custom_zne_IBMQ_not_working.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_aer import AerSimulator\n",
    "from qiskit.visualization import plot_histogram\n",
    "from aux_functions import *\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, Session\n",
    "from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.circuit import Parameter, ParameterVector\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "import numpy as np\n",
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "single_qubit_error_rate = 0.01\n",
    "two_qubit_error_rate = 0.005\n",
    "noise_model_depolarization = depolarizing_noise_model(single_qubit_error_rate, two_qubit_error_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('tocken.txt', 'r') as file:\n",
    "    token_txt = file.read().replace('\\n', '')\n",
    "\n",
    "# service = QiskitRuntimeService(\n",
    "#     channel='ibm_cloud'.channel_strategy = 'q-ctrl',\n",
    "#     instance='ibm-q/open/main',\n",
    "#     token=token_txt\n",
    "# )\n",
    "    \n",
    "service = QiskitRuntimeService(\n",
    "    channel='ibm_quantum',\n",
    "    instance='ibm-q/open/main',\n",
    "    token=token_txt\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<IBMBackend('ibm_brisbane')>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = service.least_busy(operational=True, simulator=False)\n",
    "backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        ┌───┐                ░ ┌─┐         \n",
      "   q_0: ┤ H ├──■─────────────░─┤M├─────────\n",
      "        └───┘┌─┴─┐           ░ └╥┘┌─┐      \n",
      "   q_1: ─────┤ X ├──■────────░──╫─┤M├──────\n",
      "             └───┘┌─┴─┐      ░  ║ └╥┘┌─┐   \n",
      "   q_2: ──────────┤ X ├──■───░──╫──╫─┤M├───\n",
      "                  └───┘┌─┴─┐ ░  ║  ║ └╥┘┌─┐\n",
      "   q_3: ───────────────┤ X ├─░──╫──╫──╫─┤M├\n",
      "                       └───┘ ░  ║  ║  ║ └╥┘\n",
      "meas: 4/════════════════════════╩══╩══╩══╩═\n",
      "                                0  1  2  3 \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_qubits = 4\n",
    "circ1 = generate_GHZ(n_qubits)\n",
    "print(circ1)\n",
    "sim_ideal = AerSimulator()\n",
    "result_ideal = sim_ideal.run(circ1).result()\n",
    "plot_histogram(result_ideal.get_counts(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "ename": "IBMInputValueError",
     "evalue": "'The instruction rx on qubits (0,) is not supported by the target system. Circuits that do not match the target hardware definition are no longer supported after March 4, 2024. See the transpilation documentation (https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and the primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see this coupled with operator transformations.'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIBMInputValueError\u001b[0m                        Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[54], line 5\u001b[0m\n\u001b[1;32m      3\u001b[0m sim_noise \u001b[38;5;241m=\u001b[39m AerSimulator(noise_model\u001b[38;5;241m=\u001b[39mnoise_model_depolarization)\n\u001b[1;32m      4\u001b[0m circ_noise \u001b[38;5;241m=\u001b[39m transpile(circ1, sim_noise)\n\u001b[0;32m----> 5\u001b[0m job \u001b[38;5;241m=\u001b[39m \u001b[43msampler\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43mcirc_noise\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      6\u001b[0m result_noise \u001b[38;5;241m=\u001b[39m job\u001b[38;5;241m.\u001b[39mresult()[\u001b[38;5;241m0\u001b[39m]\n\u001b[1;32m      7\u001b[0m counts_noise \u001b[38;5;241m=\u001b[39m result_noise\u001b[38;5;241m.\u001b[39mdata\u001b[38;5;241m.\u001b[39mcr\u001b[38;5;241m.\u001b[39mget_counts()\n",
      "File \u001b[0;32m~/.pyenv/versions/3.11.6/envs/QuTiP/lib/python3.11/site-packages/qiskit_ibm_runtime/sampler.py:123\u001b[0m, in \u001b[0;36mSamplerV2.run\u001b[0;34m(self, pubs, shots)\u001b[0m\n\u001b[1;32m    116\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28many\u001b[39m(\u001b[38;5;28mlen\u001b[39m(pub\u001b[38;5;241m.\u001b[39mcircuit\u001b[38;5;241m.\u001b[39mcregs) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m pub \u001b[38;5;129;01min\u001b[39;00m coerced_pubs):\n\u001b[1;32m    117\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mwarn(\n\u001b[1;32m    118\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mOne of your circuits has no output classical registers and so the result \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    119\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mwill be empty. Did you mean to add measurement instructions?\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m    120\u001b[0m         \u001b[38;5;167;01mUserWarning\u001b[39;00m,\n\u001b[1;32m    121\u001b[0m     )\n\u001b[0;32m--> 123\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_run\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcoerced_pubs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/.pyenv/versions/3.11.6/envs/QuTiP/lib/python3.11/site-packages/qiskit_ibm_runtime/base_primitive.py:154\u001b[0m, in \u001b[0;36mBasePrimitiveV2._run\u001b[0;34m(self, pubs)\u001b[0m\n\u001b[1;32m    152\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m pub \u001b[38;5;129;01min\u001b[39;00m pubs:\n\u001b[1;32m    153\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtarget\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m is_simulator(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend):\n\u001b[0;32m--> 154\u001b[0m         \u001b[43mvalidate_isa_circuits\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43mpub\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcircuit\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_backend\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtarget\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    156\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend, IBMBackend):\n\u001b[1;32m    157\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend\u001b[38;5;241m.\u001b[39mcheck_faulty(pub\u001b[38;5;241m.\u001b[39mcircuit)\n",
      "File \u001b[0;32m~/.pyenv/versions/3.11.6/envs/QuTiP/lib/python3.11/site-packages/qiskit_ibm_runtime/utils/utils.py:92\u001b[0m, in \u001b[0;36mvalidate_isa_circuits\u001b[0;34m(circuits, target)\u001b[0m\n\u001b[1;32m     90\u001b[0m message \u001b[38;5;241m=\u001b[39m is_isa_circuit(circuit, target)\n\u001b[1;32m     91\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m message:\n\u001b[0;32m---> 92\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m IBMInputValueError(\n\u001b[1;32m     93\u001b[0m         message\n\u001b[1;32m     94\u001b[0m         \u001b[38;5;241m+\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m Circuits that do not match the target hardware definition are no longer \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     95\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msupported after March 4, 2024. See the transpilation documentation \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     96\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m(https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     97\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mthe primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     98\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mthis coupled with operator transformations.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     99\u001b[0m     )\n",
      "\u001b[0;31mIBMInputValueError\u001b[0m: 'The instruction rx on qubits (0,) is not supported by the target system. Circuits that do not match the target hardware definition are no longer supported after March 4, 2024. See the transpilation documentation (https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and the primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see this coupled with operator transformations.'"
     ]
    }
   ],
   "source": [
    "with Session(service=service, backend=backend) as session:\n",
    "    sampler = Sampler(session=session)\n",
    "    sim_noise = AerSimulator(noise_model=noise_model_depolarization)\n",
    "    circ_noise = transpile(circ1, sim_noise)\n",
    "    job = sampler.run([circ_noise])\n",
    "    result_noise = job.result()[0]\n",
    "    counts_noise = result_noise.data.cr.get_counts()\n",
    "    counts_noise_dict = {int(z, 2): counts for z, counts in counts_noise.items()}\n",
    "    plot_histogram(counts_noise_dict)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# another trial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import Kraus, SuperOp\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "from qiskit_aer import AerSimulator\n",
    "from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
    "from aux_functions import *\n",
    " \n",
    "\n",
    "from qiskit_aer.noise import (\n",
    "    NoiseModel,\n",
    "    QuantumError,\n",
    "    ReadoutError,\n",
    "    depolarizing_error,\n",
    "    pauli_error,\n",
    "    thermal_relaxation_error,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "\n",
    "with open('tocken.txt', 'r') as file:\n",
    "    token_txt = file.read().replace('\\n', '')\n",
    "   \n",
    "service = QiskitRuntimeService(\n",
    "    channel='ibm_quantum',\n",
    "    instance='ibm-q/open/main',\n",
    "    token=token_txt\n",
    ")\n",
    "\n",
    "backend = service.backend(\"ibm_brisbane\")\n",
    "noise_model = NoiseModel.from_backend(backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "ename": "IBMInputValueError",
     "evalue": "'The instruction h on qubits (0,) is not supported by the target system. Circuits that do not match the target hardware definition are no longer supported after March 4, 2024. See the transpilation documentation (https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and the primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see this coupled with operator transformations.'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIBMInputValueError\u001b[0m                        Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[18], line 5\u001b[0m\n\u001b[1;32m      3\u001b[0m sampler \u001b[38;5;241m=\u001b[39m Sampler(backend\u001b[38;5;241m=\u001b[39mbackend)\n\u001b[1;32m      4\u001b[0m sampler\u001b[38;5;241m.\u001b[39moptions\u001b[38;5;241m.\u001b[39mdefault_shots \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m10_000\u001b[39m\n\u001b[0;32m----> 5\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43msampler\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43mcirc1\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mresult()\n\u001b[1;32m      6\u001b[0m dist \u001b[38;5;241m=\u001b[39m result[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m.\u001b[39mdata\u001b[38;5;241m.\u001b[39mmeas\u001b[38;5;241m.\u001b[39mget_counts()\n",
      "File \u001b[0;32m~/.pyenv/versions/3.11.6/envs/QuTiP/lib/python3.11/site-packages/qiskit_ibm_runtime/sampler.py:123\u001b[0m, in \u001b[0;36mSamplerV2.run\u001b[0;34m(self, pubs, shots)\u001b[0m\n\u001b[1;32m    116\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28many\u001b[39m(\u001b[38;5;28mlen\u001b[39m(pub\u001b[38;5;241m.\u001b[39mcircuit\u001b[38;5;241m.\u001b[39mcregs) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m pub \u001b[38;5;129;01min\u001b[39;00m coerced_pubs):\n\u001b[1;32m    117\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mwarn(\n\u001b[1;32m    118\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mOne of your circuits has no output classical registers and so the result \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    119\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mwill be empty. Did you mean to add measurement instructions?\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m    120\u001b[0m         \u001b[38;5;167;01mUserWarning\u001b[39;00m,\n\u001b[1;32m    121\u001b[0m     )\n\u001b[0;32m--> 123\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_run\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcoerced_pubs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/.pyenv/versions/3.11.6/envs/QuTiP/lib/python3.11/site-packages/qiskit_ibm_runtime/base_primitive.py:154\u001b[0m, in \u001b[0;36mBasePrimitiveV2._run\u001b[0;34m(self, pubs)\u001b[0m\n\u001b[1;32m    152\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m pub \u001b[38;5;129;01min\u001b[39;00m pubs:\n\u001b[1;32m    153\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtarget\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m is_simulator(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend):\n\u001b[0;32m--> 154\u001b[0m         \u001b[43mvalidate_isa_circuits\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43mpub\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcircuit\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_backend\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtarget\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    156\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend, IBMBackend):\n\u001b[1;32m    157\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_backend\u001b[38;5;241m.\u001b[39mcheck_faulty(pub\u001b[38;5;241m.\u001b[39mcircuit)\n",
      "File \u001b[0;32m~/.pyenv/versions/3.11.6/envs/QuTiP/lib/python3.11/site-packages/qiskit_ibm_runtime/utils/utils.py:92\u001b[0m, in \u001b[0;36mvalidate_isa_circuits\u001b[0;34m(circuits, target)\u001b[0m\n\u001b[1;32m     90\u001b[0m message \u001b[38;5;241m=\u001b[39m is_isa_circuit(circuit, target)\n\u001b[1;32m     91\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m message:\n\u001b[0;32m---> 92\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m IBMInputValueError(\n\u001b[1;32m     93\u001b[0m         message\n\u001b[1;32m     94\u001b[0m         \u001b[38;5;241m+\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m Circuits that do not match the target hardware definition are no longer \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     95\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msupported after March 4, 2024. See the transpilation documentation \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     96\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m(https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     97\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mthe primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     98\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mthis coupled with operator transformations.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     99\u001b[0m     )\n",
      "\u001b[0;31mIBMInputValueError\u001b[0m: 'The instruction h on qubits (0,) is not supported by the target system. Circuits that do not match the target hardware definition are no longer supported after March 4, 2024. See the transpilation documentation (https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and the primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see this coupled with operator transformations.'"
     ]
    }
   ],
   "source": [
    "n_qubits = 4\n",
    "circ1 = generate_GHZ(n_qubits)\n",
    "sampler = Sampler(backend=backend)\n",
    "sampler.options.default_shots = 10_000\n",
    "result = sampler.run([circ1]).result()\n",
    "dist = result[0].data.meas.get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NoiseModel on ['ecr', 'x', 'reset', 'id', 'measure', 'sx']>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QuantumError on 1 qubits. Noise circuits:\n",
      "  P(0) = 0.05, Circuit = \n",
      "   ┌───┐\n",
      "q: ┤ X ├\n",
      "   └───┘\n",
      "  P(1) = 0.95, Circuit = \n",
      "   ┌───┐\n",
      "q: ┤ I ├\n",
      "   └───┘\n",
      "QuantumError on 1 qubits. Noise circuits:\n",
      "  P(0) = 0.05, Circuit = \n",
      "   ┌───┐\n",
      "q: ┤ Z ├\n",
      "   └───┘\n",
      "  P(1) = 0.95, Circuit = \n",
      "   ┌───┐\n",
      "q: ┤ I ├\n",
      "   └───┘\n"
     ]
    }
   ],
   "source": [
    "# Construct a 1-qubit bit-flip and phase-flip errors\n",
    "p_error = 0.05\n",
    "bit_flip = pauli_error([('X', p_error), ('I', 1 - p_error)])\n",
    "phase_flip = pauli_error([('Z', p_error), ('I', 1 - p_error)])\n",
    "print(bit_flip)\n",
    "print(phase_flip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QuantumError on 1 qubits. Noise circuits:\n",
      "  P(0) = 0.0025000000000000005, Circuit = \n",
      "   ┌───┐┌───┐\n",
      "q: ┤ X ├┤ Z ├\n",
      "   └───┘└───┘\n",
      "  P(1) = 0.0475, Circuit = \n",
      "   ┌───┐┌───┐\n",
      "q: ┤ X ├┤ I ├\n",
      "   └───┘└───┘\n",
      "  P(2) = 0.0475, Circuit = \n",
      "   ┌───┐┌───┐\n",
      "q: ┤ I ├┤ Z ├\n",
      "   └───┘└───┘\n",
      "  P(3) = 0.9025, Circuit = \n",
      "   ┌───┐┌───┐\n",
      "q: ┤ I ├┤ I ├\n",
      "   └───┘└───┘\n"
     ]
    }
   ],
   "source": [
    "# Compose two bit-flip and phase-flip errors\n",
    "bitphase_flip = bit_flip.compose(phase_flip)\n",
    "print(bitphase_flip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QuantumError on 2 qubits. Noise circuits:\n",
      "  P(0) = 0.0025000000000000005, Circuit = \n",
      "     ┌───┐\n",
      "q_0: ┤ X ├\n",
      "     ├───┤\n",
      "q_1: ┤ Z ├\n",
      "     └───┘\n",
      "  P(1) = 0.0475, Circuit = \n",
      "     ┌───┐\n",
      "q_0: ┤ I ├\n",
      "     ├───┤\n",
      "q_1: ┤ Z ├\n",
      "     └───┘\n",
      "  P(2) = 0.0475, Circuit = \n",
      "     ┌───┐\n",
      "q_0: ┤ X ├\n",
      "     ├───┤\n",
      "q_1: ┤ I ├\n",
      "     └───┘\n",
      "  P(3) = 0.9025, Circuit = \n",
      "     ┌───┐\n",
      "q_0: ┤ I ├\n",
      "     ├───┤\n",
      "q_1: ┤ I ├\n",
      "     └───┘\n"
     ]
    }
   ],
   "source": [
    "# Tensor product two bit-flip and phase-flip errors with\n",
    "# bit-flip on qubit-0, phase-flip on qubit-1\n",
    "error2 = phase_flip.tensor(bit_flip)\n",
    "print(error2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kraus([[[ 9.74679434e-01+0.j,  0.00000000e+00+0.j],\n",
      "        [ 0.00000000e+00+0.j,  9.74679434e-01+0.j]],\n",
      "\n",
      "       [[ 0.00000000e+00+0.j,  2.23606798e-01+0.j],\n",
      "        [ 2.23606798e-01+0.j, -4.96506831e-17+0.j]]],\n",
      "      input_dims=(2,), output_dims=(2,))\n"
     ]
    }
   ],
   "source": [
    "# Convert to Kraus operator\n",
    "bit_flip_kraus = Kraus(bit_flip)\n",
    "print(bit_flip_kraus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SuperOp([[1. +0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
      "         [0. +0.j, 0.9+0.j, 0. +0.j, 0. +0.j],\n",
      "         [0. +0.j, 0. +0.j, 0.9+0.j, 0. +0.j],\n",
      "         [0. +0.j, 0. +0.j, 0. +0.j, 1. +0.j]],\n",
      "        input_dims=(2,), output_dims=(2,))\n"
     ]
    }
   ],
   "source": [
    "# Convert to Superoperator\n",
    "phase_flip_sop = SuperOp(phase_flip)\n",
    "print(phase_flip_sop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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