content/lab_2/lab-2-es.ipynb

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   ]
  },
  {
   "cell_type": "markdown",
   "id": "869e0a2b",
   "metadata": {
    "id": "869e0a2b"
   },
   "source": [
    "# Lab 2: El Transpiler\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "GMWViIAFk0Pz",
   "metadata": {
    "id": "GMWViIAFk0Pz"
   },
   "source": [
    "# Tabla de contenido\n",
    "\n",
    "* [Prólogo - ¿Qué es el transpiler?](#prologue)   \n",
    "* [Transpilar con administradores de pases preestablecidos](#preset_passmanager)    \n",
    "* [Niveles de optimización](#optimization_level)\n",
    "    * [Nivel de optimización = 0](#opt_lv_0)\n",
    "    * [Nivel de optimización = 1](#opt_lv_1)\n",
    "    * [Nivel de optimización = 2](#opt_lv_2)\n",
    "    * [Nivel de optimización = 3](#opt_lv_3)    \n",
    "* [Opciones del Transpiler](#transpiler_options)\n",
    "    * [Etapa inicial](#init)\n",
    "    * [Etapa de diseño](#layout)\n",
    "    * [Etapa de enrutamiento](#routing)\n",
    "    * [Etapa de traducción](#translation)\n",
    "    * [Etapa de optimización](#optimization)\n",
    "    * [Etapa de post-procesamiento](#scheduling)    \n",
    "* [Crea tus propios Pass Managers con Staged Pass Manager](#staged_pm)    \n",
    "    * [Construir pase de desacoplamiento dinámico](#dd)\n",
    "* [(Bonus) Ecosistema y Qiskit Transpiler Plugin](#plugin)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c998067",
   "metadata": {
    "id": "9c998067"
   },
   "source": [
    "<a id='toc2_'></a>\n",
    "<a name='toc2_'></a>\n",
    "\n",
    "# Configuración\n",
    "\n",
    "Para ejecutar este laboratorio correctamente, necesitamos varios paquetes de software. Si aún no ha instalado Qiskit y los paquetes relevantes, ejecute las celdas siguientes después de descomentar y reiniciar el kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b8150ce-b900-4adf-a2c7-f5d80a1e6d70",
   "metadata": {
    "id": "1b8150ce-b900-4adf-a2c7-f5d80a1e6d70"
   },
   "outputs": [],
   "source": [
    "### Instalar Qiskit y otros paquetes necesarios\n",
    "\n",
    "%pip install qiskit[visualization]==1.0.2\n",
    "%pip install qiskit_ibm_runtime\n",
    "%pip install qiskit_aer\n",
    "%pip install prototype-zne\n",
    "%pip install graphviz\n",
    "%pip install git+https://github.com/qiskit-community/Quantum-Challenge-Grader.git"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "EgHX0RuznCvl",
   "metadata": {
    "id": "EgHX0RuznCvl"
   },
   "outputs": [],
   "source": [
    "### Guarde el token API\n",
    "\n",
    "%set_env QXToken=deleteThisAndPasteYourTokenHere\n",
    "\n",
    "# Asegúrese de que no haya espacio entre el signo igual.\n",
    "# y el comienzo de tu token"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "684bbb4a-9576-474c-83fe-31d712ceb87c",
   "metadata": {
    "id": "684bbb4a-9576-474c-83fe-31d712ceb87c"
   },
   "source": [
    "Ahora, ejecutemos nuestras importaciones y configuremos el clasificador."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9pEFjWUcxKm-",
   "metadata": {
    "id": "9pEFjWUcxKm-"
   },
   "outputs": [],
   "source": [
    "# Importaciones\n",
    "\n",
    "from qiskit.circuit.random import random_circuit\n",
    "from qiskit.circuit.library import XGate, YGate\n",
    "from qiskit_ibm_runtime.fake_provider import FakeTorino, FakeOsaka\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler\n",
    "from qiskit.transpiler import InstructionProperties, PassManager\n",
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "from qiskit.transpiler.preset_passmanagers.plugin import list_stage_plugins\n",
    "from qiskit.transpiler.timing_constraints import TimingConstraints\n",
    "from qiskit.transpiler.passes.scheduling import ASAPScheduleAnalysis,PadDynamicalDecoupling\n",
    "from qiskit.visualization.timeline import draw, IQXStandard\n",
    "from qiskit.transpiler import StagedPassManager\n",
    "from qiskit.visualization import plot_circuit_layout\n",
    "from qiskit.quantum_info.analysis import hellinger_fidelity\n",
    "from qiskit.visualization import plot_distribution\n",
    "from qiskit_aer import AerSimulator\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b59eb187",
   "metadata": {
    "id": "b59eb187"
   },
   "outputs": [],
   "source": [
    "# Configurar el grader\n",
    "from qc_grader.challenges.iqc_2024 import (\n",
    "    grade_lab2_ex1,\n",
    "    grade_lab2_ex2,\n",
    "    grade_lab2_ex3,\n",
    "    grade_lab2_ex4,\n",
    "    grade_lab2_ex5\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "g_Uy-O8nnpNR",
   "metadata": {
    "id": "g_Uy-O8nnpNR"
   },
   "source": [
    "Para completar este laboratorio debe utilizar Qiskit v1.0.2. Antes de comenzar, revisemos su entorno."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "rwT3zn80nrOL",
   "metadata": {
    "id": "rwT3zn80nrOL"
   },
   "outputs": [],
   "source": [
    "from util import version_check\n",
    "\n",
    "version_check()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "438aa753",
   "metadata": {
    "id": "438aa753"
   },
   "source": [
    "# Prólogo - ¿Qué es el transpilador?<a name=\"prologue\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50aaaa14",
   "metadata": {
    "id": "50aaaa14"
   },
   "source": [
    "Comencemos con una pregunta hipotética:\n",
    "\n",
    "Cuando alguien te entrega las llaves de su automóvil y te dice \"¿podrías llenar mi auto con combustible?\" - ¿Cómo sabes qué hacer?\n",
    "\n",
    "Teniendo el carnet de conducir, tú sabes que legalmente puedes conducir el automóvil. ¿Pero sabrás cómo? ¿Qué tipo de automóvil tienen? ¿Cómo se enciende el intermitente? ¿Como se llena el tanque de combustible? ¿Y si es eléctrico? ¿Cómo se carga?\n",
    "\n",
    "Afortunadamente, el cerebro humano es inteligente. Somos capaces de seguir instrucciones y adaptarlas al vehículo que nos entregan.\n",
    "\n",
    "Eso es el transpilador."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dc37876",
   "metadata": {
    "id": "0dc37876"
   },
   "source": [
    "La transpilación es el proceso transformar un circuito inicial a un circuito equivalente diseñado para un dispositivo cuántico específico. La transpilación nos permite ejecutar y optimizar un circuito en un sistema cuántico real.\n",
    "\n",
    "Este proceso es necesario, ya que los dispositivos cuánticos funcionan de maneras diferentes, y es posible que las instrucciones que usted envíe a un dispositivo no sean compatibles con un backend (computadora) cuántico diferente. La transpilación conlleva una adaptación al conjunto de compuertas básicas del dispositivo, la topología del chip cuántico, las restricciones de tiempo y más propiedades que exploraremos en esta práctica de laboratorio.\n",
    "\n",
    "El objetivo de un transpilador es obtener el mejor rendimiento posible de un hardware cuántico ruidoso. La mayoría de los circuitos deben ser transformados de manera compatible con un dispositivo objetivo determinado. También deben ser optimizados para reducir los efectos del ruido en los resultados.\n",
    "\n",
    "**Por ejemplo:** el proceso de transpilación puede tomar un circuito simple que contenga las instrucciones:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1401a733-a9bb-432b-a2e4-e3160c2ad9ce",
   "metadata": {
    "id": "1401a733-a9bb-432b-a2e4-e3160c2ad9ce"
   },
   "source": [
    "<img src=\"data:image/webp;base64,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\" alt=\"\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edca4ed8",
   "metadata": {
    "id": "edca4ed8"
   },
   "source": [
    "y transformarlo en un circuito que solo contenga las compuertas básicas o instrucciones que una computadora cúantica determinada sea capaz de aceptar. La transpilación también optimizará dichas instrucciones para minimizar los efectos del ruido:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edf24741-adb2-4d0f-b64f-572ab3ff7657",
   "metadata": {
    "id": "edf24741-adb2-4d0f-b64f-572ab3ff7657"
   },
   "source": [
    "<img 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\" alt=\"\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1b3564f-b96a-4cf2-9bdb-8fa63b104505",
   "metadata": {
    "id": "c1b3564f-b96a-4cf2-9bdb-8fa63b104505"
   },
   "source": [
    "El transpilador, un componente central del SDK de Qiskit, está diseñado para ofrecer modularidad y extensibilidad. Su objetivo principal es transformar circuitos (con pases de transpilador) y combinarlas con otros pases existentes, reduciendo la profundidad y complejidad de los circuitos cuánticos. La manera en la cual los pases se encadenan y su orden, tiene un efecto importante en el resultado final. Este sistema de organizacion de pases está determinado por los objetos: [PassManager](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.PassManager) y [StaggedPassManager](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.StaggedPassManager).\n",
    "\n",
    "El `StaggedPassManager` organiza la ejecución de uno o más `PassManager` y determina el orden en el que se ejecutan, mientras que el `PassManager` es simplemente una colección de uno o más pases. Piense en el `StagedPassManager` como el director de una orquesta, los `PassManagers` como diferentes grupos de instrumentos y los objetos `Pass` como músicos individuales.\n",
    "\n",
    "De esta manera, puede componer circuitos cuánticos eficientes en hardware que le permitan ejecutar trabajos a escala de servicios públicos manteniendo el ruido manejable. Para obtener más detalles sobre el transpilador, visite la sección [Transpile](https://docs.quantum.ibm.com/transpile) en los documentos de la plataforma IBM Quantum."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f5929ce-0456-47a3-87e1-e24f9877dc4d",
   "metadata": {
    "id": "9f5929ce-0456-47a3-87e1-e24f9877dc4d"
   },
   "source": [
    "## Las seis etapas\n",
    "\n",
    "Reescribir circuitos cuánticos para que coincidan con las limitaciones del hardware y optimizar el rendimiento puede estar lejos de ser trivial. Qiskit proporciona a los usuarios las seis etapas estándar de flujos de compilación con cuatro canales de transpilación prediseñados. Por defecto, los administradores de pases preestablecidos se componen de seis etapas, con varias opciones en cada etapa:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc0f3d06",
   "metadata": {
    "id": "fc0f3d06"
   },
   "source": [
    "\n",
    "- `Init`: Este pase ejecuta cualquier pases iniciale necesario antes de comenzar a integrar el circuito en el sistema. Por lo general, esto implica desarrollar instrucciones personalizadas y transformar las compuertas del circuito en compuertas de uno y dos qubits. (Esto simplemente validará las instrucciones del circuito y traducirá las compuertas de múltiples qubits en compuertas de uno y dos qubits).\n",
    "\n",
    "- `Layout`: Esta etapa aplica un diseño, asignando los qubits virtuales en el circuito a los qubits físicos en un backend.\n",
    "\n",
    "- `Routing`: Esta etapa se ejecuta tras la aplicion del layout, e inyecta las compuertas (es decir, los swaps o intercambios) en el circuito original para hacerlo compatible con el backend.\n",
    "  \n",
    "- `Translation`: Esta etapa \"traduce\" las compuertas en el circuito al conjunto básico del backend objetivo.\n",
    "\n",
    "- `Optimization`: Esta etapa ejecuta la optimización principal repetidamente hasta que se alcanza una condición predeterminada (como una profundidad fija).\n",
    "\n",
    "- `Scheduling`: Esta etapa es para cualquier hardware-aware pase de programación.\n",
    "\n",
    "Qiskit también proporciona cuatro niveles de transpilación predefinidos que los usuarios pueden elegir según sus necesidades. Puede modificar estos administradores de pases preestablecidos y, además, puede crear un administrador de pases para diseñar un proceso personalizado de transformación.\n",
    "\n",
    "Para la mayoría de los usuarios que no están familiarizados con la optimización de circuitos cuánticos mediante transpilación, sugerimos utilizar una de las rutinas ya preparadas. Sin embargo, en este laboratorio profundizaremos (¡profundamente!) en cada etapa y las opciones que contienen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be8171e2",
   "metadata": {
    "id": "be8171e2"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "<a id='ex1'></a>\n",
    "<a name='ex1'></a>\n",
    "\n",
    "### Ejercicio 1:\n",
    "\n",
    "**Tu tarea:** Empareja la descripción de lo que sucede en cada etapa con el nombre de la etapa de transpilación correspondiente en la siguiente celda.\n",
    "\n",
    "- **A.** Esta etapa se centra en la reducción del número de operaciones y profundidad del circuito con varias opciones de optimización.\n",
    "- **B.** Esta etapa inserta el número apropiado de compuertas SWAP para ejecutar los circuitos usando el diseño seleccionado.\n",
    "- **C.** Esta etapa se utiliza para traducir cualquier compuerta que opere en más de dos qubits, en compuertas que solo operen en uno o dos qubits.\n",
    "- **D.** Esta etapa ejecuta una secuencia de compuertas, un mapeo, de los qubits \"virtuales\" a los qubits \"físicos\" en un dispositivo cuántico real.\n",
    "- **E.** Se puede considerar que este paso inserta explícitamente operaciones que tienen en cuenta el hardware, como instrucciones de retraso, para controlar el tiempo de inactividad entre las compuertas.\n",
    "- **F.** Esta etapa traduce las compuertas especificadas en un circuito a las compuertas básicas nativas del backend (computadora) seleccionado."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "137bfd35",
   "metadata": {
    "id": "137bfd35"
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "<b>Consejo: La respuesta será siempre una única letra mayúscula encerrada entre comillas. </b>\n",
    "\n",
    "Por ejemplo: \"A\"\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3094f28d-79b4-4758-bd0e-1024cc337740",
   "metadata": {
    "id": "3094f28d-79b4-4758-bd0e-1024cc337740"
   },
   "outputs": [],
   "source": [
    "ans = {}\n",
    "\n",
    "# Coloca la letra correcta al lado de la etapa correspondiente\n",
    "# ejemplo: ans[\"prueba\"] = \"M\"\n",
    "\n",
    "ans[\"init\"] =\n",
    "ans[\"layout\"] =\n",
    "ans[\"routing\"] =\n",
    "ans[\"translation\"] =\n",
    "ans[\"optimization\"] =\n",
    "ans[\"scheduling\"] ="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12684450",
   "metadata": {
    "id": "12684450"
   },
   "outputs": [],
   "source": [
    "# Envíe su respuesta usando el siguiente código\n",
    "\n",
    "grade_lab2_ex1(ans)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "MmoeFQ-tS_1k",
   "metadata": {
    "id": "MmoeFQ-tS_1k"
   },
   "source": [
    "Buen trabajo comprobando tu comprensión en cada etapa de transpilación! A continuación, veremos cómo utilizar las seis etapas de transpilación de Qiskit con `preset_pass_managers`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f8c1263",
   "metadata": {
    "id": "5f8c1263"
   },
   "source": [
    "<a name='preset_passmanager'></a>\n",
    "\n",
    "# Transpilar con administradores de pases preestablecidos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cf174f3",
   "metadata": {
    "id": "1cf174f3"
   },
   "source": [
    "En esta sección, aprenderemos a utilizar las seis etapas estándar del transpilador de Qiskit. Primero nos centraremos en las cuatro vertientes de transpilación predefinidas y veremos cómo crear nuestro propio PassManager mediante las opciones de cada pass en las vertientes predefinidas.\n",
    "\n",
    "Primero, veamos qué son el Passmanager y el `generate_preset_pass_manager`. Esta parte del laboratorio y partes posteriores hacen referencia a los [documentos de la plataforma IBM Quantum](https://docs.quantum.ibm.com/transpile) y la [documentación de referencia de API](https://docs.quantum.ibm.com/api/qiskit/transpiler) del transpiler, por lo que le recomendamos revisarlos.\n",
    "\n",
    "## ¿Qué es un staged pass manager (administrador de pases por etapas)?\n",
    "\n",
    "Un administrador de pases es un objeto que almacena una lista de pases del transpilador y los ejecuta en un circuito. Usted puede crear un administrador de pases inicializando un [PassManager](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.PassManager) con una lista de pases de transpilador. Para ejecutar la transpilación en un circuito, llama al método [ejecutar](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.PassManager#run) con un circuito inicial.\n",
    "\n",
    "Un administrador de pases por etapas, representado por la clase [`StaggedPassManager`](https://docs.quantum.ibm.com/transpile/transpiler-stages), es un tipo especial de administrador de pases que representa un nivel de abstracción superior al de un administrador de pases normal. Mientras que un administrador de pases normal se compone de varios pases transpiladores, un administrador de pases por etapas está compuesto de varios administradores de pases. Esta es una abstracción útil porque la transpilación normalmente ocurre en etapas discretas, y cada etapa está representada por un administrador de pases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ubXQdqLjU6mD",
   "metadata": {
    "id": "ubXQdqLjU6mD"
   },
   "source": [
    "## `Preset Passmanagers`\n",
    "\n",
    "Preset Passmanagers (`qiskit.transpiler.preset_passmanagers`) contiene funciones para generar administradores de pases preestablecidos para la transpilación. Los administradores de pases preestablecidos son instancias de StagedPassManager, que se utilizan para ejecutar las transformaciones del circuito en los diferentes niveles de optimización en un proceso de transpilación predefinido. Aquí presentamos las funciones utilizadas para generar el administrador de pases completo usando `generate_preset_pass_manager`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "K4i2qhtGWR89",
   "metadata": {
    "id": "K4i2qhtGWR89"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "### Metáforas\n",
    "\n",
    "Es fácil perderse en la terminología, te recomendamos volver a nuestra metáfora sobre un director de orquesta, secciones y músicos individuales, cuando todo se vuelva demasiado complicado.\n",
    "\n",
    "**Ejercicio adicional:** Crea tu propia metáfora relacionando un \"StaggedPassManager\", un \"PassManager\" y un \"pase\".  \n",
    "\n",
    "No dudes en compartir tu metáfora con otras personas en el servidor de Discord de IBM Quantum Challenge o con tus amigos.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fyAG5j89V8PY",
   "metadata": {
    "id": "fyAG5j89V8PY"
   },
   "source": [
    "## `generate_preset_pass_manager`\n",
    "\n",
    "En Qiskit, `generate_preset_pass_manager` se utiliza para generar rápidamente un administrador de pases preestablecido. Esta función proporciona un método conveniente y simple para construir un objeto `PassManager` independiente con niveles de **optimización** y opciones para cada paso.\n",
    "A continuación exploraremos esta opción."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "w5oPSJWPWuO2",
   "metadata": {
    "id": "w5oPSJWPWuO2"
   },
   "source": [
    "# Niveles de optimización <a name='optimization_level'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4A6jQvq2v-T5",
   "metadata": {
    "id": "4A6jQvq2v-T5"
   },
   "source": [
    "La función `generate_preset_pass_manager` tiene un argumento posicional requerido, `optimization_level`, que controla cuánto esfuerzo dedica el transpilador a optimizar los circuitos. Este argumento es un número entero que toma uno de los valores 0, 1, 2 o 3.\n",
    "\n",
    "Los niveles de optimización más altos generan circuitos cada vez más optimizados a costa de tiempos de compilación más largos y viceversa."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "417605eb-15ae-47e2-886e-446275648831",
   "metadata": {
    "id": "417605eb-15ae-47e2-886e-446275648831"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "<a id='ex2'></a>\n",
    "<a name='ex2'></a>\n",
    "\n",
    "### Ejercicio 2: Construya una función para \"evaluar\" el circuito transpilado\n",
    "\n",
    "\n",
    "Dado que el objetivo de la transpilación es mejorar el rendimiento de ejecución real del circuito, su objetivo es crear una función que mida el rendimiento del circuito traducido. Utilizará esta función más adelante en esta práctica de laboratorio.\n",
    "\n",
    "**Tu tarea:** Crea una función llamada `scoring`. La función debe recibir el circuito transpilado, su *diseño final* y su backend como entradas. Luego, la función debería devolver una puntuación del circuito. Cuanto más cerca esté la puntuación de 0, mejor.\n",
    "\n",
    "Otras notas:\n",
    "* Utiliza `FakeTorino` del paquete `qiskit-ibm-runtime` para toda este laboratorio.\n",
    "* El algoritmo para calcular la puntuación real en `util.py` es de [Mapomatic](https://github.com/qiskit-community/mapomatic), y el código principal se actualizó para adaptarse a PrimitiveV2.\n",
    "* Hemos construido algunas de estas funciones para usted.\n",
    "* Necesitaras obtener el trazado final del circuito transpilado. Estas dos páginas deberían ayudarte a completar el código siguiente para finalizar la función.\n",
    "  * [La sección de diseño de la documentación de la API QuantumCircuit](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.QuantumCircuit#layout)\n",
    "  * [La sección TranspileLayout de la documentación de la API de Qiskit Transpiler](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.TranspileLayout)\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "768bc71b-be76-4e96-a870-b17f99f1e479",
   "metadata": {
    "id": "768bc71b-be76-4e96-a870-b17f99f1e479"
   },
   "outputs": [],
   "source": [
    "### Cree la función de puntuación\n",
    "\n",
    "def scoring( qc, backend):\n",
    "    from util import transpile_scoring\n",
    "\n",
    "    layout = #Añada su código aquí\n",
    "    fidelity = transpile_scoring(qc, layout, backend)\n",
    "    score = #Añada su código aquí\n",
    "\n",
    "    return score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7b84a84-7c87-4419-adf0-fc646d93effd",
   "metadata": {
    "id": "a7b84a84-7c87-4419-adf0-fc646d93effd"
   },
   "outputs": [],
   "source": [
    "# Envíe su respuesta usando el siguiente código\n",
    "\n",
    "grade_lab2_ex2(scoring)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17b2bd07",
   "metadata": {
    "id": "17b2bd07"
   },
   "source": [
    "Ahora tienes una función para medir el rendimiento de un circuito transpilado. Antes de pasar a la siguiente parte, terminemos de configurar todo lo que necesitamos para probar adecuadamente nuestro circuito en un backend falso.\n",
    "\n",
    "Es decir, un circuito y un backend falso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f16a1d6b-8336-47ed-bf79-8e759679bc09",
   "metadata": {
    "id": "f16a1d6b-8336-47ed-bf79-8e759679bc09"
   },
   "outputs": [],
   "source": [
    "### Crea un circuito aleatorio\n",
    "\n",
    "## NO CAMBIE EL NÚMERO DE SEMILLA\n",
    "seed = 10000\n",
    "\n",
    "## Cree un circuito\n",
    "\n",
    "num_qubits = 6\n",
    "depth = 4\n",
    "qc = random_circuit(num_qubits,depth,measure=False, seed=seed)\n",
    "\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "LO757dUbd3IW",
   "metadata": {
    "id": "LO757dUbd3IW"
   },
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "\n",
    "<b>¡Ten cuidado!</b>\n",
    "    \n",
    "Para aprobar la evaluación, no cambies los valores de semilla de `seed` o `seed_transpiler` a lo largo del laboratorio.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cdc7d66-67b0-4988-953f-dfab85139d3c",
   "metadata": {
    "id": "4cdc7d66-67b0-4988-953f-dfab85139d3c"
   },
   "source": [
    "Para probar el rendimiento de cada nivel de optimización, haz un llamado a \"FakeTorino\" y guárdalo con el nombre de `backend`.\n",
    "\n",
    "`FakeTorino` tiene las características de conectividad y ruido de ibm_torino, que es el último backend de IBM Quantum con un procesador Heron."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a76391b8",
   "metadata": {
    "id": "a76391b8"
   },
   "outputs": [],
   "source": [
    "## Guarde FakeTorino como backend\n",
    "\n",
    "backend = FakeTorino()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vYeXBPVFhgmG",
   "metadata": {
    "id": "vYeXBPVFhgmG"
   },
   "source": [
    "Revisaremos la ejecución de los cuatro niveles de optimización y luego compararemos nuestros resultados. Para hacer esto, crearemos algunas matrices para guardar la información producida mientras trabajamos. Ya que usaremos estos resultados más adelante.\n",
    "\n",
    "En la siguiente celda de código, construimos estas matrices. Ejecútala y continúa con el laboratorio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "j-vk3nR2hk7H",
   "metadata": {
    "id": "j-vk3nR2hk7H"
   },
   "outputs": [],
   "source": [
    "circuit_depths = {\n",
    "    'opt_lv_0': None,\n",
    "    'opt_lv_1': None,\n",
    "    'opt_lv_2': None,\n",
    "    'opt_lv_3': None,\n",
    "}\n",
    "gate_counts = {\n",
    "    'opt_lv_0': None,\n",
    "    'opt_lv_1': None,\n",
    "    'opt_lv_2': None,\n",
    "    'opt_lv_3': None,\n",
    "}\n",
    "\n",
    "scores = {\n",
    "    'opt_lv_0': None,\n",
    "    'opt_lv_1': None,\n",
    "    'opt_lv_2': None,\n",
    "    'opt_lv_3': None,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "N4vMMKVSh4c6",
   "metadata": {
    "id": "N4vMMKVSh4c6"
   },
   "source": [
    "## Nivel de optimización = 0 <a name='opt_lv_0'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4rhnU1G4iIJm",
   "metadata": {
    "id": "4rhnU1G4iIJm"
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "<b>Consejo: Si en algún momento durante estas cuatro secciones necesitas ayuda o aclaración, </b>\n",
    "consulta <a href=\"https://docs.quantum.ibm.com/transpile/set-optimization\">esta documentación</a> para obtener una mejor comprensión del `optimization_level`.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "LHW01CZnhlNq",
   "metadata": {
    "id": "LHW01CZnhlNq"
   },
   "source": [
    "El nivel de optimización 0 está destinado a **experimentos de caracterización del dispositivo** y, como tal, solo asigna el circuito de entrada a las limitaciones del backend de destino sin realizar ninguna optimización. El nivel realiza un diseño/enrutamiento con [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout), donde selecciona el mismos número de qubit físicos y virtuales e inserta SWAP (usando [StochasticSwap](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.StochasticSwap#stochasticswap)).\n",
    "\n",
    "Construyamos un administrador de pases con `optimization_level = 0` usando nuestro backend `FakeTorino`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88992669",
   "metadata": {
    "id": "88992669"
   },
   "outputs": [],
   "source": [
    "# Creae un administrador de pases con nuestro nivel de optimización y backend deseados\n",
    "pm_lv0 = generate_preset_pass_manager(backend=backend, optimization_level=0, seed_transpiler=seed)\n",
    "\n",
    "# Corra por nuestro circuito aleatorio.\n",
    "tr_lv0 = pm_lv0.run(qc)\n",
    "\n",
    "# Descomente la siguiente línea para dibujar el circuito\n",
    "#tr_lv0.draw('mpl', idle_wires=False, fold=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce7135c2-a804-4898-baf2-49bad0049f1c",
   "metadata": {
    "id": "ce7135c2-a804-4898-baf2-49bad0049f1c"
   },
   "source": [
    "Como mencionamos anteriormente, optimización_level=0 realiza una descomposición básica de las compuertas utilizando compuertas de base del backend y asignando qubits lógicos a qubits físicos con el mismo orden de número. Asigna el qubit lógico 0 al qubit físico 0 y asigna el qubit lógico 1 al qubit físico 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "A34yXFCFjE1K",
   "metadata": {
    "id": "A34yXFCFjE1K"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "<a id='ex3'></a>\n",
    "<a name='ex3'></a>\n",
    "\n",
    "### Ejercicio 3: (El comienzo)\n",
    "\n",
    "\n",
    "**Tu tarea:** Encuentra la profundidad del circuito aleatorio, la suma del número total de compuertas y calcula la puntuación de rendimiento de este circuito utilizando el `scoring`. Utiliza el código proporcionado para guardar cada uno de estos resultados en nuestra matriz.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "j4y7E6yvjIZR",
   "metadata": {
    "id": "j4y7E6yvjIZR"
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Consejos:\n",
    "- para `circuit_ depths`: [Documentación de IBM](https://docs.quantum.ibm.com/api/qiskit/0.42/circuit)\n",
    "- para `gate_counts`: [Esta discusión de stackexchange puede ayudarle](https://quantumcomputing.stackexchange.com/questions/25931/qiskit-count-of-each-gates)\n",
    "- para las `scores`: utilice la función `scoring` que creamos anteriormente\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24b96a0c",
   "metadata": {
    "id": "24b96a0c"
   },
   "outputs": [],
   "source": [
    "### Añada su código aquí ###\n",
    "\n",
    "circuit_depths['opt_lv_0'] =\n",
    "gate_counts['opt_lv_0'] =\n",
    "scores['opt_lv_0'] =\n",
    "\n",
    "### No cambie el programa más allá de esta línea ###\n",
    "\n",
    "print(\"Optimization level 0 results\")\n",
    "print(\"====================\")\n",
    "print(\"Circuit depth:\", circuit_depths['opt_lv_0'])\n",
    "print(\"Gate count:\", gate_counts['opt_lv_0'])\n",
    "print(\"Score:\", scores['opt_lv_0'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52defeb3",
   "metadata": {
    "id": "52defeb3"
   },
   "source": [
    "\n",
    "## Nivel de optimización = 1 <a name='opt_lv_1'></a>\n",
    "\n",
    "El nivel de optimización 1 realiza una **`optimización ligera`**. Esto significa:\n",
    "\n",
    "- Diseño/Enrutamiento: el diseño se intenta primero con [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout). Si se requieren SWAPs adicionales, se encuentra un diseño con un número mínimo de SWAP utilizando [SabreSWAP](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.SabreSwap#sabreswap), luego utiliza [VF2LayoutPostLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.VF2PostLayout)` para intentar seleccionar los mejores qubits en el gráfico.\n",
    "- [Cancelación inversa](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.InverseCancellation#inversecancellation)\n",
    "- [Optimización de 1Qgates](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.Optimize1qGates#optimize1qgates)\n",
    "\n",
    "Esta vez intenta crear un administrador de pases por su cuenta. Una vez más utiliza el backend de FakeTorino con `generate_preset_pass_manager`. Configura también `optimization_level` en 1 y `seed_transpiler` = `seed`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c81db96e-aa03-4418-a089-5d5b5ffa90bf",
   "metadata": {
    "id": "c81db96e-aa03-4418-a089-5d5b5ffa90bf"
   },
   "outputs": [],
   "source": [
    "# Cree un administrador de pases con nuestro nivel de optimización y backend deseados\n",
    "pm_lv1 = ### Añada su código aquí ###\n",
    "\n",
    "# Corra por nuestro circuito aleatorio.\n",
    "tr_lv1 = pm_lv1.run(qc)\n",
    "\n",
    "# Descomente la siguiente línea para dibujar el circuito\n",
    "#tr_lv1.draw('mpl', idle_wires=False, fold=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66846d83-15f9-474a-a087-0cba27ce8466",
   "metadata": {
    "id": "66846d83-15f9-474a-a087-0cba27ce8466"
   },
   "source": [
    "Ahora deberías ver qubits lógicos asignados a diferentes conjuntos de qubits físicos y una cantidad menor de compuertas. Al igual que la última vez, encontremos la profundidad del circuito aleatorio, la suma del número total de compuertas y calculemos la puntuación de rendimiento de este circuito usando `scoring`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a1e49d1",
   "metadata": {
    "id": "1a1e49d1"
   },
   "outputs": [],
   "source": [
    "### Añada su código aquí ###\n",
    "\n",
    "circuit_depths['opt_lv_1'] =\n",
    "gate_counts['opt_lv_1'] =\n",
    "scores['opt_lv_1'] =\n",
    "\n",
    "### No cambie el programa más allá de esta línea ###\n",
    "\n",
    "print(\"Optimization level 1 results\")\n",
    "print(\"====================\")\n",
    "print(\"Circuit depth:\", circuit_depths['opt_lv_1'])\n",
    "print(\"Gate count:\", gate_counts['opt_lv_1'])\n",
    "print(\"Score:\", scores['opt_lv_1'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "723c1bbc",
   "metadata": {
    "id": "723c1bbc"
   },
   "source": [
    "## Nivel de optimización = 2 <a name='opt_lv_2'></a>\n",
    "\n",
    "El nivel de optimización 2 realiza una **`optimización media`**, lo que significa:\n",
    "\n",
    "- Diseño/Enrutamiento: Nivel de optimización 1 (sin trivial) + heurística optimizada con mayor profundidad de búsqueda y pruebas optimización. Debido a que no se utiliza él [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout), no buscamos utilizar los mismos números de qubit físicos y virtuales.\n",
    "- [Cancelación conmutativa](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.CommutativeCancellation#commutativecancellation)\n",
    "\n",
    "Hagamos un administrador de pases con `optimization_level` de 2 esta vez, usando nuevamente `generate_preset_pass_manager` con el backend de FakeTorino y `seed_transpiler` = `seed`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "442d02a6-dbf6-4fdc-b0c0-1809a8a033fe",
   "metadata": {
    "id": "442d02a6-dbf6-4fdc-b0c0-1809a8a033fe"
   },
   "outputs": [],
   "source": [
    "# Cree un administrador de pases con nuestro nivel de optimización y backend deseados\n",
    "pm_lv2 = ### Añada su código aquí ###\n",
    "\n",
    "# Corra por nuestro circuito aleatorio.\n",
    "tr_lv2 = pm_lv1.run(qc)\n",
    "\n",
    "# Descomente la siguiente línea para dibujar el circuito\n",
    "#tr_lv2.draw('mpl', idle_wires=False, fold=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eb4c089-8a29-4973-af0e-558bcc39def8",
   "metadata": {
    "id": "1eb4c089-8a29-4973-af0e-558bcc39def8"
   },
   "source": [
    "Incluso a simple vista, podemos ver que el número de compuertas ha disminuido bastante. El qubit físico al que se asigna el qubit lógico permanece sin cambios. Ahora, midamos el rendimiento de la transpilación. Es el mismo código que el anterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05928c2d",
   "metadata": {
    "id": "05928c2d"
   },
   "outputs": [],
   "source": [
    "### Añada su código aquí ###\n",
    "\n",
    "circuit_depths['opt_lv_2'] =\n",
    "gate_counts['opt_lv_2'] =\n",
    "scores['opt_lv_2'] =\n",
    "\n",
    "### No cambie el programa más allá de esta línea ###\n",
    "\n",
    "print(\"Optimization level 2 results\")\n",
    "print(\"====================\")\n",
    "print(\"Circuit depth:\", circuit_depths['opt_lv_2'])\n",
    "print(\"Gate count:\", gate_counts['opt_lv_2'])\n",
    "print(\"Score:\", scores['opt_lv_2'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccc3c8b5",
   "metadata": {
    "id": "ccc3c8b5"
   },
   "source": [
    "## Nivel de optimización = 3 <a name='opt_lv_3'></a>\n",
    "\n",
    "El nivel de optimización 3 realiza una **`optimización alta`**:\n",
    "\n",
    "- Nivel de optimización 2 + heurística optimizada en diseño/enrutamiento con mayor esfuerzo/pruebas\n",
    "- Resíntesis de bloques de dos qubits mediante [Descomposición KAK de Cartan](https://arxiv.org/abs/quant-ph/0507171).\n",
    "- Pases rompedores de la unitaridad:\n",
    "    - `OptimizeSwapBeforeMeasure`: elimina los intercambios delante de las mediciones mediante la reorientación de la parte clásica de la instrucción de medida para evitar SWAPs.\n",
    "    - `RemoveDiagonalGatesBeforeMeasure`: Elimina las compuertas diagonales (como RZ, T, Z, etc.) antes\n",
    "    una medida. Incluyendo compuertas diagonales 2Q.\n",
    "\n",
    "¡Ya sabes qué hacer a continuación!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd852fe6-49c4-49d9-8619-5d326b17a5d3",
   "metadata": {
    "id": "fd852fe6-49c4-49d9-8619-5d326b17a5d3"
   },
   "outputs": [],
   "source": [
    "pm_lv3 =### Añada su código aquí ###\n",
    "\n",
    "tr_lv3 =### Añada su código aquí ###\n",
    "\n",
    "# Descomente la siguiente línea para dibujar el circuito\n",
    "#tr_lv3.draw('mpl', idle_wires=False, fold=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e83bc48a-398b-49a0-bbb0-ddcf0fa3057e",
   "metadata": {
    "id": "e83bc48a-398b-49a0-bbb0-ddcf0fa3057e"
   },
   "source": [
    "¡Sorprendentemente, obtenemos un número aún menor de compuertas! Veamos cómo funcionó..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c926c527-37c9-4b9c-8fbf-2ceaf0555668",
   "metadata": {
    "id": "c926c527-37c9-4b9c-8fbf-2ceaf0555668"
   },
   "outputs": [],
   "source": [
    "### Añada su código aquí ###\n",
    "\n",
    "circuit_depths['opt_lv_3'] =\n",
    "gate_counts['opt_lv_3'] =\n",
    "scores['opt_lv_3'] =\n",
    "\n",
    "### No cambie el programa más allá de esta línea ###\n",
    "\n",
    "print(\"Optimization level 3 results\")\n",
    "print(\"====================\")\n",
    "print(\"Circuit depth:\", circuit_depths['opt_lv_3'])\n",
    "print(\"Gate count:\", gate_counts['opt_lv_3'])\n",
    "print(\"Score:\", scores['opt_lv_3'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc0ea866-27ef-4557-8135-56c7899eae16",
   "metadata": {
    "id": "cc0ea866-27ef-4557-8135-56c7899eae16"
   },
   "source": [
    "Ahora que tenemos todos nuestros resultados, visualicemos cuánto han cambiado la profundidad del circuito, el número de compuertas y la puntuación de evaluación según cada nivel de optimización."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1f9ba7c4-0b6f-4b9c-a454-0edffc20becb",
   "metadata": {
    "id": "1f9ba7c4-0b6f-4b9c-a454-0edffc20becb"
   },
   "outputs": [],
   "source": [
    "colors = ['#FF6666', '#66B2FF']\n",
    "ax = [\"opt_lv_0\", \"opt_lv_1\", \"opt_lv_2\", \"opt_lv_3\"]\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(10, 12))\n",
    "\n",
    "# Plot 1: Profundidad del circuito\n",
    "ax1.semilogy(ax, [circuit_depths[key] for key in ax],'o-',markersize=9, color='#FF6666', label=\"Depth\")\n",
    "ax1.set_xlabel(\"Optimization Level\", fontsize=12)\n",
    "ax1.set_ylabel(\"Depth\", fontsize=12)\n",
    "ax1.set_title(\"Circuit Depth\", fontsize=14)\n",
    "ax1.legend(fontsize=10)\n",
    "\n",
    "# Plot 2: Numero total de puertas\n",
    "ax2.semilogy(ax, [gate_counts[key] for key in ax],'^-',markersize=9, color='#66B2FF', label=\"Counts\")\n",
    "ax2.set_xlabel(\"Optimization Level\", fontsize=12)\n",
    "ax2.set_ylabel(\"Gate Count\", fontsize=12)\n",
    "ax2.set_title(\"Gate Count\", fontsize=14)\n",
    "ax2.legend(fontsize=10)\n",
    "\n",
    "# Plot 3: Puntuación del circuito transpilado\n",
    "ax3.semilogy(ax, [scores[key] for key in ax],'*-',markersize=9, label=\"Score\")\n",
    "ax3.set_xlabel(\"Optimization Level\", fontsize=12)\n",
    "ax3.set_ylabel(\"Score\", fontsize=12)\n",
    "ax3.set_title(\"Score\", fontsize=14)\n",
    "ax3.legend(fontsize=10)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29f2d8e9-0bda-43f7-86a6-d0e81396fee1",
   "metadata": {
    "id": "29f2d8e9-0bda-43f7-86a6-d0e81396fee1"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "### Ejercicio 3: (Finalizar)\n",
    "\n",
    "**Tu tarea:** Arriba hicimos una gran cantidad de trabajo para construir los diferentes administradores de pases, probarlos y guardar información sobre cada uno en su matriz correspondiente. También construimos gráficos con la información resultante de cada nivel para comparar visiblemente sus resultados. Ahora, enviaremos los cuatro administradores de pases al calificador.\n",
    "\n",
    "¡Asegúrate de no haber cambiado ningún valor de semilla `seed`!\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "540ae47a",
   "metadata": {
    "id": "540ae47a"
   },
   "outputs": [],
   "source": [
    "# Envíe su respuesta usando el siguiente código\n",
    "\n",
    "ans = [pm_lv0, pm_lv1, pm_lv2, pm_lv3]\n",
    "\n",
    "grade_lab2_ex3(ans)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "342f3b06",
   "metadata": {
    "id": "342f3b06"
   },
   "source": [
    "# Opciones del transpilador <a name='transpiler_options'></a>\n",
    "\n",
    "Hasta ahora, hemos analizado cuatro vertientes de transpiler predefinidos ofrecidos por Qiskit que utilizan circuitos aleatorios. Una de las características clave del transpilador Qiskit SDK v1.0 es la facilidad con la que los usuarios pueden crear y configurar un administrador de contraseñas personalizado. Puedes configurar tu propio administrador de pases utilizando seis pases estándar junto con el nivel de optimización comentado anteriormente, eligiendo la opción o complemento para cada pase que desees. Otra opcion, es crear tu administrador de pases con tantos pases como quiera usando `StaggedPassManager`. Además, puedes crear e implementar un nuevo administrador de pases e implementarlo como un [plugin](https://docs.quantum.ibm.com/transpile/create-a-transpiler-plugin) en Qiskit para que que otros usuarios puedan utilizarlo.\n",
    "\n",
    "Veremos los tres métodos en las siguientes secciones, comenzando primero por el más sencillo."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "NZoH_tc3zm1m",
   "metadata": {
    "id": "NZoH_tc3zm1m"
   },
   "source": [
    "## Etapa inicial <a name='init'></a>\n",
    "\n",
    "Esta primera etapa hace muy poco de forma predeterminada y es principalmente útil si desea incluir sus propias optimizaciones iniciales. Debido a que la mayoría de los algoritmos de diseño y enrutamiento solo están diseñados para funcionar con compuertas de uno y dos qubits, esta etapa también se utiliza para traducir cualquier compuerta que opere en más de dos qubits en compuertas que solo operen en uno o dos qubits.\n",
    "\n",
    "Si especifica un argumento en esta etapa para los qubits que desea usar, ese valor anula todos los pasos que podrían cambiarlo. Puede encontrar más detalles en la [documentación de opciones de configuración y valores predeterminados](https://docs.quantum.ibm.com/transpile/defaults-and-configuration-options).\n",
    "\n",
    "Primero, verifiquemos las posibles opciones de la etapa de inicio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1669b5e4-b560-4138-a732-03e5c49a0d87",
   "metadata": {
    "id": "1669b5e4-b560-4138-a732-03e5c49a0d87"
   },
   "outputs": [],
   "source": [
    "list_stage_plugins(\"init\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97a46352-d341-4780-b67c-034f4ceb09db",
   "metadata": {
    "id": "97a46352-d341-4780-b67c-034f4ceb09db"
   },
   "source": [
    "Sin plugins adicionales, solo existen opciones predeterminadas. Este proceso incluye varios complementos de paso del transpilador según el `optimization_level`; echemos un vistazo a su interior.\n",
    "\n",
    "Para esto, creemos un administrador de pases con opciones `init_method=\"default\"`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3ed5d78-c784-4a14-8c1d-e70ee1da274d",
   "metadata": {
    "id": "f3ed5d78-c784-4a14-8c1d-e70ee1da274d"
   },
   "outputs": [],
   "source": [
    "print(\"Plugins run by default init stage\")\n",
    "print(\"=================================\")\n",
    "\n",
    "for i in range(4):\n",
    "    print(f\"\\nOptimization level {i}:\")\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=i, init_method=\"default\", seed_transpiler=1000)\n",
    "    for task in pm.init.to_flow_controller().tasks:\n",
    "        print(\" -\", type(task).__name__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef6244cb",
   "metadata": {
    "id": "ef6244cb"
   },
   "source": [
    "He aquí una tabla de los documentos API de cada complemento. Échales un vistazo si quieres profundizar más en alguno de ellos.\n",
    "\n",
    "| Plugin | Descripción | API docs link|\n",
    "|---- | ---- | ------|\n",
    "|UnitarySynthesis| Sintetizar unitarios sobre algunas puertas básicas | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.UnitarySynthesis#unitarysynthesis |\n",
    "|HighLevelSynthesis | Sintetizar objetos de nivel superior y desenrollar definiciones personalizadas| https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.HighLevelSynthesis#highlevelsynthesis |\n",
    "| BasisTranslator | Traduce puertas a un objetivo mediante la búsqueda de un conjunto de traducciones de una biblioteca de equivalencia determinada | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.BasisTranslator#basistranslator |\n",
    "| InverseCancellation| Cancela puertas específicas que son inversas entre sí cuando ocurren una detrás de otra | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.InverseCancellation#inversecancellation |\n",
    "| OptimizeSwapBeforeMeasure | Mueve las medidas para evitar SWAP | NA |\n",
    "| RemoveDiagonalGatesBeforeMeasure | Retira las puertas diagonales (incluidas las puertas diagonales 2Q) antes de realizar una medida | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.RemoveDiagonalGatesBeforeMeasure |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "981276aa",
   "metadata": {
    "id": "981276aa"
   },
   "source": [
    "## Etapa de diseño <a name='layout'></a>\n",
    "\n",
    "La siguiente etapa implica el diseño o la conectividad del backend al que se enviará un circuito. En general, los circuitos cuánticos son entidades abstractas cuyos qubits son representaciones \"virtuales\" o \"lógicas\" de qubits reales utilizados en los cálculos. Para ejecutar una secuencia de compuertas, es necesario un mapeo uno a uno de los qubits \"virtuales\" a los qubits \"físicos\" en un dispositivo cuántico real. Esta asignación se almacena como un objeto de layout (diseño) y es parte de las restricciones definidas dentro de la arquitectura del conjunto de instrucciones (ISA) de un servidor.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb01b502",
   "metadata": {
    "id": "cb01b502"
   },
   "source": [
    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)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8c37f20",
   "metadata": {
    "id": "b8c37f20"
   },
   "source": [
    "El mapeo escogido es extremadamente importante para minimizar el número de operación SWAP que se necesitan para hacer una mapa del circuito de entrada que se ajuste con la topología del dispositivo y asegurar el uso de los qubits mejor calibrados. Debido a la importancia de esta etapa, los \"preset pass managers\" intentan diferentes métodos para encontrar el mejor layout. Típicamente, esto involucra dos etapas: primero, intentar de encontrar un layout \"perfecto\" (un layout que no requiera de ninguna operación SWAP), y luego, un pase heurístico que intenta encontrar el mejor layout a utilizar si no se encuentra un layout perfecto. Estos son dos pases que se utilizan típicamente en este primer paso:\n",
    "\n",
    "- [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout): De manera ingénua, mapea cada qubit virtual al mismo número de qubit físicos en el dispositivo (i.e., [0,1,1,3] -> [0,1,1,3]). Esto es un comportamiento tradicional usado solamente en `optimzation_level=1` para encontrar un layout perfecto. Si falla, se intenta con `VF2Layout` a continuación.\n",
    "\n",
    "- [VF2Layout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.VF2Layout): Este es un `AnalysisPass` que escoge un layout ideal tratando esta etapa como un problema de isomorfismo de subgrafos, resoviéndolo con el algoritmo VF2++. Si se encuentra más de un layout, asigna una puntuación heurística para escoger el mapeo con el error más bajo en promedio.\n",
    "\n",
    "Luego, para la etapa heuristica, dos pases se utilizan por defecto:\n",
    "\n",
    "- [DenseLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.DenseLayout): Encuentra el subgrafo del dispositivo con la mayor conectividad y que tiene tanto número de qubits como el circuito (usado para `optimization_level=1` si las operaciones de flujo de control (tales como `IfElseOp`) están presentes en el circuito).\n",
    "\n",
    "- [SabreLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.SabreLayout): Este pase escoge un layout comenzando desde un layout inicial de manera  aleatoria y ejecutando de manera repetida el algoritmo SabreSwap. Este pase se utiliza solamente en níveles de optimización 1,2, y 3 si no se consigue un layout perfecto a través del pase VF2Layout. Para más detalles sobre este algoritmo, referirse a la publicación [arXiv:1809.02573](arXiv:1809.02573).\n",
    "\n",
    "Podemos encontrar estos cuatro pases usando el mismo código de la etapa inicial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5426f911-6672-410e-9ea2-c9bc43a7cd7a",
   "metadata": {
    "id": "5426f911-6672-410e-9ea2-c9bc43a7cd7a"
   },
   "outputs": [],
   "source": [
    "list_stage_plugins(\"layout\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28b4724c-00e7-4716-87ae-ca32bfca6b9c",
   "metadata": {
    "id": "28b4724c-00e7-4716-87ae-ca32bfca6b9c"
   },
   "source": [
    "Primero, verifiquemos qué operaciones serán activadas por cuáles `optimization_level` con la opción `layout_method='default'`, ejecutando el código a continuación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bae1c796-5625-4b3d-96ef-27db476510d3",
   "metadata": {
    "id": "bae1c796-5625-4b3d-96ef-27db476510d3"
   },
   "outputs": [],
   "source": [
    "print(\"Plugins ejecutados por defecto en la etapa layout\")\n",
    "print(\"=================================\")\n",
    "for i in range(4):\n",
    "    print(f\"\\nOptimization level {i}:\")\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=i, layout_method='default', seed_transpiler=seed)\n",
    "    qc_tr = pm.run(qc)\n",
    "\n",
    "    for controller_group in pm.layout.to_flow_controller().tasks:\n",
    "        tasks = getattr(controller_group, \"tasks\", [])\n",
    "        for task in tasks:\n",
    "            print(\" - \" , str(type(task).__name__))\n",
    "    print(qc_tr.layout.final_index_layout())\n",
    "    display(plot_circuit_layout(pm.run(qc), backend))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5718018f-1970-410c-9e5d-a6700d5e13f9",
   "metadata": {
    "id": "5718018f-1970-410c-9e5d-a6700d5e13f9"
   },
   "source": [
    "Ahora comparemos el score y el layout de cada opción con `optimization_level=3`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ca85ae0",
   "metadata": {
    "id": "8ca85ae0"
   },
   "outputs": [],
   "source": [
    "for option in list_stage_plugins(\"layout\"):\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=3, layout_method=option, seed_transpiler=seed)\n",
    "    qc_tr = pm.run(qc)\n",
    "    score = scoring(qc_tr, backend)\n",
    "\n",
    "    print(f\"Layout method = {option}\")\n",
    "    print(f\"Score: {score:.6f}\")\n",
    "    print(f\"Layout: {qc_tr.layout.final_index_layout()}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "067950f8",
   "metadata": {
    "id": "067950f8"
   },
   "source": [
    "## Etapa de enrutamiento <a name='routing'></a>\n",
    "\n",
    "Para implementar una compuerta de dos qubits entre qubits que no están conectados directamente en un dispositivo cuántico, una o más de una compuerta SWAP debe insertarse en el circuito para desplazar el estado de los qubits hasta que sean adyacentes el mapa de compuertas del dispositivo. Cada compuerta SWAP representa una operación costosa y que genera ruido al aplicarse. Por lo tanto, encontrar el mínimo número de compuertas SWAP para mapear el circuito en un dispositivo dado es un paso importante en el proceso de transpilación. Para mayor eficiencia, esta etapa se ejecuta junto con la etapa de layout por defecto, pero son lógicamente distintas la una de la otra. La etapa de layout escoge los qubits en el hardware a utilizar, al etapa de enrutamiento inserta el número apropiado de compuertas SWAP de manera que se ejecuten los circuitos usando el layout escogido.\n",
    "\n",
    "Sin embargo, conseguir el mapeao optimal de SWAPs es difícil. De hecho, es un problem NP-hard, y por lo tanto prohibitivamente costoso para calcular para todos los circuitos de entrada y los dispositivos cuánticos, salvo aquellos más pequeños. Para solucionar esto, Qiskit usa un algoritmos heurístico y estocástico llamado SabreSwap para calcular un buen, pero no necesariamente óptimo, mapa de SWAP. El uso de un método estocástico significa no se garantiza que los circuitos generados sean los mismos en ejecuciones consecutivas. Justamente, ejecutar el mismo circuito de manera repetida se muestra como una distribución de profundidades de circuito y de número de compuertas como resultado. Es por esta razón que muchos usuarios prefieren ejecutar la función de enrutamiento (o todo el StagedPassManager) varias veces y escoger los circuitos con menor profundidad de la distribución de resultados.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0132fbf8-481d-4c08-acf8-280531f01a34",
   "metadata": {
    "id": "0132fbf8-481d-4c08-acf8-280531f01a34"
   },
   "outputs": [],
   "source": [
    "list_stage_plugins(\"routing\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4ae60079-2425-4979-bcaf-128ca52e8476",
   "metadata": {
    "id": "4ae60079-2425-4979-bcaf-128ca52e8476"
   },
   "outputs": [],
   "source": [
    "print(\"Number of each gates of transpiled circuit and the score\")\n",
    "print(\"=================================\")\n",
    "for i in range(4):\n",
    "    print(f\"\\nOptimization level {i}:\")\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=i, routing_method='basic', seed_transpiler=seed)\n",
    "    qc_tr = pm.run(qc)\n",
    "    score = scoring(qc_tr, backend)\n",
    "    for key, value in qc_tr.count_ops().items():\n",
    "        print(key, \":\", value)\n",
    "    print(f\"Score: {score:.6f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a6d8504-9ed0-4045-bd09-d9b1aac2d262",
   "metadata": {
    "id": "9a6d8504-9ed0-4045-bd09-d9b1aac2d262"
   },
   "outputs": [],
   "source": [
    "print(\"Plugins run by basic routing stage\")\n",
    "print(\"=================================\")\n",
    "for i in range(4):\n",
    "    print(f\"\\nOptimization level {i}:\")\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=i, routing_method='basic', seed_transpiler=seed)\n",
    "\n",
    "    for controller_group in pm.routing.to_flow_controller().tasks:\n",
    "        tasks = getattr(controller_group, \"tasks\", [])\n",
    "        for task in tasks:\n",
    "            print(\" - \" , str(type(task).__name__))\n",
    "    display(pm.routing.draw())\n",
    "    print(pm.run(qc).layout.final_index_layout())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f8a2443",
   "metadata": {
    "id": "6f8a2443"
   },
   "outputs": [],
   "source": [
    "## process stopped due to lookahead\n",
    "options = ['basic','sabre', 'stochastic']\n",
    "\n",
    "for option in options:\n",
    "    print(f\"Layout option = {option}:\")\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=3, routing_method=option, seed_transpiler=seed)\n",
    "    qc_tr = pm.run(qc)\n",
    "    score = scoring(qc_tr, backend)\n",
    "\n",
    "    print(f\"Score: {score:.6f}\")\n",
    "\n",
    "    for key, value in qc_tr.count_ops().items():\n",
    "        print(key, \":\", value)\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adb4ca35",
   "metadata": {
    "id": "adb4ca35"
   },
   "source": [
    "## Etapa de traducción <a name='translation'></a>\n",
    "\n",
    "Al escribir un circuito cuántico, puedes utilizar cualquier compuerta cuántica (operación unitaria) que desees, junto con una colección de operaciones que no son de compuerta, como la medición de qubits o instrucciones de reinicio. Sin embargo, la mayoría de los dispositivos cuánticos solo admiten de forma nativa un puñado de operaciones de puerta y sin compuertas cuánticas. Estas compuertas nativas son parte de la definición de ISA de un objetivo y esta etapa de PassManagers preestablecidos traduce (o desenrolla) las puertas especificadas en un circuito a las puertas básicas nativas de un backend específico. Este es un paso importante, ya que permite que el circuito sea ejecutado por el backend, pero normalmente conduce a un aumento en la profundidad y el número de puertas.\n",
    "\n",
    "Es especialmente importante destacar dos casos especiales que ayudan a ilustrar lo que hace esta etapa.\n",
    "\n",
    "1. Si una puerta SWAP no es una compuerta nativa en el backend en uso, requerimos tres compuertas CNOT: ya que tres compuertas CNOT son equivalentes a un SWAP, una operación cara en dispositivos cuánticos ruidosos. Sin embargo, estas operaciones suelen ser necesarias para integrar un circuito en las limitadas conectividades de compuerta de muchos dispositivos cuánticos. Por lo tanto, minimizar la cantidad de compuertas SWAP en un circuito es una parte principal del proceso de transpilación.\n",
    "\n",
    "2. Una Toffoli, o compuerta controlled-controlled-not (ccx), es una puerta de tres qubits. Dado que nuestro conjunto de compuertas básicas incluye solo compuertas de uno y dos qubits, esta operación debe descomponerse. Sin embargo, es bastante caro descomponer compuertas: por cada puerta Toffoli en un circuito cuántico, el hardware puede ejecutar hasta seis compuertas CNOT y un puñado de compuertas de un solo qubit. Este ejemplo demuestra que cualquier algoritmo que utilice múltiples compuertas Toffoli terminará como un circuito con gran profundidad y, por lo tanto, se verá apreciablemente afectado por el ruido.\n",
    "\n",
    "Comprobemos cuántas opciones tenemos a nuestra disposición."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74c0f1fa-1d61-4cfb-bdb7-7ffc4c85ef61",
   "metadata": {
    "id": "74c0f1fa-1d61-4cfb-bdb7-7ffc4c85ef61"
   },
   "outputs": [],
   "source": [
    "list_stage_plugins(\"translation\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b414c44-0d88-4526-885e-54a8d92e84cb",
   "metadata": {
    "id": "9b414c44-0d88-4526-885e-54a8d92e84cb"
   },
   "source": [
    "Las opciones básicas en Qiskit son 'traductor' y 'síntesis'. Contemos el número total de puertas, la profundidad del circuito y las puntuaciones de los circuitos transpilados con la opción predeterminada (\"traductor\") y cada nivel de optimización."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba72bf95-812c-44e1-add0-919beb411c7b",
   "metadata": {
    "id": "ba72bf95-812c-44e1-add0-919beb411c7b"
   },
   "outputs": [],
   "source": [
    "print(\"Number of each gates of transpiled circuit\")\n",
    "print(\"=================================\")\n",
    "\n",
    "for i in range(4):\n",
    "    print(f\"\\nOptimization level {i}:\")\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=i, translation_method='translator', seed_transpiler=seed)\n",
    "    qc_tr = pm.run(qc)\n",
    "    score = scoring(qc_tr, backend)\n",
    "    for key, value in qc_tr.count_ops().items():\n",
    "        print(key, \":\", value)\n",
    "    print(f\"Score: {score:.6f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "838b6721-0a37-4926-a09a-a43b3629c60e",
   "metadata": {
    "id": "838b6721-0a37-4926-a09a-a43b3629c60e"
   },
   "source": [
    "Contemos el número total de compuertas, la profundidad del circuito y las puntuaciones de los circuitos transpilados con cada opción y nivel_optimización=3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88abac73-ba3b-4591-9909-5fb558d4a587",
   "metadata": {
    "id": "88abac73-ba3b-4591-9909-5fb558d4a587"
   },
   "outputs": [],
   "source": [
    "options = ['translator', 'synthesis']\n",
    "\n",
    "print(\"Number of each gates of transpiled circuit\")\n",
    "print(\"=================================\")\n",
    "\n",
    "for option in options:\n",
    "    print(f\"Layout option = {option}:\")\n",
    "    pm = generate_preset_pass_manager(backend=backend, optimization_level=3, translation_method=option, seed_transpiler=seed)\n",
    "    qc_tr = pm.run(qc)\n",
    "    score = scoring(qc_tr, backend)\n",
    "    for key, value in qc_tr.count_ops().items():\n",
    "        print(key, \":\", value)\n",
    "    print(f\"Score: {score:.6f}\")\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f67bb31-95da-4e2e-b83a-272d294aaef6",
   "metadata": {
    "id": "5f67bb31-95da-4e2e-b83a-272d294aaef6"
   },
   "source": [
    "Tracémoslo en un gráfico."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de289df4-9df1-4b72-99cc-d39162cc6dfa",
   "metadata": {
    "id": "de289df4-9df1-4b72-99cc-d39162cc6dfa"
   },
   "outputs": [],
   "source": [
    "tr_depths = []\n",
    "tr_gate_counts = []\n",
    "tr_scores = []\n",
    "\n",
    "options = ['translator', 'synthesis']\n",
    "\n",
    "for i in range(4):\n",
    "    for option in options:\n",
    "        pm = generate_preset_pass_manager(backend=backend, optimization_level=i, translation_method=option, seed_transpiler=seed)\n",
    "\n",
    "        tr_depths.append(pm.run(qc).depth())\n",
    "        tr_gate_counts.append(sum(pm.run(qc).count_ops().values()))\n",
    "        tr_scores.append(scoring(pm.run(qc), backend))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e764e25f",
   "metadata": {
    "id": "e764e25f"
   },
   "outputs": [],
   "source": [
    "colors = ['#FF6666', '#66B2FF']\n",
    "markers = [ '^', '*']\n",
    "linestyles = ['-.', ':']\n",
    "\n",
    "opt_list = []\n",
    "for i in range(4):\n",
    "    opt_list.append(f\"Optimization Level {i}\")\n",
    "\n",
    "ax = opt_list\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(10, 12))\n",
    "\n",
    "# Gráfico 1: Profundidad del circuito\n",
    "for i in range(2):\n",
    "    ax1.plot(ax, tr_depths[i::2], label=options[i], marker=markers[i], markersize=9, linestyle=linestyles[i], color=colors[i], linewidth=2)\n",
    "ax1.set_xlabel(\"translation options\", fontsize=12)\n",
    "ax1.set_ylabel(\"Depth\", fontsize=12)\n",
    "ax1.set_title(\"Circuit Depth of Transpiled Circuit\", fontsize=14)\n",
    "ax1.legend(fontsize=10)\n",
    "\n",
    "# Gráfico 2: Número total de compuertas\n",
    "for i in range(2):\n",
    "    ax2.plot(ax, tr_gate_counts[i::2], label=options[i], marker=markers[i], markersize=9, linestyle=linestyles[i], color=colors[i], linewidth=2)\n",
    "ax2.set_xlabel(\"translation options\", fontsize=12)\n",
    "ax2.set_ylabel(\"# of Total Gates\", fontsize=12)\n",
    "ax2.set_title(\"Total Number of Gates of Transpiled Circuit\", fontsize=14)\n",
    "ax2.legend(fontsize=10)\n",
    "\n",
    "# Gráfico 3: Puntuación del circuito transpilado\n",
    "for i in range(2):\n",
    "    ax3.plot(ax, tr_scores[i::2], label=options[i], marker=markers[i],markersize=9, linestyle=linestyles[i], color=colors[i], linewidth=2)\n",
    "ax3.set_xlabel(\"translation options\", fontsize=12)\n",
    "ax3.set_ylabel(\"Score of Transpiled Circuit\", fontsize=12)\n",
    "ax3.set_title(\"Score of Transpiled Circuit\", fontsize=14)\n",
    "ax3.legend(fontsize=10)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8b1d224",
   "metadata": {
    "id": "a8b1d224"
   },
   "source": [
    "## Etapa de optimización <a name='optimization'></a>\n",
    "\n",
    "La descomposición de los circuitos cuánticos en el conjunto de compuertas base del dispositivo de destino y la adición de compuertas de intercambio necesarias para coincidir con la topología del hardware conspiran para aumentar la profundidad y el número de compuertas de los circuitos cuánticos. Afortunadamente, existen muchas rutinas para optimizar circuitos combinando o eliminando compuertas. En algunos casos, estos métodos son tan efectivos que los circuitos de salida tienen menor profundidad que las entradas. En otros casos, no se puede hacer mucho y el cálculo puede resultar difícil de realizar en dispositivos ruidosos. Se activan diferentes optimizaciones de puerta con diferentes valores de nivel de optimización.\n",
    "\n",
    "- Con `optimization_level=`1, esta estapa prepara [Optimize1qGatesDecomposition](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.Optimize1qGatesDecomposition) y [CXCancellation](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.CXCancellation), que combinan cadenas de compuertas a un qubit y anula pares de CNOT consecutivas.\n",
    "- Con `optimization_level=2`, esta etapa utiliza el pase[CommutativeCancellation](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.CommutativeCancellation) en lugar de `CXCancellation`, que remueve compuertas redundantes usando las relaciones de conmutación de las compuertas.\n",
    "- Con optimization_level=3, esta etapa prepara los pases[Collect2qBlocks](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.Collect2qBlocks), [ConsolidateBlocks](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.ConsolidateBlocks), [UnitarySynthesis](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.UnitarySynthesis), [Optimize1qGateDecomposition](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.Optimize1qGatesDecomposition), [CommutativeCancellation](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.CommutativeCancellation). Adicionalmente, esta etapa ejecuta unas verificaciones finales para asegurarse que todas las instrucciones en el circuito están compuestas de compuertas de base disponibles en el backend deseado.\n",
    "\n",
    "En esta etapa, podemos implementar dos opciones:\n",
    "- approximation_degree (float, entre 0-1 | None) - Un marcador utilizado heurísticamente para aproximar el circuito (1.0 = ninguna aproximación, 0.0 = aproximación máxima). El valor por defecto es 1.0. Especificar `None` implementa el grado de aproximación a la tasa de error reportada. Ver la sección Selección de grado de aproximación para más detalles.\n",
    "\n",
    "- optimization_method (str) - El nombre del plugin a utilizar para la etapa de optimización. Por defector, no se utiliza un plugin externo. Puedes ver la lista de plugins al ejecutar `list_stage_plugins()` con  `optimization` como el argumento de `stage_name`.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "QNmgZ8owogWI",
   "metadata": {
    "id": "QNmgZ8owogWI"
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "#### Ejercicio bonus (no cuenta para la validación)\n",
    "\n",
    "Como esta etapa esta fuertemente relacionadad con optimizar las compuertas de los circuitos, probemos graficar  lo siguiente con cada `optimization_level`\n",
    "\n",
    "1. número total de compuertas\n",
    "2. profundidad del circuito\n",
    "3. puntuación del circuito transpilado\n",
    "\n",
    "con diferentes valores de `approximation_degree` - $[ 0, 0.1, 0.2, ... ,0.9, 1]$ completando los códigos a continuación.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3117ff4-32c6-4e8f-ba5e-b63d8fcb78d2",
   "metadata": {
    "id": "a3117ff4-32c6-4e8f-ba5e-b63d8fcb78d2"
   },
   "outputs": [],
   "source": [
    "tr_depths = []\n",
    "tr_gate_counts = []\n",
    "tr_scores = []\n",
    "\n",
    "approximation_degree_list = np.linspace(0,1,10)\n",
    "\n",
    "for i in range(4):\n",
    "    for j in approximation_degree_list:\n",
    "        # Añada su código aquí #\n",
    "\n",
    "\n",
    "        # Añada su código aquí #"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b1651cc",
   "metadata": {
    "id": "8b1651cc"
   },
   "outputs": [],
   "source": [
    "colors = ['#FF6666', '#FFCC66', '#99FF99', '#66B2FF']\n",
    "markers = ['o', 's', '^', '*']\n",
    "linestyles = ['-', '--', '-.', ':']\n",
    "\n",
    "ax = approximation_degree_list\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(10, 12))\n",
    "\n",
    "# Gráfico 1: Profundidad del circuito\n",
    "for i in range(4):\n",
    "    ax1.plot(ax, tr_depths[i*10:i*10+10], label=f\"Optimization Level {i}\", marker=markers[i], markersize=9, linestyle=linestyles[i], color=colors[i], linewidth=2)\n",
    "ax1.set_xlabel(\"Approximation Degree\", fontsize=12)\n",
    "ax1.set_ylabel(\"Depth\", fontsize=12)\n",
    "ax1.set_title(\"Circuit Depth of Transpiled Circuit\", fontsize=14)\n",
    "ax1.legend(fontsize=10)\n",
    "\n",
    "# Gráfico 2:  Número total de compuertas\n",
    "for i in range(4):\n",
    "    ax2.plot(ax, tr_gate_counts[i*10:i*10+10], label=f\"Optimization Level {i}\", marker=markers[i], markersize=9, linestyle=linestyles[i], color=colors[i], linewidth=2)\n",
    "ax2.set_xlabel(\"Approximation Degree\", fontsize=12)\n",
    "ax2.set_ylabel(\"# of Total Gates\", fontsize=12)\n",
    "ax2.set_title(\"Total Number of Gates of Transpiled Circuit\", fontsize=14)\n",
    "ax2.legend(fontsize=10)\n",
    "\n",
    "# Gráfico 3: Score\n",
    "for i in range(4):\n",
    "    ax3.plot(ax, tr_scores[i*10:i*10+10], label=f\"Optimization Level {i}\", marker=markers[i],markersize=9, linestyle=linestyles[i], color=colors[i], linewidth=2)\n",
    "ax3.set_xlabel(\"Approximation Degree\", fontsize=12)\n",
    "ax3.set_ylabel(\"Score of Transpiled Circuit\", fontsize=12)\n",
    "ax3.set_title(\"Score of Transpiled Circuit\", fontsize=14)\n",
    "ax3.legend(fontsize=10)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc823d96-35cc-4b6c-98e3-bf00bcf60d8c",
   "metadata": {},
   "source": [
    "Looking at the graph above, what do you think? Looking at the total gate number, depth, and score of the circuit, it seems like approximation_degree=0.5 returns the best performance, so did you think we should set the approximation_degree to 0.5 in the future?\n",
    "\n",
    "Here is the important feature of optimization stage comes. \n",
    "\n",
    "As you can see through an [official document about Approximation Degree](https://docs.quantum.ibm.com/transpile/common-parameters#approximation-degree), it is about \"approximating\" circuit if the value is not 1. To see what this means, let's see the difference by comparing the ideal simulation result of this target circuit and transpiled circuits with approximation_degree=[0, 0.5, 1] by using [Hellinger fidelity](https://docs.quantum.ibm.com/api/qiskit/0.31/qiskit.quantum_info.hellinger_fidelity), wich returns fidelity between two counts distributions.\n",
    "\n",
    "First, let's compute the ideal noisyless measurement, by using `AerSimulator` with `statevector` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5c72fd60-7672-4028-8105-8e200564f352",
   "metadata": {},
   "outputs": [],
   "source": [
    "#declair ideal simulator and sampler with options\n",
    "\n",
    "aer_sim = AerSimulator(method='statevector')\n",
    "sampler = Sampler(backend=aer_sim)\n",
    "sampler.options.default_shots = 20000\n",
    "\n",
    "qc_m = qc.measure_all(inplace=False)\n",
    "\n",
    "pm_sim = generate_preset_pass_manager(backend=aer_sim, optimization_level=3, seed_transpiler=seed)\n",
    "\n",
    "result = sampler.run([pm_sim.run(qc_m)]).result()[0]\n",
    "ideal_counts = result.data.meas.get_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba6fdd5c-da6b-4811-bc79-396886cdc21b",
   "metadata": {},
   "source": [
    "Next, let's create 3 circuits by using `optimization_level=3` and `approximation_degree = [0, 0.5, 1]` with our FakeTorino() and get counts with 20000 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b45cd5b7-e157-4af6-b135-2e776aa9f026",
   "metadata": {},
   "outputs": [],
   "source": [
    "pm_0 = generate_preset_pass_manager(backend=backend, optimization_level=3, approximation_degree=0, seed_transpiler=seed)\n",
    "pm_05 = generate_preset_pass_manager(backend=backend, optimization_level=3, approximation_degree=0.5, seed_transpiler=seed) \n",
    "pm_1 = generate_preset_pass_manager(backend=backend, optimization_level=3, approximation_degree=1, seed_transpiler=seed) \n",
    "\n",
    "noisy_sampler = Sampler(backend=backend)\n",
    "noisy_sampler.options.default_shots = 20000\n",
    "\n",
    "noisy0 = noisy_sampler.run([pm_0.run(qc_m)]).result()[0].data.meas.get_counts()\n",
    "noisy05 = noisy_sampler.run([pm_05.run(qc_m)]).result()[0].data.meas.get_counts()\n",
    "noisy1 = noisy_sampler.run([pm_1.run(qc_m)]).result()[0].data.meas.get_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "433f9b73-ae26-48fb-8ba4-c0a313e1921b",
   "metadata": {},
   "source": [
    "Now let's compute the fidelity of each counts by using `Hellinger fidelity`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4c3d357-be4e-4149-964e-fe8c09b84434",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"approximation_degree = 0 fidelity\", round(hellinger_fidelity(ideal_counts, noisy0), 4))\n",
    "print(\"approximation_degree = 0.5 fidelity\", round(hellinger_fidelity(ideal_counts, noisy05), 4))\n",
    "print(\"approximation_degree = 1 fidelity\", round(hellinger_fidelity(ideal_counts, noisy1), 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ed4e2e39-aa3f-40f4-9983-37f5eeabec51",
   "metadata": {},
   "outputs": [],
   "source": [
    "It shows even we can get the smallest circuit by using approximation_degree = 0.5, the transpiled circuit is too much approximated from original circuit. \n",
    "\n",
    "Please remember that, when you create or customize transpiler which affect on enrolling circuit, there are more to consider."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "812ffa80",
   "metadata": {
    "id": "812ffa80"
   },
   "source": [
    "## Etapa de programación (scheduling) <a name='scheduling'></a>\n",
    "\n",
    "Esta última etapa solo se ejecuta si ha sido invocada explicitamente (de manera similar a la etapa inicial) y no se ejecuta por defecto (sin embargo un metodo puede especificarse escogiendo el argumento 1scheduling_method1 al invocar `generate_preset_pass_manager`). La etapa de programación se usa típicamente una vez que el circuito ha sido traducido a la base deseada, mapeado al dispositivo, y optimizado. Estos pases se concentran en llevar la cuenta de todo el tiempo de inactividad del circuito. En un nivel más alto, la etapa de programación puede entenderse como insertar explícitamente instrucción de retardo para tomar en cuenta el tiempo de inactividad entre ejecuciones de compuertas e inspeccionar porcuánto tiempo va ejecutarse en el backend.\n",
    "\n",
    "Primero veamos qué opciones podemos usar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4432b76a-8b08-4be3-907a-2afddc752cab",
   "metadata": {
    "id": "4432b76a-8b08-4be3-907a-2afddc752cab"
   },
   "outputs": [],
   "source": [
    "list_stage_plugins(\"scheduling\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9dc83cd-9497-4a61-83a8-463ea7e51efd",
   "metadata": {
    "id": "f9dc83cd-9497-4a61-83a8-463ea7e51efd"
   },
   "source": [
    "Para usar opciones de programación, primero preparamos `timing_constraints`, que contiene información relevante sobre el backend para conseguir un cronograma optimizado de pulsos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b8a3687e-575c-45ab-85f0-52eda3456916",
   "metadata": {
    "id": "b8a3687e-575c-45ab-85f0-52eda3456916"
   },
   "outputs": [],
   "source": [
    "backend_timing = backend.target.timing_constraints()\n",
    "timing_constraints = TimingConstraints(\n",
    "    granularity=backend_timing.granularity,\n",
    "    min_length=backend_timing.min_length,\n",
    "    pulse_alignment=backend_timing.pulse_alignment,\n",
    "    acquire_alignment=backend_timing.acquire_alignment )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af52f511-c0dd-42cd-94ef-c175761ca96b",
   "metadata": {
    "id": "af52f511-c0dd-42cd-94ef-c175761ca96b"
   },
   "outputs": [],
   "source": [
    "# Ejecutar con optimization_level=3 y  'asap' como scheduling_method\n",
    "pm_asap = generate_preset_pass_manager(\n",
    "    optimization_level=3,\n",
    "    backend=backend,\n",
    "    timing_constraints=timing_constraints,\n",
    "    scheduling_method=\"asap\",\n",
    "    seed_transpiler=seed,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e74e1652-0910-4a6c-8415-44ea7f1339df",
   "metadata": {
    "id": "e74e1652-0910-4a6c-8415-44ea7f1339df"
   },
   "outputs": [],
   "source": [
    "my_style = {\n",
    "    'formatter.general.fig_width': 40,\n",
    "    'formatter.general.fig_unit_height': 1,\n",
    "}\n",
    "\n",
    "draw(pm_asap.run(qc), style=IQXStandard(**my_style), show_idle=False, show_delays=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9ab99c2-c7a1-4b82-a8af-10045d633e10",
   "metadata": {
    "id": "e9ab99c2-c7a1-4b82-a8af-10045d633e10"
   },
   "outputs": [],
   "source": [
    "pm_alap = generate_preset_pass_manager(\n",
    "    optimization_level=3,\n",
    "    backend=backend,\n",
    "    timing_constraints=timing_constraints,\n",
    "    scheduling_method=\"alap\",\n",
    "    seed_transpiler=seed,\n",
    ")\n",
    "draw(pm_alap.run(qc), style=IQXStandard(**my_style), show_idle=False, show_delays=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e89663c0-8818-4b22-bfe6-705d5b709e27",
   "metadata": {
    "id": "e89663c0-8818-4b22-bfe6-705d5b709e27"
   },
   "source": [
    "Como puedes ver, estos dos circuitos tienen muchos retardo, pero la posición y orden son diferentes. Dependiendo del circuito y el backend, la programación puede crear diferencias en el rendimiento. Verifiquemos y comparemos la puntuación de estos dos circuitos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58f43a87-69bc-4a39-a31e-e2b035e9937d",
   "metadata": {
    "id": "58f43a87-69bc-4a39-a31e-e2b035e9937d"
   },
   "outputs": [],
   "source": [
    "print(\"Score\")\n",
    "print(\"===============\")\n",
    "print(f\"asap: {scoring(pm_asap.run(qc), backend):.6f}\")\n",
    "print(f\"alap: {scoring(pm_alap.run(qc), backend):.6f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "042fa34d-da5d-4771-8f5f-85694cc6c0b9",
   "metadata": {
    "id": "042fa34d-da5d-4771-8f5f-85694cc6c0b9"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "<a id='ex4'></a>\n",
    "<a name='ex4'></a>\n",
    "\n",
    "### Ejercicio 4:\n",
    "\n",
    "**Tu tarea:** Ya en este punto deberías sentirte como un profesional en gestión de pases. Por favor, as un `PassManager` con las opciones siguientes:\n",
    "\n",
    "1. optimization level = 3\n",
    "2. layout \"sabre\"\n",
    "3. enrutamiento \"sabre\"\n",
    "4. traducción \"synthesis\"\n",
    "   \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c66fc960-522c-491a-a715-22a75c896ebc",
   "metadata": {
    "id": "c66fc960-522c-491a-a715-22a75c896ebc"
   },
   "outputs": [],
   "source": [
    "pm_ex4 = generate_preset_pass_manager(\n",
    "    backend=backend,\n",
    "\n",
    "    ### Añada su código aquí ###\n",
    "\n",
    "\n",
    "\n",
    "    ### No cambie el programa más allá de esta línea ###\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "41581917",
   "metadata": {
    "id": "41581917"
   },
   "outputs": [],
   "source": [
    "# Envíe su respuesta usando el siguiente código\n",
    "\n",
    "grade_lab2_ex4(pm_ex4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c538e3cb",
   "metadata": {
    "id": "c538e3cb"
   },
   "source": [
    "# Cree sus propios Pass Managers con Staged Pass Manager <a name='staged_pm'></a>\n",
    "\n",
    "Una de las propiedades más poderosas del transpilador de Qiskit v1.0 es su flexibilidad. Permite componer un `PassManager` con solo dos o tres etapas. También te permite escoger tus `Pass`  en etapas determinadas.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hrv08ixi0ZCD",
   "metadata": {
    "id": "Hrv08ixi0ZCD"
   },
   "source": [
    "## Construya un pase de desacoplamiento dinámico <a name='dd'></a>\n",
    "\n",
    "Aquí, intentaremos construir un pase personalizado de `scheduling` para llevar a cabo `Dynamical Decoupling`, que trabaja añadiendo secuencias de pulsos (conocidas como secuencias de pulsos de deacoplamiento dinámico) a qubits inactivos para invertirlos en la esfera de Bloch, anulando el efecto de canales de ruidos y así suprimiendo la decoherencia. Estas secuencias de pulsos son similares al enfoque de pulsos en resonancia magnética nuclear. Para una descripción detallada, ver [A Quantum Engineer's Guide to Superconducting Qubits](https://arxiv.org/abs/1904.06560). Para aprender más, puedes escuchar a Nick Bronn discutiendo sobre deacoplamiento dinámico en este [video de Qiskit](https://www.youtube.com/watch?v=67jRWQuW3Fk).\n",
    "\n",
    "Para más detalles, puedes chequear la documentación [Create a pass manager for dynamical decoupling](https://docs.quantum.ibm.com/transpile/dynamical-decoupling-pass-manager).\n",
    "\n",
    "Seguiremos usando el mismo circuito dinámico. Una secuencia de deacoplamiento es una serie de compuertas que llevan a la identidad y que están separadas regularmente en el tiempo. Por ejemplo, comienza creando una secuencia simple llamada XY4 que consiste de cuatro compuertas.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "23547853-16a3-40fd-ad87-a5ab538a8164",
   "metadata": {
    "id": "23547853-16a3-40fd-ad87-a5ab538a8164"
   },
   "outputs": [],
   "source": [
    "X = XGate()\n",
    "Y = YGate()\n",
    "\n",
    "dd_sequence = [X, Y, X, Y]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b24db346-b8c5-4f78-bf49-3f45149ed019",
   "metadata": {
    "id": "b24db346-b8c5-4f78-bf49-3f45149ed019"
   },
   "source": [
    "Gracias al ritmo regular de las secuencias de deacoplamiento dinámico, la información sobre la YGate debe añadirse al circuito de destino porque no es una compuerta de base, mientras que XGate lo es. Sabemos a priori que la YGate tiene la misma duración y error que la compuerta XGate, sin embargo, podemos obtener esas propiedades del circuito de destino y añadirselas de nuevo para la YGate. Es por esto que las `basis_gates` se guardan de manera separada, ya que se añade la instrucción de la YGate al destino, aunque no sea una verdadera compuerta de base de nuestro backend ibm_torino (aquí usamos FakeTorino, que tiene las mismas configuraciones incluyendo el conjunto de compuertas de base del verdadero ibm_torino)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "322b1ee1-da0b-404c-ac58-eb9c98cd5ffc",
   "metadata": {
    "id": "322b1ee1-da0b-404c-ac58-eb9c98cd5ffc"
   },
   "outputs": [],
   "source": [
    "backend=FakeTorino()\n",
    "\n",
    "target = backend.target\n",
    "\n",
    "y_gate_properties = {}\n",
    "for qubit in range(target.num_qubits):\n",
    "    y_gate_properties.update(\n",
    "        {\n",
    "            (qubit,): InstructionProperties(\n",
    "                duration=target[\"x\"][(qubit,)].duration,\n",
    "                error=target[\"x\"][(qubit,)].error,\n",
    "            )\n",
    "        }\n",
    "    )\n",
    "\n",
    "target.add_instruction(YGate(), y_gate_properties)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0129f62-3355-45a7-bdee-ed3f4e1b6c0b",
   "metadata": {
    "id": "c0129f62-3355-45a7-bdee-ed3f4e1b6c0b"
   },
   "source": [
    "En la siguiente parte, ejecuta los pases personalizados."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80da4e56-d66e-44e1-8d55-77646e8beda3",
   "metadata": {
    "id": "80da4e56-d66e-44e1-8d55-77646e8beda3"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "<a id='ex5'></a>\n",
    "<a name='ex5'></a>\n",
    "\n",
    "### Ejercicio 5:\n",
    "\n",
    "**Tu tarea:** Crea una instancia del PassManager con `ASAPScheduleAnalysis`s y `PadDynamicalDecoupling`. Ejecuta `ASAPScheduleAnalysis` primero para añadir la información del ritmo del circuito cuántico antes de poder añadir las secuencias de deacoplamiento dinámico separadas de manera regular. Estos pases se ejecutan en el circuito usando .run().\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b3253737-730c-4922-87ae-5d8c22b74719",
   "metadata": {
    "id": "b3253737-730c-4922-87ae-5d8c22b74719"
   },
   "outputs": [],
   "source": [
    "dd_pm = PassManager(\n",
    "    [\n",
    "        ## Añada su código aquí #\n",
    "\n",
    "        ## Añada su código aquí #\n",
    "\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8964f016-bcd3-46ac-97d0-76ff52ca8f21",
   "metadata": {
    "id": "8964f016-bcd3-46ac-97d0-76ff52ca8f21"
   },
   "source": [
    "Ahora, veamos como funciona comparando con un `Timing` de `asap`, una opción de programación (scheduling). Primero traigamos el dibujo del cronograma de arriba."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd96def6-31fc-4cec-a0e1-e33f14cc29e5",
   "metadata": {
    "id": "bd96def6-31fc-4cec-a0e1-e33f14cc29e5"
   },
   "outputs": [],
   "source": [
    "draw(pm_asap.run(qc), style=IQXStandard(**my_style), show_idle=False, show_delays=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bb39b5e-717a-4844-87e1-35ce48131b1d",
   "metadata": {
    "id": "3bb39b5e-717a-4844-87e1-35ce48131b1d"
   },
   "source": [
    "Ahora, hagamos un `Pass` de programación personalizada usando la función que creamos.\n",
    "\n",
    "Para este nuevo `scheduling pass` usaremos `StagedPassManager`. Podemos hacer un `PassManager` que solo tiene un pase. Después de has un  `PassManager` personlizado, aplicaremos esto al circuito transpilado con `pm_asap`, que ya creamos más arriba."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd5a1de6-5a79-4ba2-b094-cb86d8204589",
   "metadata": {
    "id": "bd5a1de6-5a79-4ba2-b094-cb86d8204589"
   },
   "outputs": [],
   "source": [
    "staged_pm_dd = StagedPassManager(\n",
    "    stages=[\"scheduling\"],\n",
    "    scheduling=dd_pm\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a4372c1-ee09-4ff3-9f39-803c18632af6",
   "metadata": {
    "id": "3a4372c1-ee09-4ff3-9f39-803c18632af6"
   },
   "outputs": [],
   "source": [
    "qc_tr = pm_asap.run(qc)\n",
    "draw(staged_pm_dd.run(qc_tr), style=IQXStandard(**my_style), show_idle=False, show_delays=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b0b108a6",
   "metadata": {
    "id": "b0b108a6"
   },
   "outputs": [],
   "source": [
    "# Envíe su respuesta usando el código siguiente\n",
    "\n",
    "grade_lab2_ex5(staged_pm_dd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4baba9e4-e53a-49e5-828e-1d444395584d",
   "metadata": {
    "id": "4baba9e4-e53a-49e5-828e-1d444395584d"
   },
   "source": [
    "## (Bonus) Ecosistema y Qiskit Transpiler Plugin <a name='plugin'></a>\n",
    "\n",
    "Para facilitar el desarrollo y la reutilización del código de transpilación por la vasta comunidad de usuarios de Qiskit, el Qiskit SDK tiene una interfaz de plugo que permite activar paquetes de Python de terceros para declarar que proveen de funcionalidades adicionales de transpilación acesibles a través de Qiskit.\n",
    "\n",
    "Actualmente, plugins de terceros pueden añadir funcionalidades de transpilación de tres maneras:\n",
    "\n",
    "- [A transpiler stage plugin](https://docs.quantum.ibm.com/api/qiskit/transpiler_plugins) proveen con una gestión de pases que puede ser usada en lugar de una de las seis etapas predeterminadas: inicializar, layout, enrutamiento, optimización y programación.\n",
    "\n",
    "- [A unitary synthesis plugin](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.synthesis.plugin.UnitarySynthesisPlugin) proveen con una funcionalidad extendida para la sintesis de compuertas unitarias.\n",
    "\n",
    "- [A high-level synthesis plugin](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.synthesis.plugin.HighLevelSynthesisPlugin) proveen con una funcionalidad extendidad para sintetizar \"objetos de alto-nivel\" como funciones lineales u operadores de Clifford. Objetos de alto nivel se representan como sub-clases de la clase [Operation](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.Operation).\n",
    "\n",
    "\n",
    "Referirse a [esta página](https://docs.quantum.ibm.com/transpile/transpiler-plugins) para más detalles, incluyendo como instalar y utilizar los plugins.\n",
    "\n",
    "¡También puedes convertirte en `contributor` de estos plugins! Creando plugins de transpilación es una gran manera de compartir códigos de transpilación con la vasta comunidad de Qiskit, permitiendo a otros usuarios beneficiars de las funcionalidades que has desarrollado. Puedes encontrar [aquí](https://docs.quantum.ibm.com/transpile/create-a-transpiler-plugin) las normas e instrucciones de cómo contribuir a la comunidad Qiskit proveyendo con buenos plugins de transpilación."
   ]
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    "# Información adicional\n",
    "\n",
    "**Creado por:** Sophy Shin, Sumit Suresh Kale, Abby Cross\n",
    "\n",
    "**Supervisado por:** Va Barbosa, Junye Huang, Brian Ingmanson\n",
    "\n",
    "**Traducido por:** María Gragera Garcés, Mauricio Gómez Viloria\n",
    "\n",
    "**Versión:** 1.2.2"
   ]
  }
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