lecture2_bonus.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b40df627",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit_textbook.tools import array_to_latex\n",
    "from qiskit import BasicAer\n",
    "# import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9fb95c44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 238.392x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 1 (a)\n",
    "\n",
    "# Defining the circuit and the initial state |psi> = |00>\n",
    "circ1 = QuantumCircuit(2)\n",
    "psi1 = Statevector.from_label('00')\n",
    "\n",
    "# Build your circuit here\n",
    "circ1.h(0)\n",
    "circ1.z(1)\n",
    "\n",
    "# circ1.draw('mpl')\n",
    "\n",
    "# Drawing the circuit you built\n",
    "display(circ1.draw('mpl'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "866c25aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([0.70710678+0.j 0.70710678+0.j 0.        +0.j 0.        +0.j], dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "# Evolving the Statevector based on the circuit you constructed\n",
    "psi1_v = psi1.evolve(circ1)\n",
    "print(psi1_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0e3108ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "\\begin{bmatrix}\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "0 \\\\\n",
       "0\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('statevector_simulator')\n",
    "final_state = execute(circ1,backend).result().get_statevector()\n",
    "array_to_latex(final_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "32e87e6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 358.792x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 1 (b)\n",
    "\n",
    "# Defining the circuit and the initial state |psi> = |00>\n",
    "circ2 = QuantumCircuit(2)\n",
    "psi2 = Statevector.from_label('00')\n",
    "\n",
    "# Build your circuit here\n",
    "circ2.h(0)\n",
    "circ2.cx(0,1)\n",
    "circ2.z(0)\n",
    "circ2.x(1)\n",
    "# Draw the circuit you built\n",
    "display(circ2.draw('mpl'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "4f1045b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([ 0.        +0.j -0.70710678+0.j  0.70710678+0.j  0.        +0.j], dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "# Evolve the Statevector based on the circuit you constructed:\n",
    "psi2_v = psi2.evolve(circ2)\n",
    "print(psi2_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8aa24dd0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "\\begin{bmatrix}\n",
       "0 \\\\\n",
       "-\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "0\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('statevector_simulator')\n",
    "final_state = execute(circ2,backend).result().get_statevector()\n",
    "array_to_latex(final_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a19b7fc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 358.792x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 1 (c)\n",
    "\n",
    "# Defining the circuit and the initial state |psi> = |00>\n",
    "circ3 = QuantumCircuit(2)\n",
    "psi3 = Statevector.from_label('00')\n",
    "\n",
    "# Build your circuit here\n",
    "circ3.h(0)\n",
    "circ3.x(1)\n",
    "circ3.h(1)\n",
    "circ3.cx(0,1)\n",
    "# Draw the circuit you built\n",
    "display(circ3.draw('mpl'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "25638772",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([ 0.5+0.j -0.5+0.j -0.5+0.j  0.5+0.j], dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "# Evolve the Statevector based on the circuit you constructed:\n",
    "psi3_v = psi3.evolve(circ3)\n",
    "print(psi3_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "5300aef3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "\\begin{bmatrix}\n",
       "\\tfrac{1}{2} \\\\\n",
       "-\\tfrac{1}{2} \\\\\n",
       "-\\tfrac{1}{2} \\\\\n",
       "\\tfrac{1}{2}\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('statevector_simulator')\n",
    "final_state = execute(circ3,backend).result().get_statevector()\n",
    "array_to_latex(final_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "57efc457",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 479.192x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#peoblem 2\n",
    "phiPlus = QuantumCircuit(2,2)\n",
    "psi2 = Statevector.from_label('00')\n",
    "\n",
    "# Build your circuit here\n",
    "phiPlus.h(0)\n",
    "phiPlus.cx(0,1)\n",
    "phiPlus.z(0)\n",
    "phiPlus.x(1)\n",
    "phiPlus.measure([0,1],[0,1])\n",
    "# Draw the circuit you built\n",
    "display(phiPlus.draw('mpl'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "ce98bd8b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.+0.0000000e+00j, -1.+2.4492936e-16j,  0.+0.0000000e+00j,\n",
       "        0.+0.0000000e+00j])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulator = BasicAer.get_backend('statevector_simulator')\n",
    "result = execute(phiPlus,backend = simulator).result()\n",
    "psi = result.get_statevector()\n",
    "psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d0e6ed13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "\\begin{bmatrix}\n",
       "0 \\\\\n",
       "-\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "\\tfrac{1}{\\sqrt{2}} \\\\\n",
       "0\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "array_to_latex(psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "af02c383",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n",
      "c:\\users\\user\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\validation\\fields\\custom.py:93: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if isinstance(value, numpy.float):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "result = execute(phiPlus,backend, shots = 420).result()\n",
    "output = result.get_counts()\n",
    "plot_histogram(output)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}