{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "62b94cf7-c3fa-481c-90d9-14867704c495",
   "metadata": {},
   "source": [
    "# Implementation of Freerider Detection using Quantum Computer\n",
    "\n",
    "Through this notebook, I demonstarete quantum energy teleportation and implement the verification of energy consumption algorithm. \n",
    "\n",
    "Documentation: Ikeda, Kazuki, \"Quantum Games and Economics through Teleportation\" (March 06, 2025). Available at SSRN: https://ssrn.com/abstract_id=5168193\n",
    "\n",
    "Copy right: Prof. Ikeda at UMass Boston (kazuki.ikeda@umb.edu)\n",
    "Website: https://kazukiikeda.studio.site/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "155975f4-2cf9-49d9-b037-7fab4f2255d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from QET import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d292b35a-e541-48b7-b2c3-50a300891ddb",
   "metadata": {},
   "source": [
    "# Chose backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "18d5d1bb-c7e2-42fd-aba1-56069d966f46",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "pm = generate_preset_pass_manager(backend=simulator, optimization_level=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf4a082e-7497-4ab7-8a22-7a9418c708dd",
   "metadata": {},
   "source": [
    "# Generate the ground state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "54427236-f4a0-47e5-90f4-95ab451896fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 305.525x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define the parameters\n",
    "k=1\n",
    "h=1.5\n",
    "minimal_model_ground_state_circuit(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fff49eb9-d739-4a0c-a99a-1eef76c5d2e7",
   "metadata": {},
   "source": [
    "# Inject energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a5b35aac-dec0-48b6-9583-f1605a494e7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 472.949x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inject_energy_circuit(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "08ec62b0-40a6-4230-acd7-271f4bd09888",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Injected energy using backend 1.2600754415067656 STD is 0.014999519992319753\n",
      "Exact injected energy 1.2480754415067656\n"
     ]
    }
   ],
   "source": [
    "shots=int(1e4)\n",
    "\n",
    "trans_inject = pm.run(inject_energy_circuit(k,h))\n",
    "counts_inject = simulator.run(trans_inject, shots=shots).result().get_counts()\n",
    "\n",
    "inject_energy_val(k,h,counts_inject,shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b8d2c71-a0eb-4678-b5aa-2f8c4c067e7c",
   "metadata": {},
   "source": [
    "# Quantum Energy Teleportation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "276cdd0d-6942-49a1-808b-6f91fe559dd5",
   "metadata": {},
   "source": [
    "## Teleport XX energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0a57a9fb-88da-4740-99e3-26926540f977",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 891.005x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_circuit_XX(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ccb1ef51-ea8a-41da-8f28-058dae64579f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Teleported XX energy is -0.4813996075495418 STD is 0.012121696910911441\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(-0.4813996075495418), np.float64(0.012121696910911441))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_XX = pm.run(QET_circuit_XX(k,h))\n",
    "counts_XX = simulator.run(QET_XX, shots=shots).result().get_counts()\n",
    "\n",
    "QET_energy_XX(k,h,counts_XX,shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08de2cd8-5b71-43df-88d9-f6894f773aa4",
   "metadata": {},
   "source": [
    "## Teleport Z energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "359396f8-b61b-41ae-86cd-5f095d5b8dfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 825.624x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_circuit_Z(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "90a47f8f-fd5b-41d6-b176-049d4ee81691",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Teleported Z energy is 0.3381754415067657 STD is 0.011925107924039932\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(0.3381754415067657), np.float64(0.011925107924039932))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_Z = pm.run(QET_circuit_Z(k,h))\n",
    "counts_Z = simulator.run(QET_Z, shots=shots).result().get_counts()\n",
    "\n",
    "QET_energy_Z(k,h,counts_Z,shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ad84e9e-78f6-4201-9970-4bb8131c7150",
   "metadata": {},
   "source": [
    "## Evaluate teleported energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0a5ba224-4fc1-477e-81fb-4b01022533c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Teleported XX energy is -0.4813996075495418 STD is 0.012121696910911441\n",
      "Teleported Z energy is 0.3381754415067657 STD is 0.011925107924039932\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(-0.1432241660427761)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_energy_XX(k,h,counts_XX,shots)[0]+QET_energy_Z(k,h,counts_Z,shots)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adfdc387-5f42-48f4-bbe6-d20b3969879c",
   "metadata": {},
   "source": [
    "# Combine QET with QST to confirm energy consumption"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abe4052b-e8ce-4074-8936-8d438ae2c94a",
   "metadata": {},
   "source": [
    "## Confirm energy consumption - XX term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "b248e067-d943-4402-a743-a46fafe24bdf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1346.13x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_QST_XX(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "52e21a71-3913-427e-a0bc-449ac2bf6cf2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed XX energy is -0.4761996075495418 STD is 0.012189637566392202\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(-0.4761996075495418), np.float64(0.012189637566392202))"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_XX = pm.run(QET_QST_XX(k,h))\n",
    "counts_XX = simulator.run(Confirm_XX, shots=shots).result().get_counts()\n",
    "\n",
    "Confirm_XX_val(k,h,counts_XX,shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9d5c2d3-95fb-40b4-aa07-81bd6950697a",
   "metadata": {},
   "source": [
    "## Confirm energy consumption - Z term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "c69c7e64-3b89-475b-bd0f-628d6dc9dc67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1262.31x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_QST_Z(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "51bf61ca-d7d8-40b1-9f78-b60e9be88829",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed Z energy is 0.34537544150676575 STD is 0.011979702458742454\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(0.34537544150676575), np.float64(0.011979702458742454))"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_Z = pm.run(QET_QST_Z(k,h))\n",
    "counts_Z = simulator.run(Confirm_Z, shots=shots).result().get_counts()\n",
    "\n",
    "Confirm_Z_val(k,h,counts_Z,shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "573484b7-9c62-4a10-8302-0eba2e50b5df",
   "metadata": {},
   "source": [
    "## Evaluate consumed energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "176f0178-56e4-43b9-9738-5ffb2afab2e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed XX energy is -0.4761996075495418 STD is 0.012189637566392202\n",
      "Confirmed Z energy is 0.34537544150676575 STD is 0.011979702458742454\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(-0.13082416604277608)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_XX_val(k,h,counts_XX,shots)[0]+Confirm_Z_val(k,h,counts_Z,shots)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b25fe8f2-a390-4b5b-8745-e53cfda83e39",
   "metadata": {},
   "source": [
    "## Confirmation of No Energy Consumption"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "77f261cb-1e7c-47b6-8f54-e30e772dd3e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 993.048x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_NO_QET_XX(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "72d5d939-6601-4bce-946d-ec2bcd4e9c9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed XX energy is 0.017800392450458474 STD is 0.016758309699966757\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(0.017800392450458474), np.float64(0.016758309699966757))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_XX = pm.run(Confirm_NO_QET_XX(k,h))\n",
    "counts_XX = simulator.run(Confirm_XX, shots=shots).result().get_counts()\n",
    "\n",
    "Confirm_XX_val(k,h,counts_XX,shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d6987fc8-42e8-4747-b5bd-557db5290560",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 909.235x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_NO_QET_Z(k,h).draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "10616687-8580-4740-b879-c33aa36862da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed Z energy is -0.0035245584932342144 STD is 0.00826739039842682\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(-0.0035245584932342144), np.float64(0.00826739039842682))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_Z = pm.run(Confirm_NO_QET_Z(k,h))\n",
    "counts_Z = simulator.run(Confirm_Z, shots=shots).result().get_counts()\n",
    "\n",
    "Confirm_Z_val(k,h,counts_Z,shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f61441d-790e-4344-8ff8-da8a7919df26",
   "metadata": {},
   "source": [
    "## Evaluate consumed energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "49feccb0-096d-4d42-a9a0-6654746c24a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed XX energy is 0.017800392450458474 STD is 0.016758309699966757\n",
      "Confirmed Z energy is -0.0035245584932342144 STD is 0.00826739039842682\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(0.01427583395722426)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_XX_val(k,h,counts_XX,shots)[0]+Confirm_Z_val(k,h,counts_Z,shots)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "276f54ff-4383-4b06-87d8-fb8f4f18fc68",
   "metadata": {},
   "source": [
    "# Experiment by Quantum Computer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "79e82e01-c0e8-4b94-9928-4449b8154df3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService, Session, SamplerV2 as Sampler, EstimatorV2 as Estimator\n",
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "from qiskit.providers.jobstatus import JobStatus\n",
    "from qiskit_ibm_runtime.fake_provider import FakeSherbrooke\n",
    "import mthree as m3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "058aa557-f18f-4fb5-b83a-d0d80a3ef043",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Enable your account on Qiskit, replace 'My_API_Token' with your newly generated token\n",
    "from qiskit_ibm_experiment import IBMExperimentService\n",
    "My_API_Token='Your token'\n",
    "IBMExperimentService.save_account(token=My_API_Token,overwrite=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bddb6d2-0a50-4909-b8ba-de1e5cd0dc11",
   "metadata": {},
   "source": [
    "## Quantum Hardware"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "98ecf2ad-7591-499a-ae5d-56bf5c8619d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Available backends: [<IBMBackend('ibm_brisbane')>, <IBMBackend('ibm_brussels')>, <IBMBackend('ibm_fez')>, <IBMBackend('ibm_kyiv')>, <IBMBackend('ibm_marrakesh')>, <IBMBackend('ibm_sherbrooke')>, <IBMBackend('ibm_strasbourg')>, <IBMBackend('ibm_torino')>]\n",
      "Name: ibm_kyiv\n"
     ]
    }
   ],
   "source": [
    "# Initialize the Qiskit runtime service\n",
    "service = QiskitRuntimeService()\n",
    "available_backends=service.backends()\n",
    "backend = service.least_busy()\n",
    "session = Session(backend=backend)\n",
    "estimator = Estimator(mode=session)\n",
    "sampler = Sampler(mode=session)\n",
    "\n",
    "# Backend details\n",
    "print(\"Available backends:\",available_backends)\n",
    "print(\"Name:\", backend.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1117,
   "id": "ca9858f2-af0b-4408-ba14-6388f2e11824",
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = service.backend(\"ibm_marrakesh\")\n",
    "session = Session(backend=backend)\n",
    "estimator = Estimator(mode=session)\n",
    "sampler = Sampler(mode=session)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59d63afc-1af1-427c-bc0b-3010c2ab7fab",
   "metadata": {},
   "source": [
    "## Fake Hardware"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "7884280d-ff71-4470-ab41-e470832317cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime.fake_provider import FakeAlmadenV2\n",
    "#backend = FakeAlmadenV2()\n",
    "#backend = Aer.get_backend('qasm_simulator')\n",
    "backend = FakeSherbrooke()\n",
    "shots = int(1e5)\n",
    "estimator = Estimator(backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "252400af-e596-4fbc-bed5-a3ed30fa8690",
   "metadata": {},
   "source": [
    "## M3 Quantum Error Mitigation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "7b024d68-71ef-4422-ad89-d5dd432aaebf",
   "metadata": {},
   "outputs": [],
   "source": [
    "pm = generate_preset_pass_manager(backend=backend, optimization_level=3)\n",
    "mit = m3.M3Mitigation(backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80a2bb5b-3f03-40bf-a2d2-c67d1d84acdc",
   "metadata": {},
   "source": [
    "## Inject energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "09e2c6cc-aa6e-4a0a-9fc3-307f78b86a04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 980.35x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k=1\n",
    "h=1.5\n",
    "\n",
    "trans_inject_energy_QC = pm.run(inject_energy_circuit(k,h))\n",
    "trans_inject_energy_QC.draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d289f585-c5a7-4703-b104-524e67b0538c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Injected energy using backend 1.2333754415067657 STD is 0.014999279682704768\n",
      "Exact injected energy 1.2480754415067656\n"
     ]
    }
   ],
   "source": [
    "counts_inject_energy_QC = backend.run(trans_inject_energy_QC, shots=shots).result().get_counts()\n",
    "inject_energy_val(k,h,counts_inject_energy_QC,shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "83152cb0-7a5f-41a6-a309-54d7079b60fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "mappings = m3.utils.final_measurement_mapping(trans_inject_energy_QC)\n",
    "mit.cals_from_system(mappings)\n",
    "quasis = mit.apply_correction(counts_inject_energy_QC, mappings,return_mitigation_overhead=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ac45f46d-b3a7-4ac5-909f-44b192a33da7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(1.2357965121540053), 0.010295973523861553)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3_QEM_Injected(k,h,quasis)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f9fbda7-5ece-44e9-bc89-5ea4487d8a89",
   "metadata": {},
   "source": [
    "## QET -XX term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a0899ca4-568d-465c-9fc1-a85139e2a66b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1398.41x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_XX_QC = pm.run(QET_circuit_XX(k,h))\n",
    "QET_XX_QC.draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ef8b3603-48a2-49d8-b5b2-fe3daeae477c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Teleported XX energy is -0.4509996075495417 STD is 0.012510602863171703\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(-0.4509996075495417), np.float64(0.012510602863171703))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts_QET_XX_QC = backend.run(QET_XX_QC, shots=shots).result().get_counts()\n",
    "QET_energy_XX(k,h,counts_QET_XX_QC,shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bced4dc0-458a-46d5-b7db-fe962948bb6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "mappings = m3.utils.final_measurement_mapping(QET_XX_QC)\n",
    "mit.cals_from_system(mappings)\n",
    "quasis = mit.apply_correction(counts_QET_XX_QC, mappings,return_mitigation_overhead=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "87f267c4-5fa2-4395-ac16-d0c7d8a46edb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(-0.4947704068049128), 0.010331242134604079)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3_QEM_XX(k,h,quasis)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e345e1c3-f0f8-4b4d-9344-b5d7274f3e8f",
   "metadata": {},
   "source": [
    "## QET -Z term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9934f42b-9fa7-4932-ae89-a5e9073e80a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1398.41x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QET_Z_QC = pm.run(QET_circuit_Z(k,h))\n",
    "QET_Z_QC.draw(\"mpl\", idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "375c54fe-ea39-4ef5-a4a7-442fb9079f5c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Teleported Z energy is 0.36877544150676567 STD is 0.012152495669614533\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(0.36877544150676567), np.float64(0.012152495669614533))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts_QET_Z_QC = backend.run(QET_Z_QC, shots=shots).result().get_counts()\n",
    "QET_energy_Z(k,h,counts_QET_Z_QC,shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b8ee6780-453f-4427-aadb-546a20348770",
   "metadata": {},
   "outputs": [],
   "source": [
    "mappings = m3.utils.final_measurement_mapping(QET_Z_QC)\n",
    "mit.cals_from_system(mappings)\n",
    "quasis = mit.apply_correction(counts_QET_Z_QC, mappings,return_mitigation_overhead=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ceff6013-2019-4f08-b82e-b24010c9522b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.35239635506000355), 0.01027095020405495)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3_QEM_Z(k,h,quasis)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e58ac76a-506b-47d1-a734-09ac00059a7c",
   "metadata": {},
   "source": [
    "## Confirm XX term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "e7ef8ad7-14d1-4eba-8fa1-cdc6428d305a",
   "metadata": {},
   "outputs": [],
   "source": [
    "pm = generate_preset_pass_manager(backend=backend, optimization_level=3)\n",
    "mit = m3.M3Mitigation(backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "c55dd57b-8931-45a0-ab22-ebea9e54fd0c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed XX energy is -0.3895996075495416 STD is 0.00418688308888605\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(-0.3895996075495416), np.float64(0.00418688308888605))"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_XX_QC = pm.run(QET_QST_XX(k,h))\n",
    "counts_XX_QC = backend.run(Confirm_XX, shots=shots).result().get_counts()\n",
    "Confirm_XX_val(k,h,counts_XX_QC,shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "87190f9c-ed5e-49e5-a550-cd970473470e",
   "metadata": {},
   "outputs": [],
   "source": [
    "mappings = m3.utils.final_measurement_mapping(Confirm_XX_QC)\n",
    "mit.cals_from_system(mappings)\n",
    "quasis_XX = mit.apply_correction(counts_XX_QC, mappings,return_mitigation_overhead=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "d4104305-c3e2-4570-a684-1e10258b6eb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(-0.42221784504496407), 0.0034155436434054076)"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3_QEM_Confirm_XX(k,h,quasis_XX)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "565efbdd-536d-4cd9-8c5d-47388b63b6d4",
   "metadata": {},
   "source": [
    "## Confirm Z term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "de460beb-cf33-4548-94d7-9eef5fba076f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confirmed Z energy is 0.3991654415067658 STD is 0.003910692792715888\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(np.float64(0.3991654415067658), np.float64(0.003910692792715888))"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Confirm_Z_QC = pm.run(QET_QST_Z(k,h))\n",
    "counts_Z_QC = backend.run(Confirm_Z, shots=shots).result().get_counts()\n",
    "Confirm_Z_val(k,h,counts_Z_QC,shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "f51538eb-5856-485c-940f-41161cffdd0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "mappings = m3.utils.final_measurement_mapping(Confirm_Z_QC)\n",
    "mit.cals_from_system(mappings)\n",
    "quasis_Z = mit.apply_correction(counts_Z_QC, mappings,return_mitigation_overhead=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "7b7e7af2-c101-436f-a0b3-5b438f66ad8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.3852191726240142), 0.00341268046268397)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3_QEM_Confirm_Z(k,h,quasis_Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb65fd02-4166-410a-8acd-881eded92f44",
   "metadata": {},
   "source": [
    "## Confirm Energy Consumption by QST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "5b404aeb-7562-435f-8a05-55c37e22a0c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(-0.036998672420949896)"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3_QEM_Confirm_XX(k,h,quasis_XX)[0]+M3_QEM_Confirm_Z(k,h,quasis_Z)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b212d0af-2cbc-4681-b8a9-83a07b3d9e80",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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