kierros1_ratkaisut.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kvanttilaskenta 2024: Kierros 1 tehtävät\n",
    "\n",
    "Seuraava lohko pitää suorittaa, jotta saat Numpy-kirjaston käyttöön muihin lohkoihin. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numpy kirjasto on nyt käytössä.\n"
     ]
    }
   ],
   "source": [
    "# ctrl+enter\n",
    "import numpy as np\n",
    "from qiskit import *\n",
    "print(\"Numpy kirjasto on nyt käytössä.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtävä 1.1\n",
    "\n",
    "Laske vektorin $a= 3i + 4j$ pituus käyttäen indeksöintiä ja Pythagoraan lausetta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3]\n",
      " [4]]\n"
     ]
    }
   ],
   "source": [
    "a = np.matrix([[3], [4]])\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vektorin 3i + 4j pituus 5.0\n"
     ]
    }
   ],
   "source": [
    "# Laske vektorin a pituus muuttujaan l\n",
    "l = (a[0,0]**2+a[1,0]**2)**0.5\n",
    "\n",
    "print(f\"Vektorin 3i + 4j pituus {l}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtävä 1.2\n",
    "\n",
    "Laske Pythonilla vektorien a ja b aritmeettinen keskiarvo kaavalla\n",
    "\n",
    "$$ \\frac{\\bar a + \\bar b}2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Keskiarvoksi saatiin\n",
      "[[2.]\n",
      " [2.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.matrix([[1], [3]])\n",
    "b = np.matrix([[3], [1]])\n",
    "\n",
    "# laske keskiarvo muuttujaan avg\n",
    "avg = (a+b)/2\n",
    "\n",
    "print(\"Keskiarvoksi saatiin\")\n",
    "print(avg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtävä 1.3\n",
    "\n",
    "Ratkaise Pythonilla ovatko vektorit a ja b kohtisuoria, eli niiden välinen pistetulo 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "pistetulo = a[0,0]*b[0,0]+a[1,0]*b[1,0]\n",
    "print(pistetulo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 3]]\n",
      "[[6]]\n"
     ]
    }
   ],
   "source": [
    "# TApa 2\n",
    "# transponoidaan vektori a\n",
    "print(a.T)\n",
    "# lasketaan vaakavektorin a.T ja pystyvektorin b tulo\n",
    "pistetulo = a.T*b\n",
    "print(pistetulo)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtävä 1.4\n",
    "\n",
    "a) Muunna binääriesitykseen luku $123_{10}$\n",
    "\n",
    "b) Muunna desimaaliesitykseen luku $1011101_{2}$\n",
    "\n",
    "\n",
    "Ratkaise tehtävä ohjelmoimalla pythonilla alla olevaan soluun."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b1111011'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "93"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(\"1011101\",2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtävä 1.5\n",
    "\n",
    "![](./images/xor_circuit.png)\n",
    "\n",
    "Täytä totuustaulusta puuttuvat kohdat (merkattu alaviivoilla \\_) ylläolevan loogisen piirin mukaan. Voit muokata taulua tuplaklikkaamalla."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| $A$ | $B$ | C = $A \\lor B$ | D = $\\neg(A \\land B)$ | Out = $ C \\land D$ |\n",
    "| :-: | :-: | :-:            | :-:                   | :-:       |\n",
    "|   0 |   0 | 0              | 1                     | 0         |\n",
    "|   0 |   1 | 1              | 1                     | 1         |\n",
    "|   1 |   0 | 1              | 1                     | 1         |\n",
    "|   1 |   1 | 1              | 0                     | 0         |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtävä 1.6\n",
    "\n",
    "Lue [johdantoartikkeli Kvanttit horitsontissa sivut 6 -8](https://raw.githubusercontent.com/otaniemenlukio/kvanttilaskenta2024-kierros1/main/kvantit_horisontissa.pdf)\n",
    "\n",
    "Kerro lyhyesti lukemasi artikkelin perusteella, mitä ovat klassisten ja kvanttitietokoneiden oleelliset erot?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vastaus: Klassisen tietokoneen bittien arvot voivat olla 0 tai 1. \n",
    "\n",
    "Kvanttitietokoneen kubitti voi ennen tilan mittaamista olla arvon 0 ja 1 yhdistelmätilassa. Mittaamisessa kubitin tila valikoituu, ja samalla menetetään informaatiota. Kvanttitietokoneen kubittien välillä on kytkentä, eli lomittuminen (entanglement).\n",
    "\n",
    "Jos kubitin kvanttitilan tila mitataan, saadaan tilastollisia vastauksia, samalla kvanttitila tuhotaan, ts. se ei enää jatka omaa elämäänsä “kvanttimaailmassa”, vaan tilan kannalta kvanttikoherenssi loppuu. Kvanttikone voidaan kuitenkin alustaa uudelleen suorittamaan samaa identtistä “koodia”. Suorittamalla riittävä määrä mittauksia aivan samalla systeemillä, saadaan selville todennäköisimmät lopputilat, joihin kubitit asettautuvat kvanttiporttien vaikutuksesta. Nämä useimmiten esiintyvät tilat ovat kvanttikoneen tulokset. Jos häiriötekijöitä ei onnistuta poistamaan, on lopputuloksissa niin paljon kohinaa, ettei oikeita tuloksia voi enää helposti tunnistaa laskentadatasta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tehtävä 1.7\n",
    "\n",
    "Tehtävä on suorittaa seuraava kvanttipiiriesimerkki. Koodiin ei tarvitse tehdä muutoksia.\n",
    "\n",
    "Huomaa, että kvanttipiirin toimintaa ei vielä tarvitse ymmärtää. Tavoite on tutustua miten kvanttitietokoneiden ohjelmoinnissa käytettävä kvanttipiiri määrittelään Pythonin avulla. Piirin toiminta ja keskeiset käsitteet selitetään myöhemmin kurssilla."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 116.552x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 146.652x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 206.852x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 327.252x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from qiskit import *\n",
    "\n",
    "# Luodaan 2 kubitin kvanttipiiri, alkutila on |0>.\n",
    "circuit = QuantumCircuit(2, 2)\n",
    "\n",
    "display(circuit.draw(output='mpl'))\n",
    "\n",
    "# Lisätään Hadamard-portti H \n",
    "circuit.h(0)\n",
    "display(circuit.draw(output='mpl'))\n",
    "\n",
    "# Lisätään kvanttipiiriin CNOT-portti cx()-komennolla\n",
    "circuit.cx(0, 1)\n",
    "display(circuit.draw(output='mpl'))\n",
    "\n",
    "# Mitataan molemmat kubitit, ja tallennetaan tulokset klassiseen rekisteriin\n",
    "circuit.measure([0, 1], [0, 1])\n",
    "display(circuit.draw(output='mpl'))\n",
    "\n",
    "# Simuloidaan piirin toiminta.\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "execute(circuit, backend=simulator)\n",
    "result = execute(circuit, backend=simulator).result()\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "plot_histogram(result.get_counts(circuit))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.0"
  },
  "vscode": {
   "interpreter": {
    "hash": "c599cb660db903d48c4a798280cd684b1e61eb2f03221ce98a1665e092e9537c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}