doc/source/notebooks/02_02_parameter_shift_rule.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "369d71c0-8afe-4e85-8d4d-a4a24b689e25",
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install qulacs\n",
    "#!pip install qulacsvis\n",
    "#!pip install matplotlib\n",
    "#!pip install numpy\n",
    "#!pip install scipy\n",
    "#!pip install tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c2e4b430-cb21-42cb-b9d4-5907a7f0d660",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qulacs import Observable, QuantumState, QuantumCircuit\n",
    "from qulacsvis import circuit_drawer\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e58c633-31f7-4f70-bb0a-aca6dfc5415b",
   "metadata": {},
   "source": [
    "# パラメータシフト法による勾配最適化"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9763dcea-ff93-464e-87db-229c4a02ca40",
   "metadata": {},
   "source": [
    "パラメータシフト法によって勾配を求めて、変分量子アルゴリズムの最適化をしてみます。ここでは前回と同様にハイゼンベルグ模型\n",
    "$$H = \\sum_{i} J_{i} (X_iX_{i+1} + Y_iY_{1+1} + Z_iZ_{i+1})$$\n",
    "に対する VQE を行います。\n",
    "\n",
    "まずハミルトニアンと適当なパラメータ付き量子回路を定義します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "21499df8-386f-4869-85cb-b60264fec7d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1490.4x367.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qulacs import ParametricQuantumCircuit\n",
    "\n",
    "n_qubits = 4\n",
    "depth = 4\n",
    "circuit = ParametricQuantumCircuit(n_qubits)\n",
    "for d in range(depth):\n",
    "    for i in range(n_qubits):\n",
    "        circuit.add_parametric_RY_gate(i, 0.0)\n",
    "        circuit.add_parametric_RZ_gate(i, 0.0)\n",
    "    for i in range(n_qubits//2):\n",
    "        circuit.add_CZ_gate((i+d%2)%n_qubits, (i+1+d%2)%n_qubits)\n",
    "\n",
    "hamiltonian = Observable(n_qubits)\n",
    "np.random.seed(1)\n",
    "J_list = 2*np.random.rand(n_qubits)-1\n",
    "for i in range(n_qubits):\n",
    "    hamiltonian.add_operator(J_list[i], f\"X {i} X {(i+1)%n_qubits}\")\n",
    "    hamiltonian.add_operator(J_list[i], f\"Y {i} Y {(i+1)%n_qubits}\")\n",
    "    hamiltonian.add_operator(J_list[i], f\"Z {i} Z {(i+1)%n_qubits}\")\n",
    "    \n",
    "circuit_drawer(circuit, \"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58dc21e9-2134-4451-9046-ab673830b872",
   "metadata": {},
   "source": [
    "道具として、与えられたパラメータにおけるコスト関数 (この場合はエネルギー期待値) を返す関数を作っておきます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5f4548cd-620f-40d0-a518-bae3722d510b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_cost(params):\n",
    "    state = QuantumState(n_qubits)\n",
    "    for i, p in enumerate(params):\n",
    "        circuit.set_parameter(i,p)\n",
    "    circuit.update_quantum_state(state)\n",
    "    return hamiltonian.get_expectation_value(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "662a9636-5c19-4a9d-bbf9-36a60574c636",
   "metadata": {},
   "source": [
    "## パラメータシフト法による勾配\n",
    "復習：$\\langle H(\\theta) \\rangle = \\langle \\psi(\\theta) | H | \\psi(\\theta) \\rangle$ で、パラメータ $\\theta$ がすべて $\\exp(-i\\theta P/2)$ ($P$はパウリ行列) の形で入っているとき、$\\frac{\\partial \\langle H(\\theta)\\rangle}{\\partial \\theta_i}$ は次のように求まります。\n",
    "$$\\frac{\\partial \\langle H(\\theta)\\rangle}{\\partial \\theta_i} = \\frac{1}{2}\\left(\\left\\langle H\\left(\\theta+\\frac{\\pi}{2}e_i\\right)\\right)-\\left\\langle H\\left(\\theta-\\frac{\\pi}{2}e_i\\right)\\right\\rangle\\right)$$\n",
    "ここで $e_i$ は $i$ 番目の成分だけ 1 でそれ以外はゼロのベクトルです。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e75b0db1-5b3e-4f06-8f51-2c2dcbe0de3b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# パラメータシフト法によって、あるパラメータ params における勾配ベクトルを求めるコードを書いてください。\n",
    "def get_gradient_by_parameter_shift(params):\n",
    "    grad_vector = np.zeros_like(params)\n",
    "    tmp_params = np.copy(params)\n",
    "    for i in range(len(params)):\n",
    "        tmp_params[i] += np.pi/2\n",
    "        plus = get_cost(tmp_params)\n",
    "        tmp_params[i] -= np.pi\n",
    "        minus = get_cost(tmp_params)\n",
    "        grad_vector[i] = (plus-minus)/2\n",
    "        tmp_params[i] = params[i]\n",
    "    return grad_vector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b25fea46-6fcf-43e1-aa1d-2cd5971d2328",
   "metadata": {},
   "source": [
    "正しく書けているか、有限差分による微分の近似値と比較しましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c5b18b9f-a6fa-45c7-b04c-dd73a907e4dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_gradient_by_finite_diff(params, eps=1e-6):\n",
    "    grad_vector = np.zeros_like(params)\n",
    "    tmp_params = np.copy(params)\n",
    "    for i in range(len(params)):\n",
    "        tmp_params[i] += eps\n",
    "        plus = get_cost(tmp_params)\n",
    "        tmp_params[i] -= 2*eps\n",
    "        minus = get_cost(tmp_params)\n",
    "        grad_vector[i] = (plus-minus)/2/eps\n",
    "        tmp_params[i] = params[i]\n",
    "    return grad_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4be3c26c-e071-45cf-97a5-4e0ff1bbd9ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.28641755 -0.00438154 -0.06712645 -0.32537361 -0.05751078  0.16557163\n",
      "  0.11887725  0.10954547 -0.17033146 -0.24962483  0.12171529  0.35254303\n",
      " -0.39434455  0.16599231  0.2278707  -0.09372357  0.17685758  0.0195437\n",
      "  0.02588595 -0.06820095  0.14981395 -0.43356911  0.27244975  0.25668482\n",
      "  0.16067643 -0.02018968  0.70788171 -0.22227356 -0.03951543  0.43888274\n",
      " -0.20362175 -0.19641951]\n",
      "[ 0.28641755 -0.00438154 -0.06712645 -0.32537361 -0.05751078  0.16557163\n",
      "  0.11887725  0.10954547 -0.17033147 -0.24962483  0.12171529  0.35254303\n",
      " -0.39434455  0.16599231  0.2278707  -0.09372357  0.17685758  0.0195437\n",
      "  0.02588595 -0.06820095  0.14981395 -0.43356911  0.27244975  0.25668482\n",
      "  0.16067643 -0.02018968  0.70788171 -0.22227356 -0.03951543  0.43888274\n",
      " -0.20362175 -0.19641951]\n"
     ]
    }
   ],
   "source": [
    "params = (2*np.random.random(circuit.get_parameter_count())-1)*np.pi\n",
    "print(get_gradient_by_parameter_shift(params))\n",
    "print(get_gradient_by_finite_diff(params))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd763d69-90a7-4e42-a652-01329221b479",
   "metadata": {},
   "source": [
    "## 最適化\n",
    "勾配降下法によって最適化しますが、先に答えを知っておきたいので、基底状態のエネルギーを得ておきましょう"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e7a87d6d-a7f2-483e-b5d3-c21b59ef8723",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ground state energy is: -2.2830906123847066\n"
     ]
    }
   ],
   "source": [
    "from utility import get_matrix\n",
    "from scipy.sparse.linalg import eigsh\n",
    "eigvals = eigsh(get_matrix(hamiltonian), which=\"SR\")[0]\n",
    "print(\"ground state energy is:\", min(eigvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cb0b60f-af9a-4190-93dc-6cc2752d2c02",
   "metadata": {},
   "source": [
    "単純な勾配降下法によって最適化を行います。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0cd2ebc7-4b0f-4af5-8aa9-fcb364a6beec",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [01:33<00:00, 10.64it/s]\n"
     ]
    }
   ],
   "source": [
    "n_steps = 1000\n",
    "rate = 0.1\n",
    "params = (2*np.random.random(circuit.get_parameter_count())-1)*np.pi\n",
    "cost_history = np.zeros(n_steps)\n",
    "for i in tqdm(range(n_steps)):\n",
    "    params -= get_gradient_by_parameter_shift(params)*rate\n",
    "    cost_history[i] = get_cost(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7fd95107-072a-494f-bcda-7abf46576e78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_history)\n",
    "plt.axhline(min(eigvals), color=\"black\", linestyle=\"dashed\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"steps\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f54e95da-d475-4313-8265-e90e7f663a1f",
   "metadata": {},
   "source": [
    "最適化できていますね。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bedafad-3823-48c1-a32b-fcdabfa0a643",
   "metadata": {},
   "source": [
    "## 発展編：統計ノイズのもとでの勾配降下法"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cd609ab-95a2-496c-b592-b91ef5c7251f",
   "metadata": {},
   "source": [
    "前回行ったように、実際の実験では必ずサンプリングに伴う統計ノイズが発生します。統計ノイズのもとでも勾配降下法が機能するか見てみましょう。\n",
    "\n",
    "まずは統計ノイズを含むコスト関数を定義します。前回のサンプリングコードを流用します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e9a1ce2a-b44d-4d43-956a-ec8c4b58c00e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_ZZ(state, _n_shots):\n",
    "    global J_list\n",
    "    samples = state.sampling(_n_shots)\n",
    "    estimated_energy = 0\n",
    "    mask_list = [0b0011, 0b0110, 0b1100, 0b1001]\n",
    "    for s in samples:\n",
    "        for J, mask in zip(J_list, mask_list):\n",
    "            bitcount = bin(s & mask).count(\"1\")\n",
    "            estimated_energy += J*(-1)**bitcount/_n_shots\n",
    "    return estimated_energy\n",
    "\n",
    "from qulacs.gate import H, Sdag\n",
    "def sample_XX(state, _n_shots):\n",
    "    global J_list\n",
    "    for i in range(n_qubits):\n",
    "        H(i).update_quantum_state(state)\n",
    "    samples = state.sampling(_n_shots)\n",
    "    estimated_energy = 0\n",
    "    mask_list = [0b0011, 0b0110, 0b1100, 0b1001]\n",
    "    for s in samples:\n",
    "        for J, mask in zip(J_list, mask_list):\n",
    "            bitcount = bin(s & mask).count(\"1\")\n",
    "            estimated_energy += J*(-1)**bitcount/_n_shots\n",
    "    return estimated_energy\n",
    "\n",
    "def sample_YY(state, _n_shots):\n",
    "    global J_list\n",
    "    for i in range(n_qubits):\n",
    "        Sdag(i).update_quantum_state(state)\n",
    "        H(i).update_quantum_state(state)\n",
    "    samples = state.sampling(_n_shots)\n",
    "    estimated_energy = 0\n",
    "    mask_list = [0b0011, 0b0110, 0b1100, 0b1001]\n",
    "    for s in samples:\n",
    "        for J, mask in zip(J_list, mask_list):\n",
    "            bitcount = bin(s & mask).count(\"1\")\n",
    "            estimated_energy += J*(-1)**bitcount/_n_shots\n",
    "    return estimated_energy\n",
    "\n",
    "def sample_cost(params, n_shots=1000):\n",
    "    state = QuantumState(n_qubits)\n",
    "    for i, p in enumerate(params):\n",
    "        circuit.set_parameter(i,p)\n",
    "    circuit.update_quantum_state(state)\n",
    "    return sample_ZZ(state, n_shots) + sample_XX(state, n_shots) + sample_YY(state, n_shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "196ab297-5e6c-40c0-a4f6-69cd506341d2",
   "metadata": {},
   "source": [
    "一応正しくサンプリングできていることを確認しておきます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c54b2530-5d8d-463d-9479-c2676d294d8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:12<00:00, 79.96it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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ORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_tests = 1000\n",
    "costs = np.zeros(n_tests)\n",
    "for i in tqdm(range(n_tests)):\n",
    "    costs[i] = sample_cost(params)\n",
    "plt.hist(costs, bins=30, alpha=0.3)\n",
    "plt.axvline(get_cost(params), color=\"black\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0f05f83-d5ab-44a2-88bd-6b207756cfc9",
   "metadata": {},
   "source": [
    "できているようなので、最適化に移ります。\n",
    "\n",
    "### 有限差分による最適化\n",
    "まずは有限差分で最適化してみましょう。サンプリングをすると少し時間がかかるので、100 step だけやります。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b64175eb-cac2-49aa-98f2-9c5e981aeca8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [01:18<00:00,  1.28it/s]\n"
     ]
    }
   ],
   "source": [
    "def sample_gradient_by_finite_diff(params, eps=1e-6):\n",
    "    grad_vector = np.zeros_like(params)\n",
    "    tmp_params = np.copy(params)\n",
    "    for i in range(len(params)):\n",
    "        tmp_params[i] += eps\n",
    "        plus = sample_cost(tmp_params)\n",
    "        tmp_params[i] -= 2*eps\n",
    "        minus = sample_cost(tmp_params)\n",
    "        grad_vector[i] = (plus-minus)/2/eps\n",
    "        tmp_params[i] = params[i]\n",
    "    return grad_vector\n",
    "n_steps = 100\n",
    "rate = 0.1\n",
    "np.random.seed(1)\n",
    "params = (2*np.random.random(circuit.get_parameter_count())-1)*np.pi\n",
    "cost_history_fd = np.zeros(n_steps)\n",
    "for i in tqdm(range(n_steps)):\n",
    "    params -= sample_gradient_by_finite_diff(params)*rate\n",
    "    cost_history_fd[i] = get_cost(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f0b560ae-0f96-4315-aa69-8d2724471fc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_history_fd)\n",
    "plt.axhline(min(eigvals), color=\"black\", linestyle=\"dashed\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"steps\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36e12890-da33-4f87-be82-835e58731ced",
   "metadata": {},
   "source": [
    "全然最適化できていないことがわかります。これは $\\langle H(\\theta+\\epsilon) \\rangle$ と $\\langle H(\\theta) \\rangle$ の差が統計誤差に負けているためだと考えられます。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eba7995f-12f1-40e0-ade5-83822de8c0b4",
   "metadata": {},
   "source": [
    "### パラメータシフト法による最適化\n",
    "次にパラメータシフト法によって最適化してみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "43a7a2ce-e411-4908-9c4e-e5264988c51e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [01:16<00:00,  1.31it/s]\n"
     ]
    }
   ],
   "source": [
    "def sample_gradient_by_parameter_shift(params, n_shots=1000):\n",
    "    grad_vector = np.zeros_like(params)\n",
    "    tmp_params = np.copy(params)\n",
    "    for i in range(len(params)):\n",
    "        tmp_params[i] += np.pi/2\n",
    "        plus = sample_cost(tmp_params, n_shots)\n",
    "        tmp_params[i] -= np.pi\n",
    "        minus = sample_cost(tmp_params,n_shots)\n",
    "        grad_vector[i] = (plus-minus)/2\n",
    "        tmp_params[i] = params[i]\n",
    "    return grad_vector\n",
    "n_steps = 100\n",
    "n_shots = 1000\n",
    "rate = 0.1\n",
    "np.random.seed(1)\n",
    "params = (2*np.random.random(circuit.get_parameter_count())-1)*np.pi\n",
    "cost_history_ps = np.zeros(n_steps)\n",
    "for i in tqdm(range(n_steps)):\n",
    "    params -= sample_gradient_by_parameter_shift(params, n_shots)*rate\n",
    "    cost_history_ps[i] = get_cost(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9c4de5cd-7485-4ef0-9d22-0e2bd8602b2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_history_fd, label=\"FD\")\n",
    "plt.plot(cost_history_ps, label=\"PS\")\n",
    "plt.axhline(min(eigvals), color=\"black\", linestyle=\"dashed\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"steps\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ee4c2de-7b60-4fe0-8aa3-6c543807da5d",
   "metadata": {},
   "source": [
    "パラメータシフト法が統計ノイズに対して圧倒的にロバストであることが確認できます。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be0e95e4-2c5a-47d8-ad01-c19acb3dda4b",
   "metadata": {},
   "source": [
    "### 確率的勾配降下法との関係\n",
    "コスト関数 $f(\\theta)$ について、$\\mathbb{E}[\\hat{g}(\\theta)] = \\nabla f(\\theta)$ となるような乱数 $\\hat{g}$ を使って、\n",
    "$$\\theta \\to \\theta - \\alpha \\hat{g}$$\n",
    "と更新することによって最適化する方法を一般に確率的勾配降下法といいます。統計誤差付きのパラメータシフト法もこれと同じことをしているとみなせます。確率的勾配降下法では、$\\hat{g}$ が $\\nabla f$ の不偏推定量になっていさえいれば良いので、原理的には `n_shots` をどれだけ減らしてもパラメータシフト法は動くはずです。試しに `n_shots=1` でやってみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c342f3ea-84ca-4b76-abee-7ed44ece4f75",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [03:24<00:00, 48.85it/s]\n"
     ]
    }
   ],
   "source": [
    "n_steps = 10000\n",
    "n_shots = 1\n",
    "rate = 0.1\n",
    "np.random.seed(1)\n",
    "params = (2*np.random.random(circuit.get_parameter_count())-1)*np.pi\n",
    "cost_history_ps_1shot = np.zeros(n_steps)\n",
    "for i in tqdm(range(n_steps)):\n",
    "    params -= sample_gradient_by_parameter_shift(params, n_shots)*rate\n",
    "    cost_history_ps_1shot[i] = get_cost(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "94f22271-1cf2-4ccc-9fd3-459efae21dc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_history_ps_1shot, label=\"PS-1shot\")\n",
    "plt.plot(cost_history_ps, label=\"PS-1000shots\")\n",
    "plt.axhline(min(eigvals), color=\"black\", linestyle=\"dashed\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"steps\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93fa7b72-a781-4972-b138-4fe963348b59",
   "metadata": {},
   "source": [
    "全然だめですね。確率的勾配降下法を収束させるためにはステップ幅 $\\alpha$ を小さくしていかないといけないからです。そこで次は $\\alpha = \\alpha_0/(\\text{number of steps})$ で変化させていきます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "67441ae8-623c-4e5d-9c9e-c158f3d2d562",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [03:05<00:00, 53.81it/s]\n"
     ]
    }
   ],
   "source": [
    "n_steps = 10000\n",
    "n_shots = 1\n",
    "rate = 0.1\n",
    "np.random.seed(1)\n",
    "params = (2*np.random.random(circuit.get_parameter_count())-1)*np.pi\n",
    "cost_history_ps_1shot = np.zeros(n_steps)\n",
    "for i in tqdm(range(n_steps)):\n",
    "    params -= sample_gradient_by_parameter_shift(params, n_shots)*rate/(i+1)\n",
    "    cost_history_ps_1shot[i] = get_cost(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4bb6f5f2-40fd-4f91-8bcd-639724861838",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_history_ps_1shot, label=\"PS-1shot\")\n",
    "plt.plot(cost_history_ps, label=\"PS-1000shots\")\n",
    "plt.axhline(min(eigvals), color=\"black\", linestyle=\"dashed\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"steps\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6e07d28-6e29-442b-96e2-637509e5a974",
   "metadata": {},
   "source": [
    "一応上よりは良くなりましたし、無限に続ければ収束しそうな雰囲気です (?)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}