quantum_embed/quantum_embed.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Embeds classial data according to the following papers:\n",
    "\n",
    "The effect of data encoding on the expressive power of variational quantum machine learning models\n",
    "Maria Schuld, Ryan Sweke, Johannes Jakob Meyer\n",
    "https://arxiv.org/abs/2008.08605\n",
    "\n",
    "Quantum embeddings for machine learning\n",
    "Seth Lloyd, Maria Schuld, Aroosa Ijaz, Josh Izaac, Nathan Killoran\n",
    "https://arxiv.org/abs/2001.03622\n",
    "\n",
    "Supervised quantum machine learning models are kernel methods\n",
    "Maria Schuld\n",
    "https://arxiv.org/abs/2101.11020\n",
    "\n",
    "Circuit-centric quantum classifiers\n",
    "Maria Schuld, Alex Bocharov, Krysta Svore, Nathan Wiebe\n",
    "https://arxiv.org/abs/1804.00633\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tensorflow/quantum/blob/research/q_embed/quantum_embed.ipynb)\n",
    "\n",
    "First we must install the required libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -q --upgrade tensorflow==2.7.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -q tensorflow-quantum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we import necessary modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt \n",
    "import numpy as np\n",
    "\n",
    "import cirq\n",
    "import tensorflow as tf\n",
    "from tensorflow_quantum.python import util\n",
    "from tensorflow_quantum.python.layers.circuit_executors import expectation\n",
    "\n",
    "import quantum_embed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we create the data to train on. The input is a range of increasing numbers and the output is a single sine function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_examples = 128\n",
    "\n",
    "data_in = np.linspace(-np.pi, np.pi, num_examples, endpoint=False)\n",
    "data_out = 0.456 * np.cos(data_in - np.pi / 3.0)\n",
    "\n",
    "plt.plot(data_in, data_out)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we have a single sine wave, the depth and number of repetions of the circuits are all one. Refer to the paper or the unit tests for more complicated use cases. We then build the quantum embedding layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "depth_input = 1\n",
    "num_repetitions = 1\n",
    "num_repetitions_input = 1\n",
    "num_unitary_layers = 1\n",
    "\n",
    "data_in = np.repeat(np.expand_dims(data_in, axis=1), depth_input, axis=1)\n",
    "data_out = np.repeat(np.expand_dims(data_out, axis=1), depth_input, axis=1)\n",
    "\n",
    "qubits = [[cirq.GridQubit(i, j) for j in range(depth_input)] for i in range(num_repetitions_input)]\n",
    "qe = quantum_embed.QuantumEmbed(qubits, num_repetitions_input, depth_input, num_unitary_layers, num_repetitions)\n",
    "\n",
    "data_circuits = util.convert_to_tensor(\n",
    "    [cirq.Circuit(qe.build_param_rotator(data_in[m, :])) for m in range(num_examples)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then use the Quantum Embedding layer with a standard training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/50\n",
      "4/4 [==============================] - 1s 10ms/step - loss: 0.4323\n",
      "Epoch 2/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.1643\n",
      "Epoch 3/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.1197\n",
      "Epoch 4/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.1004\n",
      "Epoch 5/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0256\n",
      "Epoch 6/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0200\n",
      "Epoch 7/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0082\n",
      "Epoch 8/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0126\n",
      "Epoch 9/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0056\n",
      "Epoch 10/50\n",
      "4/4 [==============================] - 0s 13ms/step - loss: 0.0051\n",
      "Epoch 11/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0030\n",
      "Epoch 12/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0030\n",
      "Epoch 13/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0013\n",
      "Epoch 14/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0011\n",
      "Epoch 15/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 0.0013\n",
      "Epoch 16/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 3.4186e-04\n",
      "Epoch 17/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.8885e-04\n",
      "Epoch 18/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 2.6582e-04\n",
      "Epoch 19/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.5691e-04\n",
      "Epoch 20/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.5304e-04\n",
      "Epoch 21/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.0533e-04\n",
      "Epoch 22/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 2.8272e-05\n",
      "Epoch 23/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 3.7456e-05\n",
      "Epoch 24/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 3.8110e-05\n",
      "Epoch 25/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.6867e-05\n",
      "Epoch 26/50\n",
      "4/4 [==============================] - 0s 11ms/step - loss: 1.7203e-05\n",
      "Epoch 27/50\n",
      "4/4 [==============================] - 0s 14ms/step - loss: 1.0662e-05\n",
      "Epoch 28/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 8.2241e-06\n",
      "Epoch 29/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 6.9262e-06\n",
      "Epoch 30/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 4.3488e-06\n",
      "Epoch 31/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 3.1238e-06\n",
      "Epoch 32/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.9310e-06\n",
      "Epoch 33/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.0506e-06\n",
      "Epoch 34/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.0935e-06\n",
      "Epoch 35/50\n",
      "4/4 [==============================] - 0s 11ms/step - loss: 5.7388e-07\n",
      "Epoch 36/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 2.7430e-07\n",
      "Epoch 37/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.2873e-07\n",
      "Epoch 38/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.0417e-07\n",
      "Epoch 39/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.1324e-07\n",
      "Epoch 40/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 7.5553e-08\n",
      "Epoch 41/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 4.9839e-08\n",
      "Epoch 42/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 2.9980e-08\n",
      "Epoch 43/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.9969e-08\n",
      "Epoch 44/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 2.3435e-08\n",
      "Epoch 45/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.9808e-08\n",
      "Epoch 46/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.5916e-08\n",
      "Epoch 47/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 5.7047e-09\n",
      "Epoch 48/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 1.0903e-08\n",
      "Epoch 49/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 6.0526e-09\n",
      "Epoch 50/50\n",
      "4/4 [==============================] - 0s 10ms/step - loss: 8.0883e-09\n"
     ]
    }
   ],
   "source": [
    "quantum_datum = tf.keras.Input(shape=(), dtype=tf.dtypes.string)\n",
    "model_appended = qe(quantum_datum)\n",
    "\n",
    "batch_size = tf.gather(tf.shape(quantum_datum), 0)\n",
    "operators = util.convert_to_tensor([[cirq.Z(qubits[0][0])]])\n",
    "executor = expectation.Expectation(backend='noiseless',\n",
    "                                   differentiator=None)\n",
    "tiled_up_operators = tf.tile(qe._operators, [batch_size, 1])\n",
    "\n",
    "outputs = executor(model_appended,\n",
    "                   symbol_names=qe.symbols,\n",
    "                   operators=tiled_up_operators)\n",
    "\n",
    "model = tf.keras.Model(inputs=quantum_datum, outputs=outputs)\n",
    "model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.3),\n",
    "              loss=tf.keras.losses.mean_squared_error)\n",
    "\n",
    "history = model.fit(x=data_circuits, y=data_out, epochs=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we plot the loss in log scale. We tend to zero, since it can be fit perfectly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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.semilogy(history.history['loss']);\n",
    "plt.grid();\n",
    "plt.xlabel('step');\n",
    "plt.ylabel('loss');"
   ]
  }
 ],
 "metadata": {
  "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}