qiskit_qcl_regression_sample.ipynb

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      "authorship_tag": "ABX9TyP3secmnwxKfUXCPVA1PB5E",
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        "<a href=\"https://colab.research.google.com/github/mkatouda/qclsample/blob/master/qiskit_qcl_regression_sample.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# **Qiskitによる量子回路学習のサンプルコード: １次関数の回帰問題**\n",
        "量子機械学習にパラメータ化された量子回路(PQC)を適用しNISQ量子コンピュータで実行可能としたことでブレークスルーとなった手法として，大阪大学の御手洗らにより開発された量子回路学習(Quantum Cirquit Learning: QCL)[[Phys. Rev. A. 98, 032309 (2018)]](https://doi.org/10.1103/PhysRevA.98.032309)が挙げられる．\n",
        "本ノートブックでは，量子回路学習アルゴリズムをIBMの量子コンピューティングSDKである[Qiskit](https://qiskit.org/)を用いて実装した例を紹介する．\n",
        "\n",
        "## 量子回路学習アルゴリズム\n",
        "以下1-6の手順で量子・古典ハイブリッド計算が行われる．2-4のプロセスは量子コンピュータで，1,5-6のプロセスは古典コンピュータでそれぞれ計算される．  \n",
        "\n",
        "$$\n",
        "\\def\\bra#1{\\mathinner{\\left\\langle{#1}\\right|}}\n",
        "\\def\\ket#1{\\mathinner{\\left|{#1}\\right\\rangle}}\n",
        "\\def\\braket#1{\\mathinner{\\left\\langle{#1}\\right\\rangle}}\n",
        "$$\n",
        "\n",
        "1.   学習データ$\\{(\\mathbf{x}_i, \\mathbf{y}_i)\\}$, $\\mathbf{x}_i$は入力データのベクトル, $\\mathbf{y}_i$は出力データの真の値(教師データ)}を用意する．\n",
        "2.   入力$\\mathbf{x}$を量子状態に埋め込む量子回路$U_\\text{in}(\\mathbf{x}_i)$ (特徴量マップとよぶ)を設定し，$\\mathbf{x}_i$のデータを入力量子状態$\\ket{\\psi_\\text{in}(\\mathbf{x}_i)}=U_\\text{in}(\\mathbf{x}_i)\\ket{0}^{\\otimes n}$($n$: 量子ビット数)として埋め込む．\n",
        "3.   変分最適化により調整可能なパラメータを持つ量子回路$U_\\text{out}(\\mathbf{\\theta})$を設定し，入力量子状態に作用させ，出力量子状態$\\ket{\\psi_\\text{out}(\\mathbf{x}_i,\\mathbf{\\theta})}= U_\\text{out}(\\mathbf{\\theta})\\ket{\\psi_\\text{in}(\\mathbf{x}_i)}$を得る．\n",
        "4.   出力量子状態に対し観測量の演算子(例えば、最初の量子ビット0のZ基底を測定するための射影演算子$\\hat{Z}_0=\\ket{0_0}\\bra{0_0}+\\ket{1_0}\\bra{1_0}$の期待値$\\braket{Z_0}=\\bra{\\psi_\\text{out}}\\hat{Z}_0\\ket{\\psi_\\text{out}}$)を設定し，その測定値$\\mathbf{y}(\\mathbf{x}_i,\\mathbf{\\theta})$を得る．\n",
        "5.   真の値$\\mathbf{y}_i$と測定値$\\mathbf{y}(\\mathbf{x}_i,\\mathbf{\\theta})$間の乖離を表す損失関数$L(\\mathbf{\\theta})$を設定し，その値を極小化する方向に向かう$\\mathbf{\\theta}$の候補値に更新する．\n",
        "6.   3-5のプロセスを繰り返し，損失関数$L(\\mathbf{\\theta})$を最小化するパラメータ$\\mathbf{\\theta}_\\text{min}$を探索する．探索により得られたパラメータ$\\mathbf{\\theta}_\\text{min}$を用いた$\\mathbf{y}(\\mathbf{x}_i,\\mathbf{\\theta}_\\text{min})$を予測モデルとして採用する．\n",
        "\n",
        "![qcl_algorithm.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "lSd_C02ywvKQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 参考文献\n",
        "1.   K. Mitarai, M. Negoro, M. Kitagawa, K. Fujii, Quantum circuit learning, Phys. Rev. A. 98, 032309 (2018). [DOI: 10.1103/PhysRevA.98.032309](https://doi.org/10.1103/PhysRevA.98.032309)\n",
        "2.   T. Suzuki, M. Katouda, Predicting toxicity by quantum machine learning, J. Phys. Commun. 4, 125012 (2020). [DOI: 10.1088/2399-6528/abd3d8](https://doi.org/10.1088/2399-6528/abd3d8)\n",
        "3.   御手洗 光祐, 藤井 啓祐, 量子コンピュータを用いた変分アルゴリズムと機械学習, 日本物理学会誌 74 (9), 604 (2019). [DOI: 10.11316/butsuri.74.9_604](https://www.jps.or.jp/books/gakkaishi/2019/09/74-09seriesAIphys1.pdf)\n",
        "4.   河東田 道夫, ケモインフォマティクス実課題のための量子機械学習法の共同研究, RISTニュース No. 67 (2021). [記事pdf](https://www.rist.or.jp/rnews/67/67s3.pdf)"
      ],
      "metadata": {
        "id": "GMzLTODKiJPt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Qiskitを用いた量子回路学習による回帰の実装例"
      ],
      "metadata": {
        "id": "1QgpNuXvh5EO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Qiskitのインストール"
      ],
      "metadata": {
        "id": "fpE6DUM2wcA_"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bcpIWniUu8vk",
        "outputId": "a5763116-68be-496f-99cc-4ec5a378fa1f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting qiskit[visualization]\n",
            "  Downloading qiskit-0.38.0.tar.gz (13 kB)\n",
            "Collecting qiskit-terra==0.21.2\n",
            "  Downloading qiskit_terra-0.21.2-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (6.7 MB)\n",
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            "\u001b[?25hCollecting qiskit-aer==0.11.0\n",
            "  Downloading qiskit_aer-0.11.0-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (19.2 MB)\n",
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            "\u001b[?25hCollecting qiskit-ibmq-provider==0.19.2\n",
            "  Downloading qiskit_ibmq_provider-0.19.2-py3-none-any.whl (240 kB)\n",
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            "  Downloading requests_ntlm-1.1.0-py2.py3-none-any.whl (5.7 kB)\n",
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            "Collecting websockets>=10.0\n",
            "  Downloading websockets-10.3-cp37-cp37m-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_12_x86_64.manylinux2010_x86_64.whl (112 kB)\n",
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            "  Downloading symengine-0.9.2-cp37-cp37m-manylinux2010_x86_64.whl (37.5 MB)\n",
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            "Collecting tweedledum<2.0,>=1.1\n",
            "  Downloading tweedledum-1.1.1-cp37-cp37m-manylinux_2_12_x86_64.manylinux2010_x86_64.whl (943 kB)\n",
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            "\u001b[?25hCollecting ply>=3.10\n",
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            "\u001b[?25hCollecting retworkx>=0.11.0\n",
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            "Collecting jedi>=0.10\n",
            "  Downloading jedi-0.18.1-py2.py3-none-any.whl (1.6 MB)\n",
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            "Collecting cryptography>=1.3\n",
            "  Downloading cryptography-38.0.1-cp36-abi3-manylinux_2_24_x86_64.whl (4.0 MB)\n",
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            "\u001b[?25hCollecting ntlm-auth>=1.0.2\n",
            "  Downloading ntlm_auth-1.5.0-py2.py3-none-any.whl (29 kB)\n",
            "Requirement already satisfied: cffi>=1.12 in /usr/local/lib/python3.7/dist-packages (from cryptography>=1.3->requests-ntlm>=1.1.0->qiskit-ibmq-provider==0.19.2->qiskit[visualization]) (1.15.1)\n",
            "Requirement already satisfied: pycparser in /usr/local/lib/python3.7/dist-packages (from cffi>=1.12->cryptography>=1.3->requests-ntlm>=1.1.0->qiskit-ibmq-provider==0.19.2->qiskit[visualization]) (2.21)\n",
            "Collecting rustworkx==0.12.0\n",
            "  Downloading rustworkx-0.12.0-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (1.9 MB)\n",
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            "Collecting pbr!=2.1.0,>=2.0.0\n",
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            "Requirement already satisfied: webencodings in /usr/local/lib/python3.7/dist-packages (from bleach->nbconvert->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.3.0->qiskit[visualization]) (0.5.1)\n",
            "Building wheels for collected packages: qiskit, pylatexenc\n",
            "  Building wheel for qiskit (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for qiskit: filename=qiskit-0.38.0-py3-none-any.whl size=12147 sha256=b17160cb7d8c65a1eefed9c61a3fadbc9fd95f1c9181255dbe283929a75123a8\n",
            "  Stored in directory: /root/.cache/pip/wheels/0b/30/78/04c91b7e82655f191b8f6238b6e74af67f3cc618cfca429189\n",
            "  Building wheel for pylatexenc (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pylatexenc: filename=pylatexenc-2.10-py3-none-any.whl size=136835 sha256=9b03c64e8e8a4f1906a04081bc3aeefab6120430e7de5f5f8e993381e3f7d4d8\n",
            "  Stored in directory: /root/.cache/pip/wheels/f1/8a/f5/33ee79d4473eb201b519fa40f989b842e373237395a3421f52\n",
            "Successfully built qiskit pylatexenc\n",
            "Installing collected packages: jedi, rustworkx, pbr, tweedledum, symengine, stevedore, shared-memory38, retworkx, ply, ntlm-auth, cryptography, websockets, websocket-client, requests-ntlm, qiskit-terra, qiskit-ibmq-provider, qiskit-aer, qiskit, pylatexenc\n",
            "Successfully installed cryptography-38.0.1 jedi-0.18.1 ntlm-auth-1.5.0 pbr-5.10.0 ply-3.11 pylatexenc-2.10 qiskit-0.38.0 qiskit-aer-0.11.0 qiskit-ibmq-provider-0.19.2 qiskit-terra-0.21.2 requests-ntlm-1.1.0 retworkx-0.12.0 rustworkx-0.12.0 shared-memory38-0.1.2 stevedore-3.5.0 symengine-0.9.2 tweedledum-1.1.1 websocket-client-1.4.1 websockets-10.3\n"
          ]
        }
      ],
      "source": [
        "!pip install qiskit[visualization]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "必要なモジュールのインポート"
      ],
      "metadata": {
        "id": "KAkUz2xvwSOz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, Aer, transpile\n",
        "from qiskit.algorithms.optimizers import COBYLA"
      ],
      "metadata": {
        "id": "SFEqvIzavGyU"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "QCLモデルの入力パラメータの設定\n"
      ],
      "metadata": {
        "id": "8NmUW0iewZ9q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "########  パラメータ  #############\n",
        "# 乱数のシード\n",
        "random_seed = 0\n",
        "# 乱数発生器の初期化\n",
        "np.random.seed(random_seed)\n",
        "\n",
        "# Qubit数，回路の深さ，期待値の増幅係数\n",
        "nqubit = 2\n",
        "c_depth = 5\n",
        "Mfac = 2.0\n",
        "\n",
        "# 量子コンピュータシミュレータの設定\n",
        "backendname = 'aer_simulator'\n",
        "num_shots = 8192\n",
        "\n",
        "# パラメータオプティマイザの設定\n",
        "maxiter = 100\n",
        "tol = 0.05"
      ],
      "metadata": {
        "id": "E4aMSSUTvayP"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "回帰する元データの設定"
      ],
      "metadata": {
        "id": "4Ho_LutylBc7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "########  学習データ  #############\n",
        "# 回帰する関数の定義: y=sin(x)\n",
        "func_to_learn = lambda x: np.sin(x*np.pi)\n",
        "\n",
        "# 回帰データの設定\n",
        "x_min = -1.; x_max = 1.; num_x_train = 100\n",
        "x_train = x_min + (x_max - x_min) * np.random.rand(num_x_train)\n",
        "y_train = func_to_learn(x_train)\n",
        "\n",
        "x_pred = np.arange(x_min, x_max, 0.02)\n",
        "y_pred = func_to_learn(x_pred)\n",
        "\n",
        "# 関数に正規分布ノイズを付加\n",
        "mag_noise = 0.05\n",
        "y_train += mag_noise * np.random.randn(num_x_train)"
      ],
      "metadata": {
        "id": "vIaHAWFik6PI"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "回帰する元データの可視化"
      ],
      "metadata": {
        "id": "3mDi6DCPB_gB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig = plt.figure()\n",
        "plt.plot(x_train, y_train, \"o\", label='Training Data (with Noise)')\n",
        "plt.plot(x_pred, y_pred, label='Original Function')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "#plt.savefig('./inputdata-plot.png')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "R52wIDSj0l7e",
        "outputId": "47c9416c-bc9d-492d-94eb-63caa6018288"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "入力回路$U_\\text{in}(x)$の設定: 入力回路は御手洗&藤井のQCLオリジナル論文[[Phys. Rev. A. 98, 032309 (2018)]](https://doi.org/10.1088/2399-6528/abd3d8)の回路($R_Y(\\arcsin{x})-R_Z(\\arccos(x^2)$)から鈴木&河東田の論文[[J. Phys. Commun. 4, 125012 (2020)]](https://doi.org/10.1088/2399-6528/abd3d8)で検討した最良モデルの回路($R_Y(x)-R_Z(x)-\\text{CNOT}-R_Y(x)-R_Z(x)-\\text{CNOT}$)へ変更"
      ],
      "metadata": {
        "id": "3vsZ1jcBzuDs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def U_in(x, nqubit):\n",
        "    qr = QuantumRegister(nqubit)\n",
        "    U = QuantumCircuit(qr)\n",
        "    for j in range(2):\n",
        "        for i in range(nqubit):\n",
        "            U.ry(x, i)\n",
        "            U.rz(x, i)\n",
        "        for i in range(nqubit-1):\n",
        "            U.cz(i, i+1)\n",
        "        if nqubit >=3: U.cz(nqubit-1, 0)\n",
        "\n",
        "    return U\n",
        "\n",
        "U_in(0.0, nqubit).draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "id": "v7FOfLlYvjnM",
        "outputId": "c7bdc3ec-6e0c-4ffe-a644-99a8b752945a"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 460.633x144.48 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "出力回路$U_\\text{out}(\\mathbf{\\theta})$の設定"
      ],
      "metadata": {
        "id": "LaV8ltB0vo-p"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def U_out(nqubit, c_depth, params):\n",
        "    qr = QuantumRegister(nqubit)\n",
        "    U = QuantumCircuit(qr)\n",
        "    for d in range(c_depth):\n",
        "        for i in range(nqubit-1):\n",
        "            U.cz(i, i+1)\n",
        "        if nqubit >=3: U.cz(nqubit-1, 0)\n",
        "        for i in range(nqubit):\n",
        "            U.rx(params[nqubit*3*d+3*i], i)\n",
        "            U.rz(params[nqubit*3*d+3*i+1], i)\n",
        "            U.rx(params[nqubit*3*d+3*i+2], i)\n",
        "\n",
        "    return U\n",
        "\n",
        "num_vars = 3 * nqubit * c_depth\n",
        "U_out(nqubit, c_depth, np.zeros(num_vars)).draw('mpl')"
      ],
      "metadata": {
        "id": "l_WaSr23z4GL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "outputId": "92fdc40d-49d1-4e75-d47c-a77890438803"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1303.58x144.48 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "量子回路学習モデルの設定:  \n",
        "観測量の演算子に密度演算子を用いた場合  "
      ],
      "metadata": {
        "id": "6Q0DoEW2-RZ5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def pred_circ(x, nqubit, c_depth, params):\n",
        "    qr = QuantumRegister(nqubit, name='q')\n",
        "    cr = ClassicalRegister(1, name='c')\n",
        "    qc = QuantumCircuit(qr, cr)\n",
        "    u_in = U_in(x, nqubit).to_instruction()\n",
        "    u_out = U_out(nqubit, c_depth, params).to_instruction()\n",
        "    qc.append(u_in, qr)\n",
        "    qc.append(u_out, qr)\n",
        "    qc.measure(0, 0)\n",
        "\n",
        "    return qc\n",
        "\n",
        "def get_expval(qc, backendname, num_shots):\n",
        "    backend = Aer.get_backend(backendname)\n",
        "    qc = transpile(qc, backend=backend)\n",
        "    result = backend.run(qc, shots=num_shots).result()\n",
        "    counts = result.get_counts(qc)\n",
        "    expval = (counts['0'] - counts['1']) / num_shots\n",
        "\n",
        "    return expval\n",
        "\n",
        "def qcl_reg(x_pred, nqubit, c_depth, params, Mfac, backendname, num_shots):\n",
        "    y_pred = []\n",
        "    for x in x_pred:\n",
        "        qc = pred_circ(x, nqubit, c_depth, params)\n",
        "        y_pred.append(Mfac*get_expval(qc, backendname, num_shots))\n",
        "\n",
        "    return np.array(y_pred)"
      ],
      "metadata": {
        "id": "MCSeyJlB3dSZ"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "学習モデルの量子回路の可視化"
      ],
      "metadata": {
        "id": "nUP8a5DZzrC9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "num_vars = 3 * nqubit * c_depth\n",
        "pred_circ(0.0, nqubit, c_depth, np.zeros(num_vars)).decompose().draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        },
        "id": "1dF3jzFjz5KB",
        "outputId": "60da853d-eb43-4f91-d08f-c08362084806"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1591.45x445.48 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "出力回路$U_\\text{out}(\\mathbf{\\theta})$の変分回路パラメータ$\\mathbf{\\theta}$の初期化"
      ],
      "metadata": {
        "id": "wWE171DO-UFw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "num_vars = 3 * nqubit * c_depth\n",
        "params_init = np.random.rand(num_vars) * 2.0 * np.pi"
      ],
      "metadata": {
        "id": "YzyS7nBU1ZNd"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "初期化した変分回路パラメータ$\\theta$を用いて回帰計算実行"
      ],
      "metadata": {
        "id": "nQrLsMK1_qgj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Initial params\\n', params_init)\n",
        "\n",
        "y_pred_reg_init = qcl_reg(x_pred, nqubit, c_depth, params_init, Mfac, backendname, num_shots)\n",
        "print('y_pred_reg_init:\\n', y_pred_reg_init)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6v3eJ9n5_j_D",
        "outputId": "e470c7dc-a3eb-43cf-c8f8-58f89d2e7864"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial params\n",
            " [1.30357293 2.6683775  2.35097932 2.9127303  1.74439261 3.68687478\n",
            " 5.42776485 0.73847443 3.2507888  0.82980839 4.50416222 2.48851651\n",
            " 3.55264688 1.15158117 0.91010531 3.06654805 2.23438073 5.90890818\n",
            " 4.80868039 4.70399226 5.67823859 0.52415862 3.46952761 3.67237145\n",
            " 6.04402452 1.83561705 1.51317185 0.63016542 0.10323041 5.84040495]\n",
            "y_pred_reg_init:\n",
            " [-1.91894531 -1.88916016 -1.84521484 -1.81542969 -1.73388672 -1.67138672\n",
            " -1.59814453 -1.50048828 -1.41845703 -1.31640625 -1.22265625 -1.11035156\n",
            " -1.02148438 -0.90722656 -0.81347656 -0.68505859 -0.58105469 -0.49023438\n",
            " -0.40869141 -0.27734375 -0.17431641 -0.05224609  0.07470703  0.12353516\n",
            "  0.27929688  0.27294922  0.33447266  0.4296875   0.53662109  0.59521484\n",
            "  0.62695312  0.68652344  0.76660156  0.7578125   0.80371094  0.79785156\n",
            "  0.8515625   0.8203125   0.84472656  0.83007812  0.83398438  0.80908203\n",
            "  0.79052734  0.74658203  0.71972656  0.70605469  0.66699219  0.61767578\n",
            "  0.58837891  0.53564453  0.45361328  0.43212891  0.37255859  0.30322266\n",
            "  0.2421875   0.234375    0.18212891  0.06835938  0.06054688 -0.02441406\n",
            " -0.05810547 -0.14501953 -0.20849609 -0.21435547 -0.3046875  -0.29345703\n",
            " -0.34912109 -0.37841797 -0.41455078 -0.42333984 -0.44384766 -0.44384766\n",
            " -0.47607422 -0.50292969 -0.52294922 -0.47216797 -0.47314453 -0.44433594\n",
            " -0.47460938 -0.42871094 -0.39453125 -0.38671875 -0.33642578 -0.33691406\n",
            " -0.265625   -0.30712891 -0.25634766 -0.23632812 -0.16357422 -0.11572266\n",
            " -0.078125   -0.02734375 -0.03857422  0.03369141  0.07275391  0.11767578\n",
            "  0.16503906  0.1875      0.18701172  0.22753906]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "変分回路パラメータ学習用の損失関数の設定"
      ],
      "metadata": {
        "id": "uEyWj0SI_4-L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def loss_function(params):\n",
        "    loss_total = 0.0\n",
        "    for i in range(len(x_train)):\n",
        "        qc = pred_circ(x_train[i], nqubit, c_depth, params)\n",
        "        loss = (y_train[i] - Mfac * get_expval(qc, backendname, num_shots))**2\n",
        "        loss_total += loss\n",
        "\n",
        "    return loss_total\n",
        "\n",
        "def obj_function(params):\n",
        "    global iter\n",
        "    loss_total = loss_function(params)\n",
        "    print('Iter: %d, Loss: %f' % (iter, loss_total))\n",
        "    losses.append(loss_total)\n",
        "    iter += 1\n",
        "\n",
        "    return loss_total"
      ],
      "metadata": {
        "id": "9ODJOIHX_yav"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "パラメータシフト法を用いた損失関数の回路パラメータ微分計算  \n",
        "(計算が遅いため，現バージョンでは回路パラメータ学習には使用していない)"
      ],
      "metadata": {
        "id": "WiCrBDaxv8sc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def loss_grad(params):\n",
        "    gradient = np.empty(len(params))\n",
        "    shifted = params.copy()\n",
        "    pipt = 0.5 * np.pi\n",
        "    for i in range(len(params)):\n",
        "        tmp = shifted[i]\n",
        "        shifted[i] = tmp + pipt\n",
        "        forward = loss_function(shifted)\n",
        "        shifted[i] = tmp - pipt\n",
        "        backward = loss_function(shifted)\n",
        "        gradient[i] = 0.5 * (forward - backward)\n",
        "        shifted[i] = tmp\n",
        "\n",
        "    return gradient"
      ],
      "metadata": {
        "id": "mUM-weUJv52J"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "変分回路パラメータ学習実行：回路パラメータの最適化アルゴリズムには  \n",
        "[COBYLA(Constrained Optimization By Linear Approximation)法](https://qiskit.org/documentation/stubs/qiskit.algorithms.optimizers.COBYLA.html)を使用"
      ],
      "metadata": {
        "id": "g7iaOBHlAciA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "iter = 0; losses = []\n",
        "optimizer = COBYLA(maxiter=maxiter, tol=tol)\n",
        "result = optimizer.minimize(obj_function, params_init)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "syhIbYwDAc74",
        "outputId": "cd8f6240-479d-4543-99a4-84894ed11158"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iter: 0, Loss: 111.651037\n",
            "Iter: 1, Loss: 86.675475\n",
            "Iter: 2, Loss: 78.103026\n",
            "Iter: 3, Loss: 79.862534\n",
            "Iter: 4, Loss: 48.319133\n",
            "Iter: 5, Loss: 38.006034\n",
            "Iter: 6, Loss: 24.560602\n",
            "Iter: 7, Loss: 102.872722\n",
            "Iter: 8, Loss: 40.714477\n",
            "Iter: 9, Loss: 35.865713\n",
            "Iter: 10, Loss: 49.451233\n",
            "Iter: 11, Loss: 50.005896\n",
            "Iter: 12, Loss: 96.300558\n",
            "Iter: 13, Loss: 55.720041\n",
            "Iter: 14, Loss: 13.192888\n",
            "Iter: 15, Loss: 121.858836\n",
            "Iter: 16, Loss: 43.033265\n",
            "Iter: 17, Loss: 12.325874\n",
            "Iter: 18, Loss: 49.150376\n",
            "Iter: 19, Loss: 114.719335\n",
            "Iter: 20, Loss: 3.772490\n",
            "Iter: 21, Loss: 15.729260\n",
            "Iter: 22, Loss: 123.483241\n",
            "Iter: 23, Loss: 27.051256\n",
            "Iter: 24, Loss: 94.050733\n",
            "Iter: 25, Loss: 7.159241\n",
            "Iter: 26, Loss: 70.572818\n",
            "Iter: 27, Loss: 52.788798\n",
            "Iter: 28, Loss: 3.821022\n",
            "Iter: 29, Loss: 3.799649\n",
            "Iter: 30, Loss: 3.856151\n",
            "Iter: 31, Loss: 61.110662\n",
            "Iter: 32, Loss: 1.914945\n",
            "Iter: 33, Loss: 5.618155\n",
            "Iter: 34, Loss: 16.952736\n",
            "Iter: 35, Loss: 60.817625\n",
            "Iter: 36, Loss: 18.056984\n",
            "Iter: 37, Loss: 8.765050\n",
            "Iter: 38, Loss: 3.960323\n",
            "Iter: 39, Loss: 9.725826\n",
            "Iter: 40, Loss: 19.909029\n",
            "Iter: 41, Loss: 2.950663\n",
            "Iter: 42, Loss: 4.681752\n",
            "Iter: 43, Loss: 4.888164\n",
            "Iter: 44, Loss: 26.685952\n",
            "Iter: 45, Loss: 7.521257\n",
            "Iter: 46, Loss: 15.326879\n",
            "Iter: 47, Loss: 3.769081\n",
            "Iter: 48, Loss: 4.434419\n",
            "Iter: 49, Loss: 2.410415\n",
            "Iter: 50, Loss: 6.021566\n",
            "Iter: 51, Loss: 4.176976\n",
            "Iter: 52, Loss: 1.578560\n",
            "Iter: 53, Loss: 13.024182\n",
            "Iter: 54, Loss: 10.805491\n",
            "Iter: 55, Loss: 3.512780\n",
            "Iter: 56, Loss: 15.246310\n",
            "Iter: 57, Loss: 1.806182\n",
            "Iter: 58, Loss: 2.554214\n",
            "Iter: 59, Loss: 1.854140\n",
            "Iter: 60, Loss: 4.716654\n",
            "Iter: 61, Loss: 1.388397\n",
            "Iter: 62, Loss: 14.441875\n",
            "Iter: 63, Loss: 1.132625\n",
            "Iter: 64, Loss: 35.635008\n",
            "Iter: 65, Loss: 1.059289\n",
            "Iter: 66, Loss: 4.694512\n",
            "Iter: 67, Loss: 2.164495\n",
            "Iter: 68, Loss: 3.406883\n",
            "Iter: 69, Loss: 4.701760\n",
            "Iter: 70, Loss: 6.594170\n",
            "Iter: 71, Loss: 1.890926\n",
            "Iter: 72, Loss: 27.828553\n",
            "Iter: 73, Loss: 4.561313\n",
            "Iter: 74, Loss: 0.841584\n",
            "Iter: 75, Loss: 5.188673\n",
            "Iter: 76, Loss: 1.274311\n",
            "Iter: 77, Loss: 5.520744\n",
            "Iter: 78, Loss: 1.221470\n",
            "Iter: 79, Loss: 4.160393\n",
            "Iter: 80, Loss: 1.004909\n",
            "Iter: 81, Loss: 1.681541\n",
            "Iter: 82, Loss: 1.425482\n",
            "Iter: 83, Loss: 2.421330\n",
            "Iter: 84, Loss: 1.409029\n",
            "Iter: 85, Loss: 0.918803\n",
            "Iter: 86, Loss: 0.946594\n",
            "Iter: 87, Loss: 2.785601\n",
            "Iter: 88, Loss: 1.437492\n",
            "Iter: 89, Loss: 3.108382\n",
            "Iter: 90, Loss: 9.784056\n",
            "Iter: 91, Loss: 2.303957\n",
            "Iter: 92, Loss: 1.136215\n",
            "Iter: 93, Loss: 1.412242\n",
            "Iter: 94, Loss: 0.950263\n",
            "Iter: 95, Loss: 0.879096\n",
            "Iter: 96, Loss: 1.030487\n",
            "Iter: 97, Loss: 4.114678\n",
            "Iter: 98, Loss: 1.037028\n",
            "Iter: 99, Loss: 2.277801\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "学習結果の表示"
      ],
      "metadata": {
        "id": "ypSmpD5HCOzw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "params_final = result.x\n",
        "print('Final params\\n', params_final)\n",
        "\n",
        "y_pred_reg_final = qcl_reg(x_pred, nqubit, c_depth, params_final, Mfac, backendname, num_shots)\n",
        "print('y_pred_reg_final:\\n', y_pred_reg_final)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DLJoTd-QA7Rj",
        "outputId": "70ddcd57-f805-4eeb-eba4-9b7534d52b68"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final params\n",
            " [ 3.08900194  3.65960204  2.40827051  3.96204569  2.75857422  4.70443724\n",
            "  5.58200348  0.64303679  3.20254424  0.6833514   4.47026023  2.34291089\n",
            "  3.47660214  2.14161767  0.77940117  3.03749811  3.2423927   5.73173444\n",
            "  4.99424737  5.71590844  5.65928914  0.29709969  3.4291064   3.50185612\n",
            "  6.04165728  1.71095748  1.42251147  0.44497493 -0.02955375  5.61297378]\n",
            "y_pred_reg_final:\n",
            " [ 9.76562500e-04 -6.25000000e-02 -1.86523438e-01 -2.47070312e-01\n",
            " -2.98828125e-01 -3.73046875e-01 -4.28222656e-01 -5.13671875e-01\n",
            " -5.21972656e-01 -6.07910156e-01 -6.71875000e-01 -7.03125000e-01\n",
            " -7.75390625e-01 -7.98828125e-01 -8.37890625e-01 -8.62304688e-01\n",
            " -8.63281250e-01 -9.16992188e-01 -8.98437500e-01 -9.65332031e-01\n",
            " -9.86328125e-01 -1.00146484e+00 -9.79003906e-01 -9.73632812e-01\n",
            " -9.96093750e-01 -1.01660156e+00 -9.74121094e-01 -9.70703125e-01\n",
            " -9.68750000e-01 -9.94140625e-01 -9.16015625e-01 -9.13574219e-01\n",
            " -8.74511719e-01 -8.82812500e-01 -8.33007812e-01 -8.12988281e-01\n",
            " -7.87597656e-01 -7.42187500e-01 -7.00195312e-01 -6.23535156e-01\n",
            " -6.11816406e-01 -5.42480469e-01 -5.52734375e-01 -4.50195312e-01\n",
            " -4.12597656e-01 -3.21777344e-01 -2.53417969e-01 -2.21679688e-01\n",
            " -1.38671875e-01 -1.06933594e-01 -5.17578125e-02  2.78320312e-02\n",
            "  7.86132812e-02  1.69921875e-01  2.76855469e-01  3.01757812e-01\n",
            "  3.61816406e-01  3.96972656e-01  4.89746094e-01  5.65429688e-01\n",
            "  6.28417969e-01  6.28417969e-01  6.92382812e-01  7.89550781e-01\n",
            "  7.92968750e-01  8.04687500e-01  8.76464844e-01  9.26757812e-01\n",
            "  9.69726562e-01  1.03613281e+00  1.05419922e+00  1.10839844e+00\n",
            "  1.10498047e+00  1.10986328e+00  1.15771484e+00  1.11181641e+00\n",
            "  1.14843750e+00  1.12792969e+00  1.14697266e+00  1.13818359e+00\n",
            "  1.13818359e+00  1.15136719e+00  1.09228516e+00  1.05761719e+00\n",
            "  1.01416016e+00  9.88769531e-01  9.38476562e-01  9.23339844e-01\n",
            "  8.11523438e-01  7.75390625e-01  7.54882812e-01  6.83105469e-01\n",
            "  6.25000000e-01  5.20507812e-01  4.34082031e-01  4.26269531e-01\n",
            "  3.00781250e-01  2.20703125e-01  1.49902344e-01  5.27343750e-02]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "損失関数の最適化結果の可視化"
      ],
      "metadata": {
        "id": "1aQhNZH7CH3m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig = plt.figure()\n",
        "plt.plot([i for i in range(len(losses))], losses, c='black', linewidth=1.5)\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Loss')\n",
        "plt.show()\n",
        "#plt.savefig('./qcl-epoch.png')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "RKMh64pJjmKT",
        "outputId": "eb67d183-54d7-49f2-bc23-307973df1358"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "量子回路学習で決定した回帰モデルの可視化"
      ],
      "metadata": {
        "id": "RuPUnEzafz-E"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig = plt.figure()\n",
        "plt.plot(x_train, y_train, 'o', label='Training Data (with Noise)', c='gray')\n",
        "plt.plot(x_pred, y_pred_reg_init, '--', label='Predicted result (Initial model)', c='black', linewidth=1.0)\n",
        "plt.plot(x_pred, y_pred_reg_final, label='Predicted result (Final model)', c='red', linewidth=1.5)\n",
        "plt.legend()\n",
        "plt.show()\n",
        "#plt.savefig('./qcl-regplot.png')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "sPX5pzyPBMRr",
        "outputId": "e5a2e9a3-255b-412f-b7e2-d30be6d12ebf"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}