4.-Teleportación cuántica y codificación superdensa.ipynb

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   "source": [
    "# Teleportación cuántica y codificación superdensa"
   ]
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   "source": [
    "## Teleportación cuántica\n",
    "$$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}$$\n",
    "Vamos a implementar el circuito de la figura, que nos servirá para teleportar el qubit $\\ket{\\psi}$ \n",
    "\n",
    "<img src=\"Images/teleport_circuit.png\" width=80%>"
   ]
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    "import projectq, random, time\n",
    "from projectq.ops import Measure, H, CNOT, Z, X\n",
    "\n",
    "#Primero creamos un qubit al azar (establecemos el valor de las\n",
    "#amplitudes directamente, mediante números generados aleatoriamente)\n",
    "\n",
    "a1 = random.random()\n",
    "a2 = random.random()\n",
    "b1 = random.random()\n",
    "b2 = random.random()\n",
    "\n",
    "# Hay que normalizar\n",
    "\n",
    "norma = (a1**2 + a2**2 + b1**2 + b2**2)**0.5\n",
    "\n",
    "a = complex(a1/norma,a2/norma) #Amplitud de |0> \n",
    "b = complex(b1/norma,b2/norma) #Amplitud de |1>\n",
    "\n",
    "eng = projectq.MainEngine()\n",
    "\n",
    "psi = eng.allocate_qubit()\n",
    "eng.flush()\n",
    "\n",
    "eng.backend.set_wavefunction([a,b],psi)\n",
    "\n",
    "print(\"El qubit que tiene Alice es:\")\n",
    "print(eng.backend.get_amplitude(\"0\",psi),\"|0> + \",\n",
    "      eng.backend.get_amplitude(\"1\",psi),\"|1>\")\n",
    "\n",
    "# Ahora creamos el par entrelazado que van a compartir Alice y Bob\n",
    "\n",
    "bell = eng.allocate_qureg(2)\n",
    "H | bell[0]\n",
    "CNOT | (bell[0],bell[1])\n",
    "\n",
    "# Aplicamos la CNOT a |psi> y a la parte de Alice del par de Bell\n",
    "# También aplicamos la puerta H\n",
    "\n",
    "CNOT | (psi,bell[0])\n",
    "H | psi\n",
    "\n",
    "# Medimos los qubits de Alice y guardamos el resultado\n",
    "\n",
    "Measure | psi \n",
    "Measure | bell[0]\n",
    "\n",
    "a = int(bell[0])\n",
    "b = int(psi)\n",
    "\n",
    "print(\"\")\n",
    "print(\"Teleporting\", end='')\n",
    "for _ in range(10):\n",
    "    time.sleep(.4)\n",
    "    print(\".\",end='')\n",
    "print(\"\")\n",
    "print(\"\")\n",
    "\n",
    "# Alice comunica sus medidas a Bob y este aplica X y Z en consecuencia\n",
    "\n",
    "if(a==1):\n",
    "    X | bell[1]\n",
    "if(b==1):\n",
    "    Z | bell[1]\n",
    "    \n",
    "# Accedemos a las amplitudes para ver el qubit que tiene ahora Bob\n",
    "\n",
    "eng.flush()\n",
    "\n",
    "str0 = str(b)+str(a)+\"0\"\n",
    "str1 = str(b)+str(a)+\"1\"\n",
    "\n",
    "print(\"El qubit que ahora tiene Bob es:\")\n",
    "print(eng.backend.get_amplitude(str0,psi+bell),\"|0> + \",\n",
    "      eng.backend.get_amplitude(str1,psi+bell),\"|1>\")\n",
    "\n",
    "Measure | bell[1]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Codificación superdensa\n",
    "\n",
    "Ahora, vamos a implementar el circuito de la codificación superdensa, que nos permite enviar dos bits clásicos mediante un único qubit, siempre que tengamos un par de bell compartido previamente\n",
    "\n",
    "<img src=\"Images/superdense.png\" width=100%>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "source": [
    "from projectq.ops import All\n",
    "\n",
    "# Comenzamos creando el par entrelazado compartido por Alice y Bob\n",
    "\n",
    "eng=projectq.MainEngine()\n",
    "\n",
    "bell = eng.allocate_qureg(2)\n",
    "H | bell[0]\n",
    "CNOT | (bell[0],bell[1])\n",
    "\n",
    "# Alice decide los bits que quiere enviar\n",
    "\n",
    "b1 = random.randint(0,1)\n",
    "b2 = random.randint(0,1)\n",
    "\n",
    "print(\"Alice quiere enviar \",b1,b2)\n",
    "\n",
    "# Y aplica las puertas correspondientes\n",
    "\n",
    "if(b2==1):\n",
    "    X | bell[0]\n",
    "if(b1==1):\n",
    "    Z | bell[0]\n",
    "    \n",
    "# Envía su parte del qubit a Bob\n",
    "\n",
    "print(\"\")\n",
    "print(\"Sending\", end='')\n",
    "for _ in range(10):\n",
    "    time.sleep(.2)\n",
    "    print(\".\",end='')\n",
    "print(\"\")\n",
    "print(\"\")\n",
    "\n",
    "# Bob procede a aplicar sus puertas y a medir\n",
    "\n",
    "CNOT | (bell[0],bell[1])\n",
    "H | bell[0]\n",
    "\n",
    "All(Measure) | bell\n",
    "\n",
    "print(\"Bob ha recibido \",int(bell[0]),int(bell[1]))\n"
   ]
  }
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