{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "f5d21946", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "---\n", "title: \"反復コード\"\n", "description: \"このチュートリアルでは、 IBM 動的回路を用いた基本的な反復コードの構築方法を示します。これは基本的な量子誤り訂正（QEC）の一例です。\"\n", "---\n", "\n", "\n", "\n", "# 反復コード\n", "\n", "*使用時間の目安：Heronプロセッサーで1分未満（注：あくまでも目安です。 ランタイムは異なるかもしれない)。*\n", "\n", "\n", "\n", "## 背景\n", "\n", "リアルタイムの量子エラー訂正（QEC）を可能にするためには、量子プログラムの実行中に量子プログラムの流れを動的に制御し、測定結果に応じて量子ゲートを条件付けできるようにする必要がある。 このチュートリアルでは、QEC の非常に単純な形式である bit-flip コードを実行します。 符号化量子ビットを1回のビット反転エラーから保護できる動的量子回路を実証し、ビット反転符号の性能を評価する。\n", "\n", "さらにアンシラ量子ビットとエンタングルメントを利用すれば、符号化された量子情報を変換することなく*安定化装置を*測定することができる。 量子スタビライザーコードは、 $k$ 論理量子ビットを $n$ 物理量子ビットにエンコードする。 スタビライザー符号は、パウリ群 $\\Pi^n$ からの支持を得て、離散的な誤り集合を訂正することに重点を置いている。\n", "\n", "QECに関する詳細については、 [『初心者向け量子エラー訂正』](https://arxiv.org/abs/0905.2794) を参照してください。\n", "\n" ] }, { "cell_type": "markdown", "id": "88672bd6", "metadata": {}, "source": [ "\n", "\n", "## 要件\n", "\n", "このチュートリアルを始める前に、以下のものがインストールされていることを確認してください：\n", "\n", "* Qiskit SDK v2.0 またはそれ以降、 [可視化](/docs/api/qiskit/visualization)サポート付き\n", "* Qiskit Runtime v0.40 またはそれ以降 (`pip install qiskit-ibm-runtime`)\n", "\n" ] }, { "cell_type": "markdown", "id": "14c29e8b", "metadata": {}, "source": [ "\n", "\n", "## セットアップ\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "1b9fd8ad", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# Qiskit imports\n", "from qiskit import (\n", " QuantumCircuit,\n", " QuantumRegister,\n", " ClassicalRegister,\n", ")\n", "\n", "# qiskit-ibm-runtime\n", "from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler\n", "\n", "from qiskit_ibm_runtime.circuit import MidCircuitMeasure\n", "\n", "service = QiskitRuntimeService()" ] }, { "cell_type": "markdown", "id": "4d01e8d3", "metadata": {}, "source": [ "\n", "\n", "## ステップ 1. 古典的な入力を量子問題にマッピングする\n", "\n" ] }, { "cell_type": "markdown", "id": "cdee0b18", "metadata": {}, "source": [ "\n", "\n", "### ビット反転安定化回路を構築する\n", "\n", "ビット反転符号は、スタビライザー符号の最も単純な例である。 これは、符号化量子ビットのいずれかが1つのビット反転（X）エラーから状態を保護する。 $|0\\rangle \\rightarrow |1\\rangle$ $\\epsilon = \\{E_0, E_1, E_2 \\} = \\{IIX, IXI, XII\\}$ と を任意の量子ビットにマップする、ビット反転エラー の作用を考える。このコードには5つの量子ビットが必要です。3つは保護された状態をエンコードするのに使われ、残りの2つはスタビライザー測定アンシラとして使われます。 $|1\\rangle \\rightarrow |0\\rangle$ $X$\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "b588703a", "metadata": {}, "outputs": [], "source": [ "# Choose the least busy backend that supports `measure_2`.\n", "\n", "backend = service.least_busy(\n", " filters=lambda b: \"measure_2\" in b.supported_instructions,\n", " operational=True,\n", " simulator=False,\n", " dynamic_circuits=True,\n", ")" ] }, { "cell_type": "code", "execution_count": null, "id": "606dff18", "metadata": {}, "outputs": [], "source": [ "qreg_data = QuantumRegister(3)\n", "qreg_measure = QuantumRegister(2)\n", "creg_data = ClassicalRegister(3, name=\"data\")\n", "creg_syndrome = ClassicalRegister(2, name=\"syndrome\")\n", "state_data = qreg_data[0]\n", "ancillas_data = qreg_data[1:]\n", "\n", "\n", "def build_qc():\n", " \"\"\"Build a typical error correction circuit\"\"\"\n", " return QuantumCircuit(qreg_data, qreg_measure, creg_data, creg_syndrome)\n", "\n", "\n", "def initialize_qubits(circuit: QuantumCircuit):\n", " \"\"\"Initialize qubit to |1>\"\"\"\n", " circuit.x(qreg_data[0])\n", " circuit.barrier(qreg_data)\n", " return circuit\n", "\n", "\n", "def encode_bit_flip(circuit, state, ancillas) -> QuantumCircuit:\n", " \"\"\"Encode bit-flip. This is done by simply adding a cx\"\"\"\n", " for ancilla in ancillas:\n", " circuit.cx(state, ancilla)\n", " circuit.barrier(state, *ancillas)\n", " return circuit\n", "\n", "\n", "def measure_syndrome_bit(circuit, qreg_data, qreg_measure, creg_measure):\n", " \"\"\"\n", " Measure the syndrome by measuring the parity.\n", " We reset our ancilla qubits after measuring the stabilizer\n", " so we can reuse them for repeated stabilizer measurements.\n", " Because we have already observed the state of the qubit,\n", " we can write the conditional reset protocol directly to\n", " avoid another round of qubit measurement if we used\n", " the `reset` instruction.\n", " \"\"\"\n", " circuit.cx(qreg_data[0], qreg_measure[0])\n", " circuit.cx(qreg_data[1], qreg_measure[0])\n", " circuit.cx(qreg_data[0], qreg_measure[1])\n", " circuit.cx(qreg_data[2], qreg_measure[1])\n", " circuit.barrier(*qreg_data, *qreg_measure)\n", " circuit.append(MidCircuitMeasure(), [qreg_measure[0]], [creg_measure[0]])\n", " circuit.append(MidCircuitMeasure(), [qreg_measure[1]], [creg_measure[1]])\n", "\n", " with circuit.if_test((creg_measure[0], 1)):\n", " circuit.x(qreg_measure[0])\n", " with circuit.if_test((creg_measure[1], 1)):\n", " circuit.x(qreg_measure[1])\n", " circuit.barrier(*qreg_data, *qreg_measure)\n", " return circuit\n", "\n", "\n", "def apply_correction_bit(circuit, qreg_data, creg_syndrome):\n", " \"\"\"We can detect where an error occurred and correct our state\"\"\"\n", " with circuit.if_test((creg_syndrome, 3)):\n", " circuit.x(qreg_data[0])\n", " with circuit.if_test((creg_syndrome, 1)):\n", " circuit.x(qreg_data[1])\n", " with circuit.if_test((creg_syndrome, 2)):\n", " circuit.x(qreg_data[2])\n", " circuit.barrier(qreg_data)\n", " return circuit\n", "\n", "\n", "def apply_final_readout(circuit, qreg_data, creg_data):\n", " \"\"\"Read out the final measurements\"\"\"\n", " circuit.barrier(qreg_data)\n", " circuit.measure(qreg_data, creg_data)\n", " return circuit" ] }, { "cell_type": "code", "execution_count": null, "id": "dbe02949", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "\"Output" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def build_error_correction_sequence(apply_correction: bool) -> QuantumCircuit:\n", " circuit = build_qc()\n", " circuit = initialize_qubits(circuit)\n", " circuit = encode_bit_flip(circuit, state_data, ancillas_data)\n", " circuit = measure_syndrome_bit(\n", " circuit, qreg_data, qreg_measure, creg_syndrome\n", " )\n", "\n", " if apply_correction:\n", " circuit = apply_correction_bit(circuit, qreg_data, creg_syndrome)\n", "\n", " circuit = apply_final_readout(circuit, qreg_data, creg_data)\n", " return circuit\n", "\n", "\n", "circuit = build_error_correction_sequence(apply_correction=True)\n", "circuit.draw(output=\"mpl\", style=\"iqp\", cregbundle=False)" ] }, { "cell_type": "markdown", "id": "609c0c47", "metadata": {}, "source": [ "\n", "\n", "## ステップ 2. 量子実行向けに問題を最適化する\n", "\n", "ジョブの実行時間を短縮するため、 Qiskit primitives は、ターゲットシステムがサポートする命令および接続仕様に準拠した回路およびオブザーバブルのみを受け入れます（これらは命令セットアーキテクチャ（ISA）回路およびオブザーバブルと呼ばれます）。 [トランスパイレーションについて詳しく知る](/docs/guides/transpile)。\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "c8ea2716", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "\n", "\n", "### ISA回路を生成する\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "67b55eef", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "\"Output" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "\n", "pm = generate_preset_pass_manager(backend=backend, optimization_level=1)\n", "isa_circuit = pm.run(circuit)\n", "\n", "isa_circuit.draw(\"mpl\", style=\"iqp\", idle_wires=False)" ] }, { "cell_type": "code", "execution_count": 7, "id": "67acea4f", "metadata": {}, "outputs": [], "source": [ "no_correction_circuit = build_error_correction_sequence(\n", " apply_correction=False\n", ")\n", "\n", "isa_no_correction_circuit = pm.run(no_correction_circuit)" ] }, { "cell_type": "markdown", "id": "bcd61a1f", "metadata": {}, "source": [ "\n", "\n", "## ステップ 3. Qiskit primitives を使用して実行する\n", "\n" ] }, { "cell_type": "markdown", "id": "e68d10d2", "metadata": {}, "source": [ "補正を適用したバージョンと補正なしのバージョンを実行する。\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "d53319ba", "metadata": {}, "outputs": [], "source": [ "sampler_no_correction = Sampler(backend)\n", "job_no_correction = sampler_no_correction.run(\n", " [isa_no_correction_circuit], shots=1000\n", ")\n", "result_no_correction = job_no_correction.result()[0]" ] }, { "cell_type": "code", "execution_count": null, "id": "df7421d0", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "sampler_with_correction = Sampler(backend)\n", "\n", "job_with_correction = sampler_with_correction.run([isa_circuit], shots=1000)\n", "result_with_correction = job_with_correction.result()[0]" ] }, { "cell_type": "code", "execution_count": 10, "id": "1cba37f5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Data (no correction):\n", "{'111': 878, '011': 42, '110': 35, '101': 40, '100': 1, '001': 2, '000': 2}\n", "Syndrome (no correction):\n", "{'00': 942, '10': 33, '01': 22, '11': 3}\n" ] } ], "source": [ "print(f\"Data (no correction):\\n{result_no_correction.data.data.get_counts()}\")\n", "print(\n", " f\"Syndrome (no correction):\\n{result_no_correction.data.syndrome.get_counts()}\"\n", ")" ] }, { "cell_type": "code", "execution_count": 11, "id": "7b7697f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Data (corrected):\n", "{'111': 889, '110': 25, '000': 11, '011': 45, '101': 17, '010': 10, '001': 2, '100': 1}\n", "Syndrome (corrected):\n", "{'00': 929, '01': 39, '10': 20, '11': 12}\n" ] } ], "source": [ "print(f\"Data (corrected):\\n{result_with_correction.data.data.get_counts()}\")\n", "print(\n", " f\"Syndrome (corrected):\\n{result_with_correction.data.syndrome.get_counts()}\"\n", ")" ] }, { "cell_type": "markdown", "id": "1b652319", "metadata": {}, "source": [ "\n", "\n", "## ステップ 4. 後処理を行い、結果を従来の形式で返す\n", "\n", "ビット・フリップ・コードによって多くのエラーが検出され、修正された結果、全体的にエラーが少なくなっていることがわかる。\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "fa59fb42", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def decode_result(data_counts, syndrome_counts):\n", " shots = sum(data_counts.values())\n", " success_trials = data_counts.get(\"000\", 0) + data_counts.get(\"111\", 0)\n", " failed_trials = shots - success_trials\n", " error_correction_events = shots - syndrome_counts.get(\"00\", 0)\n", " print(\n", " f\"Bit flip errors were detected/corrected on \"\n", " f\"{error_correction_events}/{shots} trials.\"\n", " )\n", " print(\n", " f\"A final parity error was detected on \"\n", " f\"{failed_trials}/{shots} trials.\"\n", " )" ] }, { "cell_type": "code", "execution_count": null, "id": "5b1ff3a3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed bit code experiment data measurement counts (no correction): {'111': 878, '011': 42, '110': 35, '101': 40, '100': 1, '001': 2, '000': 2}\n", "Completed bit code experiment syndrome measurement counts (no correction): {'00': 942, '10': 33, '01': 22, '11': 3}\n", "Bit flip errors were detected/corrected on 58/1000 trials.\n", "A final parity error was detected on 120/1000 trials.\n" ] } ], "source": [ "# non-corrected marginalized results\n", "data_result = result_no_correction.data.data.get_counts()\n", "marginalized_syndrome_result = result_no_correction.data.syndrome.get_counts()\n", "\n", "print(\n", " f\"Completed bit code experiment data measurement counts (no correction): \"\n", " f\"{data_result}\"\n", ")\n", "print(\n", " f\"Completed bit code experiment syndrome measurement counts (no correction): \"\n", " f\"{marginalized_syndrome_result}\"\n", ")\n", "decode_result(data_result, marginalized_syndrome_result)" ] }, { "cell_type": "code", "execution_count": null, "id": "7f1c2d48", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed bit code experiment data measurement counts (corrected): {'111': 889, '110': 25, '000': 11, '011': 45, '101': 17, '010': 10, '001': 2, '100': 1}\n", "Completed bit code experiment syndrome measurement counts (corrected): {'00': 929, '01': 39, '10': 20, '11': 12}\n", "Bit flip errors were detected/corrected on 71/1000 trials.\n", "A final parity error was detected on 100/1000 trials.\n" ] } ], "source": [ "# corrected marginalized results\n", "corrected_data_result = result_with_correction.data.data.get_counts()\n", "corrected_syndrome_result = result_with_correction.data.syndrome.get_counts()\n", "\n", "print(\n", " f\"Completed bit code experiment data measurement counts (corrected): \"\n", " f\"{corrected_data_result}\"\n", ")\n", "print(\n", " f\"Completed bit code experiment syndrome measurement counts (corrected): \"\n", " f\"{corrected_syndrome_result}\"\n", ")\n", "decode_result(corrected_data_result, corrected_syndrome_result)" ] }, { "cell_type": "markdown", "id": "b66026c4", "metadata": {}, "source": [ "\n", "\n", "## チュートリアル調査\n", "\n", "このチュートリアルに関するご意見・ご感想をお寄せください。 あなたの洞察は、私たちのコンテンツの提供とユーザーエクスペリエンスを向上させるのに役立ちます。\n", "\n", "[アンケートへのリンク](https://your.feedback.ibm.com/jfe/form/SV_5onAlfA2Y7ac1FA)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "id": "a1b8767d", "source": "© IBM Corp., 2017-2026" } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3" }, "hours": 1.5, "qpuSeconds": 60 }, "nbformat": 4, "nbformat_minor": 5 }