{
 "cells": [
  {
   "attachments": {
    "circuit.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Superdense Coding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
    "from braket.tracking import Tracker\n",
    "t = Tracker().start()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, we construct an implementation of the superdense coding protocol via Amazon Braket's SDK. Superdense coding is a method of transmitting two classical bits by sending only one qubit. Starting with a pair of entanged qubits, the sender (aka Alice) applies a certain quantum gate to their qubit and sends the result to the receiver (aka Bob), who is then able to decode the full two-bit message.\n",
    "\n",
    "If Alice wants to send a two-bit message to Bob using only classical channels, she would need to send two classical bits. However, with the help of quantum entanglement, Alice can do this by sending just one qubit. By ensuring that Alice and Bob initially share an entangled state of two qubits, they can devise a strategy such that Alice can transmit her two-bit message by sending her single qubit.\n",
    "\n",
    "To implement superdense coding, Alice and Bob need to share or otherwise prepare a maximally entangled pair of qubits (i.e., a Bell pair). Alice then selects one of the four possible messages to send with two classical bits: 00, 01, 10, or 11. Depending on which two-bit string she wants to send, Alice applies a corresponding quantum gate to encode her desired message. Finally, Alice sends her own qubit to Bob, which Bob then uses to decode the message by undoing the initial entangling operation.\n",
    "\n",
    "Note that superdense coding is closely related to quantum teleportation.  In teleportation, one uses an entangled pair (an e-bit) and two uses of a classical channel to simulate a single use of a quantum channel.  In superdense coding, one uses an e-bit and a single use of a quantum channel to simulate two uses of a classical channel.\n",
    "\n",
    "\n",
    "## Detailed Steps\n",
    "1. Alice and Bob initially share a Bell pair.  This can be prepared by starting with two qubits in the |0⟩ state, then applying the Hadamard gate (𝐻) to the first qubit to create an equal superposition, and finally applying a CNOT gate (𝐶𝑋) between the two qubits to produce a Bell pair.  Alice holds one of these two qubits, while Bob holds the other.\n",
    "2. Alice selects one of the four possible messages to send Bob. Each message corresponds to a unique set of quantum gate(s) to apply to her own qubit, illustrated in the table below.  For example, if Alice wants to send the message \"01\", she would apply the Pauli X gate.\n",
    "3. Alice sends her qubit to Bob through the quantum channel.\n",
    "4. Bob decodes Alice's two-bit message by first applying a CNOT gate using Alice's qubit as the control and his own qubit as the target, and then a Hadamard gate on Alice's qubit to restore the classical message.\n",
    "\n",
    "| Message | Alice's encoding | State Bob receives<br>(non-normalized) | After 𝐶𝑋 gate<br>(non-normalized) | After 𝐻 gate |\n",
    "| :---: | :---: | :---: | :---: | :---: |\n",
    "| 00 | 𝐼 | \\|00⟩ + \\|11⟩ | \\|00⟩ + \\|10⟩ | \\|00⟩\n",
    "| 01 | 𝑋 | \\|10⟩ + \\|01⟩ | \\|11⟩ + \\|01⟩ | \\|01⟩\n",
    "| 10 | 𝑍 | \\|00⟩ - \\|11⟩ | \\|00⟩ - \\|10⟩ | \\|10⟩\n",
    "| 11 | 𝑍𝑋 | \\|01⟩ - \\|10⟩ | \\|01⟩ - \\|11⟩ | \\|11⟩\n",
    "\n",
    "\n",
    "## Circuit Diagram\n",
    "\n",
    "Circuit used to send the message \"00\". To send other messages, swap out the identity (𝐼) gate.\n",
    "<div align=\"center\"><img src=\"circuit.png\"/></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Version: 1.0.0.post1\r\n"
     ]
    }
   ],
   "source": [
    "# Print version of SDK\n",
    "!pip show amazon-braket-sdk | grep Version\n",
    "\n",
    "# Import Braket libraries\n",
    "from braket.circuits import Circuit, Gate, Moments\n",
    "from braket.circuits.instruction import Instruction\n",
    "from braket.aws import AwsDevice\n",
    "from braket.devices import LocalSimulator\n",
    "import matplotlib.pyplot as plt\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Typically, we recommend running circuits with fewer than 25 qubits on the local simulator to avoid latency bottlenecks. The on-demand, high-performance simulator SV1 is better suited for larger circuits up to 34 qubits. For demonstration purposes, we are going to continue this example with the local simulator, but it is easy to switch over to SV1 by commenting out the LocalSimulator line below and uncommenting the sv1 line.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up device: local simulator or the on-demand simulator\n",
    "device = LocalSimulator()\n",
    "# device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to run quantum task, check the status thereof and collect results\n",
    "def get_result(device, circ):\n",
    "    \n",
    "    # get number of qubits\n",
    "    num_qubits = circ.qubit_count\n",
    "\n",
    "    # specify desired results_types\n",
    "    circ.probability()\n",
    "\n",
    "    # submit task: define task (asynchronous)\n",
    "    if device.name == 'StateVectorSimulator':\n",
    "        task = device.run(circ, shots=1000)\n",
    "    else:\n",
    "        task = device.run(circ, shots=1000)\n",
    "\n",
    "    # Get ID of submitted task\n",
    "    task_id = task.id\n",
    "#     print('Task ID :', task_id)\n",
    "\n",
    "    # Wait for job to complete\n",
    "    status_list = []\n",
    "    status = task.state()\n",
    "    status_list += [status]\n",
    "    print('Status:', status)\n",
    "\n",
    "    # Only notify the user when there's a status change\n",
    "    while status != 'COMPLETED':\n",
    "        status = task.state()\n",
    "        if status != status_list[-1]:\n",
    "            print('Status:', status)\n",
    "        status_list += [status]\n",
    "\n",
    "    # get result\n",
    "    result = task.result()\n",
    "\n",
    "    # get metadata\n",
    "    metadata = result.task_metadata\n",
    "\n",
    "    # get output probabilities\n",
    "    probs_values = result.values[0]\n",
    "\n",
    "    # get measurement results\n",
    "    measurement_counts = result.measurement_counts\n",
    "\n",
    "    # print measurement results\n",
    "    print('measurement_counts:', measurement_counts)\n",
    "\n",
    "    # bitstrings\n",
    "    format_bitstring = '{0:0' + str(num_qubits) + 'b}'\n",
    "    bitstring_keys = [format_bitstring.format(ii) for ii in range(2**num_qubits)]\n",
    "\n",
    "    # plot probabalities\n",
    "    plt.bar(bitstring_keys, probs_values)\n",
    "    plt.xlabel('bitstrings')\n",
    "    plt.ylabel('probability')\n",
    "    plt.xticks(rotation=90)\n",
    "    plt.show() \n",
    "    \n",
    "    return measurement_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alice and Bob initially share a Bell pair.  Let's create this now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)]))])\n"
     ]
    }
   ],
   "source": [
    "circ = Circuit()\n",
    "circ.h([0])\n",
    "circ.cnot(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define Alice's encoding scheme according to the table above.  Alice selects one of these messages to send."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Four possible messages and their corresponding gates\n",
    "message = {\"00\": Circuit().i(0),\n",
    "           \"01\": Circuit().x(0),\n",
    "           \"10\": Circuit().z(0),\n",
    "           \"11\": Circuit().x(0).z(0)\n",
    "          }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Select message to send.  Let's start with '01' for now\n",
    "m = \"01\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alice encodes her message by applying the gates defined above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
     {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)])), Instruction('operator': X('qubit_count': 1), 'target': QubitSet([Qubit(0)]))])\n"
     ]
    }
   ],
   "source": [
    "# Encode the message\n",
    "circ.add_circuit(message[m])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alice then sends her qubit to Bob so that Bob has both qubits in his lab.  Bob decodes Alice's message by disentangling the two qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit('instructions': [Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)])), Instruction('operator': X('qubit_count': 1), 'target': QubitSet([Qubit(0)])), Instruction('operator': CNot('qubit_count': 2), 'target': QubitSet([Qubit(0), Qubit(1)])), Instruction('operator': H('qubit_count': 1), 'target': QubitSet([Qubit(0)]))])\n"
     ]
    }
   ],
   "source": [
    "circ.cnot(0,1)\n",
    "circ.h([0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The full circuit now looks like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T  : |0|1|2|3|4|\n",
      "                \n",
      "q0 : -H-C-X-C-H-\n",
      "        |   |   \n",
      "q1 : ---X---X---\n",
      "\n",
      "T  : |0|1|2|3|4|\n"
     ]
    }
   ],
   "source": [
    "print(circ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By measuring the two qubits in the computational basis, Bob can read off Alice's two qubit message"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status: COMPLETED\n",
      "measurement_counts: Counter({'01': 1000})\n"
     ]
    },
    {
     "data": {
      "image/png": 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HLkry5VkUtMzcAtzAPR9DUt36Q2ZS0fJzDvDvwNFV9d8ASX6KwR8jHwKeNcPafuwlOWKhXcATp1lL3wyC/tya5PnAv1TVjwCS3At4PnDrTCtbHq4DnlFVXx3dkeTGMe21ozVVdY9H5XWB8OYkL59RTcvJFuDTjH8m2oOmXEuvDIL+nMDg/QqnJ9neBX8QcD57/x3Ue8JfAw8GdggC4C1TrmW5uiHJ7wFnVtU3AJI8FHgp93wysMa7BnhVVX1ldMfe9seIcwQ9SnIog3cuHMTgMRtfBT5aVdfMtLBlIsljufv8FYOHFm7y/E0myYOBkxmcw+3Dad9g8Iyv06rKnukikjwPuKKqdnjsfZLnVNVHZlBWL7xqqCdJ3gD8E4P/gX0R+Hy366xxr+3UPXV/yZ7NoFv+JQbd9OD5m1hV3VpVb6iqx1bVgd3PoVX1BgYTyFpEVZ07LgQ6D55qMT2zR9CTbkL4Z6rqByPb9wOuqqq1s6lsefD89SvJV6tq9azrWK72tvPnHEF/fgQ8nMGVL8Me1u3T4jx/uynJ5QvtAh46zVqWo5bOn0HQn5OATyX5CndPzK0GHgWcOLOqlg/P3+57KPAr7HiVWrh7qFILa+b8GQQ9qapPJnk0cCSDyc4wuI9gS1X9cKbFLQOevz3iY8ADqurS0R1JLph+OctOM+fPOQJJapxXDUlS4wwCSWqcQaDmJFmT5Mox29+TZF23/AcTHOekJPdbZP9dx5N+nDlHoOYkWQN8rKoet0ib71TVA5Y4zvXAXFV9c8y+fZzU1nJhj0Ct2jfJmd27Is5Ncr8kFySZS3IacN8klyb5xyT3T/Lx7p0SVyZ5YZLXMLjP4fwk58MgPJKcmuSLwJO3H29o3591x7ioe+YPSX66W9/SffY73faHJflMV8OVSX5hNqdJLTAI1KrHABur6gnAbcCrt++oqpOB71XVE6vq14FjgJuq6rCuF/HJqnoHg2cfPb2qnt599P7AlVV1VFVdOPJ99wcuqqrDgM8Ar+y2vx14e1X9bHe87V4EnFdVTwQOA3a4hFHaUwwCterGqvpct/xB4KmLtL0CeGaSNyf5har69gLtfgj8ywL77mBwXTrAxcCabvnJDN4NAINnU223BXhZkjcBj6+q2xepT9otBoFaNTo5tuBkWVV9GXgSg0D48ySnLND0+4vMC/yg7p6Q+yFL3MxZVZ8BfhH4GvCBJC9erL20OwwCtWp1kid3y+uB0aGcH2x/t3SShwPfraoPAn8BbH9z1e3A/rtZx0XAc7vlu95TkeQRwM1V9ffAe4e+U9rjDAK16hrgJd2DxQ4E3j2yfyNweZJ/BB4PfCnJpcAfAn861OYT2yeLd9FJwGuTfInBA/W2DzsdDVya5BIGQfH23fgOaVFePirNUHcfwveqqpKcAKyvquNnXZfa4kPnpNl6EvCuJAG+BfguYU2dPQJJapxzBJLUOINAkhpnEEhS4wwCSWqcQSBJjTMIJKlx/w8+J9WNgQGuTgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter({'01': 1000})\n"
     ]
    }
   ],
   "source": [
    "counts = get_result(device, circ)\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that this scheme works for the other possible messages too:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status: COMPLETED\n",
      "measurement_counts: Counter({'00': 1000})\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Message: 00. Results:\n",
      "Counter({'00': 1000})\n",
      "Status: COMPLETED\n",
      "measurement_counts: Counter({'01': 1000})\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Message: 01. Results:\n",
      "Counter({'01': 1000})\n",
      "Status: COMPLETED\n",
      "measurement_counts: Counter({'10': 1000})\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Message: 10. Results:\n",
      "Counter({'10': 1000})\n",
      "Status: COMPLETED\n",
      "measurement_counts: Counter({'11': 1000})\n"
     ]
    },
    {
     "data": {
      "image/png": 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JvjSLgpaZ24CbuO9jSKpbf8RMKlp+zgP+GTimqv4bIMmPMfhj5CPAc2ZY2w+9JEcutAt48jRr6ZtB0J/bk7wA+Ieq+gFAkvsBLwBun2lly8MNwLOq6iujO5LcPKa9drSmqu7zmLIuEF6f5DdnVNNysgX4LOOfifawKdfSK4OgPycxeL/CmUm2d8EfBlzI3n8H9Z7wFuDhwA5BALxhyrUsVzcl+QPg7Kr6GkCSRwK/zn2fDKzxrgN+q6q+PLpjb/tjxDmCHiU5jME7Fw5i8JiNrwAfr6rrZlrYMpHkCdx7/orBQws3ef4mk+ThwKkMzuH24bSvMXjG1xlVZc90EUlOBK6qqh0ee5/keVX1sRmU1QuvGupJktcAH2bwH9gXgH/tdp0z7rWduq/uL9lzGXTLv8igmx48fxOrqtur6jVV9YSqOrD7OayqXsNgAlmLqKrzx4VA5+FTLaZn9gh60k0I/0RVfW9k+37ANVW1djaVLQ+ev34l+UpVrZ51HcvV3nb+nCPozw+AH2dw5cuwR3X7tDjP325KcuVCu4BHTrOW5ail82cQ9OcU4DNJvsy9E3OrgccBJ8+squXD87f7Hgn8IjtepRbuHarUwpo5fwZBT6rq00keDxzFYLIzDO4j2FJV359pccuA52+P+ATwkKq6fHRHkoumX86y08z5c45AkhrnVUOS1DiDQJIaZxCoOUnWJLl6zPb3JFnXLf/RBMc5JcmDFtl/z/GkH2bOEag5SdYAn6iqJy7S5ltV9ZAljnMjMFdVXx+zbx8ntbVc2CNQq/ZNcnb3rojzkzwoyUVJ5pKcATwwyeVJPpTkwUk+2b1T4uokL0rySgb3OVyY5EIYhEeS05N8AXjq9uMN7fuL7hiXdM/8Iclju/Ut3We/1W1/VJLPdTVcneRnZ3Oa1AKDQK06FNhYVU8C7gBesX1HVZ0KfKeqnlxVvwIcC9xSVYd3vYhPV9XbGDz76JlV9czuow8Grq6qo6vq4pHvezBwSVUdDnwOeHm3/a3AW6vqp7rjbfdi4IKqejJwOLDDJYzSnmIQqFU3V9Xnu+UPAk9fpO1VwLOTvD7Jz1bVNxdo933gHxbYdxeD69IBLgXWdMtPZfBuABg8m2q7LcBvJHkd8JNVdeci9Um7xSBQq0YnxxacLKuqLwFPYRAIf5nktAWafneReYHv1b0Tct9niZs5q+pzwM8BXwU+kOQli7WXdodBoFatTvLUbnk9MDqU873t75ZO8uPAt6vqg8BfAdvfXHUnsP9u1nEJ8Pxu+Z73VCR5NHBrVb0beO/Qd0p7nEGgVl0HvLR7sNiBwDtH9m8ErkzyIeAngS8muRz4Y+DPh9p8avtk8S46BXhVki8yeKDe9mGnY4DLk1zGICjeuhvfIS3Ky0elGeruQ/hOVVWSk4D1VXXCrOtSW3zonDRbTwHekSTANwDfJayps0cgSY1zjkCSGmcQSFLjDAJJapxBIEmNMwgkqXEGgSQ17v8BVnjVjbMQPTQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Message: 11. Results:\n",
      "Counter({'11': 1000})\n"
     ]
    }
   ],
   "source": [
    "for m in message:\n",
    "    \n",
    "    # Reproduce the full circuit above by concatenating all of the gates:\n",
    "    newcirc = Circuit().h([0]).cnot(0,1).add_circuit(message[m]).cnot(0,1).h([0])\n",
    "    \n",
    "    # Run the circuit:\n",
    "    counts = get_result(device, newcirc)\n",
    "    \n",
    "    print(\"Message: \" + m + \". Results:\")\n",
    "    print(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Task Summary\n",
      "{}\n",
      "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
      "Estimated cost to run this example: 0.00 USD\n"
     ]
    }
   ],
   "source": [
    "print(\"Task Summary\")\n",
    "print(t.quantum_tasks_statistics())\n",
    "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
    "print(f\"Estimated cost to run this example: {t.qpu_tasks_cost() + t.simulator_tasks_cost():.2f} USD\")"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3.8.10 ('venv': venv)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
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  "vscode": {
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 },
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