Notebook_10.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b4386340-74f7-4569-9eb9-eafa1a0371d6",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Notebook 10 \n",
    "# Sunint Bindra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a714bdf2-f616-451c-995e-a0177a4d498d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Libraries imported successfully!\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Importing standard Qiskit libraries\n",
    "from qiskit import QuantumCircuit, execute, transpile, Aer, IBMQ\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from ibm_quantum_widgets import *\n",
    "\n",
    "# Loading your IBM Quantum account(s)\n",
    "provider = IBMQ.load_account()\n",
    "print('Libraries imported successfully!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8c7dbab5-aff4-4b5c-94f9-f7b4d737a00c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 206.852x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quantum circuit with 2 qubits \n",
    "# Adding an H gate to qubit 0, and an CX gate with qubit 0 as control and qubit 1 as target.\n",
    "\n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a9155783-2c2f-4395-a5fa-3d895e4237b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\text{Statevector} = \n",
       "\\begin{bmatrix}\n",
       "\\tfrac{1}{\\sqrt{2}} & 0 & 0 & \\tfrac{1}{\\sqrt{2}}  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulating circuit using Statevector simulator and visualizing in vector form\n",
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(qc,backend) \n",
    "result = job.result()\n",
    "\n",
    "state = result.get_statevector()\n",
    "array_to_latex(state, prefix=\"\\\\text{Statevector} = \")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2492fe5e-29bc-43bc-862e-063107791ce1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 267.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quantum Circuit for 2nd Bell State \n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "qc.x(0)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "97a2011a-b0fb-4fdc-818c-48b73eb08d6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\text{Statevector} = \n",
       "\\begin{bmatrix}\n",
       "0 & \\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}} & 0  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulating circuit using Statevector simulator and visualizing in vector form\n",
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(qc,backend) \n",
    "result = job.result()\n",
    "\n",
    "state = result.get_statevector()\n",
    "array_to_latex(state, prefix=\"\\\\text{Statevector} = \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "229598d7-216c-47ac-9089-f1dcb039404f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 267.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quantum Circuit for 3rd Bell State \n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "qc.z(0)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b41b1064-8993-4913-9c51-27383216960a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\text{Statevector} = \n",
       "\\begin{bmatrix}\n",
       "\\tfrac{1}{\\sqrt{2}} & 0 & 0 & -\\tfrac{1}{\\sqrt{2}}  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulating circuit using Statevector simulator and visualizing in vector form\n",
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(qc,backend) \n",
    "result = job.result()\n",
    "\n",
    "state = result.get_statevector()\n",
    "array_to_latex(state, prefix=\"\\\\text{Statevector} = \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "02762b62-31c0-4baa-9cd5-16d544348730",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 327.252x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quantum Circuit for 4th Bell State \n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "qc.z(0)\n",
    "qc.x(0)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c316b922-7661-48a0-8a94-d2e574a7c3e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\text{Statevector} = \n",
       "\\begin{bmatrix}\n",
       "0 & \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulating circuit using Statevector simulator and visualizing in vector form\n",
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(qc,backend) \n",
    "result = job.result()\n",
    "\n",
    "state = result.get_statevector()\n",
    "array_to_latex(state, prefix=\"\\\\text{Statevector} = \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "16587837-c9dc-491b-b31a-6d999879a0ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Which of the four Bell states do you want to make? 3\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 267.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Bell State Abstraction - Creates Bell State and corresponding circuit given user input  \n",
    "\n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "state_choice = input(\"Which of the four Bell states do you want to make?\")\n",
    "if state_choice == \"1\":\n",
    "    pass\n",
    "elif state_choice ==\"2\":\n",
    "    qc.x(0)\n",
    "elif state_choice ==\"3\":\n",
    "    qc.z(0)\n",
    "elif state_choice ==\"4\":\n",
    "    qc.z(0)\n",
    "    qc.x(0)\n",
    "qc.draw()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "25f44762-f27b-4260-b304-320e134ab650",
   "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": [
    "# 2-Qubit quantum circuit. Addinng X gates to both qubits \n",
    "# Adding a CZ gate with q0 as control and q1 as target\n",
    "qc = QuantumCircuit(2)\n",
    "qc.x(0)\n",
    "qc.x(1)\n",
    "qc.cz(0,1)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5d882dfa-c731-4b22-bef7-ffaea09e2dba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\text{Statevector} = \n",
       "\\begin{bmatrix}\n",
       "0 & 0 & 0 & -1  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulating circuit using Statevector simulator and visualizing in vector form\n",
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(qc,backend) \n",
    "result = job.result()\n",
    "\n",
    "state = result.get_statevector()\n",
    "array_to_latex(state, prefix=\"\\\\text{Statevector} = \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9d0f193c-e13b-40da-8153-ed0e16831bc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 267.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating Bell State using H and CZ gates \n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.h(1)\n",
    "qc.cz(0,1)\n",
    "qc.h(1)\n",
    "qc.draw()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d2c30fbd-b0de-4603-9b15-629158760ef0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\text{Statevector} = \n",
       "\\begin{bmatrix}\n",
       "\\tfrac{1}{\\sqrt{2}} & 0 & 0 & \\tfrac{1}{\\sqrt{2}}  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulating circuit using Statevector simulator and visualizing in vector form\n",
    "backend = Aer.get_backend('statevector_simulator') \n",
    "job = execute(qc,backend)\n",
    "result = job.result()\n",
    "\n",
    "state = result.get_statevector()\n",
    "array_to_latex(state, prefix=\"\\\\text{Statevector} = \")"
   ]
  }
 ],
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