content/lab_2/lab-2-ko.ipynb

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   ]
  },
  {
   "cell_type": "markdown",
   "id": "869e0a2b",
   "metadata": {
    "id": "869e0a2b"
   },
   "source": [
    "# Lab 2: The Transpiler\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "GMWViIAFk0Pz",
   "metadata": {
    "id": "GMWViIAFk0Pz"
   },
   "source": [
    "# 목차\n",
    "\n",
    "* [Prologue - 트랜스파일러란?](#prologue)   \n",
    "* [Preset Pass Manager를 사용해 트랜스파일하기](#preset_passmanager)    \n",
    "* [Optimization levels](#optimization_level)\n",
    "    * [Optimization level = 0](#opt_lv_0)\n",
    "    * [Optimization level = 1](#opt_lv_1)\n",
    "    * [Optimization level = 2](#opt_lv_2)\n",
    "    * [Optimization level = 3](#opt_lv_3)    \n",
    "* [트랜스파일러 스테이지와 옵션](#transpiler_options)\n",
    "    * [Init stage](#init)\n",
    "    * [Layout Stage](#layout)\n",
    "    * [Routing Stage](#routing)\n",
    "    * [Translation Stage](#translation)\n",
    "    * [Optimization Stage](#optimization)\n",
    "    * [Scheduling Stage](#scheduling)    \n",
    "* [Staged Pass Manager를 사용해 여러분만의 패스 매니저를 만들어 보세요](#staged_pm)    \n",
    "    * [`Dynamical Decoupling` 패스를 만들어 봅시다](#dd)\n",
    "* [(보너스) Qiskit ecosystem과 트랜스파일러 플러그인](#plugin)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dacee2d4",
   "metadata": {
    "id": "dacee2d4"
   },
   "source": [
    "# 셋업 <a name='toc2_' id='toc2_'></a>\n",
    "\n",
    "이 lab을 실행하기 위해 몇 가지 필요한 패키지들이 있습니다. 아직 Qiskit과 추가 패키지들을 설치하지 않으신 경우, 커널을 재시작하고 아래의 셀들을 실행해주세요."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b8150ce-b900-4adf-a2c7-f5d80a1e6d70",
   "metadata": {
    "id": "1b8150ce-b900-4adf-a2c7-f5d80a1e6d70"
   },
   "outputs": [],
   "source": [
    "### 필요한 경우, 이 코드를 실행해 Qiskit과 추가 패키지들을 설치해주세요\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": [
    "### 아직 API 토큰을 등록하지 않으신 경우, 이 코드를 실행해 토큰을 등록해주세요\n",
    "\n",
    "%set_env QXToken=deleteThisAndPasteYourTokenHere\n",
    "\n",
    "# 등호 앞뒤에 공백이 없도록 주의해주세요"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "684bbb4a-9576-474c-83fe-31d712ceb87c",
   "metadata": {
    "id": "684bbb4a-9576-474c-83fe-31d712ceb87c"
   },
   "source": [
    "자, 이제 사용할 함수와 grader를 불러오도록 하겠습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9pEFjWUcxKm-",
   "metadata": {
    "id": "9pEFjWUcxKm-"
   },
   "outputs": [],
   "source": [
    "# 사용할 함수를 불러옵니다\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": [
    "# 답안을 채점할 grader 함수를 불러옵니다\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": [
    "이 lab은 Qiskit v1.0.2 에서만 정상적으로 동작합니다. 시작하기 전에 사용중인 Qiskit 버전을 확인해보도록 하겠습니다."
   ]
  },
  {
   "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": [
    "# Prologue - 트랜스파일러란? <a name=\"prologue\" id=\"prologue\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d18fa3b-416a-4de6-bae4-09dbd863ed90",
   "metadata": {
    "id": "0d18fa3b-416a-4de6-bae4-09dbd863ed90"
   },
   "source": [
    "다음과 같은 상황을 가정해 봅시다:\n",
    "\n",
    "누군가가 당신에게 자동차 키를 건네며 \"제 차에 연료를 넣어 주시겠어요?\"라고 말했다고 생각해 봅시다 - 이때 당신은 어떻게 할 수 있을 까요?\n",
    "\n",
    "확실히 운전 면허증은 가지고 있지만, 상대방의 자동차 타입은? 시프트 레버는 어디에 있는지? 코너를 돌기 위한 방향 지시등은 어떻게 켜야 하는지, 또 주유소에 도착한 후 연료 탱크는 어떻게 열어야 할까요? 만약 건네 받은 자동차가 연로 탱크조차 없는 전기차라면 어떻게 할까요?  \n",
    "\n",
    "다행히도 인간의 뇌는 똑똑합니다. 여러가지 지시를 전달 받아서 그것을 바로 탑승할 자동차에 적용 시킬 수 있습니다. \n",
    "\n",
    "요약하자면, 이것이 바로 트랜스파일러입니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Xz013UUMKMxk",
   "metadata": {
    "id": "Xz013UUMKMxk"
   },
   "source": [
    "트랜스파일레이션(transpilation)은 주어진 입력 회로를 특정 양자 장치에 실행할 수 있는 등가 회로로 다시 쓰는 과정 이나, 실제 양자 시스템에서 실행할 수 있도록 회로를 최적화하는 과정을 뜻합니다. \n",
    "\n",
    "이 과정은 모든 양자 소자가 같은 방식으로 작동하는 것은 아니기 때문에 필요합니다. 하나의 양자 백엔드에 사용되는 명령이 다른 양자 백엔드와 호환되지 않을 수도 있습니다. 트랜스파일레이션은 이 랩에서 알아보게 될 양자 소자의 기본 게이트 집합, 연결 구조, 마이크로파 신호의 타이밍 제약 등을 포함한 여러가지에 대해 작용합니다.\n",
    "\n",
    "트랜스파일러의 목표는 노이즈가 많은 양자 하드웨어에서 최고의 성능을 얻는 것입니다. 대부분의 회로는 실행되어야 하는 대상 장치와 호환되도록 하는 일련의 변환을 거쳐야 하며, 결과의 노이즈를 줄이기 위해 회로를 최적화해야 합니다.\n",
    "\n",
    "**예시:** 여러분이 작성한 아주 간단한 회로를 사용해서도 트랜스파일 과정을 살펴 볼 수 있습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1401a733-a9bb-432b-a2e4-e3160c2ad9ce",
   "metadata": {},
   "source": [
    "<img src=\"data:image/webp;base64,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\" alt=\"\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79697b94-47d5-4fc7-a007-5fd6df339b69",
   "metadata": {},
   "source": [
    "이 회로를 사용해야 하는 양자 컴퓨터가 실행할 수 있는 기본 게이트나 연산만을 사용하도록 변환합니다. 이 과정에는 주어진 연산이나 게이트들을 노이즈의 영향을 최소화하기 위해 최적화 하는 것이 포함됩니다. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edf24741-adb2-4d0f-b64f-572ab3ff7657",
   "metadata": {},
   "source": [
    "<img 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\" alt=\"\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1b3564f-b96a-4cf2-9bdb-8fa63b104505",
   "metadata": {
    "id": "c1b3564f-b96a-4cf2-9bdb-8fa63b104505"
   },
   "source": [
    "Qiskit SDK의 핵심 구성 요소인 트랜스파일러는 모듈화와 확장성을 기반으로 설계되었습니다. 이것의 주요 목표는 새로운 회로 변환기(트랜스파일러 패스)를 작성하고 기존의 다른 패스와 결합하여 양자 회로의 깊이와 복잡성을 크게 줄이는 것입니다. 어떤 패스가 어떤 순서로 연결되는지에 따라 최종 결과는 크게 달라질 수 있습니다. 이 일련의 과정은 [PassManager](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.PassManager) 및 [StagedPassManager](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.StagedPassManager) 객체에 의해 결정됩니다.\n",
    "\n",
    "`PassManager` 객체는 하나 혹은 그 이상의 패스들의 모임에 해당하며, `StagedPassManager`는 하나 혹은 그 이상의 `PassManagers`의 실행을 조정하여 어느 순서로 실행될지를 결정합니다. `StagedPassManager`는 오케스트라의 지휘자로, `PassManagers`는 각기 다른 악기들의 섹션으로, `Pass`는 개개인의 음악가로 빗대어 이해할 수 있을 것입니다. \n",
    "\n",
    "이러한 방식으로, 여러분은 하드웨어에서 효과적으로 실행될 수 있는 양자 회로를 만들 수 있으며, 회로의 노이즈를 관리할 수 있는 수준으로 유지하여 유틸리티 규모의 작업을 실행할 수 있게 됩니다. 더 자세한 내용은 IBM Platform의 공식 문서 [Transpile 페이지](https://docs.quantum.ibm.com/transpile)를 참고하세요. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f5929ce-0456-47a3-87e1-e24f9877dc4d",
   "metadata": {
    "id": "9f5929ce-0456-47a3-87e1-e24f9877dc4d"
   },
   "source": [
    "## 6개의 스테이지\n",
    "\n",
    "하드웨어 제약 조건에 맞게 양자 회로를 다시 작성하고 성능을 최적화하는 것이 쉽지만은 않습니다. Qiskit은 사용자에게 미리 구축된 4개의 트랜스파일 파이프라인과 함께 표준 6단계의 컴파일 흐름을 제공합니다. 기본적으로 사전 설정된 패스 매니저는 6단계로 구성되며 각 단계마다 여러 옵션이 있습니다:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc0f3d06",
   "metadata": {
    "id": "fc0f3d06"
   },
   "source": [
    "- `Init`: 이 단계는 시스템에 맞게 회로를 재설정하기 전에 필요한 모든 초기 패스를 실행하는 단계입니다. 일반적으로 사용자 지정 명령을 분해하여 회로를 단일 및 2-큐비트 게이트로 변환하는 것을 포함합니다. (회로의 게이트와 연산을 검증하고 다중 큐비트 게이트를 단일 및 2-큐비트 게이트로 변환합니다.)\n",
    "- `Layout`: 이 단계에서는 회로의 가상 큐비트를 실제 백엔드의 물리적인 큐비트로 매핑하는 레이아웃을 적용합니다.\n",
    "- `Routing`: 이 단계는 레이아웃이 적용된 후에 진행되며, 백엔드의 연결 구조와 호환되도록 원래 회로에 게이트(즉, SWAP)를 삽입합니다. \n",
    "- `Translation`: 이 단계에서는 회로의 게이트를 대상 백엔드의 기본 게이트 세트로 변환합니다.\n",
    "- `Optimization`: 이 단계에서는 조건(예: 지정된 회로의 깊이)에 도달할 때까지 주요 최적화 루프를 반복적으로 실행합니다.\n",
    "- `Scheduling`: 이 단계는 실제 양자 하드웨어에서 실행되는 일련의 (마이크로파의) 스케쥴을 조정하는 패스들로 구성되어 있습니다.\n",
    "\n",
    "Qiskit은 사용자가 필요에 따라 미리 지정된 네 가지 수준의 트랜스파일레이션을 선택할 수 있도록 제공하고 있습니다. 여러분은 이 미리 지정된 패스 매니저들을 수정할 수 있으며, 패스 매니저를 활용해 입력 회로를 변환하기 위한 여러분만의 파이프라인을 구축할 수도 있습니다.\n",
    "\n",
    "트랜스파일을 통한 양자 회로의 최적화에 익숙하지 않은 대부분의 사용자들에게는 이 프리셋 루틴을 사용할 것을 추천합니다. 하지만 이 랩에서 여러분은 아주 깊~~~이! 각각의 단계들과 그 옵션들에 대해 알아보게 될 것입니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf273e41-76a0-4986-9257-cd592373f77c",
   "metadata": {
    "id": "cf273e41-76a0-4986-9257-cd592373f77c"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "<a id='ex1'></a>\n",
    "<a name='ex1'></a>\n",
    "\n",
    "### 문제 1:\n",
    "\n",
    "**미션:** 아래의 셀에 트랜스파일레이션의 각 단계에 대한 설명을 올바른 순서로 대응시켜보세요.\n",
    "\n",
    "- **A.** 이 단계에서는 몇 가지 최적화 옵션에 따라 회로의 양자 연산의 숫자와 회로의 깊이를 줄입니다.\n",
    "- **B.** 이 단계에서는 양자 회로를 정해진 레이아웃에 맞게 실행하기 위해 회로에 적절한 숫자의 SWAP 게이트를 삽입합니다.\n",
    "- **C.** 이 단계에서는 두 개의 큐비트 이상에 가해지는 게이트들을 단일 또는 2-큐비트 게이트로 변환합니다.\n",
    "- **D.** 이 단계에서는 \"가상의\" 큐비트를 양자 장치의 \"물리적\" 큐비트에 매핑하는 연산을 실행합니다.\n",
    "- **E.** 이 단계에서는 게이트 실행 사이의 유휴 시간(idle time)을 조절하는 지연(delay) 명령과 같이, 실제 하드웨어 레벨에서 필요한 동작을 삽입합니다.\n",
    "- **F.** 이 단계에서는 특정 백엔드의 기본 게이트 세트들로 양자 회로의 게이트들을 분해하는 작업을 진행합니다.\n",
    "\n",
    "<b>힌트: </b> 정답은 반드시 대문자 한 글자로 따옴표와 함께 입력되어야 합니다. 예시: \"A\"\n",
    "\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",
    "# Place the correct letter next to the corresponding stage, inside a parenthesis\n",
    "# 예시:  ans[\"test\"] = \"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": [
    "# 아래의 grader 함수를 사용해 답안을 제출해주세요\n",
    "\n",
    "grade_lab2_ex1(ans)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "MmoeFQ-tS_1k",
   "metadata": {
    "id": "MmoeFQ-tS_1k"
   },
   "source": [
    "각 트랜스파일 단계에 대해 이해하게 되셨습니다! 다음으로 Qiskit의 여섯 개의 트랜스파일 단계들을 `preset_pass_managers`와 함께 사용하는 방법을 살펴보겠습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f8c1263",
   "metadata": {
    "id": "5f8c1263"
   },
   "source": [
    "# Preset Pass Manager를 사용해 트랜스파일하기 <a name='preset_passmanager' id='preset_passmanager'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cf174f3",
   "metadata": {
    "id": "1cf174f3"
   },
   "source": [
    "이 파트에서, 여러분은 Qiskit의 6개의 트랜스파일러 단계에 대해서 알아보게 될 것입니다. 우선 먼저 네 가지의 프리셋 트랜스파일 파이프라인을 살펴 본 후,이 사전 정의된 파이프라인과 함께 6개의 각 단계의 옵션과 기능을 사용해 여러분만의 `PassManager`를 구성하는 방법에 대해 알아보도록 하겠습니다.\n",
    "\n",
    "가장 먼저, `Passmanager`와 `generate_preset_pass_manager`가 무엇인지 살펴봅시다. 이어질 파트들에서는 트랜스파일러에 대한 [IBM Quantum Platform docs](https://docs.quantum.ibm.com/transpile)와 [API reference documentation](https://docs.quantum.ibm.com/api/qiskit/transpiler)을 많이많이 인용할 예정이니, 이 문서들을 꼭 함께 살펴보실 것을 추천드립니다.\n",
    "\n",
    "## (Staged) Pass Manager란?\n",
    "패스 매니저는 트랜스파일러 패스들의 목록을 저장하고 패스들을 회로에 실행할 수 있게 해주는 객체입니다. 트랜스파일러 패스들의 리스트로 [PassManager](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.PassManager)를 선언하는 방식으로 패스 매니저를 정의할 수 있습니다. 주어진 회로에 트랜스파일러 패스를 실행하려면 회로를 입력으로 하여 [run](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.PassManager#run) 함수를 실행합니다.\n",
    "\n",
    "[`StagedPassManager`](https://docs.quantum.ibm.com/transpile/transpiler-stages) 클래스로 대표되는 StageedPassManager는 일반 패스 매니저보다 더 높은 추상화 수준을 나타내는 특수한 종류의 패스 매니저입니다. 일반적인 패스 매니저는 여러 개의 트랜스파일러 패스로 구성되는 반면, StageedPassManager는 여러 개의 패스 매니저로 구성됩니다. 이는 편리한 높은 단계의 추상화로, 패스 매니저로 대표되는 각 단계에 따라 트랜스파일을 순서대로 진행시킬 수 있습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ubXQdqLjU6mD",
   "metadata": {
    "id": "ubXQdqLjU6mD"
   },
   "source": [
    "## `Preset Passmanagers`\n",
    "\n",
    "Preset Passmanagers(`qiskit.transpiler.preset_passmanagers`)는 트랜스파일에 필요한 패스 매니저를 미리 정의된 규칙에 따라 생성합니다. 이 `preset passmanager`들은 미리 정의된 트랜스파일 파이프라인인 optimization level에 맞추어 회로의 변환을 실행하는 StagedPassManager입니다. 이 곳에서는 전 과정을 포함하는 패스 매니저를 `generate_preset_pass_manager`를 사용해 손쉽게 생성하는 방법을 알아보도록 하겠습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "K4i2qhtGWR89",
   "metadata": {
    "id": "K4i2qhtGWR89"
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "### 비유\n",
    "\n",
    "지금까지 새로 배운 용어들이 너무 많아 헷갈리고 계신다면 오케스트라 지휘자, 섹션 및 개별 음악가에 대한 비유로 다시 돌아가봅시다.\n",
    "\n",
    "**Bonus Exercise:** 여러분이 각각 이해한 방식으로 `StagedPassManager`, `PassManager`, `pass`의 관계를 비유적으로 설명해 봅시다.\n",
    "\n",
    "여러분의 비유적 설명을 IBM Quantum Challenge Discord나 친구들과 자유롭게 나누어 보세요.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fyAG5j89V8PY",
   "metadata": {
    "id": "fyAG5j89V8PY"
   },
   "source": [
    "## `generate_preset_pass_manager`\n",
    "\n",
    "`generate_preset_pass_manager` 함수는 Qiskit에서 빠르게 프리셋 패스 매니저를 생성하는 데에 사용될 수 있습니다. 이 함수는 쉽고 간편하게 독립적인 `PassManager`를  **optimization** 레벨과 각 패스들의 옵션을 사용해 만들어냅니다. 이어지는 내용에서 자세한 내용을 공부해봅시다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "w5oPSJWPWuO2",
   "metadata": {
    "id": "w5oPSJWPWuO2"
   },
   "source": [
    "# Optimization levels <a name='optimization_level' id='optimization_level'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4A6jQvq2v-T5",
   "metadata": {
    "id": "4A6jQvq2v-T5"
   },
   "source": [
    "`generate_preset_pass_manager` 함수는 반드시 optimization_level 값을 입력으로 요구하며, 이 값은 트랜스파일러가 회로를 최적화할 때 얼마 만큼의 노력을 기울일지를 결정합니다. 이 옵션의 값은 0, 1, 2, 3 중 하나의 값을 가질 수 있습니다. \n",
    "\n",
    "높은 optimization_level의 값은 더 긴 시간을 소요해 더 많은 최적화 과정이 적용된 회로를 만들어 내며, 반대로 낮은 레벨의 값은 적은 시간으로 적은 최적화 과정만을 적용해 회로를 트랜스파일합니다. "
   ]
  },
  {
   "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",
    "### 문제 2: 트랜스파일된 회로를 ` 평가(evaluate) ` 하는 함수를 만들어봅시다.\n",
    "\n",
    "트랜스파일링의 실제 목표가 양자 회로의 실제 실행 결과를 개선하는 것이기 때문에, 이곳에서 여러분의 목표는 변환된 회로의 성능을 계산할 수 있는 함수를 만들어 보는 것입니다. 이 랩의 이어지는 부분에서 이 함수를 계속 사용하게 될 것입니다. \n",
    "\n",
    "**미션:** `scoring` 이라는 이름의 함수를 만들어 봅시다. 이 함수는 트랜스파일된 회로와 그것의 *최종 레이아웃*, 그리고 회로가 실행될 대상 백엔드를 입력으로 전달 받습니다. 이 함수는 회로의 결과를 실행 결과로 반환합니다. 0에 가까울수록 좋은 점수입니다. \n",
    "\n",
    "기타 유념할 내용들:\n",
    "* 이 랩 전체에서 `qiskit-ibm-runtime` 패키지의 `FakeTorino`를 사용해 주세요.\n",
    "* `util.py` 속의 실제 점수를 계산하는 알고리즘은 [Mapomatic](https://github.com/qiskit-community/mapomatic)으로부터 정의되었으며, 코드는 `PrimitiveV2`와 호환되도록 업데이트 되었습니다.\n",
    "* 함수의 일부는 미리 구현되어 있습니다.\n",
    "* 여러분은 회로의 최종 레이아웃을 구해야 합니다. 이 두 페이지가 여러분이 아래의 함수 선언 코드를 완성하는데 도움이 될 것입니다.\n",
    "  * [The layout section from the QuantumCircuit API documentation](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.QuantumCircuit#layout)\n",
    "  * [The TranspileLayout section from the Qiskit Transpiler API documentation](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": [
    "### scoring 함수를 정의해보세요\n",
    "\n",
    "def scoring( qc, backend):\n",
    "    from util import transpile_scoring\n",
    "\n",
    "    layout = ##여기에 코드를 작성해주세요\n",
    "    fidelity = transpile_scoring(qc, layout, backend)\n",
    "    score = ##여기에 코드를 작성해주세요\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": [
    "# 아래의 grader 함수를 사용해 답안을 제출해주세요\n",
    "\n",
    "grade_lab2_ex2(scoring)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cad37e66-b684-419c-9cc0-9f14ef393cff",
   "metadata": {
    "id": "cad37e66-b684-419c-9cc0-9f14ef393cff"
   },
   "source": [
    "이제 여러분은 트랜스파일된 회로의 성능을 계산할 수 있는 함수를 마련하셨습니다. 다음 부분으로 넘어가기 전에, Fake 백엔드에 회로를 테스트 할 수 있도록 준비를 마무리 해 봅시다. \n",
    "\n",
    "말 그대로, 회로와 fake backend를 정의하는 것이죠!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f16a1d6b-8336-47ed-bf79-8e759679bc09",
   "metadata": {
    "id": "f16a1d6b-8336-47ed-bf79-8e759679bc09"
   },
   "outputs": [],
   "source": [
    "### 무작위 회로를 생성합니다\n",
    "\n",
    "## seed 숫자를 절대 변경하지 마세요\n",
    "seed = 10000\n",
    "\n",
    "## 주어진 seed로 무작위 회로를 생성합니다\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> 주의!</b>\n",
    "\n",
    "채점을 위해, 랩 전체 코드에서 `seed`나 `seed_transpiler`의 값을 변경하지 마세요.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cdc7d66-67b0-4988-953f-dfab85139d3c",
   "metadata": {
    "id": "4cdc7d66-67b0-4988-953f-dfab85139d3c"
   },
   "source": [
    "각 최적화 레벨의 성능을 테스트하기 위해, 먼저 `FakeTorino`를 호출하여 `backend`로 지정합시다.\n",
    "\n",
    "`FakeTorino`는 IBM Quantum의 가장 최신의 Heron 칩을 탑재한 ibm_torino의 연결 구조와 노이즈 특성을 가져옵니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a76391b8",
   "metadata": {
    "id": "a76391b8"
   },
   "outputs": [],
   "source": [
    "## 백엔드를 FakeTorino로 설정합니다\n",
    "\n",
    "backend = FakeTorino()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vYeXBPVFhgmG",
   "metadata": {
    "id": "vYeXBPVFhgmG"
   },
   "source": [
    "여러분은 네 개의 모든 최적화 레벨을 사용해 본 후 마지막에 결과들을 비교해 보게 될 것입니다. 그러기 위해서, 각 계산 결과를 저장하고 사용하기 위한 변수(dict 타입)을 만들어 봅시다.\n",
    "\n",
    "다음의 코드 셀에 필요한 변수를 선언해 두었습니다. 수정 할 것 없이 실행해둡시다."
   ]
  },
  {
   "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": [
    "## Optimization level = 0 <a name='opt_lv_0' id='opt_lv_0'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4rhnU1G4iIJm",
   "metadata": {
    "id": "4rhnU1G4iIJm"
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "이 네 개의 섹션을 진행하면서 도움이 필요하거나 내용을 명확히 이해하기 어렵다면, <a href=\"https://docs.quantum.ibm.com/transpile/set-optimization\">이 문서</a>를 통해 optimization_level에 대해 알아보세요.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "LHW01CZnhlNq",
   "metadata": {
    "id": "LHW01CZnhlNq"
   },
   "source": [
    "최적화 레벨 0은 **장비의 특성을 실험하기** 위한 것으로 최적화를 수행하지 않고 입력 회로를 대상 백엔드의 제약 조건에 매핑합니다. [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout)을 사용하여 회로를 큐비트를 각 번호에 따라 동일한 번호의 물리적 큐비트에 배정하며, 백엔드의 연결성을 고려하여 이 회로가 실행되도록 적절한 SWAP을 [StochasticSwap](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.StochasticSwap#stochasticswap)를 사용하여 삽입합니다..\n",
    "\n",
    "\n",
    "최적화 레벨 0을 사용해 FakeTorino에 대해 회로를 트랜스파일하는 패스 매니저를 생성하고 결과를 살펴봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2193548-33ea-4fe7-ade3-8a919c5bf447",
   "metadata": {
    "id": "b2193548-33ea-4fe7-ade3-8a919c5bf447"
   },
   "outputs": [],
   "source": [
    "# 지정된 optimization level과 백엔드에 기반해 pass manager를 생성합니다\n",
    "pm_lv0 = generate_preset_pass_manager(backend=backend, optimization_level=0, seed_transpiler=seed)\n",
    "\n",
    "# Pass manager에 무작위 회로를 넣어 실행시킵니다\n",
    "tr_lv0 = pm_lv0.run(qc)\n",
    "\n",
    "# 아래의 코드를 주석 해제하여 트랜스파일된 회로를 그려보세요\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": [
    "앞서 언급한 바와 같이 optimization_level=0은 백엔드의 기본 게이트를 이용하여 논리 큐비트를 같은 순서의 물리 큐비트에 매핑하고 2큐비트 이상의 양자 게이트나 사용자 지정 게이트의 분해를 수행합니다. 예를 들어 논리 큐비트 0을 물리 큐비트 0에 매핑하고 논리 큐비트 1을 물리 큐비트 1에 매핑하는 식입니다.\n"
   ]
  },
  {
   "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",
    "### 문제 3: (Start)\n",
    "\n",
    "**미션:** 주어진 랜덤회로를 트랜스파일하여 회로의 깊이와, 전체 게이트 수의 합, 그리고 회로의 성능을 'scoring' 함수를 사용하여 계산한 후 앞서 만들어둔 변수에 저장합시다. \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "j4y7E6yvjIZR",
   "metadata": {
    "id": "j4y7E6yvjIZR"
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "팁들:\n",
    "- `circuit_depths`: [IBM Documentation](https://docs.quantum.ibm.com/api/qiskit/0.42/circuit)\n",
    "- `gate_counts`: 숫자입니다. [이 stackexchange 스레드에서 진행된 논의가 도움이 될 수 있습니다.](https://quantumcomputing.stackexchange.com/questions/25931/qiskit-count-of-each-gates)\n",
    "- scores`: 앞서 만들어둔 `scoring` 함수를 사용 합시다.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24b96a0c",
   "metadata": {
    "id": "24b96a0c"
   },
   "outputs": [],
   "source": [
    "### 아래에 코드를 작성해주세요 ###\n",
    "\n",
    "circuit_depths['opt_lv_0'] =\n",
    "gate_counts['opt_lv_0'] =\n",
    "scores['opt_lv_0'] =\n",
    "\n",
    "### 아래의 코드는 수정하지 마세요 ###\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": "d2210488",
   "metadata": {
    "id": "d2210488"
   },
   "source": [
    "## Optimization level = 1 <a name='opt_lv_1' id='opt_lv_1'></a>\n",
    "\n",
    "최적화 레벨 1은 **`가벼운 최적화`**를 수행합니다. 그 의미를 간단히 살펴봅시다:\n",
    "\n",
    "- Layout/Routing: 회로의 레이아웃은 먼저 [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout)을 사용합니다. 추가적으로 회로가 백엔드의 연결성에 맞도록 가장 적은 숫자의 SWAP을 [SabreSWAP](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.SabreSwap#sabreswap)을 사용해 추가합니다. 그 다음 [VF2LayoutPostLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.VF2PostLayout)`을 사용해 생성된 회로의 그래프에 맞게 최적의 큐비트를 선택합니다.\n",
    "- [InverseCancellation](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.InverseCancellation#inversecancellation)\n",
    "- [1Q gate optimization](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.Optimize1qGates#optimize1qgates)\n",
    "\n",
    "여러분이 직접 `generate_preset_pass_manager`를 사용해 `FakeTorino`를 위한 패스 매니저를 만들어보세요. `optimization_level`은 1이어야 하며, `seed_transpiler` = `seed`이어야 합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c81db96e-aa03-4418-a089-5d5b5ffa90bf",
   "metadata": {
    "id": "c81db96e-aa03-4418-a089-5d5b5ffa90bf"
   },
   "outputs": [],
   "source": [
    "# 지정된 optimization level과 백엔드에 기반해 pass manager를 생성합니다\n",
    "pm_lv1 = ### 여기에 코드를 작성해주세요 ###\n",
    "\n",
    "# Pass manager에 무작위 회로를 넣어 실행시킵니다\n",
    "tr_lv1 = pm_lv1.run(qc)\n",
    "\n",
    "# 아래의 코드를 주석 해제하여 트랜스파일된 회로를 그려보세요\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": [
    "여러분은 가상의 큐비트들이 물리적 큐비트 세트에 제대로 대응되어 있는 것을 보실 수 있으며, 회로에 사용된 양자 게이트의 숫자가 적어진 것을 확인 할 수 있습니다. 조금 전에 했던 것과 마찬가지로 회로의 깊이와 전체 게이트 숫자의 합 그리고 이 회로의 성능을 `scoring`을 사용해 계산하여 저장해 봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a1e49d1",
   "metadata": {
    "id": "1a1e49d1"
   },
   "outputs": [],
   "source": [
    "### 아래에 코드를 작성해주세요 ###\n",
    "\n",
    "circuit_depths['opt_lv_1'] =\n",
    "gate_counts['opt_lv_1'] =\n",
    "scores['opt_lv_1'] =\n",
    "\n",
    "### 아래의 코드는 수정하지 마세요 ###\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": [
    "## Optimization level = 2 <a name='opt_lv_2' id='opt_lv_2'></a>\n",
    "\n",
    "최적화 레벨 2는 **`중간 단계의 최적화`**를 수행하며, 그 뜻은:\n",
    "\n",
    "- Layout/Routing: trivial 방식을 제외한 최적화 레벨 1(without trivial)의 방식과 최적화 기능을 사용하여 여러 번의 발견적 최적화(heuristic optimize)를 추가적으로 수행합니다. [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout)이 사용되지 않기 때문에, 가상의 큐비트와 물리적 큐비트가 같은 값으로 매핑되지 않습니다.\n",
    "- [CommutativeCancellation](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.CommutativeCancellation#commutativecancellation)\n",
    "\n",
    "다시 한 번  `generate_preset_pass_manager`를 사용해 `FakeTorino`를 위한 패스 매니저를 만들어 봅시다. `optimization_level`은 2여야 하며, `seed_transpiler` = `seed`이어야 합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "442d02a6-dbf6-4fdc-b0c0-1809a8a033fe",
   "metadata": {
    "id": "442d02a6-dbf6-4fdc-b0c0-1809a8a033fe"
   },
   "outputs": [],
   "source": [
    "# 지정된 optimization level과 백엔드에 기반해 pass manager를 생성합니다\n",
    "pm_lv2 = ### 여기에 코드를 작성해주세요 ###\n",
    "\n",
    "# Pass manager에 무작위 회로를 넣어 실행시킵니다\n",
    "tr_lv2 = pm_lv2.run(qc)\n",
    "\n",
    "# 아래의 코드를 주석 해제하여 트랜스파일된 회로를 그려보세요\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": [
    "간단히 훑어봐도, 게이트의 숫자가 상당히 줄어든 것을 확인 할 수 있을 것입니다. 물리적인 큐비트와 가상의 큐비트가 매핑된 방식은 변하지 않습니다. 위와 같은 방식으로 트랜스파일된 회로의 특성들을 저장해 봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05928c2d",
   "metadata": {
    "id": "05928c2d"
   },
   "outputs": [],
   "source": [
    "### 아래에 코드를 작성해주세요 ###\n",
    "\n",
    "circuit_depths['opt_lv_2'] =\n",
    "gate_counts['opt_lv_2'] =\n",
    "scores['opt_lv_2'] =\n",
    "\n",
    "### 아래의 코드는 수정하지 마세요 ###\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": [
    "## Optimization level = 3 <a name='opt_lv_3' id='opt_lv_3'></a>\n",
    "\n",
    "최적화 레벨 3은 **`높은 수준의 최적화`**를 수행합니다:\n",
    "\n",
    "- 최적화 레벨 2의 작업 + layout/routing에 더 많은 노력과 시도를 더해 발견적 최적화(heuristic optimize)를 수행합니다.\n",
    "- [Cartan's KAK Decomposition](https://arxiv.org/abs/quant-ph/0507171)을 사용해 2-큐비트 게이트들을 다시 조합힙니다.\n",
    "- Unitarity-breaking passes:\n",
    "    - `OptimizeSwapBeforeMeasure`: 측정 직전의 SWAP을 제거하고 고전 비트를 재배치 하여 SWAP 게이트들을 줄입니다. \n",
    "    - `RemoveDiagonalGatesBeforeMeasure`: 측정 직전의 대각화 게이트들(like RZ, T, Z, etc.)을 2큐비트 대각화 게이트를 포함하여 제거합니다. \n",
    "\n",
    "무엇을 해야할지 알고 계시죠?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd852fe6-49c4-49d9-8619-5d326b17a5d3",
   "metadata": {
    "id": "fd852fe6-49c4-49d9-8619-5d326b17a5d3"
   },
   "outputs": [],
   "source": [
    "pm_lv3 =### 여기에 코드를 작성해주세요 ###\n",
    "\n",
    "tr_lv3 =### 여기에 코드를 작성해주세요 ###\n",
    "\n",
    "# 아래의 코드를 주석 해제하여 트랜스파일된 회로를 그려보세요\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": [
    "놀랍지 않나요? 게이트가 얼마 남지 않았습니다. 이제 성능은 어떤지 확인해 봅시다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c926c527-37c9-4b9c-8fbf-2ceaf0555668",
   "metadata": {
    "id": "c926c527-37c9-4b9c-8fbf-2ceaf0555668"
   },
   "outputs": [],
   "source": [
    "### 아래에 코드를 작성해주세요 ###\n",
    "\n",
    "circuit_depths['opt_lv_3'] =\n",
    "gate_counts['opt_lv_3'] =\n",
    "scores['opt_lv_3'] =\n",
    "\n",
    "### 아래의 코드는 수정하지 마세요 ###\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": [
    "이제 모든 결과를 얻었으니 각각의 최적화 수준에 따라 회로의 깊이와, 게이트의 전체 숫자 그리고 성능 점수를 그래프로 그려봅시다."
   ]
  },
  {
   "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",
    "# 그래프 1: 회로의 깊이 (Circuit Depth)\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",
    "# 그래프 2: 게이트의 개수 (Total Number of Gates)\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",
    "# 그래프 3: 점수\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",
    "### 문제 3: (마무리)\n",
    "\n",
    "**미션:** \n",
    "앞서 여러분은 각기 다른 패스 매니저를 구성하고, 테스트하고, 트랜스파일된 회로의 정보를 각각에 상응하는 어레이에 저장했습니다. 또한 그 결과를 그래프로 그려 비교도 해보았습니다. 이제 만들어 둔 네 개의 패스 매니저를 Grader에 보내 채점해봅시다.\n",
    "\n",
    "seed 값을 바꾸지 않았는지 다시 한번 살펴보세요!\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "540ae47a",
   "metadata": {
    "id": "540ae47a"
   },
   "outputs": [],
   "source": [
    "# 아래의 grader 함수를 사용해 답안을 제출해주세요\n",
    "\n",
    "ans = [pm_lv0, pm_lv1, pm_lv2, pm_lv3]\n",
    "\n",
    "grade_lab2_ex3(ans)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed3972d",
   "metadata": {
    "id": "3ed3972d"
   },
   "source": [
    "# 트랜스파일러 스테이지와 옵션 <a name='transpiler_options' id='transpiler_options'></a>\n",
    "\n",
    "지금까지 우리는 Qiskit에서 제공하는 4개의 미리 정의된 트랜스파일러 파이프라인(optimizatin_level)을 랜덤 회로를 사용해 살펴보았습니다. Qiskit SDK v1.0 트랜스파일러의 주요 특징 중 하나는 사용자가 사용자 지정 패스 매니저를 쉽게 구축하고 구성할 수 있다는 점입니다. 위에서 설명한 최적화 수준과 함께 6개의 표준 스테이지들을 사용하지만 각 스테이지에 대한 옵션이나 플러그인도 원하는 대로 선택하여 자신만의 패스 매니저를 구성할 수 있습니다. 또 다른 방법은 `StagedPassManager`를 사용하여 원하는 만큼의 패스를 가진 패스 매니저를 만드는 것입니다. 또한 새로운 패스 매니저를 생성 및 배포하고 다른 사용자가 사용할 수 있도록 Qiskit에서 [plugin](https://docs.quantum.ibm.com/transpile/create-a-transpiler-plugin) 형태로 구현할 수도 있습니다.\n",
    "\n",
    "언급된 세 가지 방법들을 모두 이어서 살펴보도록 합시다. 먼저 가장 쉬운 방법을 살펴보겠습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "NZoH_tc3zm1m",
   "metadata": {
    "id": "NZoH_tc3zm1m"
   },
   "source": [
    "## Init stage <a name='init' id='init'></a>\n",
    "\n",
    "이 첫 번째 스테이지는 기본적으로 작은 역할만을 수행하며, 여러분만의 초기 최적화 과정을 적용하고 싶을 때 특히 유용합니다. 대부분의 레이아웃과 라우팅 스테이지의 알고리즘은 단일/2-큐비트 게이트에서만 작동하기 때문에, 이 단계는 두 개 이상의 큐비트, 또는 사용자 지정 연산자나 게이트를 한 개 또는 두 개의 큐비트에서만 작동하는 게이트로 변환하는 작업을 주로 수행합니다.\n",
    "\n",
    "만약 여러분이 이 단계에서 큐비트에 사용할 옵션을 따로 지정한다면 기본 옵션은 모두 덮어씌워질 것입니다. 더 자세한 내용은 [Default settings and configuration options documentation](https://docs.quantum.ibm.com/transpile/defaults-and-configuration-options)에서 확인하실 수 있습니다. \n",
    "\n",
    "우선 우리가 사용할 수 있는 init 스테이지의 옵션들을 확인해 봅시다."
   ]
  },
  {
   "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": [
    "추가적인 플러그인을 설치하지 않았다면, default 옵션만이 보일 것입니다. 이 옵션은 `optimization_level`에 따른 몇 가지 패스(플러그인으로 취급되기도 함)들을 지니고 있습니다. 하나씩 들여다 보도록 합시다.\n",
    "\n",
    "이것을 위해, `init_method=\"default\"`의 값을 지닌 패스 매니저를 생성하고 아래의 셀을 실행시켜 각 optimization_level 별로 실행되는 패스들을 살펴봅시다."
   ]
  },
  {
   "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": [
    "\n",
    "각 플러그인들의 API 문서들을 아래의 테이블에 정리해 두었습니다. 각 플러그인에 대해 궁금하신 것이 있으시면 하나씩 살펴보세요.\n",
    "\n",
    "| Plugin | Description | API docs link|\n",
    "|---- | ---- | ------|\n",
    "|UnitarySynthesis| Synthesize unitaries over some basis gates | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.UnitarySynthesis#unitarysynthesis |\n",
    "|HighLevelSynthesis |Synthesize higher-level objects and unroll custom definitions| https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.HighLevelSynthesis#highlevelsynthesis |\n",
    "| BasisTranslator | Translates gates to a target basis by searching for a set of translations from a given EquivalenceLibrary | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.BasisTranslator#basistranslator |\n",
    "| InverseCancellation| Cancel specific gates which are inverses of each other when they occur back-to- back | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.InverseCancellation#inversecancellation |\n",
    "| OptimizeSwapBeforeMeasure | Moves the measurements around to avoid SWAPs | NA |\n",
    "| RemoveDiagonalGatesBeforeMeasure | Remove diagonal gates (including diagonal 2Q gates) before a measurement | https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.RemoveDiagonalGatesBeforeMeasure |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "981276aa",
   "metadata": {
    "id": "981276aa"
   },
   "source": [
    "## Layout stage <a name='layout' id='layout'></a>\n",
    "\n",
    "다음 스테이지는 회로가 전송될 백엔드의 레이아웃 또는 큐비트의 연결 상태와 관련이 있습니다. 일반적으로 양자 회로는 큐비트가 계산에 사용되는 실제 큐비트의 \"가상\" 또는 \"논리\"적인 추상적인 실체입니다. 일련의 게이트를 실행하기 위해서는 \"가상\" 큐비트에서 실제 양자 장치의 \"물리적\" 큐비트로 일대일 매핑이 필요합니다. 이 매핑은 레이아웃 객체로 저장되며 백엔드의 명령어 세트 아키텍처(ISA, Instruction set architecture)에 정의된 제약 조건을 따르게 됩니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb01b502",
   "metadata": {
    "id": "cb01b502"
   },
   "source": [
    "![layout_mapping](data:image/webp;base64,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)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8c37f20",
   "metadata": {
    "id": "b8c37f20"
   },
   "source": [
    "큐비트를 매핑하는 과정에서는 입력된 회로를 장치의 연결 구조에 맞게 매핑하면서도, 필요한 SWAP 연산의 수를 최소화하고 노이즈가 적은 큐비트를 사용하도록 하는 것이 중요합니다. 따라서 프리셋 패스 매니저는 최상의 레이아웃을 찾기 위해 몇 가지의 다른 방법들을 시도합니다. 이 과정은 일반적으로 두 단계로 구성되어 있습니다: 먼저 SWAP을 전혀 필요로 하지 않는 '완벽한' 레이아웃을 찾습니다. 완벽한 레이아웃이 발견되지 않았을 경우, 발견적인(heuristic) 패스들이 실행됩니다. 우선 첫 번째 단계에는 일반적으로 두 가지 패스가 사용됩니다:\n",
    "\n",
    "- [TrivialLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.TrivialLayout#triviallayout): 회로의 각 가상 큐비트를 장치의 동일한 번호의 물리적 큐비트(즉, [0,1,1,3] -> [0,1,1,3])에 매핑합니다. 이는 '완벽한' 레이아웃을 찾기 위해 optimization_level=1에서만 사용됩니다. 실패하면 이어서 VF2Layout을 시도합니다.\n",
    "- [VF2Layout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.VF2Layout): 이 과정을 하위 그래프 동형화 문제(subgraph isomorphism problem)로 취급하여 VF2++ 알고리즘으로 해결하여 이상적인 레이아웃을 선택하는 AnalysisPass입니다. 두 개 이상의 레이아웃이 발견되면 발견적인 점수매김(heuristic scoring)을 실행하여 평균 오차가 가장 낮은 매핑을 선택합니다.\n",
    "\n",
    "다음으로 발견(heuristic) 단계에서는, 일반적으로 다음의 두 가지 패스가 사용됩니다:\n",
    "\n",
    "- [DenseLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.DenseLayout): 회로와 동일한 큐비트 숫자를 지닌, 가장 좋은 연결성을 지닌 장비의 서브그래프를 찾습니다. (만약 제어 연산자 (IfElseOp와 같은)가 있는 경우 optimization level 1에서 사용됨.)\n",
    "- [SabreLayout](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.SabreLayout): 이 패스는 초기 무작위 레이아웃에서 시작하여 SabreSwap 알고리듬을 반복적으로 실행하여 더 좋은 레이아웃을 선택합니다. VF2Layout 패스를 통해 완벽한 레이아웃을 찾을 수 없는 경우 이 패스는 최적화 레벨 1, 2, 3에서만 사용됩니다. 이 알고리즘에 대한 자세한 내용은 다음 논문을 참조하십시오 [arXiv:1809.02573](arXiv:1809.02573). \n",
    "\n",
    "init 스테이지에서 사용했던 것과 같은 방식으로 layout 스테이지에 대해 이 옵션들을 다음의 명령어로 확인할 수 있습니다."
   ]
  },
  {
   "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": [
    "가장 먼저, 각 optimization_level 값에 대하여 `layout_method='default'` 옵션에서 어떤 패스들이 실행되는지 다음의 셀을 실행하여 확인해 봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bae1c796-5625-4b3d-96ef-27db476510d3",
   "metadata": {
    "id": "bae1c796-5625-4b3d-96ef-27db476510d3"
   },
   "outputs": [],
   "source": [
    "print(\"Plugins run by default layout 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, 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": [
    "\n",
    "이번에는 optimization_level=3일때 각 옵션들의 `score`를 계산하여 비교해 봅시다."
   ]
  },
  {
   "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": [
    "## Routing stage <a name='routing' id='routing'></a>\n",
    "\n",
    "\n",
    "양자 장비에서 실제로 연결되지 않은 큐비트 사이에 2-큐비트 게이트를 가하기 위해서는, 하나나 그 이상의 SWAP 게이트를 삽입하여 장비의 게이트 맵 상에서 각 큐비트들이 연결될 수 있도록 해야 합니다. 각각의 SWAP 게이트는 실행 비용이 비싸며 노이즈가 생기기 쉬운 연산입니다. 따라서 트랜스파일 과정에서는 회로를 주어진 장비에 필요한 SWAP게이트의 숫자를 최소화 할 수 있는 매핑 방법을 찾아내는 것이 상당히 중요합니다. 효율성을 위해, 이 단계는 일반적으로 layout 단계에 이어서 수행되지만, 각각의 단계는 서로 독립적으로 수행됩니다. Layout 단계는 사용할 하드웨어의 물리적인 큐비트를 선택하며, Routing 단계에서는 선택된 레이아웃에서 회로를 실행하기 위해 적절한 숫자의 SWAP 게이트들을 삽입합니다.\n",
    "\n",
    "그러나 최적의 SWAP 매핑을 찾는 것은 쉽지 않습니다. 이 문제는 사실 NP-hard 문제에 해당하기 때문에, 가장 작은 양자 디바이스와 회로만을 사용하는 것이 아니면 모든 회로를 계산하는 데에는 엄청나게 많은 계산 비용이 소모될 수밖에 없습니다. 이 문제를 해결하기 위해 Qiskit은 SabreSwap이라는 확률적 발견(stochastic heuristic) 알고리즘을 사용하여 반드시 최적은 아니지만 적당한 성능을 얻을 수 있는 SWAP 매핑을 얻습니다. 확률적 방법을 사용하기 때문에 회로 생성을 반복 실행할 때마다 결과가 달라질 수 있습니다. 실제로 같은 회로를 대상으로 반복적으로 계산했을 때 회로의 깊이나 게이트 숫자와 같은 결과는 어떤 분산을 갖게 됩니다. 따라서 많은 사용자들이 Routing 함수들(또는 전체 StagePassManager)을 여러번 실행하고 출력의 분포에서 가장 낮은 깊이를 지닌 회로를 선택하곤 합니다."
   ]
  },
  {
   "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": [
    "## Translation stage <a name='translation' id='translation'></a>\n",
    "\n",
    "양자 회로를 작성할 때는 측정 또는 재설정(reset)과 같은 비게이트 연산과 함께 원하는 모든 양자 게이트(유니터리 연산)를 자유롭게 사용할 수 있습니다. 그러나 대부분의 양자 장치는 기본적으로 소수의 양자 게이트 및 비게이트 연산만을 지원합니다. 이러한 기본 게이트는 백엔드의 ISA로 정의되어 있으며, `preset pass managers`의 `Translation` 단계에서는 회로에 사용된 게이트들을 지정된 백엔드의 기본 게이트로 변환(또는 분해)합니다. 이 과정은 백엔드에서 실제로 회로를 실행할 수 있게 해주기 때문에 중요한 과정이지만 일반적으로 이 과정에서 게이트의 깊이와 수는 증가하게 됩니다.\n",
    "\n",
    "이 단계의 중요성을 이해하는데 도움이 되는 두 가지 특수 사례를 소개해보겠습니다.\n",
    "\n",
    "1. SWAP 게이트가 대상 백엔드가 지원하는 기본 게이트가 아닌 경우, SWAP 게이트를 구현하기 위해서는 세 개의 CNOT 게이트가 필요합니다. 세 개의 CNOT 게이트가 소요되기 때문에 SWAP은 노이즈가 있는 양자 장치에서 수행하기에는 계산 비용이 많이 드는 작업입니다. 그러나 SWAP 작업은 많은 양자 장비의 제한된 게이트 연결 구조로 회로를 실행하기 위해 보편적으로 요구되는 작업입니다. 따라서 회로에 있는 SWAP 게이트의 수를 최소화하는 것은 트랜스파일 과정에서 매우 중요합니다. \n",
    "\n",
    "2. 토폴리 또는 제어-제어-반전게이트(ccx)는 3-큐비트 게이트입니다. 기본 게이트 세트는 일반적으로 단일 및 2-큐비트 게이트만 포함한다는 점을 고려할 때, 이 게이트는 백엔드에서 실행되기 위해 분해 되어야 합니다. 하지만 이것은 꽤 많은 계산 비용을 소모합니다. 양자 회로의 모든 토폴리 게이트는 하드웨어에서 실행되기 위해 최대 6개의 CNOT 게이트와 몇 개의 단일 큐비트 게이트로 분해됩니다. 이러한 문제는 여러 개의 토폴리 게이트를 사용하는 모든 양자 알고리즘이 결국 깊이가 깊은 회로로 변환되어 노이즈에 상당한 영향을 받게 되는 결과로 이어집니다. \n",
    "\n",
    "우선은 어느 옵션들을 사용할 수 있는지를 먼저 확인해 봅시다."
   ]
  },
  {
   "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": [
    "Qiskit이 제공하는 기본적인 옵션은 `translator`와 `synthesis` 입니다. 그 중 기본 옵션으로 지정되어 있는 `translator`를 사용해서 각 최적화 레벨에서의 회로의 깊이와, 게이트의 숫자, 그리고 점수를 계산해봅시다."
   ]
  },
  {
   "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": [
    "이번에는 optimization_level=3을 유지하고 `transpilation` 옵션을 바꿔가면서 전체 게이트의 숫자와, 회로의 깊이, 그리고 트랜스파일된 회로의 점수를 계산해봅시다. "
   ]
  },
  {
   "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": [
    "그래프로 그려서 확인해봅시다."
   ]
  },
  {
   "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",
    "# 그래프 1: 회로의 깊이 (Circuit Depth)\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",
    "# 그래프 2: 게이트의 개수 (Total Number of Gates)\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",
    "# 그래프 3: 점수\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": [
    "## Optimization stage <a name='optimization' id='optimization'></a>\n",
    "\n",
    "양자 회로를 대상 백엔드의 기본 게이트 세트로 변환하거나 하드웨어 연결 구조에 맞추기 위해 SWAP 게이트를 추가하는 과정들은 회로의 깊이와 사용되는 게이트의 숫자를 증가시킵니다. 다행히도, 존재하는 게이트들의 숫자를 줄이거나 합치는 여러 가지 방법들이 존재합니다. 어떤 경우에는 이 방법들이 너무도 효과적이어서, 최종 회로가 입력 회로에 비해 현저히 낮은 깊이를 가지기도 합니다. 물론 큰 효과가 없는 경우도 있고, 노이즈가 있는 장비에서는 실행하기 어려운 회로를 얻게 되는 경우도 있습니다. optimization_level의 값에 따라 다양한 게이트 최적화 방법들이 사용됩니다. \n",
    "\n",
    "- optimization_level=1 에서는 [Optimize1qGatesDecomposition](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.Optimize1qGatesDecomposition)과 [CXCancellation](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.CXCancellation)이 실행되는데 이 패스들은 연속적인 단일 큐비트 게이트를 합치거나 앞뒤로 이어져있는 CNOT 게이트들을 상쇄합니다. \n",
    "- optimization_level=2 에서는 [CommutativeCancellation](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.CommutativeCancellation) 패스가 `CXCancellation` 대신에 실행되며 이 패스는 교환 관계(commutation relations)를 탐색하여 잉여 게이트들을 제거합니다.\n",
    "- optimization_level=3 에서는 다음의 패스들을 실행합니다 - [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).\n",
    "\n",
    "추가적으로, 이 단계에서는 회로가 최종적으로 대상 백엔드의 기본 게이트들로 잘 구성되어 있는지에 대한 몇 가지 확인도 수행됩니다.\n",
    "\n",
    "Optimization 단계에서는 다음의 두 가지 옵션을 설정할 수 있습니다:\n",
    "\n",
    "- approximation_degree (float, in the range 0-1 | None) - 경험적인 (heuristic) 다이얼로 회로의 근사도를 설정합니다. (1.0 = 근사하지 않음, 0.0 = 최대로 근사함). 기본값은 1.0입니다. None으로 설정하게 되면 근사 수치를 지저된 에러율로 설정합니다. 더 자세한 내용은 [Approximation Degree](https://docs.quantum.ibm.com/transpile/common-parameters#approximation-degree) 부분을 참고하세요. \n",
    "- optimization_method (str) - 사용될 플러그인의 이름. 기본적으로 외부 플러그인은 사용하지 않습니다. list_stage_plugins() 함수의 stage_name을 optimization으로 설정하여 사용할 수 있는 옵션들을 확인할 수 있습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "QNmgZ8owogWI",
   "metadata": {
    "id": "QNmgZ8owogWI"
   },
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "#### 보너스 문제 ( 채점되지 않습니다 )\n",
    "\n",
    "이 단계는 회로의 게이트를 최적화하는 것과 관련이 깊습니다. 이어지는 코드를 완성하여 각각의 optimization_level에 대한 다음의 값들을\n",
    "\n",
    "1. 회로의 총 게이트의 숫자\n",
    "2. 회로의 깊이\n",
    "3. 트랜스파일 된 회로의 score\n",
    "\n",
    "다양한 approximation_degree 값 - $[ 0, 0.1, 0.2, ... ,0.9, 1]$에 대해 계산하여 그려봅시다.\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",
    "        ### 아래에 코드를 작성해주세요 ###\n",
    "\n",
    "\n",
    "        ### 아래의 코드는 수정하지 마세요 ###"
   ]
  },
  {
   "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",
    "# 그래프 1: 회로의 깊이 (Circuit Depth)\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",
    "# 그래프 2: 게이트의 개수 (Total Number of Gates)\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",
    "# 그래프 3: 점수\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": "9dbc7d56-58b5-412c-bdc1-9b8cabac8eae",
   "metadata": {},
   "source": [
    "위의 그래프를 보면서 무슨 생각이 드나요? 총 게이트 숫자, 회로의 깊이 그리고 회로의 점수를 볼 때, approximation_degree=0.5가 가장 좋은 성능을 내고 있는 것 같아서 앞으로 approximation_degree=0.5를 사용해야겠다는 생각이 드나요? \n",
    "\n",
    "바로 여기에 Optimiztation 단계의 중요한 점이 있습니다.\n",
    "\n",
    "여러분이 [Approximation Degree에 대한 공식 문서](https://docs.quantum.ibm.com/transpile/common-parameters#approximation-degree)에서 살펴 볼 수 있듯이, 이 것은 회로를 값이 1이 아닌 경우 \"근사하는\" 기능을 수행합니다. 이것이 무엇인이 이해하기 위해, 아주 이상적인 회로의 실행 결과와 대상 백엔드에 대해 approximation_degree=0, 0.5, 1로 각각 트랜스파일된 회로의 측정결과를 두 측정 결과 사이의 정확도(fidelity)를 계산하는 [Hellinger fidelity](https://docs.quantum.ibm.com/api/qiskit/0.31/qiskit.quantum_info.hellinger_fidelity)함수를 사용해 확인해 봅시다. \n",
    "\n",
    "우선, 노이즈가 없는 측정 결과를 `AerSimulator`를 `statevector`로 사용하여 얻어봅시다. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "844dc7cb-60c2-4325-b5b2-69698c03cc70",
   "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": "de2a6885-362c-45f9-9139-8c962e101989",
   "metadata": {},
   "source": [
    "다음으로, `optimization_level=3`과 `approximation_degree = [0, 0.5, 1]`을 사용하여 FakeTorino()에 대해 트랜스파일된 세개의 회로를 얻고 20000번 측정하여 카운트를 얻어봅시다.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2c5c509-621b-4cfd-aa7b-301e1071b55f",
   "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": "060bb565-021e-4e31-b29b-e54099117a57",
   "metadata": {},
   "source": [
    "`Hellinger fidelity`를 사용하여 이상적인 측정 결과와 세 회로의 측정 결과를 비교해 봅시다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "177e1d60-4ca2-4796-a740-dc09c6339618",
   "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": "markdown",
   "id": "52726e8c-0960-4ba8-b80f-a76a15c496db",
   "metadata": {},
   "source": [
    "이 결과는 여러분이 approximation_degree = 0.5를 사용하여 가장 작은 트랜스파일된 회로를 얻었더라도, 이 회로는 원래 회로에서 너무 많이 근사 되어 있음을 나타냅니다. \n",
    "\n",
    "기억하세요, 여러분이 회로를 분해나 합성에 영향을 미치는 여러분만의 트랜스파일러를 만들 때에는, 고려애햐 할 사항이 더 많다는 것을요."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "812ffa80",
   "metadata": {
    "id": "812ffa80"
   },
   "source": [
    "## Scheduling stage <a name='scheduling' id='scheduling'></a>\n",
    "\n",
    "이 마지막 단계는 (시작 단계와 유사하게) 명시적으로 호출된 경우에만 실행되며, 기본적으로는 실행되지 않습니다 ('generate_preset_pass_manager'를 호출할 때 `scheduling_method` 인수를 설정하여 방법을 지정할 수는 있습니다). 일반적으로 스케줄링 단계는 회로가 백엔드의 기본 게이트로 변환되고, 장치에 매핑되고, 최적화되고 나서 적용됩니다. 이 패스들은 회로의 모든 유휴 시간(idle time)을 최적화에 사용하는 것에 초점을 맞춥니다. 요약하면, 스케줄링 패스는 게이트 실행 사이의 유휴 시간을 계산하며, 백엔드에서 회로의 작동 시간을 조절하는 지연 명령을 명시적으로 삽입하는 역할을 한다고 생각할 수 있습니다.\n",
    "\n",
    "사용할 수 있는 옵션들을 확인해 봅시다."
   ]
  },
  {
   "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": [
    "스케쥴링 옵션을 사용하기 위해서는, 백엔드의 펄스 스케쥴을 최적화 하는데 필요한 `timing_constraints`들을 설정해야 합니다."
   ]
  },
  {
   "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": [
    "# Optimization level은 3, scheduling pass는 'asap' 으로 실행합니다\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": [
    "여러분이 보시는 바와 같이, 이 두 회로는 많은 delay들을 가지고 있지만 그 위치와 순서가 옵션에 따라 상이합니다. 회로와 백엔드에 따라 이 스케쥴링이 성능에 주는 영향은 달라질 수 있습니다. 두 회로의 성능을 비교해 봅시다."
   ]
  },
  {
   "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",
    "### 문제 4:\n",
    "\n",
    "**미션:** 이제 여러분은 각기 다른 패스 매니저를 만드는 전문가가 되셨습니다! 다음의 옵션들을 사용해 패스 매니저를 구성해 보면서 실력을 확인해 보세요:\n",
    "1. optimization level = 3\n",
    "2. \"sabre\" layout\n",
    "3. \"sabre\" routing\n",
    "4. \"synthesis\" translation\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",
    "    ### 아래에 코드를 작성해주세요 ###\n",
    "\n",
    "\n",
    "\n",
    "    ### 아래의 코드는 수정하지 마세요 ###\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "41581917",
   "metadata": {
    "id": "41581917"
   },
   "outputs": [],
   "source": [
    "# 아래의 grader 함수를 사용해 답안을 제출해주세요\n",
    "\n",
    "grade_lab2_ex4(pm_ex4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c538e3cb",
   "metadata": {
    "id": "c538e3cb"
   },
   "source": [
    "# Staged Pass Manager를 사용해 여러분만의 패스 매니저를 만들어 보세요 <a name='staged_pm' id='staged_pm'></a>\n",
    "\n",
    "Qiskit 1.0 트랜스파일러의 강력한 특징 중 하나는 바로 \"유연성\"입니다. 여러분은 이 유연성을 이용해 두 개 혹은 세 개의 스테이지만을 갖는 `PassManager`를 구성할 수도 있고, 여러분이 만든 `Pass`를 원하는 스테이지에 넣을 수도 있습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hrv08ixi0ZCD",
   "metadata": {
    "id": "Hrv08ixi0ZCD"
   },
   "source": [
    "## `Dynamical Decoupling` 패스를 만들어 봅시다 <a name='dd' id='dd'></a>\n",
    "\n",
    "이번에는 `Dynamic Decoupling`을 수행하는 여러분만의 `scheduling` 패스를 만들어 볼 것입니다. 이것은 아무런 동작을 하지 않는 유휴 큐비트에 dynamic decoupling sequence라 불리는 일련의 펄스신호를 삽입해서, 큐비트를 블로흐 구면에서 회전시키며 결잃음에서 오는 노이즈를 상쇄시키는 방법입니다. 이 펄스 신호들은 핵 자기 공명(nuclear magnetic resonance)에서 사용되는 펄스 재초점(refocusing pulses)과 유사한 기능을 합니다. 이에 대한 전체 설명은 [A Quantum Engineer's Guide to Superconducting Qubits](https://arxiv.org/abs/1904.06560)를 참고해주세요. 더 쉬운 설명으로 배우고자 하신다면 Nick Bronn 이 dynamic decoupling에 대해 설명하는 [이 유튜브 비디오](https://www.youtube.com/watch?v=67jRWQuW3Fk)를 시청해보세요.\n",
    "\n",
    "기술적인 세부 사항에 대해서는 IBM의 [Create a pass manager for dynamical decoupling](https://docs.quantum.ibm.com/transpile/dynamical-decoupling-pass-manager) 문서를 살펴보시기 바랍니다.\n",
    "\n",
    "앞서 사용한 것과 같은 양자 회로를 이어서 사용하도록 하겠습니다. Dynamic decoupling 신호는 궁극적으로 항등 (identity) 연산이 되는 연속적인 게이트들을 일정한 시간 간격으로 배치하는 것입니다. 예시로 간단하게 XY4라 불리는 네 개의 게이트 세트로 시작해봅시다.  "
   ]
  },
  {
   "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": [
    "Dynamic decoupling sequence들의 펄스 신호 간격은 동일해야 하며, XGate는 백엔드의 기본 게이트 중 하나이지만 YGate는 그렇지 않기 때문에, YGate의 펄스 신호에 대한 정보를 수동으로 백엔드에 추가해 주어야 합니다. 우리는 경험적으로 YGate가 XGate와 동일한 지속 시간과 에러율을 가지고 있다는 것을 알고 있으므로, 백엔드에서 해당 속성을 검색하여 YGate의 속성을 정의한 후 백엔드에 추가할 수 있습니다. "
   ]
  },
  {
   "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": [
    "다음으로 사용자 지정 패스 매니저를 작성하고 실행해 봅시다."
   ]
  },
  {
   "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",
    "### 문제 5:\n",
    "\n",
    "**미션:** PassManager를  `ASAPScheduleAnalysis` 와 `PadDynamicalDecoupling` 를 사용해 선언해 봅시다. 양자 회로의 타이밍 정보를 추가하기 위해 `ASAPScheduleAnalysis` 를 같은 간격의 dynamic decoupling sequence를 삽입하기 전 실행합니다. 이 패스들은 양자회로에 `.run()` 명령어를 사용해 실행할 수 있습니다. \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",
    "        ### 아래에 코드를 작성해주세요 ###\n",
    "\n",
    "        ### 아래의 코드는 수정하지 마세요 ###\n",
    "\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8964f016-bcd3-46ac-97d0-76ff52ca8f21",
   "metadata": {
    "id": "8964f016-bcd3-46ac-97d0-76ff52ca8f21"
   },
   "source": [
    "이제 이 패스가 어떻게 작동하는지 `asap` 스케쥴링의 `Timing`과 비교해 보도록 합시다. 우선 위에서 만들어둔 asap 패스 매니저의 타이밍을 먼저 그려봅시다. "
   ]
  },
  {
   "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": [
    "이제 우리가 만들어둔 패스를 사용해 사용자 지정 스케쥴링 `Pass`를 만들어 봅시다.\n",
    "\n",
    "새 `scheduling pass`를 만들기 위해서  `StagedPassManager`를 사용해 봅시다. 이 기능을 사용해 오직 하나의 패스만을 갖는 패스 매니저를 구성해 봅시다. 사용자 지정 스테이지 패스 매니저를 구성한 다음 이 것을 이미 만들어둔 pm_asap를 사용해 트랜스파일된 회로에 적용하고 타이밍 정보를 위와 비교해 봅시다. "
   ]
  },
  {
   "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": [
    "# 아래의 grader 함수를 사용해 답안을 제출해주세요\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": [
    "## (보너스) Qiskit ecosystem과 트랜스파일러 플러그인 <a name='plugin' id='plugin'></a>\n",
    "\n",
    "Qiskit SDK에서는 Qiskit 커뮤니티의 더 많은 사용자들이 더 쉽게 사용자 지정 트랜스파일 함수를 개발하고 배포할 수 있도록 플러그인 인터페이스를 지원합니다. 이것은 서드파티 파이썬 패키지가 Qiskit을 통해 확장된 트랜스파일 기능을 제공할 수 있도록 합니다.\n",
    "\n",
    "현재까지 서드파티 플러그인을 사용할 수 있는 방법은 총 세 가지가 있습니다:\n",
    "\n",
    "- [A transpiler stage plugin](https://docs.quantum.ibm.com/api/qiskit/transpiler_plugins)은 preset staged passmanger의 표준 여섯 가지 트랜스파일 스테이지 (init, layout, routing, translation, optimization, scheduling) 중 하나에 사용될 수 있는 패스 매니저를 제공합니다.\n",
    "- [A unitary synthesis plugin](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.synthesis.plugin.UnitarySynthesisPlugin)은 유니터리 게이트의 조합에 사용할 수 있는 확장 기능을 제공합니다.\n",
    "- [A high-level synthesis plugin](https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.synthesis.plugin.HighLevelSynthesisPlugin)은 `high-level 오브젝트`를 조합할 수 있는 확장 기능, 예를 들어 선형 함수나 클리포드 연산자 등에 대한 확장을 제공합니다. High-level 오브젝트는 [Operation](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.Operation) 클래스의 하위 클래스로 표현됩니다.\n",
    "\n",
    "\n",
    "[이 페이지](https://docs.quantum.ibm.com/transpile/transpiler-plugins)를 통해 플러그인을 설치하고 사용하는 방법에 대해 더 자세히 알아보실 수 있습니다.\n",
    "\n",
    "또한 여러분이 직접 이 플러그인들의 `contributor`가 될 수도 있습니다! 여러분만의 트랜스파일러를 만들고, 플러그인으로 제작하여, 다른 Qiskit 커뮤니티의 멤버들과 공유함으로써 다른 개발자들이 여러분이 개발한 플러그인을 활용할 수 있게 할 수 있습니다. [여기](https://docs.quantum.ibm.com/transpile/create-a-transpiler-plugin)에서 어떻게 트랜스파일러 플러그인을 만들어 공유하고, 커뮤니티에 기여할 수 있는지에 대해 알아보세요."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac270f3d",
   "metadata": {
    "id": "ac270f3d"
   },
   "source": [
    "# Additional information\n",
    "\n",
    "**Created by:** Sophy Shin, Sumit Suresh Kale, Abby Cross\n",
    "\n",
    "**Advised by:** Va Barbosa, Junye Huang, Brian Ingmanson\n",
    "\n",
    "**Translated by:** Sophy Shin, Boseong Kim\n",
    "\n",
    "**Version:** 1.2.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d74ce35c-9475-4649-a7ab-5128934ce347",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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