Session2_Demo_Deutsch_Jozsa.ipynb

{
 "cells": [
  {
   "cell_type": "raw",
   "id": "599aa1a4-d91f-4c81-83d0-3d4192e3fb92",
   "metadata": {},
   "source": [
    "Deutsch Jozsa Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb52c208-0903-4dda-a554-795487e9cdf1",
   "metadata": {},
   "source": [
    "First let's consider an oracle made of a function which takes 1 bit as the input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f835973a-81f3-4164-8499-53d4c03cec16",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialization\n",
    "import numpy as np\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, Aer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit import QuantumCircuit, assemble, transpile\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e07f4970-b7cf-4b61-a964-a52aa895c411",
   "metadata": {},
   "source": [
    "n=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a731bef6-b097-417c-895a-7e91c6dc7ef9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 116.552x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "const_oracle1 = QuantumCircuit(2)\n",
    "\n",
    "\n",
    "#constant oracle 1 --- identity \n",
    "\n",
    "const_oracle1.draw()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fa6fed80-3800-4d27-b460-a980250161d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH0AAAB7CAYAAABZ2Y84AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAFw0lEQVR4nO3df0iUdxzA8ffznGc/UIIQKjOdVifoPE23Ef2Rta3wn9EQbMkUcwdZc8JoG9tg9sdkspXbZCA0Rq3B0EHOxgbmH4PO9YuFtAUxmFCWHTT7SXgQN7v77g/hxs2VZ5jPc34+L7g//Prj+ejb5/FR8atljDEoUWynB1BzT6MLpNEF0ugCaXSBNLpAGl0gjS6QRhdIowuk0QXS6AJpdIE0ukAaXSCNLpBGF0ijC6TRBdLoAml0gTS6QBpdII0ukEYXSKMLpNEF0ugCaXSBNLpAGl0gjS6QRhdIowuk0QXS6AJpdIFcHT0Wi9HR0cHatWtZuHAhpaWlDA4OUlhYyK5du5weL2WlOT3AowQCAfr6+mhtbaWiooIzZ85QW1vLzZs32bt3r9PjpS7jUt3d3QYwwWAwYb26utoA5ty5cw5Nlvpce3lvb2+nqqqKysrKhPU1a9bg9Xrx+/0AXLlyhcrKSnw+HyUlJZw8edKJcVOL0591/+fatWsGMIcOHZryvB07dpiysrL401u3bjVdXV3GGGNOnz5tsrOzTSQSmfYYwLx6zIQrz/RQKATA8uXLE9bv37/P4OAg5eXlANy6dYtTp04RCAQA2LBhA9nZ2Zw4cWJuB04xroyelZUFwPDwcML6/v37uX79OhUVFQCMjo6ybNkyFixYEH+Z/Px8rl69Ou0xjDHz6jETrrx7LygowO/3097eztKlS1m5ciW9vb309/cDxKOrx+PKM922bY4ePUpxcTF79uyhsbGRrKwsmpub8Xg88Zu43NxcxsbGiEQi8dcdGRkhLy/PqdFTw4zuABxWV1dnSkpKEta2bNmScCO3YsWKpG7kJHPl5f1hhoaGWL9+fcLawYMH2blzJ52dnaSnp9PT00N6erpDE6YGy5jU2OQ/HA6zZMkSOjs7aWlpcXqclJYy0dXsceWNnHqyNLpAGl0gjS6QRhdIowuk0QXS6AJpdIE0ukAaXSCNLpBGF0ijC6TRBdLoAml0gTS6QBpdII0ukEYXSKMLlFJ/7OCEt/78gwvj444cuzQzk08Li2b97Wr0aVwYH+eXu3ecHmNW6eVdII0ukEYXSKMLpNEF0ugCaXSBNLpAro6uGwI/Ga6OHggEaGtro6mpiePHj7N9+3Zqa2u5fPmya7cVMxMTTOx+g+iXXyWsR4/9wERdAyYcdmiyf7n2x7A9PT0cOXKEYDAY3x928+bNnD9/nr6+vviukW5jeb2kvfcOD1rexHruWex1ZZiREWKHv8Hz0YdYGRlOj+jeMz3ZDYH37duHz+fDtm16e3udGHUK66k87NcaiHZ8jrlzhwcfH8De9hK2v8Tp0QCXRg+FQly8eJGampopzxsdHaW4uDi+NWhVVRUDAwNs3Lhxrsd8JPvlbVi5q3jQ1AweD3ZDvdMjxbk2Oky/ITBMbgJcUFAw42NYlpXUIxgMPtb7YFkWlr8E7t3DfuF5LK93xm8jGAwmPedMuDJ6shsCu5kZGSHW/R32KzXEvu3G3Ljh9EhxrryRm4sNgZPdPu/FoV9n/Pt08/fE5Nfx6pfxNDZg7t4leuAzPJ+0Y9nJn2ebNm3i5yewzZ8rz/RkNwR2q9jhr7HS0rDrXwXA8/puzF9jxL4/5vBkk1x5pgP4fL4pm/XX19dTVFTEokWLHJpqerHffifWP0Ba1xdYaZMfXmvxYjzvvk30/Q+wnynHys93dEZXnukPMzQ0NOXS3traSk5ODmfPnqWpqYmcnBwuXbrk0IRgryvD+2Mf1qqcxPWni/H+dMzx4JBC0cPhMMPDw1N+KNPW1kYoFCISiXD79m1CoRCrV692aMrU4NrL+39lZGQQjUadHmNeSJkzXc0ejS6QRhdIowuk0QXS6AJpdIFS5vt0p5RmZs67Y+t/axJIL+8CaXSBNLpAGl0gjS6QRhdIowuk0QXS6AJpdIE0ukAaXSCNLpBGF0ijC6TRBdLoAml0gf4Bw2IX96Z9iHYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 146.652x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# constant oracle 2 \n",
    "const_oracle2 = QuantumCircuit(2)\n",
    "\n",
    "const_oracle2.x(1)\n",
    "\n",
    "const_oracle2.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7b6b927f-fffe-4c4c-9adb-ece37b2f907c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.652x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "balanced_oracle1= QuantumCircuit(2)\n",
    "#balanced_oracle2= QuantumCircuit(2)\n",
    "balanced_oracle1.cx(0,1)\n",
    "balanced_oracle1.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cdd52b57-7fb8-42e8-bc20-3a3a918d9805",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 206.852x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "balanced_oracle2=QuantumCircuit(2)\n",
    "balanced_oracle2.cx(0,1)\n",
    "balanced_oracle2.x(1)\n",
    "balanced_oracle2.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87132deb-0173-41d6-aa96-a12498b64c3a",
   "metadata": {},
   "source": [
    "Choosing 4 possible oracles to understand the quantum algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "294efa3d-4aba-4b8f-8a8a-690262cc3df1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# chosing the oracle to simulate \n",
    "# select one of these and comment the rest\n",
    "\n",
    "#oracleF= const_oracle1\n",
    "oracleF= const_oracle2\n",
    "# oracleF= balanced_oracle1\n",
    "#oracleF= balanced_oracle2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "460f97eb-9aa5-4292-a81a-e18a013737a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_135/1700680483.py:14: DeprecationWarning: The QuantumCircuit.__iadd__() method is being deprecated. Use the compose() (potentially with the inplace=True argument) and tensor() methods which are more flexible w.r.t circuit register compatibility.\n",
      "  dj_circuit += oracleF\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 568.052x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dj_circuit = QuantumCircuit(2, 1)\n",
    "\n",
    "# Apply H-gates\n",
    "for qubit in range(1):\n",
    "    dj_circuit.h(qubit)\n",
    "\n",
    "# Put qubit in state |->\n",
    "dj_circuit.x(1)\n",
    "dj_circuit.h(1)\n",
    "\n",
    "dj_circuit.barrier()\n",
    "\n",
    "# Add oracle\n",
    "dj_circuit += oracleF\n",
    "\n",
    "dj_circuit.barrier()\n",
    "\n",
    "# Repeat H-gates\n",
    "for qubit in range(1):\n",
    "    dj_circuit.h(qubit)\n",
    "dj_circuit.barrier()\n",
    "\n",
    "# Measure\n",
    "for i in range(1):\n",
    "    dj_circuit.measure(i, i)\n",
    "\n",
    "# Display circuit\n",
    "dj_circuit.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2fe5205f-675c-43f2-9236-b56cb3792ae7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use local simulator\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "qobj = assemble(dj_circuit, aer_sim)\n",
    "results = aer_sim.run(qobj).result()\n",
    "answer = results.get_counts()\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74325017-fafe-4a55-85d7-7148c9a3747b",
   "metadata": {},
   "source": [
    "Now we will look at a generalized version \n",
    "\n",
    "Reference : https://qiskit.org/textbook/ch-algorithms/deutsch-jozsa.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d09ff7a3-b006-475b-92ac-df8ce03a7393",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dj_oracle(case, n):\n",
    "    # We need to make a QuantumCircuit object to return\n",
    "    # This circuit has n+1 qubits: the size of the input,\n",
    "    # plus one output qubit\n",
    "    oracle_qc = QuantumCircuit(n+1)\n",
    "    \n",
    "    # First, let's deal with the case in which oracle is balanced\n",
    "    if case == \"balanced\":\n",
    "        # First generate a random number that tells us which CNOTs to\n",
    "        # wrap in X-gates:\n",
    "        b = np.random.randint(1,2**n)\n",
    "        # Next, format 'b' as a binary string of length 'n', padded with zeros:\n",
    "        b_str = format(b, '0'+str(n)+'b')\n",
    "        # Next, we place the first X-gates. Each digit in our binary string \n",
    "        # corresponds to a qubit, if the digit is 0, we do nothing, if it's 1\n",
    "        # we apply an X-gate to that qubit:\n",
    "        for qubit in range(len(b_str)):\n",
    "            if b_str[qubit] == '1':\n",
    "                oracle_qc.x(qubit)\n",
    "        # Do the controlled-NOT gates for each qubit, using the output qubit \n",
    "        # as the target:\n",
    "        for qubit in range(n):\n",
    "            oracle_qc.cx(qubit, n)\n",
    "        # Next, place the final X-gates\n",
    "        for qubit in range(len(b_str)):\n",
    "            if b_str[qubit] == '1':\n",
    "                oracle_qc.x(qubit)\n",
    "\n",
    "    # Case in which oracle is constant\n",
    "    if case == \"constant\":\n",
    "        # First decide what the fixed output of the oracle will be\n",
    "        # (either always 0 or always 1)\n",
    "        output = np.random.randint(2)\n",
    "        if output == 1:\n",
    "            oracle_qc.x(n)\n",
    "    \n",
    "    oracle_gate = oracle_qc.to_gate()\n",
    "    oracle_gate.name = \"Oracle\" # To show when we display the circuit\n",
    "    return oracle_gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9fc53834-7514-4909-aa7f-1521d135f252",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create circuit\n",
    "\n",
    "def dj_algorithm(oracle, n):\n",
    "    dj_circuit = QuantumCircuit(n+1, n)\n",
    "    # Set up the output qubit:\n",
    "    dj_circuit.x(n)\n",
    "    dj_circuit.h(n)\n",
    "    # And set up the input register:\n",
    "    for qubit in range(n):\n",
    "        dj_circuit.h(qubit)\n",
    "    # Let's append the oracle gate to our circuit:\n",
    "    dj_circuit.append(oracle, range(n+1))\n",
    "    # Finally, perform the H-gates again and measure:\n",
    "    for qubit in range(n):\n",
    "        dj_circuit.h(qubit)\n",
    "    \n",
    "    for i in range(n):\n",
    "        dj_circuit.measure(i, i)\n",
    "    \n",
    "    return dj_circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c867d29e-3466-41cf-ad4f-5843ef4f0ae4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 507.997x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2\n",
    "oracle_gate = dj_oracle('balanced', n)\n",
    "dj_circuit = dj_algorithm(oracle_gate, n)\n",
    "dj_circuit.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e1e6f80c-6c6f-4d99-b29b-7197d58558b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulator\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "transpiled_dj_circuit = transpile(dj_circuit, aer_sim)\n",
    "qobj = assemble(transpiled_dj_circuit)\n",
    "results = aer_sim.run(qobj).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d41e1a9-f286-48bd-a630-c496fe5c3061",
   "metadata": {},
   "source": [
    "With real quantum devices "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "567e8fbe-3056-437f-867e-218d3046f3b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ibmqfactory.load_account:WARNING:2023-01-13 07:07:59,304: Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "least busy backend:  ibmq_belem\n"
     ]
    }
   ],
   "source": [
    "# Load our saved IBMQ accounts and get the least busy backend device with greater than or equal to (n+1) qubits\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub='ibm-q')\n",
    "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= (n+1) and\n",
    "                                   not x.configuration().simulator and x.status().operational==True))\n",
    "print(\"least busy backend: \", backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5e0e1f26-8de0-4225-8e8d-56140727bfc1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "\n",
    "transpiled_dj_circuit = transpile(dj_circuit, backend, optimization_level=3)\n",
    "job = backend.run(transpiled_dj_circuit)\n",
    "job_monitor(job, interval=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "440b1602-e3a7-413a-aac7-692712fb08b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the results of the computation\n",
    "results = job.result()\n",
    "answer = results.get_counts()\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a74debc6-d6da-46f9-a64e-ea137aed92ab",
   "metadata": {},
   "source": [
    "Similarly, for a constant function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "db84a6a3-3eca-4810-aeee-723e21c85ee8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 507.997x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2\n",
    "oracle_gate = dj_oracle('constant', n)\n",
    "dj_circuit = dj_algorithm(oracle_gate, n)\n",
    "dj_circuit.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5eb42b94-1feb-460f-8763-7af3f5083227",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulator\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "transpiled_dj_circuit = transpile(dj_circuit, aer_sim)\n",
    "qobj = assemble(transpiled_dj_circuit)\n",
    "results = aer_sim.run(qobj).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "88d999ba-0eac-4c11-8eee-5a65c5b79c08",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "least busy backend:  ibm_oslo\n"
     ]
    }
   ],
   "source": [
    "# Load our saved IBMQ accounts and get the least busy backend device with greater than or equal to (n+1) qubits\n",
    "#IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub='ibm-q')\n",
    "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= (n+1) and\n",
    "                                   not x.configuration().simulator and x.status().operational==True))\n",
    "print(\"least busy backend: \", backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3e1547ce-448f-436a-99fe-1293ba02e3d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "\n",
    "transpiled_dj_circuit = transpile(dj_circuit, backend, optimization_level=3)\n",
    "job = backend.run(transpiled_dj_circuit)\n",
    "job_monitor(job, interval=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ce0b8331-49b9-4cfa-84ed-162d86a1a16d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the results of the computation\n",
    "results = job.result()\n",
    "answer = results.get_counts()\n",
    "\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b38c2d1-ea27-45fe-995d-489e9e5f0fc3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.13"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}