Ex3_Hessian_vs_metric_tensor.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example: Compare Hessian, metric tensor and vanilla SGD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "import pennylane as qml\n",
    "from pennylane import expval, var\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from vqc_loss_landscapes.hess_vs_metrictensor import *\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from pennylane.utils import _flatten, unflatten\n",
    "from pennylane.optimize import GradientDescentOptimizer\n",
    "\n",
    "from tqdm.notebook import tqdm as tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Draw circuit with Qiskit.Aer device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">      ┌────────────┐┌────────────┐ ┌────────────┐   ┌───────────┐ »\n",
       "q_0: ─┤ RZ(5.3773) ├┤ RY(2.2459) ├─┤ RZ(2.0572) ├─■─┤ RZ(1.934) ├─»\n",
       "     ┌┴────────────┤├────────────┤┌┴────────────┤ │ ├───────────┴┐»\n",
       "q_1: ┤ RZ(0.24209) ├┤ RY(0.4382) ├┤ RZ(0.55355) ├─■─┤ RZ(4.2309) ├»\n",
       "     └─────────────┘└────────────┘└─────────────┘   └────────────┘»\n",
       "c_0: ═════════════════════════════════════════════════════════════»\n",
       "                                                                  »\n",
       "c_1: ═════════════════════════════════════════════════════════════»\n",
       "                                                                  »\n",
       "«     ┌────────────┐┌────────────┐   ┌──────────┐┌─┐   \n",
       "«q_0: ┤ RY(2.0928) ├┤ RZ(1.0993) ├─■─┤1         ├┤M├───\n",
       "«     ├────────────┤├────────────┤ │ │  unitary │└╥┘┌─┐\n",
       "«q_1: ┤ RY(0.5574) ├┤ RZ(3.8018) ├─■─┤0         ├─╫─┤M├\n",
       "«     └────────────┘└────────────┘   └──────────┘ ║ └╥┘\n",
       "«c_0: ════════════════════════════════════════════╩══╬═\n",
       "«                                                    ║ \n",
       "«c_1: ═══════════════════════════════════════════════╩═\n",
       "«                                                      </pre>"
      ],
      "text/plain": [
       "      ┌────────────┐┌────────────┐ ┌────────────┐   ┌───────────┐ »\n",
       "q_0: ─┤ RZ(5.3773) ├┤ RY(2.2459) ├─┤ RZ(2.0572) ├─■─┤ RZ(1.934) ├─»\n",
       "     ┌┴────────────┤├────────────┤┌┴────────────┤ │ ├───────────┴┐»\n",
       "q_1: ┤ RZ(0.24209) ├┤ RY(0.4382) ├┤ RZ(0.55355) ├─■─┤ RZ(4.2309) ├»\n",
       "     └─────────────┘└────────────┘└─────────────┘   └────────────┘»\n",
       "c_0: ═════════════════════════════════════════════════════════════»\n",
       "                                                                  »\n",
       "c_1: ═════════════════════════════════════════════════════════════»\n",
       "                                                                  »\n",
       "«     ┌────────────┐┌────────────┐   ┌──────────┐┌─┐   \n",
       "«q_0: ┤ RY(2.0928) ├┤ RZ(1.0993) ├─■─┤1         ├┤M├───\n",
       "«     ├────────────┤├────────────┤ │ │  unitary │└╥┘┌─┐\n",
       "«q_1: ┤ RY(0.5574) ├┤ RZ(3.8018) ├─■─┤0         ├─╫─┤M├\n",
       "«     └────────────┘└────────────┘   └──────────┘ ║ └╥┘\n",
       "«c_0: ════════════════════════════════════════════╩══╬═\n",
       "«                                                    ║ \n",
       "«c_1: ═══════════════════════════════════════════════╩═\n",
       "«                                                      "
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "width = 2  # must be odd\n",
    "layers = 2\n",
    "\n",
    "target = np.ones((2**width,))*(1/np.sqrt(2**width))\n",
    "rho_target = np.outer(target ,np.conj(target).T)\n",
    "\n",
    "init_params = np.random.uniform(low=0.0, high=2 * np.pi, size=width * layers *3)\n",
    "\n",
    "model = Setup_For_Training(layers, width, rho_target, device=\"qiskit.aer\")\n",
    "\n",
    "theta = init_params.copy()\n",
    "\n",
    "circuit = model.qcircuit\n",
    "\n",
    "circuit(theta)\n",
    "a = model.dev._circuit\n",
    "a.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize with SGD, metric tensor and Hessian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "normal SGD\n"
     ]
    },
    {
     "data": {
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       "model_id": "619b1200ce184727a994c08bf0346d86",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Metric Tensor\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9663965087d44ea3b6026487ec022eae",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hessian\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9e7489e8ad074c31b12cf58c05e1f86b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "shots = 8192\n",
    "epochs = 100\n",
    "\n",
    "width = 2\n",
    "layers = 2\n",
    "\n",
    "target = np.ones((2**width,))*(1/np.sqrt(2**width))\n",
    "rho_target = np.outer(target ,np.conj(target).T)\n",
    "\n",
    "model = Setup_For_Training(layers, width, rho_target, device=\"default.qubit\")\n",
    "\n",
    "theta = init_params.copy()\n",
    "\n",
    "circuit = model.qcircuit\n",
    "\n",
    "init_params = np.random.uniform(low=0.0, high=2 * np.pi, size=width * layers*3)\n",
    "plot_lists = []\n",
    "lr_list = []\n",
    "for run in range(3):\n",
    "    lr=0.1\n",
    "    opt = qml.GradientDescentOptimizer(lr)\n",
    "    epochs=100\n",
    "    if run==0:\n",
    "        print(\"normal SGD\")\n",
    "        get_hessian=False\n",
    "        get_metr_tens=False\n",
    "    if run==1:\n",
    "        print(\"Metric Tensor\")\n",
    "        get_hessian=False\n",
    "        get_metr_tens=True\n",
    "    if run==2:\n",
    "        print(\"Hessian\")\n",
    "        get_hessian=True\n",
    "        get_metr_tens=False\n",
    "\n",
    "    loss_list = []\n",
    "    learning_rates = []\n",
    "    metric_tensor_list = []\n",
    "    params = init_params.copy()\n",
    "    progress = tqdm(range(epochs), bar_format='{desc}')\n",
    "    for it in progress:\n",
    "        loss = model.cost_fidelity(params, circuit)\n",
    "        loss_list.append(loss)\n",
    "        if get_hessian==True:\n",
    "            H = model.Hessian(params, circuit)\n",
    "            Hev, Hv = np.linalg.eigh(H)\n",
    "            lr = 1/Hev.max()\n",
    "            opt = qml.GradientDescentOptimizer(lr)\n",
    "            params = opt.step(lambda v: model.cost_fidelity(v, circuit), params)\n",
    "        elif get_metr_tens == True:\n",
    "            params, tensor = step(params, lr, \n",
    "                                  circuit.metric_tensor([params], diag_approx=False), \n",
    "                                  opt, model, circuit, lam=0.00000001)\n",
    "            metric_tensor_list.append(tensor)\n",
    "        else:\n",
    "            params = opt.step(lambda v: model.cost_fidelity(v, circuit), params)\n",
    "\n",
    "        progress.set_description_str('loss: {:3f}'.format(loss))\n",
    "        learning_rates.append(lr)\n",
    "    plot_lists.append(loss_list)\n",
    "    lr_list.append(learning_rates)\n",
    "    plt.plot(loss_list)\n",
    "    plt.show()\n",
    "for plot in plot_lists:\n",
    "    plt.plot(plot)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}