = 4\n",
    "nb_trial = 10\n",
    "is_psi_1 = False\n",
    "fname = 'results_real_device_exp2_4qubits'\n",
    "\n",
    "device = 'IBMQ'\n",
    "#device = 'QASM'\n",
    "\n",
    "if True:\n",
    "    fake_device = QasmSimulator.from_backend(mock.FakeSydney())\n",
    "    coupling_map = fake_device.configuration().coupling_map\n",
    "    noise_model = NoiseModel.from_backend(fake_device)\n",
    "else:\n",
    "    noise_model, coupling_map = None, None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "scientific-ratio",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rename to your config file\n",
    "with open('ibmq_config.yaml') as file:\n",
    "    config = yaml.safe_load(file)\n",
    "    \n",
    "IBMQ.save_account(config['token'], overwrite=True)\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub=config['provider']['hub'], group=config['provider']['group'], project=config['provider']['project'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "working-henry",
   "metadata": {},
   "outputs": [],
   "source": [
    "quantum_instance_statevec = QuantumInstance(Aer.get_backend('statevector_simulator'), seed_simulator=seed, seed_transpiler=seed)\n",
    "quantum_instance_qasm     = QuantumInstance(Aer.get_backend('qasm_simulator'), shots=shots, seed_simulator=seed, seed_transpiler=seed, coupling_map=coupling_map, noise_model=noise_model)\n",
    "quantum_instance_ibmq     = QuantumInstance(provider.get_backend(config['backend']), seed_transpiler=seed, shots=shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "strange-karaoke",
   "metadata": {},
   "outputs": [],
   "source": [
    "def experiments(psi_0_list, psi_1_list, mat_A_list, meas_list, qasm=True, ibmq=True):\n",
    "\n",
    "    expectation_gt_list = []\n",
    "    for psi_0, psi_1, mat_A in zip(psi_0_list, psi_1_list, mat_A_list):\n",
    "        p0 = quantum_instance_statevec.execute(psi_0).get_statevector()\n",
    "        if psi_1 is not None:\n",
    "            p1 = quantum_instance_statevec.execute(psi_1).get_statevector()\n",
    "            expectation_gt = (np.conjugate(p0)*(mat_A @ p1)).sum()\n",
    "        else:\n",
    "            expectation_gt = (np.conjugate(p0)*(mat_A @ p0)).sum()\n",
    "        expectation_gt_list += [expectation_gt]\n",
    "\n",
    "    expectation_statevec_list, results = eval_expectation_listed(copy.deepcopy(meas_list), quantum_instance_statevec, params_dict=None)\n",
    "    \n",
    "    res = {'GT':expectation_gt_list, 'statevec':expectation_statevec_list}\n",
    "    \n",
    "    if not all(np.isclose(np.ravel(expectation_gt_list), np.ravel(expectation_statevec_list))):\n",
    "        print(expectation_gt_list)\n",
    "        print(expectation_statevec_list)\n",
    "        plt.scatter(np.real(np.ravel(expectation_gt_list)), np.real(np.ravel(expectation_statevec_list)))\n",
    "        plt.scatter(np.imag(np.ravel(expectation_gt_list)), np.imag(np.ravel(expectation_statevec_list)))\n",
    "        plt.axes().set_aspect('equal')\n",
    "        raise ValueError()\n",
    "\n",
    "    if qasm:\n",
    "        expectation_qasm_list, results = eval_expectation_listed(copy.deepcopy(meas_list), quantum_instance_qasm, params_dict=None)\n",
    "        res.update({'QASM':expectation_qasm_list})\n",
    "\n",
    "    if ibmq:\n",
    "        expectation_ibmq_list, results = eval_expectation_listed(copy.deepcopy(meas_list), quantum_instance_ibmq, params_dict=None)\n",
    "        res.update({'IBMQ':expectation_ibmq_list})\n",
    "    \n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "finnish-wheel",
   "metadata": {},
   "outputs": [],
   "source": [
    "if device=='IBMQ':\n",
    "    qasm, ibmq = False, True\n",
    "elif device=='QASM':\n",
    "    qasm, ibmq = True, False\n",
    "else:\n",
    "    raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "sunset-collaboration",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "nb_elements = 4**nb_qubits\n",
    "psi_0_list = []\n",
    "psi_1_list = []\n",
    "mat_A_list = []\n",
    "meas_pauli_list = []\n",
    "meas_xbm_list = []\n",
    "\n",
    "for trial in range(nb_trial):\n",
    "    for j in range(nb_elements):\n",
    "        np.random.seed(trial)\n",
    "        random.seed(trial)\n",
    "        psi_0 = QuantumCircuit(nb_qubits)\n",
    "        for i in range(nb_qubits):\n",
    "            psi_0.h(i)\n",
    "\n",
    "        mat_A = np.zeros((4**nb_qubits,)).astype(np.complex128)\n",
    "        foo = np.random.random() * random.choice([1,-1])\n",
    "        foo += 1j * np.random.random() * random.choice([1,-1])\n",
    "        mat_A[j] = foo\n",
    "        mat_A = np.reshape(mat_A, (2**nb_qubits,2**nb_qubits))\n",
    "        psi_1 = None\n",
    "        psi_0_list += [psi_0]\n",
    "        psi_1_list += [None]\n",
    "        mat_A_list += [mat_A]\n",
    "        meas_pauli_list += [get_all_meas_circs_bits_coefs_pauli(psi_0, psi_1, mat_A, reduce=False)]\n",
    "        meas_xbm_list += [get_all_meas_circs_bits_coefs(psi_0, psi_1, mat_A)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "thorough-innocent",
   "metadata": {},
   "outputs": [],
   "source": [
    "if False:\n",
    "    with open(fname+'.pkl', 'rb') as f:\n",
    "        results = pickle.load(f)\n",
    "        res_xbm = results['XBM']\n",
    "        res_pauli = results['Pauli']\n",
    "else:\n",
    "    res_xbm = experiments(psi_0_list, psi_1_list, mat_A_list, meas_xbm_list, qasm=qasm, ibmq=ibmq)\n",
    "    res_pauli = experiments(psi_0_list, psi_1_list, mat_A_list, meas_pauli_list, qasm=qasm, ibmq=ibmq)\n",
    "    with open(fname+'.pkl', 'wb') as f:\n",
    "        pickle.dump({'XBM':res_xbm, 'Pauli':res_pauli}, f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "loved-thursday",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_abs_errors(res, nb_trial=10):\n",
    "    \n",
    "    abs_errors = []\n",
    "    for gt, evaluated in zip(res['GT'],res[device]):\n",
    "        abs_error = np.abs(gt-evaluated)\n",
    "        abs_errors += [abs_error]\n",
    "    abs_errors = np.array(abs_errors).reshape((nb_trial,2**nb_qubits,2**nb_qubits))\n",
    "    \n",
    "    return abs_errors\n",
    "\n",
    "\n",
    "def get_rel_errors(res, nb_trial=10):\n",
    "    \n",
    "    rel_errors = []\n",
    "    for gt, evaluated in zip(res['GT'],res[device]):\n",
    "        rel_error = np.abs(gt-evaluated)/np.abs(gt)\n",
    "        rel_errors += [rel_error]\n",
    "    rel_errors = np.array(rel_errors).reshape((nb_trial,2**nb_qubits,2**nb_qubits))\n",
    "    \n",
    "    return rel_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "norwegian-landscape",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vmax = get_rel_errors(res_xbm).mean(0).max()\n",
    "sns.heatmap(get_rel_errors(res_xbm).mean(0), annot=False, vmin=0, vmax=vmax)\n",
    "plt.axes().set_aspect('equal')\n",
    "plt.savefig('elementwise-error-xbm.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "stuffed-magazine",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ASS+RtBE4FbhQ0uo0/PnASkm3AFcDnxx1V/Np3Jw0s6ZPAI+Iy4HLRx07p2Z/BUkzc3TcdcALi6TVsBCrqQr+ISJ+KentwMtJStdlEdHetZ3NrCUq/LCjzJrY19Jrpko6HZgO/BA4kWQsyOmtzZ6ZtUPQeXMi88oqxF4YES+S1Edyd+HgiBiW9G0aPMItHTeyFGBK/wEMTNqvaRk2s+Yb6tb1xICetEk5A5gK7HmEywAwqV5Q7SoWLsDMOl+g3FunyaqJfRW4A+gFzgZ+IGk98DLg4hbnzczapGv7xCLiAknfT/f/IOmbwEnAlyPit+3IoJm1XifWsPLKHGIREX+o2X8MuLSVGTKz9uvampiZTQzD3VwT21dlJtAO9PaXSusFU+YVjrlp24bsi8awcPLcUnEXP3Jz4Zglc15UKq3bhrYUjrnu4TtKpTXQW/c+T0Mz+qcUjnli945SafX19JaKK+OwyQeWihsaGWpyTvLpwFWnc3NNzMwYcU3MzKqsAx9ilJsLMTNzx76ZVduI3Jw0swort75xZ8gsxNIlYv+MZKXGYeB3wHcjYmuL82ZmbVLlu5MN505Keh/wJWAy8BKSOZOHANdLOqFB3FMPEnhi5yPNy62ZtcQIyr11mqya2HuBo9KVKz4HXB4RJ0i6EPgxydrXT1P7IIFFc/5LlW98mE0IVf4jzdMn1kfSjBwgWU+MiLhPUrnRjWbWcarcnMwqxL5C8vTeG4A/Bs4HkHQAUHw4uJl1pK4dYhERn5f0S5LF+z8bEXekxx8CjmtD/sysDYa7uCZGRKwGVmddZ2bV1bU1MTObGFyINTBr0vTCMUsGFpZK618eXVE4puzKBsMlf+2HTDugcMzFm1eWSuu0gxYXjrl9YGqptKb2DZSL651cOGZyb7m0osQ9uK27t5VK6/Yn7ysV9+TgzlJx+6rCS+y7JmZmromZWcV19bQjM+t+3TxOzMwmADcnzazSXIiZWaVVee5k1hPAS6ldxeLh7Q+0Igkza6IR5d86TdZSPDMlfVLSHZK2SHpE0tr02Kx6cRGxLCIWR8TiuVOf0fRMm1lzDRfY8pB0sqQ7Ja2TdNYY54+TdJOkIUlvGXXudEl3pdvpWWll1cQuAR4FToiI/SNiDvCq9NglOd+PmXW4ESL3lkVSL/AF4HXAEcDbJB0x6rL7gHcB3x0Vuz/wEeClwLHARyTNbpReViG2MCLOj4in2oQR8UBEnA8cmvluzKwSRgpsORwLrIuI9RGxG7gYWFJ7QUTcExG3jvGSrwWuiogtEfEocBVwcqPEsgqxeyV9SNJBew5IOkjSh4FyT501s44TBbbaPu90Wzrq5eazd/mwMT2WR+HYrLuTbwXOAq6VtOeRxpuB5cCpOTNlZh2uyBCL2pWbO0HWemKPAh9Ot71IejfwtawEPlqi1XnB8ObCMQD79U8rHPPE4PZSaW3YWW5NyFOmP6dwzPbhXaXS+o9t95aKK2M4yo00emKo+M9/oKe/VFqP7XqycExPyUeZPbar3MTxXrVkwECmITV1kMUmkmdx7LEgPZY39oRRsdc0CtiXn9i5+xBrZh2kSHMyhxXA4ZIWSeoHTiNpveVxBfAaSbPTDv3XpMfqalgTk3RrvVPAQXXOmVnFNHPEfkQMSTqTpPDpBS6KiNWSzgNWRsRySS8BfgTMBv5U0rkRcWREbJH0MZKCEOC8iGjY7MnqEzuI5G7Bo6OOC7iu2Fszs06VZ+hEERFxOXD5qGPn1OyvIGkqjhV7EXBR3rSyCrGfAtMjYtXoE5KuyZuImXW2Kk87yurYP6PBubc3PztmNh48AdzMKm24wnUxF2JmVumaWOkhFpJ+3uDcUyN6r9i+rmwSZtYmUeBfp8kaYnFMvVPAUfXiakf0/vgZb++8d21me6lyTSyrObkCuJak0BptVtNzY2bjotlDLNopqxBbC/zXiLhr9AlJngBu1iWqW4RlF2IfpX6/2X9vblbMbLwMVbgYyxondmmD0w0XKjOz6ujEDvu89mWIxbnkWMXijO0rC7/wa2YfWSY/LCmxFPaBQ6WS4gPbVmRfNIbLtq4uHPP47nIrbbxgZvEVRHaWXDFjcKTc41d7e4rfIH98d/HVKAC2DxZ/b0Ml39cBU2eWihspuRrIvurajn1PADebGLq5JuYJ4GYTQNfWxPAEcLMJYTi6tCbmCeBmE0M3jxMzswmgm/vEzGwCqHKfWEueSlA7AXzn7sdbkYSZNVEzH57bbg0LMUn7Sfpfkr4l6e2jzv1rvbiIWBYRiyNi8eT+cuNlzKx9qryKRVZN7GskwykuA06TdJmkgfTcy1qaMzNrm+GI3FunyeoTe1ZE/Hm6/2+SzgZ+LemUFufLzNqoE5uJeWUVYgOSeiKSuRAR8XFJm4B/B6a3PHdm1hbd3LH/E+BPag9ExNeBvwV2tyhPZtZmVe4Tyxrs+qE6x38h6ROtyZKZtVs3NycbybWKxWdmHFv4hT/8WPGVLwC+cu7xhWM+f8G2UmntHi63/EWU6Bg9aEq5VY/WPH5f4Zhp/ZNLpbX/wIxScQ/vLD4EZ2rfQPZFTbJwWrl1Dn63dVOpOGmsRZRbr8znslN4FQsz6+pHtnkVC7MJoJubk17FwmwC6NrmpFexMJsYurkmZmYTQCcOncirJRPAzaxamj3tSNLJku6UtE7SWWOcH5D0/fT8DZIWpscXStohaVW6fSkrrawJ4M+Q9EVJX5A0R9JHJd0m6RJJ8xrEPbWKxTXbnvbISjPrMM1cxUJSL/AF4HXAEcDbJB0x6rIzgEcj4tnABcD5Nefujoij0u2vstLLqol9HVgDbACuBnYArwd+A9QtIWtXsThh2uFZeTCzcdbkpXiOBdZFxPqI2A1cDCwZdc0S4Bvp/qXAiSo5SC6rEDsoIv45Ij4JzIqI8yNiQ0T8M1D8eWBm1pEiIvdW29JKt6WjXm4+ScVnj43psTGviYgh4HFgTnpukaSbJV0r6Y+z8p7VsV9byH1z1LnerBc3s2oocncyIpYBy1qUlfuBZ0bEI5JeTLJ6zpERsbVeQFZN7MeSpgNExP/cc1DSs4E7m5FjMxt/TZ4Avgk4pOb7BemxMa+R1AfMBB6JiF0R8QhARNwI3A08p1FiDQuxiDgnIp72uOWIWAf8rPH7MLOqGI6R3FsOK4DDJS2S1A+cBiwfdc1y4PR0/y3AryMiJB2Q3hhA0mHA4cD6Rom1fAL4QImRwBvvvrxMfphz6EmFYz44949KpVV2UvZJ0w4rHPO1zTeUSmvmwNTCMVt3bS+V1mDJCfFl+nIHR4ZLpTW5r79wzIbtD5VK68hZ5bqMN+wol96+auaI/YgYknQmcAVJt9NFEbFa0nnAyohYDnwV+JakdcAWkoIO4DjgPEmDJMuc/VVEbGmUnieAm1nTR+xHxOXA5aOOnVOzvxM4dYy4y0iWw8/NE8DNrNIj9j0B3MwY8QRwM6uybq6JmdkEkPOuY0dyIWZmlW5OFl7FQtKBOa55alrCr7avK5czM2ubrn3akaT9Rx8CfivpaED1xm/UTkv43sHv6Lx3bWZ7qXJNLKs5+TBw76hj84GbgACKj9w0s47TiTWsvLIKsb8HXg38fUTcBiDp9xGxqOU5M7O2GY5ysyA6QdYQi89K+j5wgaQNwEegwkW2mY2pax8UAhARG4FTJZ0CXAUUn5BnZh2tyg8KyX13Mp20+SrgJABJ725VpsysvYosithpVDZTku6LiGdmXbftvOJ3Jy+7sNyj3O/pK/5eLty6qlRa/zD96FJxXx5suKrImB7d/USptLbsfNoqSpmm908uldbUvnJxU3qLryxx//aGixrUT6vEKhb9PeWGUk7qmVQqbtfI7lJx9z5ya7k/mtS8WUfk/uO5/7E1+5RWs3kVCzPr6ruTXsXCbALo5mlHXsXCbALoxL6uvLyKhZl19Yh9M5sAurYmZmYTw4QYJ1ZE7SoWF630KhZmna7K48QaFmKSTq7Znynpq5JulfRdSXWHWETEsohYHBGL/3Lxs5uZXzNrgSY/sq2tsmpin6jZ/yzJ03n/lOS5che2KlNm1l4jEbm3TlOkT2xxRByV7l8g6fRGF5tZdXRiMzGvrELsQEkfJBncup8kxX++25b0p5lZ+3XziP0vAzPS/W8Ac4GHJD0DWNXCfJlZG3VtTSwizq1z/AFJV7cmS2bWbp3Y15VbkVuro26z3lc2tuY1lrYrrlvTqkIeuzWtquSx27eGS/FkrGLxnIgYKFFu1r7+yohY3I64bk2rbJzTGr+4duex23kVCzOrNK9iYWaVNt6rWCxrY1y3plU2zmmNX1y789jVSi9PbWbWCTxg1cwqzYWYmVXauBRikk6WdKekdZLOKhB3kaQHJd1eIOYQSVdLWiNptaT354iZLOm3km5JY8Yc9NsgvlfSzZJ+WiDmHkm3SVolaWXOmFmSLpV0h6S1kv4oR8xz0zT2bFslfSBH3P9Ifxa3S/qepFyPN5L0/jRmdaN0xvrdStpf0lWS7kq/zs4Rc2qa1oikMYcj1In7dPpzvFXSjyTNyhHzsfT6VZKulHRwnrRqzv2tpJA0N2cePyppU83v7vVjvb8Jp90D04Be4G7gMKAfuAU4ImfsccAxwO0F0psHHJPuzwB+l5UeyRCS6en+JOAG4GUF0vwg8F3gpwVi7gHmFvxZfgN4T7rfD8wq8bt4ADg047r5wO+BKen3lwDvyvH6LwBuJ3ngch/wS+DZeX+3wKeAs9L9s4Dzc8Q8H3gucA3JogV503oN0Jfun58zrf1q9t8HfCnvZxY4BLgCuHes33ud9D4K/F2R3/FE2MajJnYssC4i1kfEbuBiYEmewIj4d6DQQwcj4v6IuCndfwJYS/JH2SgmImLPQxsnpVuuOyCSFgBvAL5SJJ9FSZpJ8kH/KkBE7I6Ixwq+zInA3RFxb45r+4ApkvpICqU/5Ih5PnBDRGyPiCHgWuDPxrqwzu92CUlBTfr1TVkxEbE2Iu5slKk6cVemeQS4HliQI2ZrzbfTGOMz0uAzewHwobFiMuJslPEoxOYDG2q+30hGodIskhYCR5PUrLKu7ZW0CngQuCoiMmNS/5vkw1l09bgArpR0o6SlOa5fBDwEfC1tun5F0rSCaZ4GfC8zYxGbgM8A95GsKfd4RFyZ4/VvB/5Y0hxJU4HXk9RA8jooIu5P9x+gfc86/Uvg53kulPRxSRuAdwDn5IxZAmyKiFtK5O3MtAl70ejm9UQ1YTr2JU0HLgM+MOp/0DFFxHAk66ctAI6V9IIcabwReDAibiyRxVdGxDHA64C/kXRcxvV9JM2NL0bE0cA2kiZXLpL6gVOAH+S4djZJrWgRcDAwTdI7s+IiYi1J0+xK4BckK58M583jqNcKctaG94Wks4Eh4Dt5ro+IsyPikPT6M3O8/lTgH8lZ4I3yReBZwFEk/5l8tsRrdJ3xKMQ2sff/xgvSYy0jaRJJAfadiPhhkdi0iXY1cHLGpQCvAE6RdA9JM/lPJH07Zzqb0q8PAj8iaXY3shHYWFNDvJSkUMvrdcBNEbE5x7UnAb+PiIciYhD4IfDyPIlExFcj4sURcRzJ9LXfFcjjZknzANKvDxaILUzSu4A3Au9IC80ivgP8eY7rnkXyn8Et6edkAXCTkuWtGoqIzel/riMky2RlfUYmhPEoxFYAh0talNYGTgOWtyoxSSLpN1obEZ/LGXPAnrtTkqYArwbuyIqLiH+IiAURsZDkff06IjJrLJKmSZqxZ5+kk7nhHdiIeADYIOm56aETgTVZadV4Gzmakqn7gJdJmpr+PE8k6VvMJOnA9OszSfrDvlsgj8uBPSsInw78uEBsIUqeJ/Eh4JSI2J4z5vCab5eQ7zNyW0QcGBEL08/JRpIbTw/kSG9ezbdvJuMzMmGMx90Ekr6R35HcpTy7QNz3SKrRgyS//DNyxLySpBlyK0lzZhXw+oyYFwE3pzG3A+eUeI8nkPPuJMmd2lvSbXXenwlJs2Jlms9/A2bnjJsGPALMLPB+ziX5I70d+BYwkDPuNySF6y3AiUV+t8Ac4FfAXSR3NvfPEfPmdH8XsBm4Imda60j6avd8Rr6UI+ay9OdxK/ATYH7Rzyx17krXSe9bwG1pesuBec34e6z65mlHZlZpE6Zj38y6kwsxM6s0F2JmVmkuxMys0lyImVmluRAzs0pzIWZmlfb/AYLG01DPFXC0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(get_rel_errors(res_xbm).std(0), annot=False)\n",
    "plt.axes().set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "chronic-claim",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(get_rel_errors(res_pauli).mean(0), annot=False, vmin=0, vmax=vmax)\n",
    "plt.axes().set_aspect('equal')\n",
    "plt.savefig('elementwise-error-naive.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "explicit-bunch",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(get_rel_errors(res_pauli).std(0), annot=False)\n",
    "plt.axes().set_aspect('equal')"
   ]
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}