Fazis_visszahatas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fázis-visszahatás/visszarúgás\n",
    "\n",
    "Megtanultuk, hogy a CNOT kapu az ellenkezőjére változtatja a target (második) qubit állapotát, ha a kontroll (első) qubit értéke $|1\\rangle$, egyébként változatlanul hagyja a targetet. \n",
    "* $|00\\rangle$ $\\rightarrow$ $|00\\rangle$\n",
    "* $|01\\rangle \\rightarrow |01\\rangle$\n",
    "* $|10\\rangle \\rightarrow |11\\rangle$\n",
    "* $|11\\rangle \\rightarrow |10\\rangle$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vizsgáljuk most meg, hogy mi történik az alábbi áramkörben!\n",
    "\n",
    "<img src=\"https://github.com/gubazoltan/QBronze2023/blob/main/%C3%A1br%C3%A1k/X1_H2_CNOT_circuit.png?raw=true\" width=\"150\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Megj.: feltételezzük, hogy mindkét qubit a $|0\\rangle$ kvantumállapotban kerül inicializálásra.)\n",
    "\n",
    "A CNOT-kapu **bemenete** tehát:\n",
    "\n",
    "$\\left.\n",
    "\\begin{array}{l}\n",
    "X:|0\\rangle \\rightarrow |1\\rangle \\\\\n",
    "H:|0\\rangle \\rightarrow |+\\rangle=\\frac{1}{\\sqrt{2}}(|0\\rangle+|1\\rangle)\n",
    "\\end{array} \\quad\n",
    "\\right\\rbrace\n",
    "\\quad\n",
    "|1\\,+\\rangle=|1\\rangle \\cdot \\frac{1}{\\sqrt{2}}(|0\\rangle+|1\\rangle)=\\frac{1}{\\sqrt{2}}(|10\\rangle+|11\\rangle)$\n",
    "\n",
    "A CNOT **kimenete**:\n",
    "\n",
    "$|1\\,+\\rangle \\rightarrow \\frac{1}{\\sqrt{2}}(|11\\rangle+|10\\rangle)=|1\\rangle \\cdot \\frac{1}{\\sqrt{2}}(|0\\rangle+|1\\rangle)=|1\\,+\\rangle$\n",
    "\n",
    "#### Vagyis itt hiába 1 a kontroll qubit értéke, a target állapota mégsem változik meg.\n",
    "- Megj.: Ha a kontroll értéke nem $|1\\rangle$, hanem $|0\\rangle$ (azaz nincs X kapu) akkor természetesen nem is várhatnánk, hogy a target állapota megváltozzon "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nézzünk egy másik áramkört\n",
    "\n",
    "<img src=\"https://github.com/gubazoltan/QBronze2023/blob/main/%C3%A1br%C3%A1k/X1_X2_H2_CNOT_circuit.png?raw=true\" width=\"200\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mivel $H: |1\\rangle \\rightarrow |-\\rangle=\\frac{1}{\\sqrt{2}}(|0\\rangle-|1\\rangle)$\n",
    "\n",
    "A CNOT-kapu **bemenete** most:\n",
    "\n",
    "$|1\\,-\\rangle=\\frac{1}{\\sqrt{2}}|1\\rangle(|0\\rangle-|1\\rangle)=\\frac{1}{\\sqrt{2}}(|10\\rangle-|11\\rangle)$\n",
    "\n",
    "A CNOT **kimenete** tehát:\n",
    "\n",
    "$|1\\,-\\rangle \\rightarrow \\frac{1}{\\sqrt{2}}(|11\\rangle-|10\\rangle)=-|1\\rangle \\cdot \\frac{1}{\\sqrt{2}}(|0\\rangle-|1\\rangle)=-|1\\,-\\rangle$\n",
    "\n",
    "- **Itt is hiába 1 a kontroll qubit értéke, a target állapota most sem változik meg**\n",
    "    - Magyarázat: a CNOT lényegében egy feltételes X-kapu, aminek a $|-\\rangle$ (illetve a $|+\\rangle$) állapot a \"sajátállapota\".\n",
    "    \n",
    "    \n",
    "- **Viszont mivel a target állapota $|-\\rangle$, a kontroll qubit kap egy fázist $=$ _fázis visszahatás/visszarúgás_**\n",
    "\n",
    "    - Ez a fázis itt most éppen \"nem számít\", mert globális fázis, de máskor számíthat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nézzük meg, mi történik, ha szuperpozíció a bemenet!\n",
    "\n",
    "\n",
    "<img src=\"https://github.com/gubazoltan/QBronze2023/blob/main/%C3%A1br%C3%A1k/H1_X2_H2_CNOT_circuit.png?raw=true\" width=\"200\"/>\n",
    "\n",
    "A CNOT **bemenete** most: \n",
    "\n",
    "$|+\\,-\\rangle=\\frac{1}{\\sqrt{2}}\\left(|0\\rangle+|1\\rangle\\right)|-\\rangle$\n",
    "\n",
    "A fentiekben láttuk, hogy a **kétfajta bemenetre** a CNOT hatása:\n",
    "\n",
    "$|0\\,-\\rangle \\rightarrow |0\\,-\\rangle$\n",
    "\n",
    "$|1\\,-\\rangle \\rightarrow -|1\\,-\\rangle$\n",
    "\n",
    "Tehát a CNOT **kimenete** most:\n",
    "\n",
    "$|+\\,-\\rangle \\rightarrow \\frac{1}{\\sqrt{2}}(|0\\rangle-|1\\rangle)|-\\rangle=|-\\,-\\rangle$\n",
    "\n",
    "#### Vegyük észre, hogy ha ezután még mindkét qubitre hatunk egy-egy H-kapuval, \n",
    "\n",
    "<img src=\"https://github.com/gubazoltan/QBronze2023/blob/main/%C3%A1br%C3%A1k/01_to_11_inverted_CNOT.png?raw=true\" width=\"300\"/>\n",
    "\n",
    "#### akkor a \"barrier\" előtti $|01\\rangle$ kezdőállapotból az $|11\\rangle$ végállapot lesz. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Feladat:** Hozzátok létre a fenti kvantumáramkört és futtassátok le szimulátoron!<br>\n",
    "A qubitek, $q_1$ és $q_0$, kezdetben legyenek a $|01\\rangle$  állapotban, azaz inicializáljátok a <br>\n",
    "- $q_1$ kvantumbitet a  $|0\\rangle$  állapotba <br>\n",
    "- $q_0$ kvantumbitet pedig az  $|1\\rangle$ állapotba.<br>\n",
    "\n",
    "Ezután alkalmazzatok egy-egy Hadamard kaput mindkét kvantumbiten.<br>\n",
    "Majd alkalmazzatok egy CNOT kaput úgy, hogy a $q_1$ a kontroll qubit és $q_0$ a target qubit legyen.<br>\n",
    "Alkalmazzatok ismét egy-egy Hadamard kaput mindkét kvantumbiten.<br>\n",
    "Végül mérjétek meg a kvantumbiteket!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 507.852x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 100}\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, execute, Aer\n",
    "\n",
    "qc = QuantumCircuit(2,2)\n",
    "\n",
    "qc.x(0)\n",
    "qc.barrier()\n",
    "\n",
    "qc.h(0)\n",
    "qc.h(1)\n",
    "\n",
    "qc.cx(1,0)\n",
    "\n",
    "qc.h(0)\n",
    "qc.h(1)\n",
    "\n",
    "qc.measure(1,1)\n",
    "qc.measure(0,0)\n",
    "\n",
    "display(qc.draw(output='mpl',reverse_bits=True))\n",
    "\n",
    "job = execute(qc,Aer.get_backend('qasm_simulator'),shots=100)\n",
    "counts = job.result().get_counts(qc)\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Feladat:** A többi számítási bázis bemenetre ($|00\\rangle$, $|10\\rangle$, $|11\\rangle$) is nézzétek meg a fenti áramkör hatását! Mit tapasztaltok?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A H-kapukkal \"szendvicselt\" CNOT tehát fordítva hat\n",
    "\n",
    "<img src=\"https://github.com/gubazoltan/QBronze2023/blob/main/%C3%A1br%C3%A1k/reversing_a_CNOT.png?raw=true\" width=\"300\"/>\n",
    "\n",
    "#### azaz a kontroll és target qubit szerepe felcserélődik."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. Feladat:** Hozzatok létre egy áramkört 3 qubittel ($q_2$,$q_1$,$q_0$) és inicializáljátok őket a $|001\\rangle$ állapotban.<br>\n",
    "Alkalmazzatok Hadamard kaput az összes kvantumbiten! <br>\n",
    "Alkalmazzatok 2 db CNOT kaput úgy, hogy a kontroll qubitek a $q_2$ és $q_1$, míg a target mindkét CNOT esetén a $q_0$ legyen. <br>\n",
    "Ismét alkalmazzatok Hadamard kapukat az összes kvantumbiten, majd mérjétek meg őket! <br>\n",
    "Értelmezzétek az eredményt!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 688.597x264.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'111': 100}\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, execute, Aer\n",
    "\n",
    "qc = QuantumCircuit(3,3)\n",
    "\n",
    "qc.x(0)\n",
    "qc.barrier()\n",
    "\n",
    "for i in range(3):\n",
    "    qc.h(i)\n",
    "\n",
    "for i in range(2):\n",
    "    qc.cx(i+1,0)\n",
    "\n",
    "for i in range(3):\n",
    "    qc.h(i)\n",
    "\n",
    "qc.barrier()\n",
    "\n",
    "for i in range(3):\n",
    "    qc.measure(i,i)\n",
    "\n",
    "display(qc.draw(output='mpl',reverse_bits=True))\n",
    "\n",
    "job = execute(qc,Aer.get_backend('qasm_simulator'),shots=100)\n",
    "counts = job.result().get_counts(qc)\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. Feladat:** Nézzétek meg mi történik, ha az egyik, vagy mindkét CNOT kaput kihagyjátok az áramkörből! Mi lesz ezekben az esetekben a mérési eredmény a $q_2$ és $q_1$ qubiteken? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. Feladat:** Végezzétek el a 4. Feladat analízisét nagyobb áramkörben is!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "2353d288b475d2cc636ad48126075a57059af323d6ffd0a5e5428d78a33005ad"
  },
  "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}